Basic Math Questions and Answers

Jaquin hopes to earn $700 in interest in 3.6 years time from $28,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds semi-annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Marsha gave the cashier $20 to pay for 3 pairs of socks. The cashier gave her $5.03 in change. Each pair of socks cost the same amount. What is the cost in dollars and cents for each pair of socks?

Sally worked 7 hours on Monday, 6 hours on Tuesday, 6.75 hours on Wednesday, 5.75 hours on Thursday, and 3.5 hours on Friday. If she is paid $10.18 per hour. Find her gross earnings for the week.

The harmonic motion function d (t) = 5cos(2t), in which dis measured in centimeters and t is measured in seconds, gives the distance a swinging pendulum is from its resting position at time t. How far was the pendulum from its resting position when the motion began? What is the period of the pendulum's motion? How far is the pendulum from its resting position after 7.5 seconds?

Carter Motor Company claims that its new sedan, the Libra, will average better than 31 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. There is not sufficient evidence to support the claim that the mean is less than 31 miles per gallon. There is not sufficient evidence to support the claim that the mean is greater than 31 miles per gallon. There is sufficient evidence to support the claim that the mean is less than 31 miles per gallon. There is sufficient evidence to support the claim that the mean is greater than 31 miles per gallon.

Eduardo wants to determine the fuel consumption of his vehicle. He knows that 20 L of gasoline will get him 220 km and that 11 L of gasoline will get him 115 km. a. What is the independent variable? b. What is the dependent variable? c. What would two coordinates be?

A radioisotope is used as a power source for a satellite. The power output is given by the equation P = 50e t/250, where P is the power in watts and t is the time in days. a. Find the power available after 100 days.

Zachary earns $8.00 per hour. He get paid time and a half for any hours over 40 that he works in a week. If Zachary works 9 hours per day from Monday through Friday, what are his gross earnings for the week?

A farmer is comparing the number of eggs laid by two hens. The first hen laid 6 eggs per week for x weeks. The second hen laid 9 eggs per week for y weeks. The total number of eggs laid by the first hen was greater than the total number of eggs laid by the second hen. Write an inequality showing this relationship.

The exponential model A = 883.1 e 0.014t describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was million.

Find the greatest common factor of 9m4 and 10n³.

Suppose there are five firms in an industry. Their sales (that is, total revenue) are as follows: • Firm 1: $96 million • Firm 2: $48 million • Firm 3: $36 million • Firm 4: $14 million • Firm 5: $6 million The Herfindahl-Hirschman Index (HHI) for this industry is (Enter your response as an integer.)

Grande Prairie to Medicine Hat, Alberta, is 1013 km and takes Suzie 10 hrs and 45 minutes to drive. Suzie's SUV is travelling at a constant rate of speed from Grande Prairie to Medicine Hat. a. What are the independent and dependent variables? b. How could you represent Suzie's starting coordinates and end coordinates?

After a 70% reduction, you purchase a new sofa on sale for $204. What was the original price of the sofa? The original price was $

A delivery truck is driving along a straight road, and after, hours its distance (in miles) east of its starting point is s = 24t² - 4t³ At time t = 2 hours, where is the truck located? B) 64 miles C) 48 miles A) 96 miles D) 100 miles

You invest $20,000 into an account that earns 5.2% interest every year. How much would you have after 18 years? a. Find the a and the b for this problem. b. Write the equation that models this situation. C. How much would you have after 18 years?

A bullet is fired straight up into the air. Its velocity after t seconds is given by v(t) = -9.81t + 345 m/sec. Find the total distance travelled by the bullet after 63 seconds. Round your answer to 2 decimal(s) Total distance: m

Aisle 2 of a furniture store stocks 4-legged chairs, 4-legged tables, and 3-legged stools. If there are t tables, cchairs, and s stools, which expressions show the total number of furniture legs in aisle 2? 4t+4c+ 3s 4t+4c+4s 4(t+c)+ 3s 4(t+c+s) t+c+s t+c+ 3s

The designers of a standardized test are interested in knowing how long people take, on average, to complete the writing portion of the test. They decide to conduct an observation study at a testing facility. To avoid blas in their study, they create a list of the test takers scheduled to take the test this week. Then, they randomly select 50 test takers from the list to be part of the study. In this situation, what does the list of test takers represent? A. the population B. a sample C. the frame D. a control group

A local hamburger shop sold a combined total of 384 hamburgers and cheeseburgers on Saturday. There were 66 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday? hamburgers

A puzzle contains rectangular wooden pieces with a length of 5 cm and a width of 6 cm. Each puzzle contains 10 of these rectangular pieces. If Tommothy wants to make 4 of these puzzles, find the amount of wood needed to make all of them.

How did Trevor Noah suggest to change the old adage: "Give 1 poin a man a fish, feed him for a day. Teach a man to fish, feed him for a lifetime."?* If you give a man a computer, he could be making a great deal of money and feed his family for the rest of his life. You should also give a man the rod so that he can fish and feed his family. If you teach the man to fish and give him a rod, then you might as well go fishing with him. Why did Trevor decide to stop involving himself in petty crimes? * He was afraid of the consequences if his mother knew of his illegal dealings. He decided to enter college and find a decent job that would help him get out of poverty. 1 point He felt guilty for stealing someone's digital camera where the family's memories were stored.

Mr. Costa randomly surveyed 20 students as they walked through the front door of the elementary school and found that 8 of them were buying hot lunch. If there are 430 students at this elementary school, how many would you expect to buy hot lunch? 172 162 152 142

A company decides to survey its employees about their job satisfaction. The company's managers are responsible for delivering the surveys. The managers Interview the employees they supervise face-to-face, asking the survey questions and writing down the responses. What is a source of blas in this sampling method? A. It is unlikely that employees will claim they are unsatisfied with their jobs while talking to their managers. B. Some people may be sick that day and unable to complete the survey. C. Employees usually complain about their jobs anyway. D. Some people may be on vacation and unable to complete the survey.

The half-life of radium (Ra226) is 1620 years. When will a 20-gram sample of radium (Ra226) be completely gone? Explain.

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t) = 750e-0.144t, where t is the time in years? Round to the nearest hundredth year.

The exponential model A = 84.3 e0.032t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 165 million. The population of the country will be 165 million in (Round to the nearest year as needed.)

A veterinarian is interested in the average number of pets her clients own. Over the course of a month, she questions each client she meets with and records their responses. The veterinarian calculates the average and draws a conclusion from her data. What kind of statistical study did the veterinarian conduct? A. experiment B. survey C. theoretical study D. observational study

Stacy Arrington is paid $.73 for sewing a jacket collar, $.86 for a sleeve with cuffs, and $.94 for a lapel. One week she sewed 318 jacket collars, 112 sleeves with cuffs, and 37 lapels. Find her gross earnings.

Suppose a rectangle has width W and length L both in feet. Choose the correct translation of the following into symbolic algebra: "Five feet more than four times the width is half of the length." 4W + 5 = L/2 (4W) = (1/2)L 4W = L/2+5 4W (L+5)/2 none of these are correct 4W+5+ (1/2)L

Suppose a certain baseball diamond is a square 95 feet on a side. The pitching rubber is located 61.5 feet from home plate on a line joining home plate and second base. How far is it from the pitching rubber to first base?

Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 100 workers 6 weeks to build 4 miles of highway. How many workers would be needed to build 16 miles of highway in 15 weeks?

Emily has 50 gallons of water to share between 6 different fish tanks. She puts an equal amount of water in each fish tank. What is the total amount of water, in gallons, in each tank? A. 3/25 gallon B. 8 1/25 gallon C. 9 2/25 gallon D. 10 1/25 gallon

The volume of a fixed amount of a gas varies directly as the temperature I' and inversely as the pressure P. Suppose that V= 120 cm³ when T=260 kelv and P=13-2 Find the pressure when T-380 kelvin and V=152 cm³.

Solve the following exponential equation. Express the solution in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. 37x+4 = 5x-2 The solution set expressed in terms of logarithms is. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is {} (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Hans will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $52 and costs an additional $0.15 per mile driven. The second plan has an initial fee of $57 and costs an additional $0.13 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same?

A car traveled at an average speed of 80 miles per hour for 3 hours and consumed fuel at a rate of 34 miles per gallon. Approximately how many gallons of fuel did the car use for the entire 3-hour trip? A) 2 B) 3 C) 6 D) 7

A biologist observed a population of bacteria that grew at a rate expressed by the exponential equation f(t) = 256e(0.0611r) where I is in minutes. How long will it take the population to reach 5 times its initial value? Round to two decimal places and do not include "t=" in your answer.

At Imelda's fruit stand, you bought 5 apples and 4 oranges for $10, and your friend bought 5 apples and 5 oranges for $11. Using this information, is it possible to determine the cost of one apple and one orange from the fruit stand? If so, what do they cost? If not, why not? Choose 1 answer: Yes; they should charge $1.00 for an apple and $1.25 for an orange. Yes; they should charge $1.20 for an apple and $1.00 for an orange. No; the system has many solutions. No: the system has no solution.

Two cyclists leave towns 180 miles apart at the same time and travel toward each other. One cyclist travels 8 slower than the other. If they meet in 5 hours, what is the rate of each cyclist? h Note that the ALEKS graphing calculator can be used to make computations easier. Rate of the slower cyclist: Rate of the faster cyclist: ?

The Jones family and the Griffin family each used their sprinklers last summer. The water output rate for the Jones family's sprinkler was 20 L per hour. The water output rate for the Griffin family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1075 L. How long was each sprinkler used?

One month Rachel rented 7 movies and 9 video games for a total of $71. The next month she rented 5 movies and 3 video games for a total of $31. Find the rental cost for each movie and each video game.

A motorboat takes 3 hours to travel 108 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

The formula d = rt is used to calculate the distance an object travels over a period of time, t, at a constant rate, r. Based on this formula, what is the rate, r, in terms of d and t? A) r = d/t B) r = dt C) r = t/d D) r = d - t

Cindy measured a community college and made a scale drawing. The scale she used was 1 centimeter: 3 meters. A building at the college is 53 centimeters long in the drawing. How long is the actual building?

A dairy farmer uses a storage silo, shown below, that is in the shape of a right circular cylinder below. If the volume of the silo is 72pi cubic yards, what is the diameter of the base of the cylinder, in yards? 3 6 7 9

Find the amount of money (Future Value) in an account where $3,700 is deposited (Present Value) at an interest rate of 2.5% per year compounded continuously and the money is left in the account for 6 years.

A population of frogs in a pond increases at an annual rate of 22%. If there are 100 frogs in the pond, which equation gives you a model for how many frogs there will be in time t years? a. Pt = 100e^0.22t b. Pt = 100e^0.22/t c. Pt = 100e^-0.22/t d. Pt = 100e^-0.22t

Point R is located at (1, 2) on a coordinate grid. Point S is located at (4,-5) on the same coordinate grid. What is the distance from point R to point S, rounded to the nearest tenth? A 3.2 units B. 4.6 units C. 7.6 units D. 10.0 units

The equation above is used to model the relationship between the number of cups, n, of hot chocolate sold per day in a coffee shop and the average daily temperature, T, in degrees Fahrenheit. According to the model, what is the meaning of the 3 in the equation? A) For every increase of 3°F, one more cup of hot chocolate will be sold. B) For every decrease of 3°F, one more cup of hot chocolate will be sold. C) For every increase of 1"F, three more cups of hot chocolate will be sold. D) For every decrease of 1"F, three more cups of hot chocolate will be sold.