Mary purchased \( 4 \) tires by mail order. She paid \( \$ 61.10 \) per tire plus \( \$ 5.40 \) per tire for shipping and handling. There is no sales tax, because the tires were purchased out of state. She also had to pay \( \$ 8.11 \) per tire for mounting and balancing. At a local store, Mary's total for the \( 4 \) tires with mounting and balancing would be \( \$ 328 \) plus \( 6 \% \) sales tax. How much did Mary save by purchasing the tires through the mail?

A plane is flying at an altitude of \( 15,000 ft \) , where the temperature is \( - 5 ^ { \circ } F \) . The nearby airport, at an altitude of \( 2000 ft \) , is reporting precipitation. If the temperature increases \( 2.7 ^ { \circ } F \) for every \( 1000 \) -ft decrease in altitude, will the precipitation at the airport be rain or snow? Assume that rain changes to snow at \( 32 ^ { \circ } F \) .

A boat leaves point A traveling south at a rate of 52 km/he. A second boat leave point A traveling east at a rate of 40 km/hr . How fast is the distance between boats increasing after 15 minutes .Give the exact answer and the answer rounded to one decimal point.

The white oak tree is an Illinois native that can grow \( 15 \) inches taller in one year, but only adds

\( 1 / 4 \) inch to its diameter each year. A tree that is \( 48 \) inches tall and \( 3 / 4 \) inches in diameter when it is planted will have what circumference when i reaches \( 50 \) feet tall (to the nearest inch)?

A) \( 9{ } ' { } ' \)

B) \( 29 ^ { \prime \prime } \)

C) \( 31 ^ { \prime \prime } \)

D) \( 462 ^ { \prime \prime } \)

10. A wooden fence that is \( 6 \) feet tall and \( 11 \) feet wide needs to be painted front and back. If two gallons of paint cover \( 5000 \) square inches, and a one-gallon can of paint costs \( \$ 3.50 \) , how much will it cost to paint the fence?

A) \( \$ 28.00 \)

B) \( \$ 33.26 \)

C) \( \$ 44.19 \)

D) \( \$ 66.52\)

11. When a bicycle is in its highest gear, the wheels (radius \( 14 \) ") rotate \( 9 \) times for every \( 2 \) revolutions of the pedals. When Hildaur is pedaling at \( 60 \) revolutions per minute, how fast will his bicycle travel down the road in miles per hour?

A) \( 1.11 \)

B) \( 3.58 \)

C) \( 5.00 \)

D) \( 22.49\)

Keisha is choosing between two exercise routines.

In Routine \( \# 1 \) , she does only running, burning \( 15.5 \) calories per minute.

In Routine #2, she burns \( 19 \) calories walking. She then runs at a rate that burns \( 10.75 \) calories per minute.

For what amounts of time spent running will Routine #1 burn at least as many calories as Routine #2? Use \( t \) for the number of minutes spent running, and solve your inequality for \( t \) .

Write the sentence in symbolic form. Use \( v , p , \) and \( t \) as defined below.

v: "I will take a vacation."

p: "I get the promotion."

t: "I will be transferred."

If I am transferred, then I will not take a vacation.

\(v \rightarrow t \)

\( v \rightarrow t \)

\( t \rightarrow \sim v \)

\( t \rightarrow v\)

Make use of one of De Morgan's laws to write the given statement in an equivalent form.

It is not true that, she received a promotion or that she received a raise.

She did not receive a promotion and she did not receive a raise.

She did not receive a promotion but she did receive a raise.

She received a promotion and she received a raise.

She received a promotion but she did not receive a raise.

She either received a promotion or she received a raise, but not both.

The numbers of students in the \( 9 \) schools in a district are given below. (Note that these are already ordered from least to greatest.)

\( 247,260,273,280,285,309,312,348,377\)

Suppose that the number \( 247 \) from this list changes to \( 346 \) . Answer the following.

(a) What happens to the median?It decreases by

It increases by

It stays the same.

(b) What happens to the mean? It decreases by

It stays the same.

It increases by

The amount of time it takes for a quantity that grows exponentially to become twice its initial amount is called its

growing time

doubling time

decaying time

increasing time

The following rational equation has denominators that conlain variables. For this equalion, a. Wrile the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Koeping the restrictions in mind, solve the cquation.

\( \frac { 2 } { x + 5 } + \frac { 5 } { x - 4 } = \frac { 45 } { ( x + 5 ) ( x - 4 ) } \)

a. What istare the value or values of the variable that make(s) the denominators zero?

\( x = \) (Simplify your answer. Use a comma to separate answers as needed.)

b. Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is ()

B. The solution set is \( \{ x | x \) is a real number].

C. The solution set is \( \varnothing \)

Center for Health Statistics (NCHS), statisticians Traci Clemons and Marcello Pagano found that the birth weights of babies in the United States are not symmetric ("Are babies normal?" The American Statistician, N \( 1999,53 : 4 \) ). However, they also found that when infants born outside of the "typical" \( 37 - 43 \) weeks and infant born to mothers with a history of diabetes are excluded, the birth weights of the remaining infants do follow a Normal model with mean \( \mu = 3432 g \) and standard deviation \( \sigma = 482 g \) . The following questions refer to infant born from \( 37 \) to \( 43 \) weeks whose mothers did not have a history of diabetes.

Compute the z-score of an infant who weighs \( 3607 g \) . (Round your answer to two decimal places.)

Approximately what fraction of infants would you expect to have birth weights between \( 2960 g \) and \( 3990 g \) ? (Express your answer as a decimal, not a percent, and round to three decimal places.) Approximately what fraction of infants would you expect to have birth weights below \( 2960 \) g? (Express your answer as a decimal, not a percent, and round to three decimal places.)

A population numbers \( 13,000 \) organisms initially and decreases by \( 18.8 \% \) each year. Suppose \( P \) represents population, and \( t \) the number of years of decline. An exponential model for the population can be written in the form \( P = a \cdot b ^ { t } \) where

\( a = 13000\) and \( b = ?\)

In supply (and demand) problems, \( y \) is the number of items the supplier will produce (or the public will buy) if the price of the item is \( x \) .

For a particular product, the supply equation is \( y = 2 x + 423\) and the demand equation is \( y = - 6 x + 671\)

What is the intersection point of these two lines?

Enter answer as an ordered pair (don't forget the parentheses).

What is the selling price when supply and demand are in equilibrium?

price \( = \$ \)

What is the amount of items in the market when supply and demand are in equilibrium?

number of items \( = \)

At \( 6 : 00 \) am, here's what we know about two airplanes: Airplane #1 has an elevation of \( 23050 ft \) . and is descending at the rate of \( 600 ft / min \) . Airplane #2 has an elevation of \( 11290 ft \) . and is climbing at the rate of \( 100 ft / min \) .

(1) Let \( t \) represent the time in minutes since \( 6 : 00 \) am, and let \( E \) represent the elewation in feet. Write an equation for the elevation of each plane in terms of \( t \) .

plane \( \# 1 : E ( t ) = \)

plane \( \# 2 : E ( t ) = \)

(2) At what time will the two airplanes have the same elevation?

\( t = \) minutes after \( 6 : 00 \) am

(3) What is the elevation at that time?

Eva was on a long \( 198 \) mile road trip. The first part of the trip there was lots of traffic, she only averaged \( 20 \) mph. The second part of the trip there was no traffic so she could drive \( 52 \) mph. If the trip took her \( 5 \) hours, how long did she travel at each speed?

In traffic she drove for \( \quad \) hours

After the traffic cleared she drove for \( \quad \) hours.

A dog food producer reduced the price of a dog food. With the price at \( \$ 10 \) the average monthly sales has been \( 22000 \) . When the price dropped to \( \$ 7 \) , the average monthly sales rose to \( 27000 \) . Assume that monthly sales is linearly related to the price.

What price would maximize revenue? \( \$ \)

Zuke's Nukes is a retailer of organic microwavable entrees. They purchase frozen meals in batches from a supplier and then sell them to customers in their store. It costs \( \$ 0.95 \) to store one frozen meal for a year. To reorder more batches of meals from their supplier, Zuke's Nukes pays a fixed fee of \( \$ 2.45 \) per batch as well as \( \$ 0.35 \) per meal. They sell \( 4000 \) meals each year.

Find how large their batch sizes should be for each of their orders from the supplier so that Zuke's Nukes can minimize their total inventory costs.

Approximately how many times will they need to order? (round to nearest order)

A dog food producer reduced the price of a dog food. With the price at \( \$ 11 \) the average monthly sales has been. \( 23000 \) . When the price dropped to \( \$ 10 , \) the average monthly sales rose to \( 27000 \) . Assume that monthly sales is linearly related to the price.

What price would maximize revenue?

A car wash reduced the price of a basic wash as a promotion and test of the market. With the price at \( \$ 11 \) the average monthly sales has been \( 27000 \) . When the price dropped to \( \$ 8 \) , the average monthly sales rose to \( 31000 \) . Assume that monthly sales is linearly related to the price.

What car wash price would maximize revenue? \( \square \)

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of \( 6.7 \) -in and a standard deviation of \( 1.2 \) -in. Due to financial constraints, the helmets will be designed to fit all men except those witly head breadths that are in the smallest \( 1.2 \% \) or largest \( 1.2 \% \) .

What is the minimum head breadth that will fit the clientele? min \( = \)

What is the maximum head breadth that will fit the clientele? min \( = \)

The planning department of Abstract Office Supplies has been asked to determine whether the company should introduce a new computer desk next year. The department estimates that \( \$ 6,000 \) of new manufacturing equipment will need to be purchased and that the cost of constructing each desk will be \( S 100 \) . The department also estimates that the revenue from each desk will be \( \$ 400 \) . a. Determine the revenue function \( R ( x ) \) from the sale of \( x \) desks. \( R ( x ) = \square \)

b. Determine the cost function \( C ( x ) \) for manufacturing \( x \) desks \( C ( x ) = \square \)

c. Find the number of desks that must be sold for the company to break even \( \square \)

If you apply the changes below to the absolute value parent function, \(f ( x ) = | x | \) , what is the equation of the new function?

Shift \(5\) units to the left.

Shift \(4\) units down.

A. \(g ( x ) = | x + 5 | - 4\)

B. \(g ( x ) = | x - 5 | - 4\)

C. \(g ( x ) = | x + 4 | - 5\)

D. \(g ( x ) = | x - 4 | - 5\)

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of \( 119 \) and standard deviation of \( 26 \) . Someone qualifies as having Stage \( 2 \) high blood pressure if their systolic blood pressure is \( 160 \) or higher.

Express your answers as a decimal and round to \( 2 \) decimal places,

a. Around what percentage of adults in the USA have stage \( 2 \) high blood pressure? Give your answer rounded to two decimal places.

b. Stage \( 1 \) high BP is specified as systolic BP between \( 140 \) and \( 160 \) . What percentage of adults in the US qualify for stage \( 1 ?\)

Which term describes the point where the three altitudes of a triangle intersect?

A. Orthocenter

B. Circumcenter

C. Incenter

D. Centroid

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of \(6.6\) -in and a standard deviation of \(0.8\) -in. Due to financi,ll constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest \(4.5 \% \) or largest \(4.5 \% \) .

What is the minimum head breadth that will fit the clientele?

\(\min = \)

What is the maximum head breadth that will fit the clientele?

min \(= \)

Enter your answer as a number accurate to \(1\) decimal place.

The relation \( R \) is defined by the ordered pairs listed below.

\( R = \{ ( - 10 , - 5 ) , ( - 4,7 ) , ( 1,2 ) , ( - 4,18 ) , ( - 10 , - 9 ) \} \)

The domain of \( R \) is __

The range of \( R \) is __

Is \( R \) a function?

Yes, the relation is a function

No, the relation is not a function

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of \( 6.6 \) -in and a standard deniation of \( 0.8 \) -in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest \( 4.5 \% \) or largest \( 4.5 \% \) .

What is the minimum head breadth that will fit the clientele?

\( \min = \)

What is the maximum head breadth that will fit the clientele?

\( \min = \)

Enter your answer as a number accurate to \( 1 \) decimal place.

How many ml of \( 50 \) percent acid should be added to pure acid to make \( 40 ml \) of \( 80 \) percent acid?

\( 24 ml \)

\( 16 ml \)

\( 20.8 ml \)

\( 13.6 ml\)

State whether the following statement is true or false. A function \( f \) has a local maximum at \( c \) if there is an open interval \( d \) containing \( c \) such that for all \( x \) in \( I , f ( x ) \leq f ( c ) \) .

Choose the correct answer below.

A. False, because if \( f \) has a local maximum at \( c \) , then the value of \( f \) at \( c \) is less than or equal to the values of \( f \) near \( c \) .

B. False, because if \( f \) has a local maximum at \( c \) , then the value of \( f \) at \( c \) is the smallest value of \( f \) in the domain.

C. True, because if \( f \) has a local maximum at \( c \) , then the value of \( f \) at \( c \) is the largest value of \( f \) in the domain.

D. True, because if \( f \) has a local maximum at \( c \) , then the value of \( f \) at \( c \) is greater than or equal to the values of \( f \) .

the product of \( 50 \) and the number of employees

A. \( 50 + n \)

B. \( \frac { 50 } { n } \)

C. \( 50 - n \)

D. \( 50 \cdot n\)

Complete the sentence below.

A set of points in the xy-plane is the graph of a function if and only if every ___line intersects the graph in at most one point.

The exponential function \( f ( x ) = 2 ^ { x } \) undergoes two transformations to

\( g ( x ) = 3 \cdot 2 ^ { x } + 5 \) . How does the graph change? Select all that apply.

\( \square \) A. It is vertically stretched.

\( \square \) B. It is vertically compressed.

\( \square \) C. It is shifted left. D. It is flipped over the \( x \) -axis.

\( \square \) E. It is shifted up.

You want to paint the walls of your bedroom. Two walls measure \( 11 ft \) by \( 9 ft \) , and the other two walls measure \( 19 ft \) by \( 9 ft . \) The paint you wish to purchase must be purchased in one-gallon cans and costs \( \$ 17 \) per gallon. Each gallon will cover \( 400 ft ^ { 2 } \) of wall. Find the total amount you will spend on paint.

Suppose that \( f ( x ) = x ^ { 2 } \) and \( g ( x ) = \frac { 4 } { 5 } x ^ { 2 } \) . Which statement best compares the graph of \( g ( x ) \) with the graph of \( f ( x ) \) ?

A. The graph of \( g ( x ) \) is the graph of \( f ( x ) \) stretched vertically.

B. The graph of \( g ( x ) \) is the graph of \( f ( x ) \) compressed vertically.

C. The graph of \( g ( x ) \) is the graph of \( f ( x ) \) stretched vertically and flipped over the \( x \) -axis.

D. The graph of \( g ( x ) \) is the graph of \( f ( x ) \) compressed vertically and flipped over the \( x \) -axis.

If \( g ( x ) = \{ ( 4 , - 5 ) , ( - 3,2 ) , ( - 6,1 ) , ( 1,0 ) \} \) , which set of ordered pairs represents the inverse of \( g ( x ) \) ?

A. \( \{ ( - 5,4 ) , ( 2 , - 3 ) , ( 1 , - 6 ) , ( 0,1 ) \} \)

B. \( \{ ( 5 , - 4 ) , ( - 2,3 ) , ( - 1,6 ) , ( 0 , - 1 ) \} \)

C. \( \{ ( 4 , - 5 ) , ( - 3,2 ) , ( - 6,1 ) , ( 1,0 ) \} \)

D. \( \{ ( - 4,5 ) , ( 3 , - 2 ) , ( 6 , - 1 ) , ( - 1,0 ) \} \)

What statement is sufficient to prove that a quadrilateral is a square?

A Opposite sides are congruent and parallel

B All four sides are congruent

C All four angles are right angles

D All four sides are congruent'and all four angles are \( 90 ^ { \circ } \)

Of all the students in a particular class, \( 50 \% \) have blue eyes. We want to run a simulation to predict how many blue eye students will be chosen if we randomly select \( 10 \) students. First, we need to assign digits to students that have blue eyes and students that do not have blue eyes. If we were to use single digits to represent both, which of the following would be a correct method of assigning these digits?

A. blue eyes: \( 0,1,2,3,4 \) other: \( 5,6,7,8,9 \)

B. blue eyes: \( 0,1,2,3 \) other: \( 4,5,6,7,8,9 \)

C. blue eyes: \( 1,2,3,4,5 \) other: \( 6,7,8,9,10 \)

D. blue eyes: \( 1,2,3,4 \) other: \( 5,6,7,8,9,10\)

Iladin alone can feed all the animals on a farm in \( 20 \) minutes. Katrina can feed all the animals on the farm in \( 30 \) minutes. From this information, is it reasonable to conclude that Iladin and Katrina together can feed all the animals in \( 12 \) minutes, and why or why not?

No, because \( 12 < 20 \) and \( 12 < 30 \) .

No, because \( 12 > 30 - 20 . \)

Yes, because \( 12 < 20 \) and \( 12 < 30 . \)

Yes, because \( 12 > 30 - 20 .\)

1) Todd was boiling two pots of soup at work. The chicken soup boiled after \( 7.7 \) minutes. The mushroom soup boiled after \( 6.41 \) minutes. Which soup boiled more quickly?

2) On a cold winter day, the temperature in Town \( A \) was \( - 6 ^ { \circ } F \) and the temperature in Town \( B \) was \( - 6.78\) .Which town was warmer?

3) Joyce and Jack were measuring the width of cardboard for a science project. Joyce recorded the width as \( 0.224 mm \) . Jack recorded the width as \( 0.186 mm \) . Who recorded a larger width?

A farmer uses the equation below to determine what she will receive after selling her wheat crop.

\(p = 0.33 b u - s\)

In the equation \( p = \) total payment, \( b = \) total bushels of wheat harvested, \( u = \) the unit price (price per bushel), and \( s = \) fee for storing wheat. The farmer had the wheat planted and harvested by farmhands, so she will receive payment on \( 33 \% \) of the total bushels harvested.

The total payment is \( \$ 45,605 \) , the price per unit is \( \$ 4.66 \) , and the storage fee is \( \$ 2467 \) . The farmer wishes to calculate the total bushels harvested. The steps to find \( b \) are shown below.

(1) \( 45,605 = 0.33 ( b ) ( 4.66 ) - 2,467 \)

(2) \( 48,072 = 0.33 ( b ) ( 4.66 ) \)

(3) \( 15,864 = ( b ) ( 4.66 ) \)

(4) \( b \approx 3,404\)

Which statement describes the validity of the solution?

The solution is not valid because both sides of the equation should be divided by \( 0.33 \) in step (2).

The solution is valid because all steps to solve for \( b \) are correct.

The solution is not valid because \( 15,864 \) minus \( 4.66 \) is \( 15.859 .34 \) in step (4).

The solution is not valid because \( \frac { 48,072 } { 0.33 } \) is \( 145,672.73 \) in step (3).

Write the decimal approximations for the given numbers as place value numbers

In 2015, the population of Tallyville was approximately \( 8.32 \) million people.

The smallest bug in Tallyville has a radius of approximately \( 3.8 \) hundredths of an inch.

The tallest building in Tallyville is approximately \( 20.1 \) thousand feet.

The width of a piece of paper in Tallyville is approximately \( 9.66 \) tenths of an inch.

Which statement is false?

A.Adding the same number to both sides of an equation gives a true statement.

B.Dividing each side of an equation by a different number gives a true statement.

C.Multiplying each side of an equation by the same number gives a true statement.

Atmospheric pressure \( P \) in pounds per square inch is represented by the formula \( P = 14.7 e ^ { - 0.21 x } \) , where \( x \) is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of \( 8.595 \) pounds per square inch? (Hint: there are \( 5,280 \) feet in a mile)

If an object is propelled upward from a height of \( 112 \) feet at an initial velocity of \( 96 \) feet per second, then its height \( h \) after \( t \) seconds is given by the equation

\( h = - 16 t ^ { 2 } + 96 t + 112 \) . After how many seconds does the object hit the ground?

\( 6 sec \)

\( 7 sec \)

\( 11 sec \)

\( 3.5 sec\)

Miranda estimates that it will take \( 1.75 \) gallons to put one coat of paint on her bedroom walls. One gallon of paint costs \( \$ 25.50 \) . For \( \$ 75 \) , her friend has offered to help paint. Miranda creates the following inequality to show the minimum amount of money needed to paint her room:

\(b \geq 25.50 p + 75.00 , \) where \( b = \) money to complete the job and

\( p = \) cans of paint. Miranda substitutes \( \$ 150 \) for \( b \) and solves for \( p \) . She determines that \( \$ 150 \) will pay for her friend's help and \( 2 \) gallons of paint.

(1) \( 150 \geq 25.50 p + 75.00 \)

(2) \( 150.00 - 75.00 \geq 25.50 p \)

(3) \( \frac { 75.00 } { 25.50 } \geq p \)

(4) \( p \leq 2.9\)

Which statement describes the validity of Miranda's solution?

The solution is not valid because both sides of the equation should be divided by \( 25.50 \) in step (2).

The solution is valid because all steps to solve for \( p \) are correct.

The solution is not valid because \( 75.00 \) minus \( 25.50 \) is \( 24.50 \) in step (4).

The solution is not valid because \( 25.50 \) should be subtracted from both sides of the inequality in step ( \( 3 ) \) .

Which source of bias is most relevant to the following situation: A researcher wants to determine average household size and asks all students at the local college how many people are in their local family.

self-interest study

voluntary response bias

nonresponse bias or missing data

perceived lack of anonymity

loaded or leading question

In \( 2000 \) , when the federal budget showed a large surplus, the Pew Research Center asked two questions of random samples of adults. Both questions stated that Social Security would be "fixed." Here are the uses suggested for the remaining surplus:

Should the money be used for a tax cut, or should it be used to fund new government programs?

Should the money be used for a tax cut, or should it be spent on programs for education, the environment, health care, crime-fighting and military defense?

Which wording pulls respondents toward a tax cut?

The second wording pulls respondents toward a tax cut because it makes the tax cut sound better. The first wording biases respondents towards a tax cut because it lists the possible uses of the surplus.

The first wording biases respondents towards a tax cut because it does not elaborate on the possible uses of the surplus.

The second wording pulls respondents toward a tax cut because it makes the government spending sound better.

In order to determine how American undergraduate college students feel about eliminating spring break in order to finish spring term a week early, a survey was conducted. \( 200 \) undergraduate students from the University of Miami (FL) were interviewed. Both of the interviewers hired to conduct the survey were told to interview \( 25 \) freshmen, \( 25 \) sophomores, \( 25 \) juniors, and \( 25 \) seniors. Of

the \( 200 \) students interviewed, \( 20 \% \) were in favor of the elimination of spring break, \( 70 \% \) were opposed, and \( 10 \% \) had no opinion.

The results of this survey are unreliable primarily because of

the absence of a control group. nonresponse bias only.

sample (selection) bias only.

both sample (selection) bias and non-response bias.

None of the above

The city of Raleigh has \( 6700 \) registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of \( 350 \) randomly selected registered voters was conducted. \( 171 \) said they'd vote for Brown, \( 166 \) said they'd vote for Feliz, and \( 13 \) were undecided. Describe the target population for this survey.

All citizens of Raleigh

All registered voters in Raleigh

The \( 350 \) voters surveyed

The \( 171 \) voters who said they'd vote for Brown

None of the above

Based on data from \( 2003 \) to \( 2007 \) , the number of members of the USAA (an insurance and financial services company) can be modeled by

\( M ( t ) = 0.05 t ^ { 2 } + 0.15 t + 5.0\)

million members, where \( t \) is the number of years since \( 2003 \) . (Source; Modeled from USAA \( 2007 \) Report to Members, \( p \) .

Explain in complete sentence(s) the meaning, in the context of this problem, the value of ' \( b \) ' in this quadratic function.

The length of a rectangle is increasing at a rate of \( 10 cm / s \) and its width is increasing at a rate of \( 9 cm / s \) . When the length is \( 4 cm \) and the width is \( 9 cm \) , how fast is the area of the rectangle increasing?

A number cube with faces labeled from \( 1 \) to \( 6 \) will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling a number from \( 3 \) to \( 6 . \) If there is more than one element in the set, separate them with commas. Sample space: \( \{ \square \} \)

Event of rolling a number from \( 3 \) to \( 6 : \{ \square \} \)

Tyrone wrote an equivalent expression for \( 28 + x + 2 n + 7 + n + 5 x + 4 \) . His equivalent expression was \( 3 n + 5 x + 39 + x \cdot \) What error did Tyrone make?

Tyrone neglected to combine the \( x \) terms.

Tyrone subtracted the constants instead of adding them.

Tyrone neglected to add the coefficients of the \( n \) terms.

Tyrone made an error when he added the constants.

The midline of a trigonometric function is

The number of cycles it completes in a given interval.

How far above the horizontal axis of symmetry is from the maximum or the minimum of the function. How long a given function takes to repeat itself.

The horizontal center line about which the function oscillates above and below.

A number cube with faces labeled from \( 1 \) to \( 6 \) will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling a number from \( 2 \) to \( 4 . \) If there is more than one element in the set, separate them with commas.

Sample space: \( { } \)

Event of rolling a number from \( 2 \) to \( 4 : \{ \} \)

The students at Southern Junior High School are divided int district and will be randomly assigned to one homeroom. Which methods can be used to simulate this situation? Sele

Flip a coin \( 4 \) times, once for each homeroom, with heads represented by that flip.

Draw a marble from a bag containing \( 5 \) white marbles, \( 5 \) each color representing a different homeroom.

Use a random number generator with \( 1,2 \) , and \( 12 \) repres second homeroom, \( 3,8 \) , and \( 11 \) representing the third ho homeroom.

Roll a number cube with \( 1 \) representing the first homeroc the third homeroom, and any other outcome representing

Spin a spinner with \( 8 \) congruent sections with \( 2 \) sections

Jenny just went shoe shopping. Now she has \(5\) more pairs of shoes than her brother does. Together, they have \(25\) pairs of shoes. Jenny has \(\square \) pairs of shoes, and her brother has \(\square \) pairs of shoes.

Let \(S = \{ 1,2,3,4,5,6,7,8,9,10 \} \) be the universal set.

Let sets \(A , B\) , and \(C\) be subsets of \(S\) , where: Set \(A = \{ 6,8,9,10 \} \)

Set \(B = \{ 2,6,7 \} \)

Set \(C = \{ 3,4,5,7,10 \} \)

LIST the elements in the set \(A \cap B \cap C\) :

LIST the elements in the set \(A \cup B \cup C\) :

A homeowner has decided to fill in his in-ground pool because it is no longer used. Assume the pool is rectangular and measures \( 20 \) feet wide, \( 40 \) feet long, and \( 5.5 \) feet deep throughout. Each cubic yard of fill dirt costs \( \$ 12 \) . How much will it cost to fill in the pool?

The fox population in a certain region has a continuous growth rate of \( 4 \) percent per year. It is estimated that the population in the year \( 2000 \) was \( 21800 \) . (a) Find a function that models the population \( t \) years after \( 2000 ( \) \( t = 0 \) for \( 2000 \) ). Your answer is \( P ( t ) = \)

(b) Use the function from part (a) to estimate the fox population in the year \( 2008 \) . Your answer is (the answer must be an integer)

When a number has been factored completely, its prime factors are written from smallest to largest. Factor \( 99 \) into the product of primes.

In June of \( 2020 \) , a study was performed to determine the extent to which trees in South Carolina had been infested by Asian Longhorn Beetles. Researchers believed that more than \( 10 \% \) of trees had been infested. After randomly selecting \( 1015 \) South Carolina trees, the reserchers determined that \( 113 \) had been infested by the Asian Longhorn Beetle. At the \( 0.1 \) significance level, test the researcher's claim.

a. Enter the null hypothesis for this test.

b. Enter the alternative hypothesis for this test.

Diana has \( 3200 \) yards of fencing and wishes to enclose a rectangular area.

(a) Express the area A of the rectangle as a function of the width \( W \) of the rectangle.

(b) For what value of \( W \) is the area largest?

(c) What is the maximum area?

A college radio station surveyed \( 410 \) incoming freshmen to see how many like rap music and how many like classical music. The Venn diagram below shows the results. (Each number gives the number of freshmen who fall into that Venn diagram category.)

(a) How many of the freshmen like rap music? \( 146 \) freshmen

(b) How many of the freshmen like neither rap music nor classical music? \( 297 \) freshmen

(c) How many of the freshmen do not like both rap music and classical music? \( 242 \) frashmen

Government agencies keep data about the income distribution of the population. The Taylor family and Jenkins family live in a county with \( 5000 \) families. The Taylor family's income is at the \(64^ \text { th} \) percentile. The Jenkins family's income is at the \(27^ \text { th} \) percentile.

(a) Which of the following must be true about the Taylor family's and the Jenkins family's incomes?

Both the Taylor family and the Jenkins family earn more than the median income.

Both the Taylor family and the Jenkins family earn less than the median income.

The Taylor family earns more than the Jenkins family.

The Jenkins family earns more than the Taylor family.

(b) Which of the following must be true about the Taylor family's income?

About \( 64 \% \) of the families in their county earn less than the Taylor family.

The Taylor family earns about \( 64 \% \) of the highest income in their county.

The Taylor family's income is in the bottom half of incomes in their county.

The Taylor family earns \( \$ 64,000\)

Here are yesterday's high temperatures (in Fahrenheit) in \( 12 \) U.S. cities.

\( 50,52,54,54,59,60,62,65,70,70,71,74\)

An experiment consists of rolling a \( 20 \) sided die:

a. How many elements are there in the sample space?

b. Let A be the event that either a \( 3 \) or \( 4 \) or a \( 5 \) is rolled.

\( P ( A ) = \)

Present your answer as a decimal rounded to four decimal places, as needed. Are the events B and \( C \) mu tually exdusive?

(C) No, they are not Mutually Exdusive Yes, they are Mutually Exdusive

Convert \( ( 1 , \infty ) \) to inequality notation use the variable \( x \) .

Now graph \( ( 1 , \infty ) \) on the grid below

Find a counterexample to show that the statement is incorrect.

The product of any two counting numbers is divisible by \( 2 \) .

Choose the correct answer below.

A. \( 3 \times 4 = 12 \) , which is not divisible by \( 2 \) .

B. \( 3 \times 5 = 15 \) , which is not divisible by \( 2 \) .

C. \( 2 \times 4 = 8 \) , which is not divisible by \( 2 \) .

D. \( 2 \times 3 = 6 \) , which is not divisible by \( 2 \) .

If Lisa were to paint her living room alone, it would take \( 2 \) hours. Her sister Naomi could do the job in \( 5 \) hours. How long would it take them working together? If needed, submit your answer as a fraction reduced to lowest terms.

Judge the following statement whether is true or false.

When solving a quadratic by completing the square one should be sure that the leading coefficient is one.

Find set \( A ^ { \prime } \cap B ^ { \prime } \)

\( U = \{ 1,2,3,4,5,6,7 \} \)

\( A = \{ 1,3,4,6 \} \)

\( B = \{ 3,5,6 \} \)

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. \( A ^ { \prime } \cap B ^ { \prime } = \{ \} \) (Use a comma to separate answers as needed.)

B. \( A ^ { \prime } \cap B ^ { \prime } \) is the empty set.

Kate multiplied two binomials using the distributive property. She made a mistake in one of the steps. Where did she first make a mistake?

\( ( x - 2 ) ( 3 x + 4 ) \)

2. \( ( x - 2 ) ( 3 x ) + ( 3 x ) + ( 2 ) ( 3 x ) + ( x ) ( 4 ) + ( 2 ) ( 4 ) \)

3. \( 3 x ^ { 2 } + 6 x + 4 x + 8 \)

4. \( 3 x ^ { 2 } + 10 x + 8 \)

A. Step \( 1 \) B. Step \( 3 \) C. Step \( 2 \) D. Step \( 4\)

Which unit of measure would be appropriate for the volume of a cube with an edge length of \( 5 \) centimeters?

A. Meters

B. Centimeters

C. Square centimeters

D. Cubic centimeters

Every fraction with a non-zero denominator or divisor is an

integer

decimal

rational number

quotient

According to Hooke's Law, a linear relationship exists between the distance that a spring stretches and the force stretching it. Suppose a weight of \( 0.5 \) kilograms causes a spring to stretch \( 2.25 \) centimeters and a weight of \( 1.2 \) kilograms causes the same spring to stretch \( 5.4 \) centimeters.

(a) Find a linear model that relates the distance d of the stretch and the weight w.

(b) What stretch is caused by a weight of \( 2.4 \) kilograms?

(c) What weight causes a stretch of \( 16.2 \) centimeters?

(a) A linear model that relates the distance \( d \) of the stretch and the weight \( w \) is \( d ( w ) = 4.5 w \) . (Simplify your answer. Use integers or decimals for any numbers in the expression.)

(b) A weight of \( 2.4 \) kilograms causes a stretch of \( 10.8 \) centimeters. (Simplify your answer. Type an integer or a decimal.)

(c) A weight of \( \square \) (Simplify your answer. Type an integer or a decimal.)

The sets \( H \) and \( J \) are given below.

\( H = \{ a , e , g \} \)

\( J = \{ d , e , h \} \)

Find the union of \( H \) and \( J .\)

Scientists are studying the temperature on a distant planet. Let \( y \) represent the temperature (in degrees Celsius). Let \( x \) represent the height above the surface (in kilometers). Suppose that \( x \) and \( y \) are related by the equation \( 41 - 3 x = y \) .

Answer the questions below.

Note that a change can be an increase or a decrease.

For an increase, use a positive number. For a decrease, use a negative number.

What is the temperature on the surface of the planet?

___\( { } ^ { \circ } C\)

What is the temperature change for each kilometer we go up from the surface?

___\( { } ^ { \circ } C\)

(a) How much higher is Checkpoint \( 2 \) than Checkpoint \( 4 \) ?

___ft higher

(b) The top of a hill rises \( 472 \) feet above Checkpoint 3: What is the altitude of the top of the hill?

___ft

An egg of a particular bird is very nearly spherical. The radius to the inside of the shell is \( 8 \) millimeters and the radius to the outside of the shell is \( 8.5 \) millimeters. Use differentials to approximate the volume of the shell. [Remember that \( V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 } \) , where \( r \) is the radius.] The volume of the shell is approximately \( mm ^ { 3 } \) . (Round to the nearest hundredth.)

Translate this phrase into an algebraic expression.

Four less than the product of \( 18 \) and Matt's age

Use the variable \( m \) to represent Matt's age.

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order.

What is the sample space showing the possible orders of the other three runners?

\( S = \{ FGI , GFI , IFG \} \)

\( S = \{ FGI , FIG , GFI , GIF \} \)

\( S = \{ FGI , FIG , GFI , GIF , IFG , IGF \} \)

\( S = \{ FGI , FIG , GFI , GIF , HFG , HGI , IFG , IGF \} \)

The weighted voting systems for the voters \( A , B , C , \ldots \) are given in the form \( \{ q : w _ { 1 } , w _ { 2 } , w _ { 3 } , w _ { 4 } , \ldots , w _ { n } \} . \) The weight of voter \( A \) is \( w _ { 1 } , \) the weight of voter

\( B \) is \( w _ { 2 } , \) the weight of voter \( C \) is \( w _ { 3 } \) , and so on.

Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If not possible, enter IMPOSSIBLE.)

\(\{ 82 : 52,35,25,19 \} \)

\( B P I ( A ) = \) ________.

\( B P I ( B ) = \) ________.

\( B P I ( C ) = \) ________.

\( B P I ( D ) = \) ________.

If Digitalis knows it will sell many of these processors, should it expect to make or lose money from selling them? How much? To answer, take into account the profit earned on each processor and the expected value of the amount refunded due to the processor being defective.

Digitalis can expect to make money from selling these processors. In the long run, they should expect to make \( \square \) dollars on each processor sold.

Digitalis can expect to lose money from selling these processors.

Digitalis should expect to neither make nor lose money from selling these processors.

Which of the following is TRUE about a number line?

On a number line, negative numbers are to the right of zero, and positive numbers are to the left of zero.

The numbers on the number line decrease as we move to the right and increase as we move to the left.

The lesser number would be to the right of the greater number on the number line.

On the number line, the location of a number and its opposite are the same

What are some properties of r? How can you determine whether a linear relation exists between two variables? Discuss the steps.

Arnold lives in Canada and is recording the outside temperature each night before he goes to bed. On Monday night, he recorded a temperature of zero degrees Celsius. On Tuesday night, he recorded a temperature of \( - 1 \) degrees Celsius. Which day is warmer and which of the following inequalities compares the rational numbers in this context?

Monday is warmer; \( 0 ^ { \circ } C > - 1 ^ { \circ } C \)

Monday is warmer; \( 0 ^ { \circ } C < - 1 ^ { \circ } C \)

Tuesday is warmer; \( 0 ^ { \circ } C > - 1 ^ { \circ } C\)

Tuesday is warmer; \( \quad 0 ^ { \circ } C < - 1 ^ { \circ } C\)

Which of the following is the converse of the statement, "If I eat too much, then I will gain weight"?

A. If I gain weight, then I will eat too much.

B. If I don't eat too much, then I won't gain weight.

C. If I don't gain weight, then I won't eat too much.

D. If I eat too much, then I won't gain weight.

A small radio transmitter broadcasts in a \( 41 \) mile radius. If you drive along a straight line from a city \( 56 \) miles north of the transmitter to a second city \( 53 \) miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

A cone has a volume of \(144 \pi \) in \(3\) and a diameter of \(12\) in. Wilson states that a cylinder with the same height and diameter has the same volume. Which statement explains whether or not Wilson is correct?

A cylinder in which \(h = 12\) and \(d = 12\) has a volume of \(144 \pi \) in \(3\) ; therefore, Wilson is correct.

A cylinder in which \(h = 4\) and \(d = 12\) has a volume of \(144 \pi \) in3; therefore, Wilson is correct. A cylinder in which \(h = 12\) and \(d = 12\) has a volume of \(432 \pi \) in3; therefore, Wilson is incorrect.

A cylinder in which \(h = 4\) and \(d = 12\) has a volume of \(432 \pi \) in3; therefore, Wilson is incorrect.

The Smith family likes to fish for trout, and they are trying to decide which lake to go fishing on for the weekend. Long Lake and Square Lake both have both trout and perch populations. If x represents perch, and y represents trout per acre in the following equations, please solve the systems of equations that represent the fish populations in each lake, and then determine which lake the family would find more optimal in terms of the possibility of catching trout. Long Lake:

A. Long Lake: \(y = 3 x - 1\), \(y = x + 3\)

B. Square Lake: \(2 x - 3 y = 5\), \(1 / 2 x - y = 1\)

Jacob makes a scale drawing for a crate with a scale factor of \( 1 : 20 \) . The dimensions of his scale drawing are \( 3 \) inches long by \( 2 \) inches wide. The builder creates a scale drawing of the crate with a scale factor of \( 1 : 10 \) . What are the dimensions of the builder's scale drawing?

A. The length is \( 4 \) inches and the width is \( 6 \) inches.

B. The length is \( 6 \) inches and the width is \( 4 \) inches.

C. The length is \( 1 \) inch and the width is \( 1.5 \) inches.

D. The length is \( 1.5 \) inches and the width is \( 1 \) inch.

At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?

positive

zero

negative

undefined

A population of beetles are growing according to a linear growth model. The initial population (week

\( 0 \) is \( P _ { 0 } = 6 \) , and the population after \( 4 \) weeks is \( P _ { 4 } = 30 \) .

Find an explicit formula for the beetle population after \( n \) weeks.

After how many weeks will the beetle population reach \( 168 ? \)

Clarissa made a scale drawing of a rectangle. She used a scale factor of \( 3 \) ta draw the new rectangle How does the Iength of the new rectangle compare to the original?

The length of the new rectangle is \( \frac { 1 } { 3 } \) the length of the original

The length of the new rectangle is \( \frac { 1 } { 12 } \) the length of the ariginal

The length of the new rectangle is \( 3 \) times the length of the original.

The length of the new rectangle is \( 12 \) times the length of the original.

Write a formula that describes how much it will cost Shawna to join the arboretum and attend classes. Let's let

\( c = \) cost of each class

\( n = \) number of classes she attends

\( t = \) total cost

Find the slope of the line going through points: \( ( 3,5 ) \) and \( ( 5,6 ) \) . Write your answer as a fraction in lowest terms.

Your answer

At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system \( \{ 4 : 3,2,1 \} \) . In this voting system, the head coach A has a weight of \( 3 \) , the assistant coach B has a weight of \( 2 \) , and the junior varsity coach C has a weight of \( 1 \) .

Compute the Banzhaf power index for each of the coaches. (Round your answers to the nearest hundredth.)

\(B P I ( A ) = \)

\( B P I ( B ) = \)

\( B P I ( C ) = \)