Mathematical Reasoning Questions and Answers

Joseph wants a television for his birthday that originally cost $740. Right now, the television is on sale for 40% off! Joseph's dad agreed to buy it, as long as Joseph pays for 30% of the cost. How much will Joseph have to pay?

Which is the contrapositive of the statement below? If you do your homework, then you will be prepared for the test. If you are prepared for the test, then you did your homework. If you are not prepared for the test,then you did not do your homework. If you do not do your homework, then you will not be prepared for the test. If you do your homework, then you will be prepared for the test.

Nicole, Pablo, and Ravi sent a total of 117 text messages over their cell phones during the weekend. Ravi sent 9 more messages than Nicole. Pablo sent 4 times as many messages as Ravi. How many messages did they each send?

In 1990, Jamaica's population of 2,466,000 was expected to grow exponentially by 1.1% each year. If you were to write an exponential function representing the situation, what should you used as the initial value? 1.011 110 1990 2,466,000

There are several statements in the table below. For each, determine whether it is a negation of this statement. The water temperature is 75°F. Statement Negation (Yes/No) The water temperature is 85°F. The water temperature is not 75°F. The water temperature is not 65°F. It is not the case that the water temperature is 75°F.

Lorenzo is planning a 285-mile trip. His car's EPA rating is 18 mpg. The number of gallons of gas that Lorenzo will need for the trip is about a. 15.8 gallons b. 18.0 gallons c. 26.7 gallons d. 28.5 gallons

Against the wind a small plane flew 210 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air? The speed of the plane in still air was mph. The speed of the wind was mph.

Ivan takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Ivan is taking a combined total of 19 credit hours at the two schools. Suppose that he is taking w credit hours at Westside. Write an expression for the combined total dollar amount he paid for his class fees.

A banana peel weighs 1/6 of the total weight of a banana. If an unpeeled banana balances a peeled banana of the same weight, plus 5/6 of an ounce, how much does the banana weigh with the peel? The weight of the banana with the peel is oz.

As part of a water quality survey, you test the water hardness in several randomly selected streams. The results are shown below. Construct a confidence interval for the population variance o2 and the population standard deviation o. Use a 99% level of confidence. Assume that the population has a normal distribution. n=17 s = 12 grains per gallon What is the confidence interval for the population variance σ²? (Round to one decimal place as needed.)

What is the volume of a cylinder that is 15-m tall and has a radius of 3 m. Use 3.14 for π, and round your answer to the nearest cubic meter. A. 141 m³ B. 283 m³ C. 339 m³ D. 424 m³

Suppose that there were a strong correlation between the variables d and f. Which of these is a true statement? A. dmust cause f B. d may cause f C. fmust cause d D. d must not cause f

If c is an explanatory variable and dis the corresponding response variable, which of these would be represented by the vertical axis on a scatterplot? A. Neither c nor d B. c C. Both cand d D. d

3/4. Looking down from the top row of Cornuelle lecture hall, you notice that the angle of depression to the floor seems to be pretty steep, about 70 degrees. If the distance you walk up the stairs to get to the top row is 28 feet, how high above the floor is the top row? Round to the nearest 10th. Picture Equation: Answer:

Gamestop wanted to find out which console its customers owned. Which best represents the population? All gamers. People window shopping outside of the store. Customers in the PS4 section. All Gamestop customers.

Suppose an investor deposits $28,000 into an account for which interest is compounded monthly. Find the amount of money in the account after 6 years using the following interest rates. 1. If r = 3.5%, then the investment is worth after 6 years. 2. If r = 5.5%, then the investment is worth after 6 years. 3. If r = 7%, then the investment is worth after 6 years. 4. If r = 9%, then the investment is worth after 6 years. • Round your answers to the nearest cent. Use a dollar sign to indicate that your answer is a monetary value.

You take a $4,500 loan to pay for a trip to the Amazon rainforest to photograph wild animals. If the loan's interest rate is 8% for 1 year, what is the interest for the first payment? $12.58 $26.00 $30.00 $80.99

Consider these statements. • All squares are equiangular. • Some rhombuses are squares. Which conclusion can be made using both statements? Some rhombuses are rectangles. A rhombus is always equiangular. All rhombuses are squares. Some rhombuses are equiangular.

A four-digit number is divisible by 10 and is smaller than 5,000. Which of the following expressions represents how many possible numbers there are? 4 x 10 x 10 x 1 4 x 10 x 10 x 10 10 × 10 × 10 × 1 10 x 10 x 10 × 10

Ron makes soap balls and sells them at his local farmers' market. First, he uses a large cylindrical pot to mix and melt the ingredients. The pot has a diameter of 10 inches, and he fills it to a height of 10 inches. When everything is melted, he pours the liquid soap into small spherical soap molds that each have a radius of 1.5 inches. What is the maximum number of soap molds that Ron can fill completely using his soap mixture?

Mike already knows that he will have $500,000 when he retires. If he sets up a payout annuity for 30 years in an account paying 10% interest, how much could the annuity provide each month (to the nearest dollar)? *

Kaleb has $850 saved for college. Kaleb expects the total cost of his first year to be $8,990. He has $850 in his savings account. He will receive grants and scholarships that total $1,445. Kaleb plans to save $210 every month. At this rate, how many months will Kaleb need to save until he has enough money to pay for the net price of his first year of college? A 31 months C 36 months B 32 months D 46 months

Tuition for one year at a state university is about $14,000. Denim would like to attend this university and will save money each month for the next 4 years. His parents will give him $6,500 for his first year of tuition. Which plan shows the minimum amount of money Denim must save to have enough money to pay for his first year of tuition? Save $625.00 per month for the next 4 years. Save $156.25 per month for the next 4 years. Save $1,875.00 per month for the next 4 years. Save $250.00 per month for the next 4 years.

Olive bought a candle for her grandmother. She wants to mail it to her, but she only has $3. It costs $3 to mail a package with the volume of 150 in³. If the candle she bought for her grandma has a diameter of 6 inches and a height of 5 inches, will she have enough money to mail the package? Show your work in the box below to justify your answer.

The slope of a ramp leading into a grocery store is 1:6 What is the angle of elevation of the ramp? Hint: you might have to use trigonometry a. 10.5° b. 80.5° c. 9.5° d. 64.4°

You want to buy a bouquet of yellow roses and baby's breath for $16. The baby's breath costs $3.50 per bunch, and the roses cost $2.50 each. You want one bunch of baby's breath and some roses for our bouquet. How many roses can you buy?

A car is purchased for $23,500. After each year, the resale value decreases by 35%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

13. Jacob gets paid $21.25 an hour to work on a surveying team, plus $40.00 per day for food. Which of the following equations shows his earnings for a workday that is h hours long? a. earnings = 21.25h + 40 b. earnings = 21.25 × 40 c. earnings (21.25 +40)h d. earnings = 40h + 21.25

A perfectly spherical balloon is being inflated such that the radius of the balloon is increasing linearly at a rate of 0.3 inches per t seconds. What would be an expression for calculating the volume of the balloon att seconds? (Remember: Volume of a sphere: V = (4πr3/3)

Find the contrapositive of the conditional "You are a vegetarian if you do not eat meat." . Caution: What is the antecedent of the conditional? If you eat meat, then you are not a vegetarian If you are not a vegetarian, then you eat meat If you are a vegetarian, then you do not eat meat If you do not eat meat, then you are a vegetarian

A Global Positioning Satellite (GPS) system uses satellite information to locate ground position. Abu's surveying firm bought a GPS system for $12,500. The GPS depreciated by a fixed rate of 6% and is now worth $8600. How long ago did Abu buy the GPS system?

The function f(x) = 34,000(1.05)* can be used to determine Noah's cost of living in Houston over time. What does the 1.05 represent? A The cost of living will increase by approximately 1% each year B The cost of living will decrease by approximately 1% each year C The cost of living will increase by approximately 5% each year D The cost of living will decrease by approximately 5% each year

Representing Proportional Relationships with Equations: Maya is interning at a law firm over the summer and is paid by the hour. her hourly wage is $56, write two equations to represent the proportional relationship between the wages she earns (w) and the number of hours (h): Start with the proportion: Then solve for one of the variables: Then solve for the other variable:

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck's revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? 77 93 99 105

The art club is raising money to go to an art museum. So far they have raised $50 by selling chalk drawings for $5 each. If they need to raise a total of $400, how many more drawings do they need to sell? a. 10 b. 70 C. 80 d. 90

A company is interested in learning if employees are satisfied with their jobs. To find out, the company hires an independent market research company to conduct a survey. Every survey filled out by an employee is anonymous. Which of the following statements is correct? A. This method of sampling is unbiased. B. This method of sampling can be considered both biased and unbiased. C. This method of sampling is blased. D. This method of sampling is neither biased nor unbiased.

Hans is performing an experiment examining how salt affects the speed at which water freezes. He fills four equally sized containers with the same amounts of water. Then, In three of the containers, he stirs in varying amounts of salt. The fourth container remains plain water. Hans places all four of the containers in the same freezer and checks the containers every five minutes, recording when the water in each container freezes solid. In this situation, what do Hans's time measurements represent? A the response group B. the explanatory variable C. the control group D. the response variable

Molly starts an IRA (Individual Retirement Account) at the age of 32 to save for retirement. She deposits $450 each month. The IRA has an average annual interest rate of 8% compounded monthly. How much money will she have saved when she retires at the age of 65? Round your answer to the nearest cent, if necessary. Answer

Write the negation of the statement. There is at least one person in this class who won't pass. Choose the correct negation for the given statement. All people in this class won't pass. Some people in this class will pass. No one in this class will pass. All people in this class will pass.

Which of the following statements are equivalent to the statement "Not all cats do not like having their belly rubbed"? Select the correct answer below: Some cats do not like having their belly rubbed. Some cats like having their belly rubbed. All cats do not like having their belly rubbed. All cats like having their belly rubbed.

What is the converse of the conditional statement, "If two angles are congruent, then they have the same measure"? A. If two angles are not congruent, then they do not have the same measure. B. If two angles have the same measure, then they are congruent. C. If two angles do not have the same measure, then they are not congruent. D. If two angles have the same measure, then they are not congruent.

Write this statement as a conditional in if-then form: A triangle is a polygon with three sides. A. If a polygon is a triangle, then it has three sides. B. If a triangle has three sides, then it is a polygon. C. If a triangle is a polygon, then it has three sides. D. If a triangle has three sides, then all polygons have three sides.

The Earth's Orbit. The maximum distance of the earth from the sun is 9.3 × 10^7 mi. The minimum dis- tance is 9.1 x 10^7 mi. The sun is at one focus of the elliptical orbit. Find the distance from the sun to the other focus.

In the spring of 2008, petrol cost £1.029 per litre in London. On the same day, the exchange rate was $1 = £0.498. What was the price of London petrol in dollars ($) per gallon? (1 gal = 3.7854 L) $1.83 /gal $7.82 /gal $3.90 /gal $7.60 /gal $1.94 /gal

A landscaping company placed two orders with a local nursery. The first order was for 13 bushes and 4 trees and totaled $487. The second order was for 6 bushes and 2 trees and totaled $232. What was the cost of each bush and each tree? Bushes $31, Trees $64 Bushes $47, Trees $23 Bushes $23, Trees $47 Bushes $23, Trees $52

Consider statements p and q. p: The path is in the park. q: A tree branch is above us. (a) Write each statement below in symbolic form using p and q. Statement 1: A tree branch is not above us or the path is not in the park. Statement 2: If a tree branch is above us, then the path is not in the park.

Angela Montery has a five-year car loan for a Jeep Wrangler at an annual interest rate of 5.9% and a monthly payment of $595.50. After 3 years, Angela decides to purchase a new car. What is the payoff on Angela's loan? (Round your answer to two decimal places.)

z = -1 is what percentile? percentile State your answer to the nearest tenth of a percent. Enter your answer as an integer or decimal number. Examples: 3, -4,

WHICH ONE DOESN'T BELONG? Which statement does not belong with the other three? Explain your reasoning. 7 + (x + 4) = 7+ (4 + x) 9 + (7 + w) = (9 + 7) + w (3 + b) + 2 = (b + 3) + 2 (4 + n) + 6 = (n + 4) + 6

A recipe for a cake calls for 3/4 of a cup of sugar, and Sherry needs to use this recipe to bake four identical cakes for a school party. Sherry makes the statement, "4 multiplied by 3/4 will give me the total amount of sugar I need for all four cakes." If Sherry's statement is true, which answer choice below is also true?