Basic Math Questions and Answers

3 days after picking apples, a family had 100 apples left. After 6 days, 76 apples were left. Assuming a linear function, write an equation in the form a(t) = mt + b that shows the number of apples, a(t), left t days after picking them. Be sure to include "a(t) =" in your answer.

Error Analysis Cheryl's math teacher asks, "7 is 50% of what number?" Cheryl incorrectly says, "350." What is the correct answer? What error did Cheryl likely make? 7 is 50% of .... What error did Cheryl likely make? A. She wrote the percent equation as whole = percent part and did not divide by 100. B. She did not divide by 100. C. She wrote the percent equation as percent = whole + part.

A motorboat travels 180 miles in 6 hours going upstream. It travels 264 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Charlie bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $200 less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 9% per year, and for the laptop it was 7% per year. The total finance charges for one year were $306. How much did each computer cost before finance charges?

Use the figure to the right to find the value of PT. T is the midpoint of PQ. PT=3x+2 and TQ = 5x-8 PT=

The drama club is printing t-shirts for its members. The printing company charges a certain amount for each shirt plus a setup fee of $40. There are 21 students in the drama club. Part A: If there are 21 students in the club and the t-shirt order costs a total of $187, how much does each t-shirt cost? Show your reasoning. Part B: The equation 201.50 = f +6.50 (21) represents the cost of printing the shirts at a second printing company. Find the solution to the equation and state what it represents in this situation.

Use the Zero Product Property and factoring, when necessary, to solve for x. The Math Notes box for Lesson 1.1.4 may be useful, if you need help. Homework Help a. (x+13)(x-7)=0 b. (2x+3)(3x − 7) = 0 c. x(x − 3) = 0 d. x² −5x=0 e. x² - 2x - 35 = 0 f. 3x² +14x − 5 = 0

A box of cereal states that there are 99 calories in a 3/4 cup serving. What is the unit rate for calories per cup? How many calories are there in 3 cups of the cereal? The unit rate is calorie(s) per cup. (Simplify your answer. Type an integer, proper fraction, or mixed number)

Find the initial value a, growth/decay factor b, and growth/decay rate, for the following exponential function: Q(t) = 0.0044(2.34) (a) The initial value is a = (b) The growth factor is b = (Retain at least four decimal places.) (c) The growth rate is r = % help (numbers) (Ensure your answer is accurate to at least the nearest 0.01%) (Note that if r gives a decay rate you should have r < 0.)

Solve each application below using systems. To receive full credit, you must 1) define all variables used, set up a system of 2 equations and 2 variables, 3) solve the system, and 4) write your solution as part of a complete sentence using appropriate units of measure. A Christmas charity party sold tickets for $45 for adults and $25 for children. The total number of tickets sold was 320 and the total for the ticket sales was $13,000. How many adult and how many children's tickets were sold?

A local race for charity has taken place since 1993. Using the actual speeds of the winners from 1993 through 1998, mathematicians obtained the formula y-0.16x+5.5, in which x represents the number of years after 1993 and y represents the winning speed in miles per hour. In what year is the winning speed predicted to be 7.42 mph?

A rectangle's width is one-third its length, and its perimeter is 96 m. Find the dimensions of the rectangle. The length is m and the width is

Stating Parametric Solutions State the standard parametric solutions with parameter k, and for inverse trig values, round your answers to four decimal places. sin(t) = 0.896 if and only if t = (primary solutions) (secondary solutions) t = cos(t) 0.05 if and only if t = (primary solutions) (secondary solutions) t tan(t) t =(primary solutions) (secondary solutions)

A random sample of size n = 616 from a population whose parameter is p = 0.31. a. What is the mean of the distribution of sample proportions? Round the answer accurate to 2 decimal places. b. What is the standard deviation of the distribution of sample proportions? Round the answer accurate to 2 decimal places.

Valentina's parents are planning a trip to the Typhoon Towers resort. They plan to get a 6- day Fun Pass, which will give Valentina access to all the slides and pools at the resort during their stay. Her parents also plan to get her a $30 arcade pass. Altogether, Valentina's parents will spend $129 on passes. What is the daily cost of a Fun Pass?

Javon is in a 26% tax bracket for his federal income tax. If the amount of money that he paid for federal income tax was $19,240, what was his taxable income?

Consider the Quadratic function f(x) = x² - 4x - 21. Its vertex is Its largest x-intercept is x = Its y-intercept is y =

The area of an 19-cm-wide rectangle is 380 cm². What is its length? The length is cm.

Car Survey In a survey of 1,700 people who owned a certain type of car, 935 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car? % of the people surveyed were satisfied with the car. (Type a whole number.)

At the time of her grandson's birth, a grandmother deposits $15,000 in an account that pays 9% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? Click the icon to view some finance formulas. The value of the account will be $ (Round to the nearest dollar as needed.)

You have a choice between going to an in-state college where you would pay $6500 per year for tuition and an out-of-state college where the tuition is $9000 per year. The cost of living is much higher at the in-state college, where you can expect to pay $700 per month in rent, compared to $450 per month at the other college. Assuming all other factors are equal, which is the less expensive choice on an annual (12-month) basis? The yearly expense of the in-state college is $ college. the and the yearly expense of the out-of-state college is $ Thus, on an annual basis, the less expensive choice is

Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 5% each year. In other words, if you have $1 this year, next year it will only buy you $0.95 worth of stuff. How much will $100 buy you in 25 years?

Select the correct answer from each drop-down menu. A square rotated about its center by 360° maps onto itself at _____ different lines of reflection. across _____ different angles of rotation. You can reflect a square onto itself

Find the linear speed v for the following. the tip of a propeller 1 m long, rotating 500 times per min (Hint: r=0.5 m) The linear speed v for the tip of a propeller 1 m long, rotating 500 times per min is min. m per min. m.

How much should you deposit at the end of each month into an investment account that pays 7% compounded monthly to have $5 million when you retire in 38 years? How much of the $5 million comes from interest? Click the icon to view some finance formulas. In order to have $5 million in 38 years, you should deposit $ each month. (Round up to the nearest dollar.)

Select the correct answer. A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation? A. 1 B. 2 C. 4 D. 8

Find all values of c that satisfy the mean value theorem for integrals on the following interval. R(v)=v²-v; [5,8] C= (Round to two decimal places as needed. Use a comma to separate answers as needed.)

A container ship left the Dania Pier and traveled north at an average speed of 20 mph. Sometime later an aircraft carrier left traveling in the same direction but at an average speed of 30 mph. After traveling for two hours the aircraft carrier caught up with the container ship. Find the number of hours the container ship traveled before the aircraft carrier caught up. 3 hours 6 hours 4 hours 5 hours 7 hours

A ball is launched into the air from the top of a building. Its initial velocity is 20 feet per second. The equation h - 16² +20 t + 50 can be used to model the height h of the ball in feet after t seconds. What is the height of the building the ball is being launched from? How long does it take for the ball to hit the ground?

Investors buy a studio apartment for $200,000. Of this amount, they have a down payment of $60,000. Their down payment is what percent of the purchase price? What percent of the purchase price would an $80,000 down payment be?

The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let v represent the number of asthma sufferers (in millions) worldwide t years after 1990. (a) Write N as a linear function of t. Use exact values in your formula, not decimal approximations. N(t) = (b) Write N as an exponential function of t. Use exact values in your formula, not decimal approximations. N(t) = (c) How many asthma sufferers are predicted worldwide in the year 2014 with the linear model? (d) How many asthma sufferers are predicted worldwide in the year 2014 with the exponential model?

Mr. Smith decides to feed his pet Doberman pinscher a combination of two dog foods. Each can of brand A contains 4 units of protein, 1 unit of carbohydrates, and 2 units of fat and costs 60 cents. Each can of brand B contains 1 unit of protein, 1 unit of carbohydrates, and 4 units of fat and costs 40 cents. Mr. Smith feels that each day his dog should have at least 8 units of protein, 5 units of carbohydrates, and 16 units of fat. How many cans of each dog food should he give to his dog each day to provide the minimum requirements at the least cost? Mr. Smith should give his dog can(s) of brand A and can(s) of brand B to provide the minimum requirements at the least cost.

Suppose that you borrow $2000.00 from a friend and promise to pay back $3170.00 in 3 years. What simple interest rate will you pay?

Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $3000 at the end of each year in an annuity that pays 7.5% compounded annually. How much will you have saved at the end of five years? Find the interest. b. Click the icon to view some finance formulas. a. After 5 years, you will have approximately $ (Do not round until the final answer. Then round to the nearest dollar as needed.)

Challenge in a company, 80% of the workers are men. If 600 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.

Use the problem-solving flowchart. The sum of three times a number and three is equal to the difference of the number and nine. Find the number. Round your answer to the neatest integer, if necessary. The number is

Karina has two investment options for $20,000 she is saving for her future college expenses. One account pays 2.5% interest compounded monthly. The second account pays 2.2% compounded weekly. Which account will have the larger balance after 5 years? First account both account none of them Second account

A rectangle has a length of x − 6 and a width of x-7. Which equation below describes the perimeter, P, of the rectangle in terms of x? P=2x-13 P-4x-26 p=x²-13x+42 P=x-13

We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use the information to the right to help find the measure of angles 1 through 5.

A company wholesales shampoo in a particular city. Their marketing research department established the following weekly supply-and-demand equations. p= x/600 + 1/2 Supply equation p= 4500/x Demand equation How many units are required for supply to equal demand? At what price per bottle will supply equal demand?

You deposit $15,000 in an account that pays 4.5% interest compounded quarterly. A. Find the future value after one year. B. Use the future value formula for simple interest to determine the effective annual yield. Click the icon to view some finance formulas. A. The future value is $

Olivia sells solar panels to homeowners. She receives a 6% commission from the first $17,000 in sales and a 22% commission for any sales over $17,000. Last month he sold $54,400 worth of solar panels. How much commission did Olivia earn from her first $17,000 in sales?

You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow changes. The college conducts a lottery, and whichever number is drawn, represents the value. Your plot has a length which is four more than five times and the width is two less than three times .x. a.) What are the dimensions of your mowing plot? Length: Width: b.) What is the area of your plot (area= length x width)? Area: c.) If x= 12 meters, how many square meters is your plot? Area:

A bank offers a CD that pays a simple interest rate of 11.5%. How much must you put in this CD now in order to have $3,000 for a home-entertainment center in 2 years. The present value that must be invested to get $3,000 after 2 years at an interest rate of 11.5% is (Round up to the nearest cent.)

The city of Raleigh has 9,200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 180 said they'd vote for Brown, 157 said they'd vote for Feliz, and 13 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Round your answer to four decimal places. Preview This sample statistic suggests that we might expect Round to the nearest whole number. Preview of the 9,200 registered voters to vote for Brown.

After you build 1 shelf, your friend wonders how long it will take you to build 9 shelves. How much time will it take to build 9 shelves, if you work at a constant rate?

A major coffee supplier has warehouses in Seattle and San Jose. The coffee supplier receives orders from coffee retailers in Salt Lake City and Reno. The retailer in Salt Lake City needs 600 pounds of coffee, and the retailer in Reno needs 450 pounds of coffee. The Seattle warehouse has 1000 pounds available, and the warehouse in San Jose has 700 pounds available. The cost of shipping from Seattle to Salt Lake City is $2.50 per pound, from Seattle to Reno $3 per pound, from San Jose to Salt Lake City $4 per pound, and from San Jose to Reno $2 per pound. Find the number of pounds to be shipped from each warehouse to each retailer to minimize the cost. Ship pounds of coffee from Seattle to Salt Lake City. pounds of coffee from Seattle to Reno, pounds of coffee from San Jose to Reno. pounds of coffee from San Jose to Salt Lake City, and

You must decide whether to buy a new car for $23,000 or lease the same car over a three-year period. Under the terms of the lease, you can make a down payment of $2000 and have monthly payments of $150. At the end of the three years, the leased car has a residual value (the amount you pay if you choose to buy the car at the end of the lease period) of $11,000. Assume you can sell the new car at the end of the three years at the same residual value. Is it less expensive to buy or to lease?

Suppose that $5000 is deposited into an account that earns 3.5% interest compounded Semiannually. Let f(t) represent the value (in dollars) of the account at t years after depositing the $5000. Find the value of the account at t = 4 years. (Round your answers to two decimal places.) {Round your final answer to two decimal places}

A nature center charges a $5 admission charge for children who are 12 years old or younger and $10 for those 13 years old and older. On Tuesday, the petting zoo took in $1620 from ticket sales and sold a total of 232 tickets. How many tickets of each type were sold? a. Clearly write the unknown quantities you're being asked to find and assign variables to represent each of them. Let x = Let y = b. Using the information in the problem, write a system of equations representing this scenario. You may consider making a table to organize the known and unknown quantities to help you write the system.