Basic Math Questions and Answers

The dollar value v (t) of a certain car model that is t years old is given by the following exponential function. v (t) = 26,000(0.92)^t Find the initial value of the car and the value after 12 years.

Scott is using a 12-foot ramp to help load furniture into the back of a moving truck. If the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck?

A company is considering expanding their production capabilities with a new machine that costs $60,000 and has a projected lifespan of 6 years. They estimate the increased production will provide a constant $11,000 per year of additional income. Money can earn 1.4% per year, compounded continuously. Should the company buy the machine?

A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolitan area during rush hour, the flat fee is 54, the cost per minute is $0.20, and the cost per mile is $1.30. Let x be the number of minutes and y the number of miles. At the end of a ride, the driver said that the passenger owed $10.30 and remarked that the number of minutes was four times the number of miles. Find the number of minutes and the number of miles for this trip.

A fishbowl shaped like a sphere is filled with water. The fishbowl has a diameter of 16 inches. Which measurement is closest to the volume of water in the fishbowl in cubic inches? A 2,144.66 in.³ B 17,157.28 in.³ C 5,461.67 in.³ D 6,433.98 in.³

Carter bought a pair of shoes online for $64. He used a coupon code to get a 10% discount. The website also applied a 5% processing fee to the price after the discount. How much did Carter pay, in the end?

A plane can fly 340 miles in the same time as it takes a car to go 120 miles. If the car travels 110 mph slower than the plane, find the speed of the plane.

A used car has a value of $15,250 when it is purchased in 2012. The value of the car decreases at a rate of 7.5% per year. 1. Write an exponential function that models the value y of the car over x years. 2. To the nearest cent, what will be the value of the car after eight years?

An electrician charges a $20 house call fee plus $30 per hour of work. Which equation represents this relationship? A. y=20+30 B. y=20x + 30 C. y = 30x + 20 D. y = 50x

Frederick's salary varies directly with the hours he works. Last week he earned $328.30 and worked 33.5 hours. If he works 35 hours this week, what will be his salary? A $314.23 B $329.80 C $343.00 D $357.14

One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 10 hours. How lo it take the pipe to fill the pool if the drain is left open?

Add and/or subtract and then simplify completely: 3p/p²-81 + p/p+9

Subtract and simplify: 7x + 5/5x² - 1x + 5/5x² Numerator preview: Denominator preview: Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

Add and/or subtract and then simplify completely: 4p + 3/p² - 6p+8 + 1/P-4 Numerator preview: Denominator preview: Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

Simplify the expression 2x - 3 / x - 3 + 3 - x / x - 3 and give your answer in the form of f(x) / g(x) Your answer for the function f(x) is : Your answer for the function g(x) is :

A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3121 tickets overall. It has sold 222 more $20 tickets than $10 tickets. The total sales are $58,770 How many tickets of each kind have been sold? How many $10 tickets were sold? How many $20 tickets were sold?

Evaluate the sine, cosine, and tangent of the angle without using a calculator. (If an answer is undefined, enter UNDEFINED.) -135° sin θ = cos θ = tan θ =

Suppose that y varies directly with x, and y=8 when x = 20. (a) Write a direct variation equation that relates x and y. Equation: (b) Find y when x = 7. y =

A lemonade seller calculates that it costs $20 to produce 100 glasses of lemonade and $35 to produce 400 glasses of lemonade. Assume the relationship between the cost and the number of glasses of lemonade produced is linear. Of the choices given, what is the most reasonable estimate for producing 700 glasses of lemonade? $35 $40 $50 $70

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 m/s². If the force is changed to 18 N, what will be the acceleration of the object?

Simplify the expression 5x³ -6x²-8x/6x² - 15x + 6 and give your answer in the form of f(x)/g(x). Your answer for the function f(x) is: Your answer for the function g(x) is:

Suppose you had $6.00 to buy bananas and apples. Bananas cost $0.49 per pound and apples cost $0.34 per pound. Write a linear equation that represents the different amounts of fruit you could buy 49x +34y = 300 49x + 34y = 600 None of the other answers are correct 49x - 34y = 600 7x + 17y=300

(a) A star is 5.37 light-years from Earth. If 1 light-year is about 5.9 trillion miles, how many miles is the star from Earth? The star is about miles from Earth. (Simplify your answer. Use scientific notation.) (b) The mean distance from Earth to the Sun is 93,000,000 miles. What is the parallax of this star? The parallax of the star is about (Simplify your answer. Round to six decimal places as needed.)

4. Brady deposited $600 into a new savings account that earns 2.5% simple interest. If Brady makes no other deposits or withdrawals, how much interest will the account have earned after 5 years? A $15 B $70 C $75 D $125

The classrooms at Lincoln Middle School are painted every summer. If 7 gallons of paint are needed to paint 4 classrooms, how many gallons of paint are needed to paint 16 classrooms? 20 gallons 24 gallons 32 gallons 28 gallons

Surface area is: a. the amount of matter contained in a three-dimensional object. b. the area covering the surfaces of a three-dimensional object. C. the amount of space occupied by a three-dimensional object. d. the area covered by a two-dimensional object.

A local bank offers an investment option with a simple interest rate of 3.60% per annum. If you invest $3200.00, how much interest will you earn in 7 years? a. $967.68 b. $806.40 c. $791.73 d. $645.12

Find the average rate of change of g(x) = -x² + 5x+1 from x=2 to x = 7,

Decide whether the sampling method could result in a biased sample. Explain your reasoning. A representative of a mall surveys every fifth person walking into an electronics store to ask if they would like there to be a new store that sells audio equipment in the mall.

Solve this problem by using a two order system. A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate? $ at 4% and $ at 3%

Tony invested his savings in two investment funds. The $6000 that he invested in Fund A returned a 3% profit. The amount that he invested in Fund B returned a 10% profit. How much did he invest in Fund B, if both funds together returned a 7% profit? Amount invested in Fund B: $

McKenna plans on attending a four-year university that costs $16,000 per year. Her parents have agreed to contribute $2,000 each year. Her grandparents have a college savings account that will be worth $30,900 when she graduates high school. How much more money will she need in scholarships, loans, or work programs to attend this university for four years? A $16,900 B $32,900 C $31,100 D $25,100

(a) Complete the square by writing ² - 16-11 in the form (x-h)² + k. Note: the numbers hand k can be positive or negative.

Danielle and her family are discussing how to pay for her college education. The cost of tuition at the college that Danielle wants to attend is $12,000 per year. Danielle's parents will pay 75% of the tuition cost every year, and she will pay the rest. Danielle has one year to save enough money to attend her first year of college. What is the minimum amount of money she should save every month in order to reach her goal? A $3,000.00 B $750.00 C $40.00 D $250.00

Charles's pay varies directly with the number of words he writes for Two Cities Magazine. The first story he wrote was 4,929 words and he was paid $345.03. How much will he be paid for his next story, which is 3,825 words? A $110.40 B $267.75 C $319.97 D $546.43

Lupita deposited $5,000 into a savings account that earns 2% interest compounded annually. Rounded to the nearest cent, how much interest will Lupita have earned after 48 months? The answer is $

The mass of a textbook is approximately 0.00165 metric ton. How is this number written in scientific notation? F 165 x 10^-5 G 1.65 x 10^-3 H 16.5 x 10^-4 J 0.165 x 10^-2

John is 5 years older than Mary. In 10 years, twice John's age decreased by Mary's age Is 35, and John's age will be twice Mary's current age. Find their ages now. If x Is Mary's age now and yis John's age now, which system of equations could not be used to solve the problem? y=x+ 5 and 2(y + 10) = x y=x+ 5 and 2(y+10)-(x+10) = 35 y=x+5 and y + 10 = 2x

Frank earns $40,000 one year and receives a 6% raise in salary. What is his new salary? Frank's new salary is $. (Simplify your answer.)

James is investing $15,000 in the bank. The investment has an interest rate of 6% compounded monthly. After ten years, how much will James have made? The answer is $ Make sure to round correctly. Think MONEY.

A kitchen is shaped like a rectangle with dimensions of 11(1/2) ft by 9(1/2) ft. The floor of the room is made of square tiles with a side length of 1/2 ft. What is the number of tiles that will cover the kitchen floor?

A guy wire that is used to support a pole is attached at a height of 55 ft and at an angle of 62.1° above the ground. How far from the base of the pole is the guy wire attached to the ground? a. 29.12 ft b. 48.61 ft c. 117.54 ft d. 62.23 ft

A principal is ordering pizza for a school pizza party. He knows that 9 pizzas will feed 25 students. If there are 300 students in the school, how many pizzas will he need to order? 108 pizzas 102 pizzas 105 pizzas 99 pizzas

Ahmad and his wife are each starting a saving plan. Ahmad will initially set aside $650 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function A = 650+ 135N, where N is the number of months he has been saving. His wife will not set an initial amount aside but will add $495 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=495N. Let I be total amount (in dollars) saved using both plans combined. Write an equation relating I to N. Simplify your answer as much as possible.

In a given year, residents of a country spent approximately $50.4 billion on their pets. Of this amount, $18.9 billion was for veterinarian bills. What percent of the total was spent on veterinary care? About % of the total was spent on veterinary care.

State the order and type of each transformation of the graph of the function f(x) = (5(x - 1))3 - 2 as compared to the graph of the base function. right 1 unit, horizontal compression by a factor if 1/5 down 2 units Oright 1 unit, vertical stretch by a factor if 5, down 2 units right 1 unit, down 2 units, vertical stretch by a factor if 5 right 1 unit, down 2 units, horizontal compression by a factor if 1/5

Three sources of finan- cial aid are government grants, private scholarships, and the colleges themselves. Susan, a financial aid director of a private college, surveyed the records of 100 sophomores and found the following: 49 receive government grants 55 receive private scholarships 43 receive aid from the college 23 receive government grants and private scholarships 18 receive government grants and aid from the college 28 receive private scholarships and aid from the college 8 receive help from all three sources. How many of the students in the survey: (a) have government grants only? (b) have scholarships but not government grants? (c) receive financial aid from only one of these sources? (d) receive aid from exactly two of these sources? (e) receive no financial aid from any of these sources? (f) receive no aid from the college or the government?

The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 9900. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Hint: Use an exponential function with base e. Your answer is P(t) (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer must be an integer)

At the movie theater all snacks are priced the same, and all movie tickets are priced the same. Jaden, Ben, and Amal bought four snacks and three movie tickets, costing their group $40. Tiara, Lisa, and Shyanne bought two snacks and three movie tickets, costing their group $32. What is the cost of a snack and what is the cost of a movie ticket?

The Kuiper Belt is estimated to be about 3, 000, 000 meters wide. Which value represents the estimated width of the Kuiper Belt, in meters, in scie 3.0 x 10 meter 30 × 10-5 meter 30 x 105 meters 3.0 x 106 meters