Basic Math Questions and Answers

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) =

Solve the following inequality. x/4 > -6 (Simplify your answer.)

The sum of three numbers is 72. The first number is 8 more than the second. The third number is 2 times the first. What are the numbers? First number: Second number: Third number:

Solve the system of equations: 4/3x-3/5y=-19/10 -1/4x+1/4y=9/16

An entry level civil engineer's annual pay is $63,648 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 civil engineers. If the firm cuts the work year to 50 weeks but keeps the same rate of pay, how much should the civil engineer expect his annual pay to decrease? Round your answer to the nearest dollar.

The label on a bottle of medicine reads "Each 5 mL teaspoonful contains glucose. 1.87 g: levulose, 1.87 g; and phosphoric acid, 21.4 mg." a. Find the amount of phosphoric acid in the recommended dosage of two teaspoons. b. If the bottle contains 5 ounces, find the quantity of phosphoric acid in the bottle. (1 oz 30 mL)

(a) The diameter of Pluto at its equator is approximately 2.39 × 10³ kilometers. Write this number in standard notation. (b) An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.000196 meters. Write this number in scientific notation.

The average of a list of numbers is their sum divided by the number of numbers in the list. A female lion had 4 cubs. They weighed 2 1/20, 3 3/20, 4 9/10, and 4 3/5 pounds. What is the average cub weight?

The equation 12x + 15y = 390 represents the total revenue during a one-day fundraiser. In the equation, x represents the number of youth T-shirts sold, and y represents the number of adult T-shirts sold. If there were 10 youth T-shirts sold, how many adult T-shirts were sold? 18 T-shirts 20 T-shirts 24 T-shirts 45 T-shirts

Subtract the polynomials: (4y² + y - 4) - (8y² + 2y - 5)

Given the solution to the following system of equations written as an ordered pair. 3.7y - 11.1x = - 33.3 3.3y + 13.2x = 62.7

MP Use Repeated Reasoning Jessie has 50 packages of sports cards. There are 10 sports cards in each package. How many sports cards does Jessie have?

Function Operations, Adding and Subtracting Given the function f(x) = 7x - 5 and the function g(x) = 2x² + 6 determine each of the following. a) Evaluate: f(7) + g(9) b) Evaluate: f(2) - g(8) c) Evaluate: f(1/4) + f(4) d) Evaluate: f(1/3) - f(4/5)

Melissa wants to put a fence around the garden in her back yard in San Antonio. Since one side is adjacent to the house, she will only need to fence three sides. There are two long sides and one shorter side parallel to the house, and she needs 165 feet of fencing to enclose the garden. The length of the long side is 5 feet less than two times the length of the short side. Write an equation for L, the length of the long side, in terms of S, the length of the short side. L = Find the dimensions of the sides of the fence.

Jennifer has $0.50 in nickels and dimes. The number of dimes is 5 less than twice the number of nickels. Find the number of nickels.

The Elimination (Addition) Method Solve the following system of equations with the ELIMINATION METHOD. Write your answer as an Ordered Pair. If infinitely many solutions exist, enter ∞ "00". If no solution exists, enter DNE System of Equations 5x + 4y = 42 10x + 8y = 84

Use the order of operations to evaluate this expression: (-2 + 1)² + 5(12 ÷ 3) - 9. Type the correct answer in the box. Use numerals instead of words. The value of the expression is

A pancake recipe that serves 30 people calls for 12 eggs. Marti wants to make enough to serve only 10 people. What is the ratio of eggs to servings for the reduced recipe? A. 2 to 5 B. 1 to 3 C. 5 to 2 D. 5 to 6

Add the following polynomials: (13s³-7s) + (38s-9s³)

Find the x-coordinate(s) of the point(s) on the graph of f where the tangent line is horizontal. (Round your answer(s) to two decimal places. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = (x² + 16x + 6) (8 - x) X =

Emily and her twin sister Erica were each given $500 for their birthday. Emily deposits her money in an account, that pays 4.75% interest compounded annually. Erica deposits her money in a 5% simple annual interest account. After 10 years how much more money will Emily have her account? F $22.41 G $45.26 H $250.00 J $295.26