Basic Math Questions and Answers

Evaluate x² - 4x - 5 /x + 1
when x = -4
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Evaluate x² - 4x - 5 /x + 1 when x = -4
The formula for the surface area S of a cone is S = r² + rs, wherer is the radius and s is the slant height. Solve the formula for s. Justify each step. Then find the slant height of the cone when the surface area is 113 square feet and the radius is 4 feet. Approximate to the nearest tenth.
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The formula for the surface area S of a cone is S = r² + rs, wherer is the radius and s is the slant height. Solve the formula for s. Justify each step. Then find the slant height of the cone when the surface area is 113 square feet and the radius is 4 feet. Approximate to the nearest tenth.
a. Graph the function f(x)= ex on the window [-5,5] by [-10,30].
b. Find f(1), f(-4), and f(4), rounded to three decimal places.
c. What is the horizontal asymptote of the graph?
d. What is the y-intercept?
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a. Graph the function f(x)= ex on the window [-5,5] by [-10,30]. b. Find f(1), f(-4), and f(4), rounded to three decimal places. c. What is the horizontal asymptote of the graph? d. What is the y-intercept?
The use of calculators in math classrooms has been on the rise over the past 15 years. Is this a good tool that supports students in their learning? Or is it causing too much harm by allowing students to go through life without having mastered basic skills like adding, subtracting, multiplying, etc.? Choose a position and explain why.
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The use of calculators in math classrooms has been on the rise over the past 15 years. Is this a good tool that supports students in their learning? Or is it causing too much harm by allowing students to go through life without having mastered basic skills like adding, subtracting, multiplying, etc.? Choose a position and explain why.
A population of rabbits doubles every year and there were 1 million rabbits at the start of 2008.
a. How many million rabbits are there in 2013? Hint: How many rabbits are there in 2009? In 2010?
b. In what year will there be 10 million rabbits? Hint: Use logs!
In the year
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A population of rabbits doubles every year and there were 1 million rabbits at the start of 2008. a. How many million rabbits are there in 2013? Hint: How many rabbits are there in 2009? In 2010? b. In what year will there be 10 million rabbits? Hint: Use logs! In the year
The denominator of a fraction is four more than the numerator. If both numerator and denominator are decreased by four, the simplified result is 5/7. Find the original fraction. (Do NOT simplify.)
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The denominator of a fraction is four more than the numerator. If both numerator and denominator are decreased by four, the simplified result is 5/7. Find the original fraction. (Do NOT simplify.)
The odds in favor of Trudy beating her friend in a round of golf are 1:6. Find the probability that Trudy will lose.
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The odds in favor of Trudy beating her friend in a round of golf are 1:6. Find the probability that Trudy will lose.
Out of a random sample of 65 freshmen at State University, 31 students have declared a major. Use the "plus-four" method to find a 96% confidence interval for the true proportion of freshmen at State University who have declared a major.
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Out of a random sample of 65 freshmen at State University, 31 students have declared a major. Use the "plus-four" method to find a 96% confidence interval for the true proportion of freshmen at State University who have declared a major.
Simplify by combining like terms.
75/7 b + 2 2/3 b
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Simplify by combining like terms. 75/7 b + 2 2/3 b
A construction worker needs to pour a rectangular slab 20 ft long, 28 ft wide, and 9 in. thick. How many cubic yards of concrete does the worker need? (Assume that the construction worker cannot buy a fraction of a cubic yard of concrete.)
The worker needs cubic yards of concrete.
(Type a whole number, rounded up to the nearest full cubic yard of concrete.)
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A construction worker needs to pour a rectangular slab 20 ft long, 28 ft wide, and 9 in. thick. How many cubic yards of concrete does the worker need? (Assume that the construction worker cannot buy a fraction of a cubic yard of concrete.) The worker needs cubic yards of concrete. (Type a whole number, rounded up to the nearest full cubic yard of concrete.)
A tool rental store charges a flat fee of $6.50 to rent a chain saw, and $3.75 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.
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A tool rental store charges a flat fee of $6.50 to rent a chain saw, and $3.75 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.
A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of o feet.
She descends 48.7 feet.
She then rises 38.3 feet.
Next, she travels down a second time, 83.6 feet.
How many feet must she now ascend to get back to sea level?
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A scientist uses a submarine to study ocean life. She begins at sea level, which is an elevation of o feet. She descends 48.7 feet. She then rises 38.3 feet. Next, she travels down a second time, 83.6 feet. How many feet must she now ascend to get back to sea level?
According to the Original Tipping Page, www.tipping.org, it is appropriate to tip waiters and waitresses 15%-20% of the pre-tax restaurant bill. The Leeseburgs' dinner costs $49.00 before tax, and the tax rate is 6%.
a) What is the tax on the Leeseburgs' dinner?
b) If the Leeseburgs decide to tip 20% of the pre-tax bill, how much is the tip?
c) What is the total cost of the dinner including the tax and tip?
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According to the Original Tipping Page, www.tipping.org, it is appropriate to tip waiters and waitresses 15%-20% of the pre-tax restaurant bill. The Leeseburgs' dinner costs $49.00 before tax, and the tax rate is 6%. a) What is the tax on the Leeseburgs' dinner? b) If the Leeseburgs decide to tip 20% of the pre-tax bill, how much is the tip? c) What is the total cost of the dinner including the tax and tip?
Complete the tables, and graph the corresponding ordered pairs. Draw the line defined by the points to represent all solutions to the equation.
x-y=-3
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Complete the tables, and graph the corresponding ordered pairs. Draw the line defined by the points to represent all solutions to the equation. x-y=-3
Malik uses an app on his phone to track how far he rides his bike. Yesterday, he biked a new trail in a total of 57.5 minutes, including a 2.5-minute water break. The app notified Malik that he rode 10 miles. What was Malik's average pace while biking? 
Write your answer as a whole number or a decimal. 
minutes per mile
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Malik uses an app on his phone to track how far he rides his bike. Yesterday, he biked a new trail in a total of 57.5 minutes, including a 2.5-minute water break. The app notified Malik that he rode 10 miles. What was Malik's average pace while biking? Write your answer as a whole number or a decimal. minutes per mile
Does the function y(t) = 4e-6t satisfy the following initial value problem?
y' (t)-6y(t) = 0, y(0) = 4
Choose the correct answer below.
No, because the initial condition does not satisfy the original function, so the original function cannot satisfy the initial value problem.
Yes, because the initial condition satisfies the original function, so the original function must satisfy the initial value problem.
No, because when y and y' are substituted into the equation, the result is not a true statement.
Yes, because when y and y' are substituted into the equation, the result is a true statement.
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Does the function y(t) = 4e-6t satisfy the following initial value problem? y' (t)-6y(t) = 0, y(0) = 4 Choose the correct answer below. No, because the initial condition does not satisfy the original function, so the original function cannot satisfy the initial value problem. Yes, because the initial condition satisfies the original function, so the original function must satisfy the initial value problem. No, because when y and y' are substituted into the equation, the result is not a true statement. Yes, because when y and y' are substituted into the equation, the result is a true statement.
Audrey Graco plans to conduct book signings in several cities to promote her new novel. She wishes to visit Knoxville, Chattanooga, Chapel Hill, Charlotte, Raleigh, and Richmond. How many different ways can she visit each of these cities and return to her starting point in Wilmington?
A. 120
B. 720
C. 29
D. 30
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Audrey Graco plans to conduct book signings in several cities to promote her new novel. She wishes to visit Knoxville, Chattanooga, Chapel Hill, Charlotte, Raleigh, and Richmond. How many different ways can she visit each of these cities and return to her starting point in Wilmington? A. 120 B. 720 C. 29 D. 30
A principal of $4900 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 8 years? Use the calculator provided and round your answer to the nearest dollar.
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A principal of $4900 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 8 years? Use the calculator provided and round your answer to the nearest dollar.
MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $983 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin $13,400. Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.
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MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $983 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin $13,400. Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.
2. Kirsten has $500 in her savings account. She is able to save $50 each month. The function S(m) = 50m + 500 represents the amount of money in her savings account S as a function of time in months m.
2.a. Find S(2). Explain what this represents in this problem.
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2. Kirsten has $500 in her savings account. She is able to save $50 each month. The function S(m) = 50m + 500 represents the amount of money in her savings account S as a function of time in months m. 2.a. Find S(2). Explain what this represents in this problem.
Calculate the surface area of each pyramid with the following values. (P = perimeter, b = one side of the base, s=side, h-height). Number of sides is given in each problem. The first two have hints to let you know what the shape of the base is
 P = 12 ft, s = 4 ft, b = 4 ft, h=2 ft, 3 sides (base is a triangle)
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Calculate the surface area of each pyramid with the following values. (P = perimeter, b = one side of the base, s=side, h-height). Number of sides is given in each problem. The first two have hints to let you know what the shape of the base is P = 12 ft, s = 4 ft, b = 4 ft, h=2 ft, 3 sides (base is a triangle)
Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?
 $70
$30
$50
$65
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Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost? $70 $30 $50 $65
A large rectangle has a total area of 102 square feet, and is divided into two portions. If one portion of the rectangle has an area of 36 square feet, what is the area of the other portion of the rectangle, in square feet?
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A large rectangle has a total area of 102 square feet, and is divided into two portions. If one portion of the rectangle has an area of 36 square feet, what is the area of the other portion of the rectangle, in square feet?
Ramon's calculator screen is not working correctly. It displays the correct digits, but it does not display any decimal points. For each of the following examples, the digits from Ramon's calculator are shown below the expression. Use estimation to determine where (if anywhere) to place a decimal point in each result to end up with a reasonable answer.  
a. (2.95)(414)
b. 7.16.5.38-10.6748
c. 9.21² +19.08
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Ramon's calculator screen is not working correctly. It displays the correct digits, but it does not display any decimal points. For each of the following examples, the digits from Ramon's calculator are shown below the expression. Use estimation to determine where (if anywhere) to place a decimal point in each result to end up with a reasonable answer. a. (2.95)(414) b. 7.16.5.38-10.6748 c. 9.21² +19.08
An architect makes a model of a new house. The model shows a tile patio in the backyard. In the  model, each tile has length 1/3 in. and width 1/4 in. The actual tiles have length 1/4 ft and width 3/16ft  What is the ratio of the length of a tile in the model to the length of an actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile? Use pencil and paper. Describe two ways to find each ratio.
The ratio of the length of a tile in the model to the length of an actual tile is (Type the ratio as a simplified fraction.)
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An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length 1/3 in. and width 1/4 in. The actual tiles have length 1/4 ft and width 3/16ft What is the ratio of the length of a tile in the model to the length of an actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile? Use pencil and paper. Describe two ways to find each ratio. The ratio of the length of a tile in the model to the length of an actual tile is (Type the ratio as a simplified fraction.)
A book publisher claims that its mean book length is 250 pages with a standard deviation of 70 pages. What is the probability that for a sample of 45 randomly selected books, the mean length of a book is less than 230 pages?
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A book publisher claims that its mean book length is 250 pages with a standard deviation of 70 pages. What is the probability that for a sample of 45 randomly selected books, the mean length of a book is less than 230 pages?
Consider the function below.
f(x) = -5x² + 30x + 3
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Consider the function below. f(x) = -5x² + 30x + 3
For the following initial value problem, compute the first two approximations u₁ and u₂ given by Euler's method using the given time step.
y' (t)=t+y. y(0) = 3; At=0.3
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For the following initial value problem, compute the first two approximations u₁ and u₂ given by Euler's method using the given time step. y' (t)=t+y. y(0) = 3; At=0.3
For the function f(x) = 1/10x,construct and simplify the difference quotient f(x+h)-f(x) / h
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For the function f(x) = 1/10x,construct and simplify the difference quotient f(x+h)-f(x) / h
A water park has pools, slides, and rides that, in total, make use of 4.1 × 106 gallons of water. They plan to add a ride that would make use of an additional 91, 000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
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A water park has pools, slides, and rides that, in total, make use of 4.1 × 106 gallons of water. They plan to add a ride that would make use of an additional 91, 000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
Jon recently drove to visit his parents who live 270 miles away. On his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 12 hours driving, find the two rates.
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Jon recently drove to visit his parents who live 270 miles away. On his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 12 hours driving, find the two rates.
Each day, Caleb feeds his horse 2.25 lb of oats. He also feeds it hay. The weight
of hay is 6.5 times the weight of oats. What is the combined weight of oats and hay Caleb feeds his horse in one week?
A 61.250 lb
B 102.375 lb
C 118.125 lb
D 259.875 lb
Naomi chose C as the correct answer. How might she have gotten that answer?
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Each day, Caleb feeds his horse 2.25 lb of oats. He also feeds it hay. The weight of hay is 6.5 times the weight of oats. What is the combined weight of oats and hay Caleb feeds his horse in one week? A 61.250 lb B 102.375 lb C 118.125 lb D 259.875 lb Naomi chose C as the correct answer. How might she have gotten that answer?
Researchers in Antarctica discovered a warm sea current under a glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate of 0.06 m per day. Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?
t(x)= 450 -0.06x
t(x)= -0.06(x+450)
t(x)= 450+ 0.06x
t(x)= 0.06 (x+450)
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Researchers in Antarctica discovered a warm sea current under a glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate of 0.06 m per day. Which function can be used to find the thickness of the ice shelf in meters x days since the discovery? t(x)= 450 -0.06x t(x)= -0.06(x+450) t(x)= 450+ 0.06x t(x)= 0.06 (x+450)
Use f(x) and g(x) to find each composition. Identify its domain. (Use a calculator if necessary to find the domain.) (a) (fog)(x) (b) (gof)(x) (c) (fof)(x)
f(x)=x². g(x)=√1-x
(a) (fog)(x) = 1-x (Simplify your answer.)
The domain of (fog)(x) is (-∞0.1).
(Type your answer in interval notation.)
(b) (gof)(x) = (Simplify your answer.)
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Use f(x) and g(x) to find each composition. Identify its domain. (Use a calculator if necessary to find the domain.) (a) (fog)(x) (b) (gof)(x) (c) (fof)(x) f(x)=x². g(x)=√1-x (a) (fog)(x) = 1-x (Simplify your answer.) The domain of (fog)(x) is (-∞0.1). (Type your answer in interval notation.) (b) (gof)(x) = (Simplify your answer.)
You earn $11 per hour working at a grocery store during the summer. The function p(x) = 11x represents the amount you earn for working x hours.
a. You work 18 hours. How much do you earn?
b. How many hours do you have to work to earn $275?
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You earn $11 per hour working at a grocery store during the summer. The function p(x) = 11x represents the amount you earn for working x hours. a. You work 18 hours. How much do you earn? b. How many hours do you have to work to earn $275?
A street sign company is making street signs in the shape of equilateral triangles. The side length of each sign is 22 inches. What is the exact altitude length so that the company will be able to know what size box to ship them in?
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A street sign company is making street signs in the shape of equilateral triangles. The side length of each sign is 22 inches. What is the exact altitude length so that the company will be able to know what size box to ship them in?
Factor the expression.
-36x-32
The positive GCF of -36x and 32 is 4. Complete each equation with an expression or integer
factor.
The expression with 4 factored out is.
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Factor the expression. -36x-32 The positive GCF of -36x and 32 is 4. Complete each equation with an expression or integer factor. The expression with 4 factored out is.
The fuel efficiency rating for a certain car is 28 miles per gallon on the highway and 20 miles per gallon in the city. During one week the car traveled 220 miles and used 9 gallons of fuel. How much fuel was used for city driving? How much fuel was used for highway driving?
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The fuel efficiency rating for a certain car is 28 miles per gallon on the highway and 20 miles per gallon in the city. During one week the car traveled 220 miles and used 9 gallons of fuel. How much fuel was used for city driving? How much fuel was used for highway driving?
For what value of x is the following true?
log(x+11) = log x + log 11
Your answer is:
x=
You may enter the exact value or round to 4 decimal places.
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For what value of x is the following true? log(x+11) = log x + log 11 Your answer is: x= You may enter the exact value or round to 4 decimal places.
If e7x = 20, then x =
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If e7x = 20, then x =
In one question on a history test, a student is asked to match 10 dates with 10 events; each date can be matched with only 1 event. In how many ways can this question be answered?
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In one question on a history test, a student is asked to match 10 dates with 10 events; each date can be matched with only 1 event. In how many ways can this question be answered?
You go to the doctor and he gives you 17 milligrams of radioactive dye. After 24 minutes, 5 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. 
If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. 
You will spend minutes at the doctor's office.
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You go to the doctor and he gives you 17 milligrams of radioactive dye. After 24 minutes, 5 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office.
Three friends are going fishing. They will share 4 1/3 gallons of water equally. How much water will each friend get?
Answer the question in the following order and number your answers
1. What is the improper fraction that 4 1/3 equals?
2. What is the multiplication expression you need to find the quotient?
3. How much water will each friend get?
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Three friends are going fishing. They will share 4 1/3 gallons of water equally. How much water will each friend get? Answer the question in the following order and number your answers 1. What is the improper fraction that 4 1/3 equals? 2. What is the multiplication expression you need to find the quotient? 3. How much water will each friend get?
Answer parts (a), (b), and (c) for a cylinder with a radius of 5 inches and height of 9 inches.
(a) Compute the volume of the cylinder if the height were increased by 3 inches and the radius stayed the same.
(b) Compute the volume of the cylinder if the radius were increased by 3 inches and the height stayed the same.
(c) Which causes the volume to increase more, increasing its radius or height? Explain.
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Answer parts (a), (b), and (c) for a cylinder with a radius of 5 inches and height of 9 inches. (a) Compute the volume of the cylinder if the height were increased by 3 inches and the radius stayed the same. (b) Compute the volume of the cylinder if the radius were increased by 3 inches and the height stayed the same. (c) Which causes the volume to increase more, increasing its radius or height? Explain.
HOW MANY DIFFERENT 4 LETTER CALL LETTERS ARE POSSIBLE FOR A RADIO STATION IF:
a) THE FIRST LETTER MUST BE K OR W AND REPEATS ARE ALLOWED?
b)THE FIRST LETTER MUST BE K OR W, IT MUST END IN R, AND NO REPEATS ARE ALLOWED?
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HOW MANY DIFFERENT 4 LETTER CALL LETTERS ARE POSSIBLE FOR A RADIO STATION IF: a) THE FIRST LETTER MUST BE K OR W AND REPEATS ARE ALLOWED? b)THE FIRST LETTER MUST BE K OR W, IT MUST END IN R, AND NO REPEATS ARE ALLOWED?
The odds against Muffy beating her friend in a round of golf are 1:6. Find the probability that Muffy will lose.
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The odds against Muffy beating her friend in a round of golf are 1:6. Find the probability that Muffy will lose.
Two boats leave the same dock in Cairo, IL at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels 4 miles per hour. The southbound boat goes 8 miles per hour. How long will it take them to be 54 miles apart?
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Two boats leave the same dock in Cairo, IL at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels 4 miles per hour. The southbound boat goes 8 miles per hour. How long will it take them to be 54 miles apart?
Find out how long it takes a $2700 investment to earn $300 interest if it is invested at 7% compounded quarterly. Round to the nearest tenth of a year. Use the formula A=P(1+r/n)nt
1.7 years
1.5 years
1.9 years
1.3 years
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Find out how long it takes a $2700 investment to earn $300 interest if it is invested at 7% compounded quarterly. Round to the nearest tenth of a year. Use the formula A=P(1+r/n)nt 1.7 years 1.5 years 1.9 years 1.3 years
Terry is feeling crafty and wants to put a ribbon border on her boring clock to jazz it up a bit. If the clock has a radius of 15 inches, how many inches of ribbon will Terry need to use to surround the clock? Your answer should be a number only. Use 3.14 for pi. Round your answer to the nearest hundredth.
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Terry is feeling crafty and wants to put a ribbon border on her boring clock to jazz it up a bit. If the clock has a radius of 15 inches, how many inches of ribbon will Terry need to use to surround the clock? Your answer should be a number only. Use 3.14 for pi. Round your answer to the nearest hundredth.
Quadrilateral ABCD is mapped to quadrilateral A'B'C'D'. Which of the following transformations would not result in the two quadrilaterals being congruent?
(1) a translation along side AB by a distance of twice AB
(2) a dilation from point d by a factor of one-half
(3) a rotation about point C by 90 counterclockwise
(4) a reflection across side BC
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Quadrilateral ABCD is mapped to quadrilateral A'B'C'D'. Which of the following transformations would not result in the two quadrilaterals being congruent? (1) a translation along side AB by a distance of twice AB (2) a dilation from point d by a factor of one-half (3) a rotation about point C by 90 counterclockwise (4) a reflection across side BC