Basic Math Questions and Answers

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.

After all the taxes are withheld, Jules's take-home pay is about 72% of his total earnings. Estimate his take-home pay if his total earnings for the pay period are $240. 75 120 180 300

A person invests money in a savings account that pays 2.5% simple interest. After one year, the person earns $24.25 in interest. How much did this person initially invest in the account (rounded to the nearest dollar)? Use the formula P=1/rtwhere P is the principle, /is the interest earned, r is the interest rate and t is the time, to find the initial investment. $1,230 $125 $1,170 $970

A college requires all incoming freshmen to live on campus. The college has two freshman dormitories, East and West. For an upcoming school year, there are 800 incoming freshmen. Which method evenly assigns the students to the two dormitories so that each Incoming freshman has a fair chance of being selected for either dormitory? A. Using a random number generator, assign each incoming freshman a number, eliminating any duplicate numbers. Assign each incoming freshman with a positive number to East dormitory, and assign each incoming freshman with a negative number to West dormitory. B. Using a two-sided coin, flip a coin for each incoming freshman. If the coin lands on heads, assign the freshman to East dormitory. If the coin lands on tails, assign the freshman to West dormitory. C. Using a random number generator, assign each incoming freshman a number, eliminating duplicate numbers. After each Incoming freshman is assigned a number, list the assigned numbers in ascending order. Assign the first 400 numbers on the list to East dormitory, and assign the last 400 numbers on the list to West dormitory. D.Using a random number generator, assign each incoming freshman a number, eliminating any duplicate numbers. Assign each incoming freshman with an even number to East dormitory, and assign each freshman with an odd number to West dormitory.

Solve the following inequality for x. -4x-6/2 > 5 Do not include spaces in your answer. Write your answer as an inequality statement with x, then the < or > sign, followed by a number.

Enrollment in a business seminar increased from 71 people to 81 people. What was the percent of increase? Round to the nearest tenth of a percent.

A student council wants to know whether students would like the council to sponsor a mid-winter dance or a mid-winter carnival this year. Classify each sampling method. a. Survey every tenth student on the school's roster. b. Survey all students in three randomly selected homerooms. c. Survey a random selection of those who happen to be in the cafeteria at noon. d. Survey those who ask the council president for a questionnaire.

A 20 foot ladder is leaning against a house. The bottom of the ladder is 3ft. from the house. To the nearest tenth of a foot, about how high does the top of the ladder reach? 19.2 ft 19.8 ft 19.4 ft 19.6 ft

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3025 feet and Plane B is just taking off. Plane A is gaining altitude at 25.25 feet per second and Plane B is gaining altitude at 85.75 feet per second. How many seconds will pass before the planes are at the same altitude? seconds What will their altitude be when they're at the same altitude? feet

A glider flies 8 miles south from the airport and then 15 miles east. Then it flies in a straight line back to the airport. What was the distance of the glider's last leg back to the airport? 17 miles 18 miles 19 miles 16 miles

The fare for a taxi cab is a $2 flat fee plus an additional $1.50 for each mile. Which equation represents the total cab fare in dollars? A y+2=1.5x,y represents miles traveled, x represents the total fare B. y = 1.5x + 2y represents the total fare, x represents miles traveled C. 1.5y=x+2y represents the total fare, x represents miles traveled D. y = (1.5+ 2)x,y represents miles traveled, x represents the total fare

Jesse drives to work. The distance Jesse's car travels (d) on a number of gallons of gas (g) is given by the equation d = 25g. The constant of proportionality in terms of distance traveled per gallon of gas is ______ ("distance traveled per gallon of gas" is your clue!)

In a company's first year in operation, it made an annual profit of $127,000. The profit of the company increased at a constant 29% per year each year. How much total profit would the company make over the course of its first 28 years of operation, to the nearest whole number?

An employee joins a certain company and earns a beginning salary of $95000. At the end of each year, this employee receives a 6% raise. An explicit formula y= A. B^x can be written to model this situation. For this model, the value of A is type your answer... and the value of B is type your answer...

The equation 2w + 5j = 60 is used to determine the number of water bottles w and the number of juice bottles j that can be bought for $60. If you purchase 4 bottles of juice, how many bottles of water can you buy? A 10 B. 15 C. 20 D. 25

The formula for the area of a triangle is A =1/2 bh where b is the base of the triangle and h is the height of the triangle. What is the length of the base if the area is 22 cm^2 and the height is 8 cm? A. 4.5 cm B. 5 cm C. 5.5 cm D. 6 cm

Jackson was offered a job that paid a salary of $93, 000 in its first year. The salary was set to increase by 1% per year every year. If Jackson worked at the job for 16 years, what was the total amount of money earned over the 16 years, to the nearest whole number?

At the state fair, admission at the gate is $8. In addition, the cost of each ride is $2. Suppose that Frank will go on x rides. Frank wants the total number of dollars he spends on admission and rides to be fewer than t. Using the values and variables given, write an inequality describing this.