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Q:

Solve this number riddle.

- I am a two-digit number. 

- The sum of my digits is \( 12 \) .

- My ones digit is \( 2 \) times greater than my tens digit. 

I am the number 

 

 

How did you begin solving this problem? To begin solving this problem, 

Q:

Pam started watching a movie at \( 2 : 53 \) P.M. The movie was \( 1 \) hour and \( 52 \) minutes long. After the movie, Pam rode her bike for \( 46 \) minutes. When did Pam finish riding her bike? 

 

5:07 P.M. 5:31 P.M. 6:07 P.M. \( \quad 6 : 31 \) P.M. 

Q:

Use the information given to answer the question. An artist paints ceramic tiles, which cost \( \$ 4 \) per tile for supplies. 

 

- The function \( g ( x ) = 4 ( x + 11 ) \) represents the total cost, in dollars, for the supplies needed to paint \( x \) square tiles and \( 11 \) triangular-shaped tiles. 

 

Part B 

 

What does \( g ( 9 ) = 80 \) represent? 

The artist paints \( 9 \) square tiles, and the total cost is \( \$ 80 \) for the supplies needed to paint the square and triangular-shaped tiles, 

The artist paints \( 9 \) square tiles, and the total profit is \( \$ 80 \) for selling the square and triangular-shaped tiles. 

The artist paints \( 80 \) square tiles, and the total cost is \( \$ 9 \) for the supplies needed to paint the square and triangular-shaped tiles. 

The artist paints \( 80 \) square tiles, and the total profit is \( \$ 9 \) for selling the square and triangular-shaped tiles. 

Q:

Which two of the tollowing statements about the law of large numbers are true? 

(Select all that apply.) 

It can be used to explain the difference between theoretical and experimental probabilities. 

It can be used to find the number of arrangements with large numbers.

 

As the number of trials increases, the difference between theoretical and experimental probabilities increases. 

As the number of trials increases, the difference between theoretical and experimental probabilities 

 

Q:

Name the quadrilateral formed by the following points. (hint: graph the quadrilateral and then apply properties) M(1, 3), A(6, 3), T(7, 6), H(4, 7)

 Name the quadrilateral formed by the following points. (hint: graph the quadrilateral and then apply properties) 

\( M ( 1,3 ) , A ( 6,3 ) , T ( 7,6 ) , H ( 4,7 ) \) 

 Kite 

Square  

Rectangle

Trapezoid 

Q:

Given (-3, 2) and (1, 2) are vertices of a square, what two sets of coordinates could form the other vertices? (hint: graph the figure and then apply properties) (Select two answers)

\(\square \) Question \( 2 \) Given \( ( - 3,2 ) \) and \( ( 1,2 ) \) are vertices of a square, \( 11 \) pts what two sets of coordinates could form the other vertices? (hint: graph the figure and then apply properties) (Select two answers) 

\( \square ( - 3,5 ) \) and \( ( 1,5 ) \) 

\( \square ( - 3,5 ) \) and \( ( - 1,5 ) \) 

\( \square ( - 3,6 ) \) and \( ( 1,6 ) \) 

\( \square ( - 3 , - 2 ) \) and \( ( 1 , - 2 )\) 

Q:

Answer

Suppose you drew \( 2 \) equilateral triangles that are congruent and share a side. What polygon is formed? Is it a regular polygon? Drawing the figure may help in solving the problem. 

A    is formed. 

 

The polygon formed ? a regular polygon,

 

 because is formed. 

 

Q:

A graphic artist wants to sketch rough plans for props and positions of all the objects and characters in a key scene to ensure the effective use of space for the scene. To make use of the entire space, including physics effects, stairs, furniture, decorations, and other props along with the characters, what kind of unit measure would be best? 

Q:

A school courtyard consists of a grassy green space surrounded by a gravel path. The dimensions of the entire courtyard, including the gravel path, are \( 30 \) feet by \( 25 \) feet. The gravel path is \( 2 \) feet wide. The school's SGA will be replacing the grass in the green space. T The gravel path will not be replaced. d A landscaping company charges \( \$ 0.15 \) per square foot for the grass and an additional \( \$ 0.50 \) per square foot installed. How much would be saved if the SGA installed the grass themselves instead of having the landscaping company install it? 

How much will the students save if they work together to install the grass themselves as opposed to having the landscaper install it? 

\(\$ 81.90 \) 

\( \$ 273.00 \) 

\( \$ 322.00 \) 

\( \$ 354.90\) 

Q:

Triangle \( A B C \) is going to be dilated by a scale factor of \( 3 / 2 \) . If A is located at \( ( 2 , - 2 ) \) , where will A' be located? (Chapter \( 11 \) ) Select the correct response: 

\( ( 3 , - 3 ) \) 

\( ( 2 , - 3 ) \) 

\( ( - 3,3 ) \) 

\( ( 3 , - 2 )\) 

Q:

When she came home she changed \( € 117 \) into pounds. The new exchange rate was \( £ 1 = € 1.50 \) 

(b) Change \( € 117 \) into pounds. 

Q:

 A bag contains \( 200 \) different types of apples. \( 85 \) of these are green (G), \( 65 \) are yellow (Y) and the rest are red (R). One apple is taken out at a time.

 a) What is the probability that the apple will be green (G)? 

b) What is the probability that the apple will be yellow (Y)? 

c) What is the probability that the apple will be red (R)? 

 

I. At a supermarket, 75\% of customers buy brown bread, \( 65 \% \) buy white bread. If \( 50 \% \) of them buy both brown and white bread, what proportion of customers buy at least one kind of bread? (Please provide the steps for calculations) 

Q:

Force is measured in newtons \( ( N ) \) . 

A force of \( 198.5 N \) is applied to a rectangular surface of length \( 4.9 cm \) and width \( 4.1 cm \) . Work out an estimate of the pressure, in \( N / cm ^ { 2 } \) , applied to this rectangular surface.  

Q:

A Ferris wheel has a radius of \( 10 m \) . When one of the passenger cars is at the bottom, it is \( 2 m \) from the ground. It takes \( 16 \) seconds to reach the top of the Ferris wheel from the very bottom. Assume that the rotation of the Ferris wheel is constant. 

a) What is the period of the sinusoidal function that models this motion? 

b) What is the amplitude of the function? 

c) Determine a cosine function that would model the rotation of this wheel. 

d) How long would it take a car on the Ferris wheel to reach a height of \( 8 m \) from the ground? 

Q:

The circle represents all of the students in a class. Each section represents the students in the class who chose a certain color as their favorite. The angle measures for some sections are given. 

Part A: What is the sum of the angle measures for Blue, Red, and Green?

Part B:  Explain how to find the angle measure for Pink. Then find the measure. 

Q:

Would you rather be paid \( \$ 10,000,000 \) now and \( \$ 100,000 \) per week for the next year, or be paid \( \$ 0.01 \) now and have your money double each week for one year? Provide mathematical evidence to explain and support your choice. 

Q:

A pizza is divided into \( 18 \) equal pieces. Some teachers and students share the pizza. Each teacher eats \( 4 \) pieces, and each student eats \( 2 \) pieces of pizza. They eat all of the pizza. How many teachers are there, and how many students are there? 

Q:

The graph below shows the weight of two different puppies. The puppies were weighed at birth and then weighed each month for one year. The blue line represents an Australian Shepherd and the red line represents a Jack Russell Terrier. Which dog weighed more at birth and how can you tell? 

A. The Australian Shepherd weighed more at birth because it reaches a weight of \( 50 \) pounds. 

B. The Australian Shepherd weighed more at birth because the slope of the blue line is steeper than the slope of the red line. 

C. The Jack Russell weighed more at birth because the y-intercept of the red line is higher than the \( y \) - intercept of the blue line. 

D. This answer cannot be determined from the graph. 

Q:

10. A cook inspects \( 20 \) hamburgers and finds \( 3 \) of them are missing a pickle. a. What is the experimental probability that a hamburger will be missing a pickle? b. The restaurant makes \( 300 \) hamburgers. Predict the number of hamburgers that are likely to be missing a pickle. 

 

 

 

11. An inspector checks \( 150 \) children with bike helmets and found that \( 21 \) children are not wearing them properly. a. What is the experimental probability that a child will not be wearing a bike helmet properly? b. The inspector checks \( 500 \) more children with bike helmets. Predict the number of those children that will not be wearing their bike helmet properly. 

Q:

Write impossible, unlikely, as likely as not , likely, or certain to describe each event

1. Selecting a green marble from a bag of white marbles 

2. Choosing a vowel from the letters A, M, O, F, P, I 

3. Correctly guessing a number from \( 1 \) to \( 3 \) when you have \( 2 \) tries 

Q:

A combination washer/dryer costs \( \$ 1,179 \) . New parts for this washer/dryer cost \( \$ 211 \) , labor to repair it costs \( \$ 553 \) , and shipping it to and from a repair center costs \( \$ 152 \) . A full warranty, which covers all aspects of repairing the washer/dryer, costs \( 30 \% \) of the price of the washer/dryer. A limited warranty, which only covers labor costs, only costs \( 14 \% \) of the price of the washer/dryer. Assuming that the washer/dryer needs repairs which include parts, labor, and shipping, which warranty is the better deal, and by how much, rounded to the nearest dollar? 

a. The limited warranty will end up costing the consumer \( \$ 189 \) less. 

b. The limited warranty will end up costing the consumer \( \$ 363 \) less. 

c. The full warranty will end up costing the consumer \( \$ 553 \) less. 

d. The full warranty will end up costing the consumer \( \$ 174 \) less.

Q:

If you cannot be on the soccer team and the football team at the same time, that is an example of a(n)_______________________ event.

\(\square \) Question \( 13 \) 6. If you cannot be on the soccer team and the football team at the same time, that is an example of a(n) event. O mutually exclusive O theoretical O inclusive O complementary 

Q:

 

A journalist is going to do a survey to find out whether people aged \( 15 \) or less spend more time playing computer games than people aged more than \( 15 . \) The journalist says their sample will be the first \( 20 \) people leaving a particular shop after \( 9 \) am next Monday. 

 

(a) Give one reason why the journalist's sample is unlikely to give reliable information. 

Q:

 Maryse, who has disliked Anna since third grade, made a list of every possible distinct six-digit positive integer that can be formed using each of the digits \( 1,2,4,5,8 \) and \( 9 \) exactly once in each integer. What is the sum of the integers on Maryse's list? 

Q:

A sdentist began astudy with a sample of \( 1,500 \) bacteria. He noticed that the number of bacteria in the sample after \( t \) days can be modeled by the equation \( P = 1,500 \) . \( 5 ^ { t } \) . In this equation, what does \( 5 ^ { t } \) 

represent? A. The number of bacteria increases by \( 5 \) bacteria each day. B. The number of bacteria increases by bacteria after \( 5 \) days. C. The number of bacteria increases day factor of \( 5 \) each day. The number of bacteria increases by a factor of each day for \( 5 \) cays 

Q:

Question \( 6 \) The following numbers are part of a data set: \( 3,6,7,6,11,12,11 \) 

Which TWO choices are TRUE based on the data set? 

 

A. The lower quartile is \( 6 \) . 

B The lower quartile is \(7\) 

C The mean is \( 8 \) . 

D. The higher quartile is \( 12 \) . 

E. The mean is \( 56 \) . 

Q:

A person't heart is pumping blood at a rate of \( 96.3 \) cubic centimeters per second. Convert this into liters per minute. Round your answer off to the nearest hundredth if necessary. 

\( \square \) liters per minute 

Q:

Darcy made a wooden toy box for his nephew for Christmas. It has length of \( 24 \) in, width of \( 13 \) in and height of \( 14 \) in. He plans to paint the box green. 

a. Determine the amount of green paint required to cover the outside of the toybox to the nearest square inch. in \( ^ { 2 } .\) 

b. The can says that it will cover \( 425 \) in \( ^ { 2 } \) . How many cans of paint will Darcy need to paint the outside of the toybox? 

Q:

Chelsea is an auditor for a large women's clothing manufacturer that produces about \( 100,000 \) 

garments daily. The company wants to know why the business is starting to lose money in the past year. In her investigation, Chelsea discovers that there is an increase in the number of rejected orders based on quality issues. All rejected orders have to be re-made at the cost of the manufacturer .To investigate where things are failing, Chelsea begins to conduct her own quality control audit. She decides to do a sample of \( 1000 \) garments per day for the \( 3 \) months. On a daily basis she find at-least \( 95 \) of them do not pass the company's quality control guidelines. How many of the garments in the population can you expect to have problems? 

\(950 \) 

\( 9500 \) 

\( 95000 \) 

\( 95\) 

Q:

Austin's rectangular flower bed measures \(4\pi\) long and \(3\pi\) wide.

He wants to cover the flower bed in mulch 

He knows the area each bag of mulch covers, but only in square centimeters. 

(a) Find the area of Austin's flower bed in square centimeters. Do not round intermediate computations and round your final answer to two decimal places. Use the table of conversion facts, as needed. 

(b) Austin wants to cover his flower bed with mulch. He doesn't have any to begin with and he can't buy partial bags of mulch. Each bag of mulch covers \( 590 cm ^ { 2 } \) . How many whole bags of mulch does Austin need to buy to completely cover his flower bed? 

(c) If each bag of mulch costs \( \$ 2.58 \) , how much will he need to spend on mulch? Write your answer to the nearest cent. 

 

Q:

Tracy plans to serve punch along with the chicken wings. According to her calculatlons, two times the amount of punch needed is more than \( 4 \) liters. Write an inequality for \( y \) , the amount of punch needed to serve at Tracy's party. 

Q:

Brad, Preston, Zack, and Steven each roll a six-sided die a different number of times, record their results, and then calculate the experimental probability of rolling a \( 6 \) . If Brad rolled his die \( 5 \) times, Preston rolled his die \( 25 \) times, Zack rolled his die \( 50 \) times, and Steven rolled his die \( 15 \) times, whose experimental probability will most likely approach the theoretical probability?

 A. Preston 

B. Zack 

C. Brad 

D. Steven 

Q:

Betsey is \( 11 \) years older than Waldo. Betsey's age is \( 15 \) years less than three times Waldo's age. The system below models the relationship between Betsey's age (b) and waldo's age (w): 

\( b = w + 11 \) 

\( b = 3 w - 15\) 

Which of the following methods is correct to find Betsey's and Waldo's age? 

 

Solve \( w + 11 = 3 w - 15 \) to find the value of \( w \) . 

Solve \( b + 11 = 3 b - 15 \) to find the value of b. 

Write the points where the graphs of the equations intersect the \( x \) -axis. 

Write the points where the graphs of the equations intersect the \( y \) -axis. 

Q:

Rylee has a pack of \( 40 \) balloons. In the pack, there are \( 7 \) red, \( 12 \) green, \( 11 \) blue, and \( 10 \) yellow balloons. When grabbing a balloon, she expects to grab a yellow balloon \( \frac { 1 } { 4 } \) of the time. After grabbing and replacing a balloon, she repeats this process four times and records the results below. 

         1                  2                  3                   4

        red              green            blue             green 

Which statement best explains why the results of her experiment did not match her expectations? 

A. She should not have replaced the balloons between trials. 

B. She really should not be able to grab a yellow balloon \( \frac { 1 } { 4 } \) of the time. 

C. She performed too many trials. 

D. She did not perform enough trials. 

 

Q:

The sides of an isosceles triangle have lengths 

\( 13 x - 2 \) and \( 7 x + 4 \) . The base has length \( 10 x \) 

\( + 4 \) . What is the length of the leg? (Hint: draw a diagram) 

\( 11 \) 

\( 6 \) 

\( 4\) 

\(1\)

Q:

Find the perimeter of the rectangle with vertices \( R ( - 4,1 ) , E ( - 1,4 ) , C ( 5 , - 2 ) \) , and 

\( Y ( 2 , - 5 ) \) . Round the answer to the nearest hundredth ( \( 2 \) decimal places). 

\( 12.73 \) 

\( 25.46 \) 

\( 36 \) 

\( 1296\) 

Q:

The force \( F \) (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length \( L \) (in inches) of the handle. A force of \( 30 \) pounds is needed when the handle is \( 8 \) inches long. If a person needs \( 15 \) pounds of force to loosen the bolt, estimate the length of the wrench handle. Round answer to two decimal places if necessary.

Q:

At the beginning of year \( 1 , \) Sam invests \( \$ 700 \) at an annual compound interest rate of \( 5 \% \) . He makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year \( 4 \) ? What is the balance? 

A. \( A ( n ) = 700 + ( n - 1 ) ( 0.05 \cdot 700 ) ; \$ 805.00 \) 

B. \( A ( n ) = 700 + ( 0.05 \cdot 700 ) ^ { ( n - 1 ) } ; \$ 825.42 \) 

C. \( A ( n ) = 700 \cdot ( 1 + 0.05 ) ^ { ( n - 1 ) } ; \$ 810.34 \) 

D. \( A ( n ) = 700 \cdot ( 1 + 0.05 ) ^ { n } ; \$ 850.85\) 

Q:

A student designs a special container as part of an egg drop experiment. She believes that the egg can survive a fall as long as the container hits the ground no faster than \( 75 ft / s \) . 

 

To predict the impact velocity, she uses the physics formula \( v = \sqrt { ( v _ { 0 } ) ^ { 2 } + 2 a d } \) , in which \( v _ { 0 } \) is the egg's velocity when it is released, a is the egg's acceleration due to gravity \( ( 32 ft / sec ^ { 2 } ) \) and \( d \) is the fall distance. 

 

Assuming the student's specifications are correct, will the egg break if the student drops the unmoving egg from shoulder height \( ( 5 ft ) \) while standing on a building \( 85 ft \) high? 

Select one: 

a. not enough information 

b. yes, the egg should break 

c. no, the egg should be okay 

Q:

The graph of \( y = \sqrt { x } \) is stretched vertically by a factor of \( 3 \) , reflected over the \( y \) -axis, translated \( 3 \) units to the left and translated \( 2 \) units upward. a) Write the equation of the transformed function. b) State its domain and range. 

Q:

Aldo's Shoes bought a shipment of \( 667 \) pairs of women's shoes for \( \$ 50.00 \) per pair. The store sold \( 102 \) pairs at the regular selling price is  \( \$ 210.00 \) per pair, \( 63 \) pairs at a clearance sale at a discount of \( 30 \% \) , and the remaining pairs during an inventory sale at a price that equal to cost plus overhead. The store's overhead is \( 17 \% \) of cost. 

(a) What was the price at which the shoes were sold during the clearance sale? 

(b) What was the selling price during the inventory sale? 

(c) What was the total profit realized on the shipment? 

(d) What was the average rate of markup based on cost that was realized on the shipment? 

Q:

A telephone pole is supported by two wires on opposite sides. At the top of the pole, the wires form an angle of \( 64 ^ { \circ } \) . On the ground, the ends of the wires are \( 15.0 m \) apart. One wire makes a 

\( 45 ^ { \circ } \) angle with the ground. How tall is the telephone pole to the nearest tenth of a meter? Select one: 

a. \( 11.2 m \) 

b. \( 15.8 m \) 

c. \( 11.8 m \) 

d. \( 15 m\) 

Q:

Jessica has some round stickers. Each sticker has a radius of \( 2 cm \) . She is trying to cover as much of a sheet of paper that is \( 24 cm \) by \( 33 cm \) as possible without any overlap and modification of the stickers. How much of the bare paper will be visible around the stickers? 

\( 188.81 \) square \( cm \) 

\( 9 \) square \( cm \) 

\( 18.81 \) square cm 

\( 0.32 \) square \( cm\) 

Q:

 A rectangle's length is \(1.5\) times its width. The perimeter of the rectangle is four more than \(3\) times the length. What are the dimensions of the rectangle? 

\(8 \times 12\) 

\(6 \times 12\) 

\(8 \times 8\) 

\(6 \times 9\) 

 

Q:

 A rectangle's length is \( 1.25 \) times its width. Its perimeter is \( 3 \) times the length plus one. What are the dimensions of the rectangle? 

\( 1.33 \times 1.67 \) 

\( 2 \times 3 \) 

\( 1.25 \times 2 \) 

\( 2.25 \times 3\) 

Q:

Sellane Appliances received an invoice dated October \( 10 \) with terms \( 4 / 10 \) E.O.M. for the items listed below. 

\(4 \) refrigerators at \( \$ 1050 \) each less \( 25 \% \) and \( 4 \% \) 

\( 3 \) dishwashers at \( \$ 715 \) each less \( 15 \frac { 1 } { 3 } \% , 12.6 \% \) , and \( 5 \% \) 

(a) What is the last day for taking the cash discount? 

(b) What is the amount due if the invoice is paid on the last day for taking the discount? 

(c) What is the amount of the cash discount if a partial payment is made such that a balance of \( \$ 2500 \) remains outstanding on the invoice? 

Q:

 

David is having a dinner party. He is making Moroccan chicken tagine for the first time. The dish requires adding ingredient at different temperatures. For example the last step requires that when the internal temperature of the dish is \( 375 ^ { \circ } F \pm 2.5 ^ { \circ } F \) , he must add the peas . If he waits too long, all the other ingredients will turn too mushy and if he does it too soon, the peas will be mushy. Which of the following internal temperatures is perfect for adding the peas? 

\( 372.2 ^ { \circ } F \) 

\( 377.57 { } ^ { \circ } F \) 

\( 376.56 { } ^ { \circ } F \) 

\( 372.46 ^ { \circ } F\) 

Q:

Phyllis (Phillip's sister) has also learned good saving habits, but she wants to know what different savings accounts will help her earn. She invests \( \$ 3000 \) in each of three different savings account types each with different interest rates as shown below. 

You will use this compounding interest formula to calculate how much her money will earn in each of the accounts based on the interest rate \( ( r ) \) as a decimal and time (t) in years. For each different account, you will change the variable for interest rate \( ( r ) \) and time \( ( t ) \) . For one month, use \( 0.083 \) years. 

Amount \( = 3000 \cdot ( 1 + r ) ^ { t }\) 

1. How much money will the accounts have after \( 1 \) month? After \( 1 \) year? After \( 10 \) years? 

 

                                       Interest (r)             \(1 \) month              \(1 \) year                  \(10 \) years

Savings                         

Money Market               

Certificate of Deposit     

 

2. How much did the money grow in each bank account from just interest over \( 10 \) years?

 

3. What brought in more money over \( 10 \) years, monthly savings or interest growth? 

Q:

"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for the same fabric specimens discussed in the previous exercise: 

\(\begin{array}{|c|c|} \hline \text{Permafresh}&\text{Hylite}\\ \hline 118&170\\\hline 127&174\\\hline 144&158\\\hline 106&169\\\hline 129&\\\hline \end{array}\)

A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. 

a. The mean and the standard deviation for the: Permafresh are: 

 

b. The mean and the standard deviation for the Hylite are: 

 

c. The standard error is: 

 

d. The critical value from the distribution for a confidence interval of \( 99.8 \% \) is: 

Q:

A study of the effects of exercise used rats bred to have high or low capacity for exercise. There were \( 13 \) high-capacity and \( 13 \) low-capacity rats. To compare the mean blood pressure of the two types of rats using the conservative Option \( 2 \) t- procedures. 

What are the associated degrees of freedom? 

Q:

In \( 1990 , \) Americans ate on average \( 386 lb \) of vegetables per year. By \( 2008 \) , this value increased to \( 449 lb \) . 

a. What was the increase in the number of pounds of vegetables?

 b. How many additional pounds of vegetables did Americans add to their diet per year? 

Q:

Dominic needs to sell at least \( 10 \) cars each month before he gets his commission check. What does the \( 10 \) car minimum represent? 

A. quota 

B. gross pay 

C. salary plus commission 

D. commission 

Q:

Depreciation is the decrease or loss in value of an item due to age, wear, or market conditions. We usually consider depreciation on expensive items like cars. Businesses use depreciation as a loss when calculating their income and taxes. 

 

One company buys a new bulldozer for \( \$ 127750 \) . The company depreciates the bulldozer linearly over its useful life of \( 23 \) years. Its salvage value at the end of \( 23 \) years is \( \$ 18500 \) . 

 

A) Express the value of the bulldozer, \( V \) , as a function of how many years old it is, \( t \) . Make sure to use function notation. 

 

B) The value of the bulldozer after \( 7 \) years is _______

Q:

Suppose that you randomly selected \( 20 \) adults. Assume \( 19 \% \) of the population smoke. Round all answers to \( 2 \) decimal places. 

a) Using the Range Rule Of Thumb, what is the minimum number of usual smokers we can expect to get out of \( 20 \) adults? 

b) Using the Range Rule of Thumb, what is the maximum number of usual smokers we can expect to get out of \( 20 \) adults? 

c) Would it be unusual to randomly select \( 20 \) adults and get \( 14 \) smokers? 

 

Yes, since \( 14 \) is not between the maximum and minimum usual values. 

No, since \( 14 \) is between the maximum and minimum usual values. 

Q:

Which one of the following statements is not true about a scatter plot? 

The dependent variable is found on the \( y \) -axis. 

A scatter plot helps you to visualize the linear relationship between two variables. 

When dealing with real-world data points, the scatter plot will usually deal with positive numbers only. If the ordered pairs of a scatter plot don't line up perfectly straight, then you can conclude that there is no relationship at all between the two variables. 

Q:

Given the sequence: \( 7,21,63,189 , \ldots , 301327047 \) 

a) Find the explicit formula for the sequence. 

 

b) Use your equation from part a) to find: What term number is the last term in the sequence? (Show the method that was demonstrated in this class, algebraically showing each step using the equation.) 

Q:

"Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for the same fabric specimens discussed in the previous exercise:

  \(\begin{array}{|r|r|} \hline \text { Permafresh } & \text { Hylite } \\ \hline 118 & 170 \\ \hline 127 & 174 \\ \hline 144 & 158 \\ \hline 106 & 169 \\ \hline 129 & \\ \hline \end{array}\)

A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. 

 

a. The mean and the standard deviation for the Permafresh are: _______

 

b. The mean and the standard deviation for the Hylite are: _______

 

c. The standard error is: _______ 

    

d. The critical value from the distribution for a confidence interval of \(99.8 \% \) is: _______

Q:

Anne owns a spinner with four equally sized segments colored red, blue, green, and yellow. The theoretical probability of any color segment having the spinner arrow land on it is \( 0.25 \) . Anne spins the arrow \( 8 \) times and records the number of times the arrow lands on each color, as follows. - red - \( 3 \) times blue - \( 4 \) times green - \( 0 \) times yellow - \( 1 \) time Anne analyzes her results and questions whether the theoretical model is consistent with her data. Which conclusion is valid? 

 

A. The theoretical model is not consistent with her data. The size of the red and blue segments on the spinner should be reduced. 

B. The theoretical model is consistent with her data. 

C. The theoretical model is not consistent with her data. More trials are needed.

D. The theoretical model is not consistent with her data. The theoretical model should be adjusted to fit her data. 

Q:

The breakfast special at the Hideout Cafe comes with a choice of three side dishes, hash browns, pancakes, or fruit, and a choice of two types of bread, toast or biscuits. List all of the possible specials. Use the first letter of each choice as an abbreviation. 

\( H - T , H - B , P - T , P - B \) 

\( H - T , H - B , P - T , P - B , F - T , F - B \) 

None of these 

\( H - B , P - T , F - T \) 

\( H - T , P - T , F - T\) 

Q:

 Select each statement that is true for all reflections in the coordinate plane. 

The distance between a point and its image will be twice the distance between the point and the line of reflection. 

A line segment connecting a point and its image will be perpendicular to the line of reflection. 

A point that is mapped to itself after a reflection is on the line of reflection. 

Q:

Since the area under the normal curve within two standard deviations of the mean is \( 0.95 \) , the area under the normal curve that corresponds to values greater than \( 2 \) standard deviations above the mean is \( 0.05 . \) 

True 

False 

Q:

9. Nathaniel wants to buy a new bicycle. His payment options are: 

Option 1: Pay \( \$ 2055.99 \) cash. He only has \(\$ 400.00 \) saved up  , so he can take out a loan for the rest from his bank at a rate of \( 7.25 \% \) per annum over \( 2 \) years. 

Option 2: Take the store payment plan of \( 12 \) monthly payments of \( \$ 180.00 \) . 

a) If he chooses Option 1, what will his monthly payments be? 

b) If he chooses Option 2, what annual rate of interest will he pay?  

c) Calculate the total cost of each option. Which option should he choose, and why?

Q:

Last weekend, Emma opened a bank account. The equation \( A = 90.76 ( 1.08 ) ^ { \wedge } n \) represents the amount of money, A. Emma has in her bank account after \( n \) months. What does the number \( 90.76 \) represent in this situation? 

-The number of months 

-The increasing interest rate 

-The initial amount to open the bank account 

-The amount of money in the account after \( 90 \) months 

Q:

Last weekend, Emma opened a bank account. The equation \( A = 90.76 ( 1.08 ) ^ { \wedge } n \) represents the amount of money, \( A , \) Emma has in her bank account after n months. What does the number \( 90.76 \) represent in this situation? 

-The number of months 

-The increasing interest rate 

-The initial amount to open the bank account 

-The amount of money in the account after \( 90 \) months 

Q:

Richard is asked to spray wash the exterior of a building that is shaped like a cube. He decides to calculate the surface area of the building in order to estimate how much water he will need. He does the calculation using the standard formula and, after doing the job, realizes he overestimated the amount of water he needed. Where was his mistake? 

A. He forgot to square the result. 

B. He forgot to subtract the area of the base from the total surface area of the cube. 

C. He forgot to add the area of the base to the total surface are of the cube. 

D. He forgot that there is no formula for the surface area of a cube. 

 

Q:

Which of the following statements about the distance formula is TRUE? 

A. The distance formula cannot be used to calculate distances in \( 3 \) dimensions. 

B. The distance formula can be written correctly in only one way. 

C. The distance formula only applies to points in one dimension. 

D. The distance formula can be derived from the Pythagorean Theorem. 

Q:

Use the following information to answer the next question 

Scenario I: The curriculum states that all students taking CALM learn about budgeting. Ryan's friend Jenna is taking CALM. Ryan therefore can conclude that Jenna will learn about budgeting,

Scenario II: Ryan has \( 5 \) friends who took PE 20. They all told Ryan that they played Basketball during their course. Ryan knows that Jenna is taking PE 20. He can therefore conclude that Jenna will play Basketball. 

Ryan is using deductive reasoning in 

A. Both Scenarios 

B. Neither Scenario 

C. Scenario II 

D. Scenario I 

Q:

If a coin has been altered so that the probability of heads coming up is \( \frac { 1 } { 10 } \) , then the probability of tails coming up is \( \frac { 9 } { 10 } \) . 

A. True

B. False 

Q:

\(\left. \begin{array} { l } { \text { The total yearly cost of the local bus service is made up of a base fee of } \$ 250 \text { plus a } } \\ { \text { per trip fee of } \$ 1 \text { . Which equation represents the relationship between the total } } \\ { \text { yearly cost } ( C ) \text { and the number of trips } ( n ) \text { ? } } \end{array} \right.\)

The total yearly cost of the local bus service is made up of a base fee of \( \$ 250 \) plus a per trip fee of \( \$ 1 \) . Which equation represents the relationship between the total yearly cost \( ( C ) \) and the number of trips \( ( n ) \) ? 

Q:

Does the y-intercept in an equation play any role in determining whether or not two lines are parallel or perpendicular? Explain and provide an example to illustrate your understanding. 

Q:

A contractor is buying shingles for a roofing job. The area of the roof is \( 400 \) square feet. The shingles cover \( 23 \) square feet per bundle. To be sure he has enough shingles, the contractor bought \( 17 \) bundles. 

Did the contractor purchase enough shingles? 

Yes, because \( 23 \times 17 \) is larger than \( 400 \) 

Yes, because \( 400 \div 17 \) is larger than \( 23 \) 

Yes, because \( 400 \div 23 \) is equal to \( 17 \) 

No, because \( 400 \div 23 \) is larger than \( 17\) 

Q:

Identify and describe the bias in each situation. 

a) Patrons of an amusement park were given surveys when leaving that read: "Tell us about how much you enjoyed our amusement park today!" 

 

b) Which type of bias is a student trying to reduce if they use a stopwatch to time a pendulum as it swings back and forth instead of using a wristwatch? 

 

c) A researcher randomly selected shoppers at a mall and gave them surveys on consumer spending. The participants were asked to complete and return the surveys to the mall office within the next month. 

Q:

The Cross Country Bus Tour Company owns five buses that tour the United States. All tours start in Los Angeles. The cost \( ( C ) \) to operate their tours is \( \$ 250.00 \) per hour plus \( \$ 1000 \) for marketing for each trip. 

Tour Destination                                      Total Hours                                   Total Miles

Texas Tour                                                     50                                                3000

Wisconsin Tour                                              66                                                3960

Florida Tour                                                    90                                                5400

New England Tour                                        110                                               6600

Alaska Tour                                                   116                                               6960

Tickets for the Wisconsin tour cost \( \$ 700 \) . How many tickets does the tour company need to sell to break even? 

Q:

Shannon likes to jog around a lake for exercise. The distance around the lake is \( 440 \) yards. If she jogs around the lake \( 4 \) times, how many miles has

                            [?] miles 

Hint: There are \( 1,760 \) yards in \( 1 \) mile 

Q:

Identify the independent and dependent variables for the given situation. Carbon dioxide levels in the air and levels of traffic. 

A. Carbon dioxide = independent; traffic = independent 

B.Carbon dioxide = independent; traffic = dependent 

C. Carbon dioxide = dependent; traffic = dependent 

D. Carbon dioxide = dependent; traffic = independent 

Q:

Identify the independent and dependent variable for the given situation. The amount of distance covered by a car in a certain amount of time.

 

distance = independent; time= dependent 

distance = dependent; time = independent 

distance = independent; time = independent 

distance = dependent; time = dependent 

Q:

If you roll a standard number cube \( 48 \) times, how many times do you expect the cube to show a two? Round your answer to the nearest whole number if needed. 

 

Q:

Based on a sample survey, a company claims that \( 90 \% \) of their customers are satisfied with their products. Out of \( 1,100 \) customers, how many would you predict to be satisfied? 

\( 890 \) customers 

\( 840 \) customers 

\( 790 \) customers 

\( 990 \) customers 

Q:

If you roll a standard number cube \( 42 \) times, how many times do you expect the cube to show a six or an eight?

 Round your answer to the nearest whole number if needed. 

 

Q:

The average monthly precipitation for October, November, and December is \( 4.21 \) in. If \( 1.65 \) in. falls in October and \( 3.04 \) in. falls in November, how many inches must fall in December so that the average monthly precipitation for these months exceeds \( 4.21 \) in.? 

Select the correct choice below and fill in the answer box(es) to complete your choice. 

 

A. The amount of precipitation that must fall in December is at most inches. 

(Type an integer or a decimal.) 

B. The amount of precipitation that must fall in December is between in. and inches. 

(Type integers or decimals. Use ascending order.) 

C. The amount of precipitation that must fall in December is greater than inches.

(Type an integer or a decimal.) 

D. The amount of precipitation that must fall in December is at least inches. 

(Type an integer or a decimal.) 

E. The amount of precipitation that must fall in December is less than inches. 

(Type an integer or a decimal.) 

Q:

A high level of LDL cholesterol ("bad cholesterol") in the blood increases a person's risk of heart disease. The table to the right shows how LDL levels affect risk of heart disease according to a certain doctor. 

 

LDL Cholester                                   Risk Category 

Less than \( 101 \)                                      Optimal 

\( 101 - 129 \)                           optimal    Near optimal/above                           

\( 130 - 157 \)                                    Borderline high             

\( 158 - 190 \)                                           High     

\( 191 \) and above                                    Very High 

 

If \( x \) represents the LDL cholesterol number, write a linear inequality or three-part inequality for the near optimal/above optimal category. Use \( x \) as the variable. Choose the correct answer below. 

A. \( 129 \leq x \leq 101 \) 

B. \( 101 < x \leq 130 \) 

C. \( x \leq 129 \) 

D. \( 101 \leq x \leq 129\) 

Q:

A zoo keeper things there is a problem with the Naked Mole-Rat population at the zoo. He starts keeping t of the animals in the tunnels. \( 7 \) days into his monitoring he counts \( 120 \) mole rats, \( 13 \) days in he counts \( 108 \) many mole rats is he getting rid of per day where x represents the number of days and y represents the number of mole rats 

Q:

Another testing center reported a pass rate of  \(83\% \)  with 620 people passing. How many people took the test at that center?(Remember that people must be a counted discretely, meaning you can't have a decimal part of a person.)

Q:

You wish to test the following claim \( ( H _ { a } ) \) at a significance level of \( \alpha = 0.005\) 

\(H _ { o } : \mu _ { 1 } = \mu _ { 2 } \) 

\( H _ { a } : \mu _ { 1 } \neq \mu _ { 2 }\) 

You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal You obtain a sample of size \( n _ { 1 } = 28 \) with a mean of \( \overline { x } _ { 1 } = 87.7 \) and a standard deviation of \( s _ { 1 } = 17.4 \) 

from the first population. You obtain a sample of size \( n _ { 2 } = 28 \) with a mean of \( \overline { x } _ { 2 } = 96.2 \) and a standard deviation of \( s _ { 2 } = 8.9 \) from the second population. 

 

a. What is the test statistic for this sample? 

 

b. What is the p-value for this sample? For this calculation, use. 

 

c. The \( p \) -value is... 

     A. less than (or equal to) \( \alpha \) 

     B. greater than \( \alpha\) 

 

d. This test statistic leads to a decision to... 

    A. reject the null 

    B.accept the null 

    C.fail to reject the null 

Q:

 

 If \( | \vec { a } | = 12 , | \vec { b } | = 8 \) , and the angle between them is \( 60 ^ { \circ } \) , determine the magnitude and direction of \( \vec { a } + \vec { b } \) . Include a diagram. (4 marks) 

Q:

In a recent study, \( 68 \% \) of high school students supported having more field trips. The study is accurate to within \( 3.0 \) percentage points, \( 19 \) times out of \( 20 \) ." What does this mean? 

 

The study was done \( 20 \) times and in \( 19 \) surveys, between \( 68 \% \) and \( 71 \% \) of respondents supported having more field trips. 

 

If this study were repeated \( 19 \) times, the result of every survey would be that between \( 65 \% \) and \( 71 \% \) of students surveyed supported having more field trips. 

 

If this study were repeated numerous times, then between \( 65 \% \) and  of high school students would support having more field trips in \( 95 \% \) of those studies. 

 

The pollsters asked \( 20 \) high school students if they supported having more field trips \( 19 \) times and the number of people who did was always \( 13 \) or \( 14 \) out of \( 20 \) . 

Q:

A provincial survey was sent to randomly selected homes across Canada. However, 

\( 99 \% \) of the respondents were from Southern Ontario, which only contains \( 94 \% \) of the population. What type of bias does this represent? 

response bias 

non-response bias 

measurement bias 

sampling bias 

Q:

 The temperatures of three solutions were recorded. The recorded temperatures were greater than the actual temperatures because the person doing the experiment gripped the thermometer too tightly. Identify the bias in this scenario. 

sampling bias 

non-response bias 

response bias 

measurement bias 

Q:

Given \( f \) of \( x \) is equal to \( 2 \) divided by the quantity 

\( x \) squared plus \( 3 x \) minus \( 10 \) end quantity, which of the following is true? 

\( f ( x ) \) is positive for all \( x < - 5 \) 

\( f ( x ) \) is negative for all \( x < - 5 \) 

\( f ( x ) \) is positive for all \( x < 2 \) 

\( f ( x ) \) is negative for all \( x > 2\) 

Q:

1. After Jane's band played at a restaurant, they sold \( 36 \) t-shirts for \( \$ 13.00 \) . They spent \( \$ 325 \) having the t- shirts made. How. much more / less than the break-point did they sell? 

A. \(\$ 143.00 \) More 

B. \( \$ 143.00 \) less 

C. \( \$ 156.00 \) Less 

D. \( \$ 156.00 \) More

 

2. At the end of a lease term, you have an option to purchase your vehicle. You will pay: 

A. the lease charge 

B. the residual value 

C. the lease rate 

D. the security deposit 

 

3. Yvette's operating costs for the bakery are \( \$ 2840.00 \) per month and her monthly revenue is \( \$ 3250.00 \) . What is her net profit each month? 

A. \(\$ 290.00 \) 

B. \( \$ 410.00 \) 

C. \( \$ 3250.00 \) 

D. \( \$ 750.00\) 

Q:

Use the ALEKS calculator to evaluate each expression. Round your answers to the nearest thousandth. Do not round any intermediate computations. 

\(e ^ { 0.1 } = \)

 

\(275 e ^ { - 0.65 }\)=

Q:

Let \( p \) and \( q \) represent the following statements. 

    p: Sue's dress is blue. 

    q: Some rockets travel faster than light. 

Express the following statement symbolically. 

No rockets travel faster than light. 

 

Symbolically, the statement is _______

Q:

A restaurant dinner menu includes the following statement. 

       "All dinners are served with a choice of: salad or soup, couscous or pasta, and carrots or peas." 

Is it permissible to select a single dinner with salad, pasta, and carrots? Explain why. 

Choose the correct answer below. 

A. It is not permissible because both salad and pasta cannot be selected at the same time. 

B. It is not permissible because both salad and carrots cannot be selected at the same time. 

C. It is permissible because only one item from each group is selected. 

D. It is not permissible because both pasta and carrots cannot be selected at the same time. 

Q:

23. The scatterplot below shows the data from a small survey to determine if there is a relationship between the number of years a person is educated and their average annual income. Select one statement below which describes the scatterplot below 

Shape: Non-Linear, Direction: positive, Strength: weak & \( 1 \) outlier 

Shape: Linear, Direction: positive, Strength: Strong & \( 0 \) outlier 

Shape: Linear, Direction: positive, Strength: Strong & \( 2 \) outlier 

Shape: Non-Linear, Direction: negative, Strength: weak & \( 2 \) outlier 

24. Derrick is the manager at a batting cage. He charges customers an admission fee of \( \$ 2.00 \) plus a charge of 

\( \$ 0.10 \) for each minute played. He writes the equation below to represent the charge for cach customer, c, based on the number of minutes of play, \( m \) . 

\( c = 0.1 m + 2 \) 

How much is a customer charged for playing \( 40 \) minutes? 

Q:

Ryan, Michelle, and Emily are at an amusement park together: 

-Ryan spent \( \$ 13.50 \) to purchase \( 3 \) tickets for the Ferris wheel and \( 2 \) tickets for the water slide.

-Michelle spent \( \$ 16.50 \) to purchase \( 1 \) ticket for the Ferris wheel and \( 4 \) tickets for the merry-go-round. 

- Emily spent \( \$ 14 \) to purchase \( 3 \) tickets for the Ferris wheel, \( 1 \) ticket for the water slide, and \( 1 \) ticket for the merry-go-round. 

Let \( x , y \) , and \( z \) represent the ticket cost for the Ferris wheel, water slide, and merry-go-round, respectively. Which matrix equation can be solved to find the cost of each type of ticket? 

A.\(\left[ \begin{array} { l l l } { 3 } & { 1 } & { 3 } \\ { 2 } & { 0 } & { 1 } \\ { 0 } & { 4 } & { 1 } \end{array} \right] \left[ \begin{array} { l } { x } \\ { y } \\ { z } \end{array} \right] = \left[ \begin{array} { c } { 13.5 } \\ { 16.5 } \\ { 14 } \end{array} \right] \) 

B.\( \left[ \begin{array} { l l l } { 3 } & { 1 } & { 3 } \\ { 0 } & { 4 } & { 1 } \\ { 2 } & { 0 } & { 1 } \end{array} \right] \left[ \begin{array} { l } { x } \\ { y } \\ { z } \end{array} \right] = \left[ \begin{array} { c } { 13.5 } \\ { 16.5 } \\ { 14 } \end{array} \right] \) 

C.\( \left[ \begin{array} { l l l } { 3 } & { 2 } & { 0 } \\ { 1 } & { 0 } & { 4 } \\ { 3 } & { 1 } & { 1 } \end{array} \right] \left[ \begin{array} { c } { x } \\ { y } \\ { z } \end{array} \right] = \left[ \begin{array} { l } { 13.5 } \\ { 16.5 } \\ { 14 } \end{array} \right] \) 

D.\( \left[ \begin{array} { l l l } { 3 } & { 0 } & { 2 } \\ { 1 } & { 4 } & { 0 } \\ { 3 } & { 1 } & { 1 } \end{array} \right] \left[ \begin{array} { c } { x } \\ { y } \\ { z } \end{array} \right] = \left[ \begin{array} { c } { 13.5 } \\ { 16.5 } \\ { 14 } \end{array} \right]\) 

Q:

What does zero represent in this situation? -25 represents the location of a dolphin \( 25 \) feet below sea level. \( 25 \) represents the location of a seagull \( 25 \) feet above sea level. 

The air temperature 

The speed at which the seagull flies 

Sea level 

The speed at which the dolphin swims 

Q:

 

\( \overline { J K } \) is dilated by a scale factor of \( n \) with the origin as the center of dilation. resulting in the image \(\overline{J ^ { \prime } K ^{ \prime }}\) . The slope of \( \overline { J K } \) is \( m \) . If the length of \( \overline { J } \overline { K } \) is \( l \) , what is the length of 

\(\overline{J ^ { \prime } K ^{ \prime }}  \)

A. \( m \times n \times l\) 

B\(\quad ( m + n ) \times l\) 

\( m \times l\) 

D. \( n \times l\) 

Q:

Select the correct answer. A transportation company hauls vehicles between three different lots of a car dealership. Their fees are based on the type of vehicle being transported, including sedans, vans, and trucks. These breakdowns give the fees for the three different lots in the same month: 

- They hauled \( 4 \) sedans, \( 11 \) vans, and \( 7 \) trucks to the first lot and charged \( \$ 6,830 \) . 

- They hauled \( 5 \) sedans, \( 14 \) vans, and \( 6 \) trucks to the second lot and charged \( \$ 7,680 \) . 

- They hauled \( 15 \) sedans, \( 3 \) vans, and \( 4 \) trucks to the third lot and charged \( \$ 6,190 \) . 

What is the fee for hauling each vehicle? 

A. \( \$ 310 \) for each sedan, \( \$ 280 \) for each van, and \( \$ 260 \) for each truck 

B. \( \$ 340 \) for each sedan, \( \$ 260 \) for each van, and \( \$ 310 \) for each truck 

C. \( \$ 280 \) for each sedan, \( \$ 290 \) for each van, and \( \$ 300 \) for each truck 

D. \( \$ 260 \) for each sedan, \( \$ 310 \) for each van, and \( \$ 340 \) for each truck 

Q:

In which pair do both decimals represent rational numbers? 

A. \( 0.752 \) and \( 0.232323 \ldots \) 

B. \( 8.3182706837521 \ldots \) and \( 0.232323 \ldots \) 

C. \( 4.32891789376287184 \ldots \) and \( 0.2323 \) 

D. \( 8.3182706837521 \ldots \) and \( 0.752\) 

Q:

In which pair do both decimals represent rational numbers? 

A. 7.0289317284164... and \( 0.3444 \) 

B. \( 5.328917830184934 \ldots \) and \( 0.3444 \ldots \) 

C. \( 5.328917830184934 \ldots \) and \( 0.318 \) 

D. \( 0.3444 \ldots\)