Basic Math Questions and Answers

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.

Renee is going bowling. The cost per game is $2.50. Renee will need to rent a pair of bowling shoes for $1.50. She can spend up to $16.00 to bowl and rent a pair of shoes. What is the maximum number of games that Renee can bowl?

The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 3 square flower beds, one on each side of the playground. The length of the playground is I and its width is w. The length of each side of the flower beds is a. Assume that the playground and beds do not overlap. The total fencing material required to fence the playground and all three flower beds is:

"The difference between the circumference and the sum of 6 feet and the radius is zero." Where C = the circumference (feet) r = the radius (feet) C-6+r C-6=r C/(6 + r) C/(6+r)=0 C-(6+r)=0 C-(6+r)

Eddie is practicing wind sprints during his summer break. He's able to run 100 meters in 28 seconds. If d represents distance and t represents time, write two equations that represent this proportional relationship: Start with the proportion: ___ = ___ Then solve for one of the variables: Then solve for the other variable:

Carlie runs two different business. She needs to pay $100 for materials, and pay her associates $12 per hour for her childcare business. And for her lawn care business, she has to pay $275 for materials, and pays her associates $10 per hour. Write two functions, C(x) and L(x), to represent the amount of money she will need to run her childcare business and her lawn care business. Complete the equations by filling in the blanks. Childcare business: C(x) = Lawn care business: L(x) =

A gym charges $35 per month for full access to their workout equipment. Mrs. Lewis has a $140 gift certificate to the gym. For how many months can Mrs. Lewis work out using the gift certificate? A 3 months B. 4 months C. 5 months D. 6 months

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 6.5%, and the tax in the second city was 4%. The total hotel tax paid for the two cities was $480. How much was the hotel charge in each city before tax? Note that the ALEKS graphing calculator can be used to make computations easier. Second city: $ First city:

Select the correct answer. It is estimated that approximately one-half of all aluminum cans will be recycled each year. If a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function? Nt = 350,000(0.52)^t A. 87,500 B. 25,591 C. 175,000 D. 21,875

Rock music accounts for 64% of the CD sales of True Tones Record Company. If next year's production is planned at 300,000 CD's, estimate how many of the CD's will be of rock music? 150,000 200,000 240,000 500,000

manager of the customer service department of an e-commerce company wants to know the average hold time for customers who call the department. The department receives about 850 calls each hour. The following data set shows the hold time, in minutes, for 10 calls picked at random. 2, 1, 4, 5, 3, 3, 7, 4, 3, 2 Calculate the approximate hold time for all customers who call the customer service department. The approximate hold time for all customers who call the customer service department

Lucy has an unpaid balance of $1200 on her credit card. The credit card company requires a minimum payment of 4.5% and charges an annual interest rate of 30%. Calculate Lucy's minimum payment, the amount of interest paid that month, and her unpaid balance. Round each to the nearest cent. The minimum payment is $ The amount of interest paid is $ The unpaid balance is $

A real estate office pays its salespeople a weekly retainer of $220 plus a commission of 2.5% for the first $200 000 of the value of each property sold and 2% of each amount after that. Calculate the commission received if a house is sold for $540,000.

Outworkers who sew T-shirts together are paid a wage of $3 per hour plus $1.45 for each T-shirt sewn together. Calculate the average hourly wage for each of the following workers. A) Kellie, who sews 90 T-shirts over 8 hours B) Nicole, who sews 47 T-shirts over 6 hours C) David, who sews 116 T-shirts over 10 hours

A map is placed on a coordinate grid. Cincinnati is located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? 15.4 16.6 16.2 15.8

Which statement is true? Point estimates are used to make Inferences about population parameters. When we use the population mean and proportion to summarize information about the entire population, we call them point estimates. The population mean and proportion are always equal to their corresponding point estimates. The sample mean and sample proportion of a population are called population parameters.

Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to the starting point? 10 miles 9.8 miles 9.6 miles 9.4 miles

Cool Down 2-24 Is this a polynomial identity? Show that this is or is not a polynomial identity: (a + b)(a²-ab + b²) = a³ + b³

Find the equation of the axis of symmetry of the following parabola algebraically. y = 2x² + 32x + 136

Part 2: Complete these problems and show work clearly (formulas used and what values you typed into the calculator). When asked for, state your answers or findings in a complete sentence. Again, limited/no help from teacher, MathLab, Learning Commons for Part 1 and Part 2). 1. In October of 1981, average interest rates were the highest they've ever been in America: 18.3% on 30-year mortgages AND 16.7% on 15-year mortgages a. Without using the table, calculate the monthly payment for a loan of $175,000 for 30 years. State your answer in a sentence.

In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch? 17 inches 16 inches 15 inches 14 inches