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A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the shaded region.



Event A and B are independent. Find the indicated Probability.


P(B)=? (round answer to three decimal places)

P(A and B)=0.16


Given \(m\parallel n\), find the value of x.



In the figure \(\overrightarrow{BA}\) and \(\overrightarrow{BC}\) are opposite rays. \(\overrightarrow{BF}\) bisects \(\angle\text{CBE}\).

If \(\text{m}\angle\text{EBF}=6x+4\) and \(\text{m}\angle\text{CBF}=7x-2\), find \(\text{m}\angle\text{EBF}\).



Last month, the online price of a powered ride-on car was $250. This month, the online price is $330. What is the percent of increase for the price of the car?


Billy's car gets 25 miles per gallon of gas. If Wilmington, DE is 150 miles away, how many gallons of gas is he going to need to get to Wilmington and come back home?


Suppose we want to choose 6 objects, without replacement, from 15 distinct objects. 


(a) How many ways can this be done, if the order of the choices does not matter?

(b) How many ways can this be done, if the order of the choices matters?


A rectangular athletic field is 100 yards wide and 500 yards long. How many square yards are there in the field?


Are the sets equal?


A={15, 16, 16, 17, 17, 17, 18, 18, 18, 18}

B={18, 17, 17, 15}


The maximum slope of a wheelchair ramp is 1:12. For a wheelchair ramp made with these specifications, what angles does the ramp make with the ground? Round your answer to the nearest hundredth.


Which list of numbers is ordered from least to greatest value?


A. \(\frac{1}{20},4.1\times10^{-1},4.8\%,\sqrt{4}\)

B. \(4.8\%,\frac{1}{20},4.1\times10^{-1},\sqrt{4}\)

C. \(\frac{1}{20},\sqrt{4},4.1\times10^{-1},4.8\%\)

D. \(4.1\times10^{-1},\frac{1}{20},\sqrt{4},4.8\%\)



Suppose Salma places $9500 in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding.


(a) Find the amount in the account at the end of 1 year.

(b) Find the amount in the account at the end of 2 years.


Given the points C(-1, -3) and D(5, 6), find the coordinates of the point E on directed line segment CD that partitions CD into the ratio 2 to 1.


(1, 0)

(-1, 0)

(3, 3)

(-3, 3)


A translation maps the point E(-3, 10) to the point E'(2, 1). If the same translation maps point F to the image point F'(7, -4) then which of the following are the coordinates of F?


(1) F(-6, 12)

(2) F(7, 4)

(3) F(12, -13)

(4) F(2, 5)


The vertices of \(\triangle\text{WED}\) are W(5, -2), E(-3, -4), and D(1, 6).


True or false. After dilation with center D and scale factor of 3, the coordinates of the images are W'(15, -6), E'(-9, -12), and D'(3, 18).


Find the volume of a pyramid with a square base, where the side length is the base is 7.5 cm and the height of the pyramid is 10.2 cm. Round your answer to the nearest tenth of a cubic centimeter.


Determine the intervals on which f(x) is concave up and concave down:



Find the perimeter of the composite geometric figure, which consists of three semicircles and a square. Use \(\pi\approx3.14\). (Round to the nearest hundredth.)



In the auditorium there are second third ,fourth and fifth graders. One sixth of the students are fifth graders, one third are fourth graders and one fourth of the remaining students are second graders. If there are 96 students in the auditorium, how many are second graders? what fraction of the students are second graders


Find the height, x, of the triangle.



A 30

B 40

C 50

D 60


\(\triangle\text{ABC}\) and \(\triangle\text{DEF}\) are congruent. If AB=DE, BC=EF, \(\text{m}\angle\text{ABC}=37^{\circ}\), and \(\text{m}\angle\text{EDF}=39^{\circ}\), what is the measure (in degrees) of \(\angle\text{EFD}\)?



Hayden says that \(\frac{3}{2}\) is a whole number because it does not repeat as a decimal. Is he correct? Why or why not?


Find the length of the hypotenuse in the following right triangle.



\(\overleftrightarrow{AD}\) is the perpendicular bisector of \(\overleftrightarrow{BC}\)\(BD=5x-10\) and \(DC=3x+10\). Determine the value of x.


In 2015, the number of graduating seniors taking the ACT exam was 1,924,887. In 2011, a total of 1,612,665 graduating seniors took the exam. By what percent did the number increase over this period of time?


Find the mean, median, and mode of the following set of data:


43, 46, 47, 47, 51, 54, 59, 50


In the figure below, if \(\text{m}\angle\text{AXC}=10x\), then \(\text{m}\angle\text{BXD}=?\).


A 10x

B 360-10x

C 90-10x

D 180-10x


Convert \(132\text{ cm}^2\) into square inches. When appropriate, round your answer off to the nearest thousandth.



If \(f(x)=x^2-6x+2\) and \(g(x)=-2x\), find the following composition.


\((g\circ f)(-5)=?\)


Triangle LMN is translated to L'M'N'. L was located at -1,3 and L' was found at -8,1. If M is at 1,3 what would be the coordinates of M' be?


Find an equation of the circle that has center (-6, 4) and passes through (-1, -2).


Find the length of the missing to the nearest tenth(do not forget your units).



Solve for \(\text{m}\angle\text{PRS}\)







Examine the following equation and determine the y-intercept and slope: \(y=-x\)


a. Slope is -x and intercept is 0

b. Slope is -x and y intercept is -1

c. Slope is -1 and y intercept is 0

d. Slope is -1 and y intercept is -1


Simplify: \(8(-9-5x)+4b\) use \(x=9\) and \(b=-9\)


a. None of these answers are correct.

b. -1044

c. -468

d. -396

e. 252


In \(\triangle\text{NOP}\), the measure of \(\angle\text{P}=90^{\circ}\)\(\text{PN}=1.1\), and \(\text{NO}=3.3\) feet. Find the measure of \(\angle\text{N}\) to the nearest degree.



This is an observation tower out in Blowing Rock, NC that is 40 feet tall. If you climb to the top and view someone's campfire at an angle of depression of 3 degrees, how far from the base of the tower is the campfire? Round your answer to the nearest foot.


At a shelter, 15% of the dogs are puppies. There are 60 dogs at the shelter. How many are puppies?


The circumference of a circle is \(16\pi\) cm. What is the area, in square centimeters? Express your answer in terms of \(\pi\).


Marlena has a bag of coins. The bag contains 8 quarters, 10 dimes, 4 nickels, and 2 pennies. She will randomly select a coin from the bag. What is the probability that Marlena will select a nickel?







The manufacturing cost of an air-conditioning unit $544, and the full-replacement extended warranty costs $113. If the manufacturer sells 506,970 units with extended warranties and must replace 20% of them as a result, how much will the replacement costs be? (Note: Assume manufacturing costs and replacement costs are the same.)


a. $55,158,336

b. $11,457,522

c. $2,129,274

d. $66,717,252


Calculate the area of a circle with a diameter of 10.8 centimeters.


Which of the following sets of lengths can represent the measures of the sides of a right triangle?


A. 4, 5, 6

B. 5, 12, 15

C. 8, 10, 17

D. 20, 21, 29


If \(f(x)=3x^2+1\) and \(g(x)=1-x\), what is the value of \((f-g)(2)\)







Two marbles are drawn randomly one after the other without replacement from a jar that contains 7 red marbles, 8 white marbles, and 9 yellow marbles. Find the probability of the following events.


(a) A red marbles is drawn first followed by a white marble.

(b) A white marble is drawn first followed by a white marble.

(c) A yellow marble is not drawn at all.


Ryan has 10 quarters. Kelly has exactly seven times as much money as Ryan. They will combine their money to buy a game. The game costs $27. How much more money do they need to save?


A sun casts a shadow of a 50-foot building. If the angle of elevation to the sun is \(64^{\circ}\), how long is the shadow? Round to the nearest tenth.


24.4 feet
114.0 feet

102.5 feet

55.6 feet


In the rectangle, if \(SQ=11x-26\) and \(PR=5x+28\), find PR.



From the top of a building 21 m tall, the angle of depression to a car on the road below is 70 degrees. How far is the car from the base of the building? Sketch a diagram to help you...


a. 61 m

b. 57.7 m

c. 7.6 m

d. 19.7 m


What is the measure of each angle of a regular 18-gon? If necessary, round to the nearest tenth.


Sam wants to buy a remote control dune buggy that is 30% off. The original price is $200.11. What is amount of discount(nearest penny)?




When a coordinate grid is superimposed on a map of Lanesville, the middle school is located at (15, 23) and the library is located at (27, 9). If each unit represents 1 mile,, how many miles apart are the middle school and the library? Round your answer to the nearest tenth.


The men's 110-meter hurdles is an event in the Olympic games. The distance from the starting line to the first hurdle is 13.72 meters. The distance from the first hurdle to the second hurdle is 9.14 meters. What is the total distance from the starting line to the second hurdle?


In a city, the record monthly high temperature for March is \(56^{\circ}\text{F}\). The record monthly low temperature for March is \(-4^{\circ}\text{F}\). What is the range of temperatures for the month of march?


In a survey of a group of people, it was found that 60% of the people liked apple, 70% liked orange and 400 people liked both of them. If 10% people liked non of them, then


(i) Represent the above information in a Venn-diagram

(ii) Find the total number of people in the survey

(iii) Find the number of people who like apple only. 


In \(\triangle\text{MNO}\), the measure of \(\angle\text{O}=90^{\circ}\)\(\text{ON}=35\)\(\text{NM}=37\), and \(\text{MO}=12\). What is the value of the tangent of \(\angle\text{M}\) to the nearest hundredth?


In the figure, the radius of circle A is twice the radius of circle B and four times the radius of circle C. If the sum of the circumferences of the three circles is \(42\pi\), find the measure of AC.


In the triangle ABC, C=90, AC=3.2m and BC=4.8m. Find B.


Find a set of side lengths that makes a right triangle.


A. 6 ft, 8 ft, 12 ft,

B. 16 ft, 30 ft, 34 ft

C. 8 ft, 15 ft, 24 ft

D. 5 ft, 10 ft, 15 ft


Yamil's rectangular garden has the measurements of 7.3 feet by 6.4 feet. Find the perimeter of Yamil's garden.


13.7 feet

46.72 feet

26.4 feet

27.4 feet


Simona has 12 quarters, 5 dimes, and 6 nickels in her piggy bank. If there are no other coins or bills, what is the amount of money in Simona's piggy bank.


A pizza shop has available toppings of anchovies, mushrooms, peppers, onions, olives, bacon, pepperoni and sausage. How many different ways can a pizza be made with 4 toppings.


3, 4, 4, 5, 5, 3, 2, 4, 6, 3, 6, 4, 2


State the mode.


Ashley wants to wallpaper the back wall of her bedroom. The wall is in the shape of a rectangle. Its length is 16 feet and its width is 13 feet. Suppose wallpaper costs $5 for each square foot. How much will wallpaper cost for the wall.


Gadget Land is an electronics store. They buy a TV from the distributer for $460.00 . Before selling the TV, it is marked up to $1610. What percentage did Gadget Land mark up the TV before selling it?


Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?



a. Yes, it does not matter If f is continuous or differentiable, every function satisfies the Mean Value Theorem.

b. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on \(\mathbb{R}\).

c. No, f is not continuous on [0, 2].

d. No, f is continuous on [0, 2] but not differentiable on (0, 2).

e. There is not enough information to verify if this function satisfies the Mean Value Theorem.


If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem.