Mathematical Reasoning Questions and Answers

Jamaican sprinter Usain Bolt won the 100 meter sprint gold medal in the 2012 Summer Olympics. He ran the 100 meter race in 9.63 seconds. There are about 3.28 feet in a met and 5280 feet in a mile. What was Usain Bolt's average speed for the 100 meter race in miles per hour?

Which breed(s) have weights that are prime numbers? Cocker Spaniel, German Shepherd Beagle A Lakeland Terrier weighs less than 20 pounds. List a new prime number and a new composite number that could be the average weight of the breed. Explain how you know.

The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam 1/4 foot wide, 1/4 foot high, and 10 feet long. Find how much a similar beam can support if the beam is 3/4 foot wide 1/3 foot high and 15 feet long

A grocery store is offering a sale on bread and soup. Khalil buys four cans of soup and three loaves of bread for $11.67. Ronda buys eight cans of soup and one loaf of bread for $12.89. Homework Help a. Write equations for both Khalil's and Ronda's purchases. b. Solve the system to find the price of one can of soup and the price of one loaf of bread.

Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is behind the simulated biker, he has a negative position. km Julian sets the simulated biker to a speed of 20 After he rides his bike for 15 minutes, Julian's app reports a h 1 position of -2- km. 4 What has Julian's average speed been so far? km h

A submarine is at the surface of the ocean. It begins its descent at a rate of 100 feet per minute. Write a linear model in the form d(t) = mt + b where d(t) represents the depth of the submarine relative to sea level, in feet, after t minutes into its descent. Be sure to include "d(t) =" in your answer. (Note: when the submarine is below sea level, its depth is a negative quantity)

Your home was recently appraised for $172,000. The balance on your existing mortgage is $120,650. If your bank is willing to loan up to 75% of the appraised value, what is the potential amount of credit available on a home equity loan? O $8,350 O $51,350 O $90,488 O $129,000

Given the three simple statements: p: The dog is orange. q:The bat is tan. r: The snake is yellow. Write the symbolic form for the following compound statement: The dog is orange, if and only if the snake is not yellow or the bat is tan. p↔ (~rVq) (~p^r) →q (p^r) → q (~p^r) ~q (~p^r) ~q q→ (p V ~r) (p^~r)→ ~q (p↔~r) Vq ~p^ (r↔~ q) (p^~r) q None of these

Mr. Brown sells horse supplies. A pair of riding gloves sells for $16. He says he will make $144 if he sells 9 pairs.

Select the contrapositive of: If the dog is blue, then the cat is pink. If the dog is blue, then the cat is not pink. The dog is not blue and the cat is pink. If the cat is pink, then the dog is blue. If the cat is not pink, then the dog is not blue. The dog is not blue or the cat is not pink. The dog is blue and the cat is not pink. The dog is not blue if and only if the cat is not pink. If the dog is not blue, then the cat is not pink. The dog is blue or the cat is not pink. The dog is not blue or the cat is pink. None of these.

Twenty one concrete blocks were sampled and tested for crushing strength in order to estimate the proportion that were sufficiently strong for a certain application. Ninteen of the 21 blocks were sufficiently strong. Use the small-sample method to construct a 95% confidence interval for the proportion of blocks that are sufficiently strong. Round the answers to at least three decimal places.

Directions: Write the following statements in if-then form. 3. A rhombus is a quadrilateral with four congruent sides 4. Those that finish the marathon will get a medal. 5. All freshman are required to attend orientation.

When the temperature stays the same, the volume of gas is inversely proportional to the pressure of the gas. If a balloon is filled with 228 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 38 cubic inches.

The number of gallons of water, W used when taking a shower varies directly as the time t, in minutes, in the shower. A shower lasting 6 minutes uses 30 gallons of water. How much water is used in a shower lasting 11 minutes?

Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month and charge their students $40 per hour. They write an equation for their profit (or loss) as y=40x-400. In this equation, what does the variable x represent?

Using a heating mantle distill at the rate of about 1 mL per 2 minutes. Collect two fractions one at temperature below 80 C and the other above 90 C. Make sure to leave about 2 mL in the flask. For data assume that you collected 23 ml in the first fraction and 20 mL in the other, report the percentage of recovery for cyclohexane and toluene. Answer the following questions in your report: 1. What is pumping and how it can be eliminated?

A rowing team rowed 50 miles while going with the current in the same amount of time as it took to row 25 miles going against the current. The rate of the current was 2 miles per hour. Find the rate of the rowing team in still water.

A class of 30 introductory statistics students took a 15 item quiz, with each item worth 1 point. The standard deviation for the resulting score distribution is 0. You know that: A. about half of the scores were above the mean. B. an arithmetic error must have been made. C. everyone correctly answered the same number of items. D. the mean, median, and mode must all be 0.

Cam and Madison were investing money into two different accounts. They both invested $550 each. Cam invested into an account at an annual interest rate of 2.7% compounded monthly and Madison invested into an account that had an annual interest rate of 3% compounded quarterly. Which statement below best describes the two accounts after 5 years? Cam's account has approximately $60 more after 5 years than Madison's account. Madison's account has approximately $9 more after 5 years than Cam's account. Cam's account has approximately $12 more after 5 years than Madison's account. Madison's account has approximately $80 more after 5 years than Sal's account.

A wildlife biologist determines that there are approximately 200 deer in a region of the national park. The population grows at a rate of 7% per year. What is an exponential function that models the expected population?

Construct a 99.5% interval for the mean score. Round the answers to two decimal places. A 99.5% confidence interval for the mean score is <μ< 0.

Convert the given number to decimal form by expanding in powers and by using the calculator shortcu 6EF sixteen Expand 6EF sixteen in powers. Use the decimal values of any digits unique to the hexadecimal system. 6EF 0+0+0 sixteen

Let p and q represent the following statements. p: Eggs make a good breakfast. q: Bacon is not healthy. Select the statement below that matches the following symbolic statement:~ p^~q Eggs__ make a good breakfast,bacon __ healthy.

Let p and q represent the following statements. p: Interest rates are low. q: It is not time to buy a house. Write the following statement in symbolic form: "Interest rates are not low, and it is not time to buy a house." To enter your response, select the appropriate statement in each of the dropdown boxes, and select the appropriate operation in the middle. If only one statement is used, select "none" for the operation in the middle and the statement in the second dropdown box. Be sure to enter the statements in the same order as in the given sentence.

A movie theatre models the revenue from ticket sales in one day as a function of the ticket price, p. Here are two expressions defining the same revenue function. p(120-4p) 120p-4p² 1. According to this model, how high would the ticket price have to be for the theater to make $0 in revenue? Explain your reasoning.

Jim rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 84 cents for each mile driven. Jim had to pay $159.11 when he returned the truck. For how many miles did he drive the truck?

Andre is setting up rectangular tables for a party. He can fit 6 chairs around a single table. Andre lines up 10 tables end-to- end and tries to fit 60 chairs around them, but he is surprised when he cannot fit them all. Write an equation for the relationship between the number of chairs c and the number of tables t when the tables are apart from each other: Complete the equation below C = Use t as your variable.

The scale on a map is drawn so that 4.5 inches corresponds to an actual distance of 225 miles. If two cities are 10.25 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) The two cities are miles apart.

The weight of 10,000 identical samples of a substance is 100 pounds. What is the weight of 10 samples?

At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts moving forward with a constant acceleration of 6 ft/sec² . At the same instant a truck traveling with a constant velocity of 30 ft/sec overtakes and passes the car. (a) How far beyond its starting point will the automobile overtake the truck?

Solve the inequality: 8 ≤ x-7 ≤ 10 Select one: a. [15, 17] b. (15, 17) c. (15, 17] d. [15, 17)

A basketball fieldhouse seats 15,000. Courtside seats sell for $9, endzone for $7, and balcony for $4. Total for a sell-out is $81,000. If half the courtside and balcony and all endzone seats are sold, the total is $47,500. How many of each type are there? 4000 courtside 3000 endzone 8000 balcony 3000 courtside 2000 endzone 10,000 balcony 3200 courtside 1800 endzone 10,000 balcony

Let p = "Sophie has been arrested" and let q = "Bubba's never been arrested." Write the statement in symbols. Sophie has been arrested if and only if Bubba has not. The statement, in symbols, is written as

A couple who borrow $50,000 for 25 years at 8.4%, compounded monthly, must make monthly payments of $399.25. (Round your answers to the nearest cent.) (a) Find their unpaid balance after 1 year. (b) During that first year, how much interest do they pay?

Form the negation of the following statement: "It is not true that wine in moderation is not good for the heart." Select all that apply: Wine in moderation is not good for the heart. Wine in moderation is good for the heart.

A vending machine sells chips for $0.50 and candy bars for $1.00. If Jim spent $5.50 on snacks in the machine over the course of a week, how many candy bars did he buy? F. 1 G. 2 H. 3 J. 4 K. Cannot be determined from the given information

Is the following a valid syllogistic argument? Identify its major and minor premise. 1. Statement: All dolphins are mammals. 2. Statement: All mammals are animals. 3. Conclusion: Dolphins are animals. Select the correct answer below: Valid; Major premise: All dolphins are mammals. Minor premise: All mammals are animals. Invalid; Major premise: All dolphins are mammals. Minor premise: All mammals are animals. Valid; Major premise: All mammals are animals. Minor premise: All dolphins are mammals. Invalid; Major premise: All mammals are animals. Minor premise: All dolphins are mammals.

Bobby opened a bag of candy and counted how many pieces were in the bag. There were 68 pieces of orange, lime, and cherry candies in total. He separated them by flavor and found that there were 2 more orange than lime and 4 more cherry than orange. How many cherry candies were in the bag? Translated Equations: F. 20 G. 22 H. 24 J. 26 K. 28 tend 02dripood we qqa ne TA E

Let E be an event. Let F be another event. We know that P(E and F) = 0.5 What can we definitely say about E & F? P(E)=P(F) = 0.25 E and F have outcomes in common E and F are mutually exclusive E and F are disjoint

Determine whether the equation is a conditional equation, an identity, or a contradiction. Give the solution set. 8(v + 1)-4v = 2(2v+4) - 12 Is the equation a conditional equation, an identity, or a contradiction? A. identity B. contradiction C. conditional equation

Experimental or Observational: A group of students is interested in knowing if the number of times they can sink a basketball is related to the color of the basketball. The students shoot a series of baskets and record their success using a regulation colored basketball. They then switch to a blue colored basketball and shoot the same series of baskets.

Three good friends are in the same Algebra class. Their scores on a recent test are three consecutive odd integers whose sum is 225. Find each score.

How are the FAFSA, SAR, and EFC related? The FAFSA is what you fill out to apply for financial aid. The SAR is a record of what you submitted in your FAFSA. The EFC is how much a college expects you and your family to contribute to your cost of college. The SAR is a record of what you submitted in your EFC form. The final step is to fill out your FAFSA to apply for financial aid. You first fill out the FAFSA for financial aid and get your EFC immediately after submitting. A few weeks later, you get your SAR to see what financial aid a college is offering you. You fill out the SAR first to let the Federal government know you intend to submit the FAFSA. After filing the FAFSA, you receive your EFC form in the mail.

Iceman and Maverick start arguing over negative radius information. Whom do you think is correct? Maverick: "A point with a negative radius is located at the same point as the positive radius (angle is unchanged)." Iceman: "A point with a negative radius is NOT located at the same point as the positive radius (angle unchanged). Explain your thinking.

Given the premises "If I am in a meeting, then my phone is on silent" and "If my phone is on silent, then I will not hear your call," is it a valid argument to conclude "If I am in a meeting, then I will not hear your call?" Select the correct answer below: There is not enough information to determine whether the argument is valid. The argument is valid. The argument is not valid.

Find the annual percentage yield for an investment at the following rates. (Round your answers to two decimal places.) (a) 7.2% compounded monthly % (b) 9% compounded continuously %

What is the negation of the statement "Some of those numbers are even"? Select the correct answer below: All of those numbers are even. All numbers are odd. None of those numbers are even. Some of those numbers are odd.

Consider statements p and q. P: The car is blue. q: The car is a sedan. For parts (a) and (b), fill in the symbolic form. For part (c), choose the descriptive form. Descriptive form (a) The car is a sedan and the car is blue. (b) The car is a sedan or the car is blue. 0 (c) (Choose one) The car is not a sedan. The car is a sedan. The car is not blue.

Ricardo obtains a 15-year, $114,250 mortgage at 4.0% on a house selling for $129,000. His monthly payment, including principal and interest is $845.09. a) Determine the total amount that Ricardo will pay for His mortgage. (Round to the nearest dollar.) Total amount: $ b) How must of the total cost will be interest? Total interest: $ (Round to the nearest dollar.) c) How much of the first payment on the mortgage is applied to the principal? Amount applied to principal: $ (Round to the nearest cent.)

An article published in Statistics Weekly claimed that a new brand of deodorant was the "Best Deodorant for High School Teenagers." The researchers at Perdue University decided to test the deodorant at a local high school. . Thirty girls and thirty boys at Park Central high were randomly selected to take part in the study. . On Monday all students used a well-known deodorant, ran a mile and rated their sweat level from 1-10. The average sweat level was 7. .On Wednesday the same 30 students used the new brand of deodorant, ran a mile, and then rated their sweat level. . The average sweat level was a 3. What was the source of the data? The researchers at Perdue University. Statistics Weekly Magazine. The high school students. The source is not stated.