Basic Math Questions and Answers

A certain forest covers an area of 1900 km2. Suppose that each year this area decreases by 8%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.

An entry level machinist's annual pay is $40,872 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its machinists. If the firm cuts the work year to 50 weeks but keeps the same rate of pay, how much should the machinist expect his annual pay to decrease? Round your answer to the nearest dollar.

Graph the function. h(x)=-3x²+5 Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values. Then click on the graph-a-function button.

Suppose that we want to examine the relationship between high school GPA and college GPA. We collect data from students at a local college. The linear regression predicted college GPA = 1.07 +0.62* high school GPA. One student has a high school GPA of 3.00 and a college GPA of 3.15. What is the residual for this student? 0.15 -0.15 -0.22 0.22

Clay's hair is 10 2/7 inches long. The barber trims off 1/4 inch. About how long is his hair now? A 9 in. B 10 in. C 11 in. D 12 in.

A social networking site recorded that 80% of the people who became members of the site one month were between 30 and 40 years old. The equation below represents this information, where x represents the total number of people who became members of the site that month: x=0.8x + 72 How many people who became members of the site that month were between 30 and 40 years of age? a. 112 b. 288 c. 360 d. 432

Kelly has 4 times as many songs on her music player as Lou. Tiffany has 6 times as many songs on her music player as Lou. Altogether, they have 682 songs on their music players. How many songs does Kelly have?

A rectangular field is to have an area of 225 m² and is to be surrounded by a fence. The cost, C, of the fence is 2 dollars per meter of length. Express the total cost of the fence in terms of the width of the field (use the variable 'w' for width). C(w) = $

Factor the following expression completely: z²+9z-1z - 9

AB has coordinates A(-3, 9) and B(6, -12) After a dilation with scale factor of 2/3 centered at the origin, the coordinates of A', are The preimage and the image are to each other. parallel not parallel

Find the domain of the function f(x) = 2x² + 3x + 1 Use interval notation to express your answer.

Factor the following expression completely: 9w(3w+1) + 3w+1

A hair stylist makes $67 each day that she works and makes approximately $13 in tips for each hair cut that she gives. If she wants to make at least $184 in one day, at least how many hair cuts does she need to give?

Devante has some quarters and dimes. He has 23 coins worth a total of $3.05. How many of each type of coin does he have? Number of quarters: Number of dimes:

If the total precipitation (rainfall and snow) for the year at a mountain town is expected to be 37.9 inches and it has already rained 26.82 inches, how many more inches of precipitation are expected?

Add the polynomials: (-x^4 - 2x² + 5) + ( -11x³ - 12x² - 1)

Let f(x) = 5x + 3 and g(x)= 2x² + 2x. Find (f + g)(x). (f+g)(x) =

Find the associated exponential decay or growth model. (Round all coefficients to three significant digits.) Q = 1,700 when t = 0; half-life = 1 Q =

Subtract the polynomials: (-x^5 +7x^4-3x³-4x) - (12x^5 - 6x³ + 2x² - 11x)

Solve the system of equations: -4/5 x - 5/3 = -7/60 3/2 x - 2/5y = 11/10

Factor the following expression completely: xy - 54 + 6y - 9x

For the play, the class sold 22 of their $10 tickets on Monday and 15 of their $10 tickets on Wednesday. On Thursday, the class added up the total number of tickets sold so far and multiplied this amount by $10. What property of operations should be used to find how much money they made in the two days? associative property of addition associative property of multiplication commutative property of multiplication distributive property

A bacteria culture starts with 800 bacteria. Two hours later there are 1,280 bacteria. Find an exponential model for the size of the culture as a function of time t in hours. f(t) = Use the model to predict how many bacteria there will be after 2 days. (Round your answer to the nearest hundred thousand.)

An oral medication is absorbed into the bloodstream at the rate of 3e^-0.04t milligrams per minute, where t is the number of minutes since the medication was taken. Find the total amount of medication absorbed within the first 20 minutes. (Round your answer to the nearest milligram.). mg

Factor the following expression completely: 64x^6 + 40x³

Given, for some series of metal cubes with variable side length: mass=2.73g/cm^3* length^3 Rewrite (including units) length as a function of mass. What measured values would you graph to linearize this function?

A farmer is packing 2,205 pounds of potatoes into boxes. Each box can hold 49 pounds. How many boxes can the farmer fill? A 10 B 20 C 45 D 46

Solve the system of equations. If there is exactly one solution, write as an ordered pair. If not, choose on the other options. x + 2y = -5 - 8y = 20 + 4x No solution Infinite number of solutions

Jia is tiling a floor. The floor is a square with side length 12 feet. Jia wants the tiles to be squares with side length 2 feet. How many tiles does Jia need to cover the entire floor? Note that the area of a square is s2, where s is the side length. Explain.

Rebecca has $75 in her savings account and she has to pay $5 each month to her parents for her cell phone. Gregory has $45 and he saves $5 each month from his job walking dogs for his neighbor. At this rate, when will Rebecca and Gregory have the same amount of money? How much will they each have? In month(s) they will both have $

7. The library at school is organized by fiction and non-fiction books. There are 3 non-fiction books for every 7 fiction books. How many total books are there if the library has 240 non-fiction books?

A travel agency will plan a tour for groups of size 53 or larger. If the group contains exactly 53 people, the price is $800 per person. However, each person's price is reduced by $10 for each additional person above the 53. If the travel agency incurs a price of $150 per person for the tour, what size group will give the agency the maximum profit? a. 6 b. 32 c. 70 d. 91 e. 59

Add the polynomials: (2y³ + 5y² + 6y - 1) + (9y³ + y² - 5y - 7)

Solve the system of equations. Give your solution as an ordered pair. 16x - 2y = 18 2/9 x + 2/9 y = 2

At the ice cream shop, there are 14 shakes sold for every 6 malts. Record the ratios below. a. malts to shakes b. malts to total

Add the following polynomials: (15t³ - 11t^6) + (24t^6 - 27t³)

Find the sum of the polynomials: (-8x^5 + 10x^4 + 2x² - 5) + (3x^5 - 11x^4 - 3x² + 11x)

Solve this system of equations using the method of elimination (addition). Use the infinity symbol if infinitely many solutions exist, or enter DNE if there are no solutions. 3x - 2y = 3 - 1x + 2y = -1

Using the decimal standard form. Compare using >, <, or =. 51 tenths 5.1 < > =

A construction company is planning to bid on a building contract. The bid costs the company $1500. The probability that the bid is accepted is 1/4 . If the bid is accepted, the company will make $38,000 minus the cost of the bid. a. What is the expected value in this situation? (Round to the nearest dollar)

A culture of bacteria is growing at the rate of 20e^0.8t cells per day, where t is the number of days since the culture was started. Suppose that the culture began with 50 cells. (a) Find a formula for the total number of cells in the culture after t days. T(t) = (b) If the culture is to be stopped when the population reaches 500, when will this occur? (Round your answer to one decimal place.) days

Two cars leave towns 1000 kilometers apart at the same time and travel toward each other. One car's rate is 12 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? Do not do any rounding.

Elsa, Rafael, and Dan sent a total of 119 text messages over their cell phones during the weekend. Dan sent 4 times as many messages as Rafael. Rafael sent 5 fewer messages than Elsa. How many messages did they each send? Number of text messages Elsa sent: Number of text messages Rafael sent: Number of text messages Dan sent:

Erica has $840 in her savings account and she has to pay $45 each month to her parents for her cell phone. Andres has $240 and he saves $30 each month from his job walking dogs for his neighbor. At this rate, when will Erica and Andres have the same amount of money? How much will they each have? In month(s) they will both have $

How long (in years) will it take a $300 investment to be worth $1000 if it is continuously compounded at 11% per year? (Give the answer to two decimal places.)

For services rendered, an attorney accepts a 120-day note for $5,200 at 7% simple interest from a client. (Both interest and principal are repaid at the end of 120 days.) Wishing to use her money sooner, the attorney sells the note to a third party for $5,270 after 60 days. What annual interest rate will the third party receive for the investment? The third party will receive an annual interest rate of %. (Type an integer or decimal rounded to two decimal places as needed.)

The sum of two numbers is 75. The difference of the two numbers is 29. What are the two numbers? Let x be the larger number and y be the smaller number. Write an equation that expresses the information in the sentence "The sum of two numbers is 75." Write an equation that expresses the information in the sentence "The difference of the two numbers is 29." Solve the system you have written above. The larger number, x is The smaller number, y is

A loan of $1,020 was repaid at the end of 12 months with a check for $1,050. What annual rate of interest was charged? The annual rate of interest was charged at %. (Round to two decimal places as needed.)

The polynomial y = -0.77⁴ +2.9x² +25.6 describes the billions of flu virus particles in a person's body z days after being infected.Round answer to 2 decimal places. There are billion virus particles in a person's body 3 days after being infected.

A law office orders business stationery. The cost is $17.05 per box. (a) Write a function that represents the cost C (x) (in $) for x boxes of stationery. (b) There is a 6% sales tax on the cost of merchandise and $9.58 for shipping. Write a function that represents the total cost T (a) for a dollars spent in merchandise and shipping. (c) Find (T ℃) (x). (d) Find (T ℃) (5) and interpret its meaning in the context of this problem. C(x) =