Basic Math Questions and Answers

A 12-oz can of soda pop costs eighty-nine cents. A 2.00 L bottle of the same variety of soda pop costs $2.29. How many times more expensive it is to buy the 12-oz can of pop compared to buying it in a 2.00 L bottle? (1.00 L =1.057 quart and 1 quart contains 32 oz) 2.8 4.2 2.2 1.9 2.6

Name the set of numbers to which √120 belongs. Enter a, b, c, d, or e. a. natural numbers b. whole numbers c. integers d. rational numbers e. irrational numbers

Find the difference quotient of f; that is, find f(x+h)-f(x)/h. h ≠ 0 for the following function f(x) = 7x+6 f(x+h)-f(x)/h=

Fill in the blank, then answer the following questions. The greatest integer function is defined by int(x) = the greatest integer that is The greatest integer function is defined by int(x) = the greatest integer that is less than or equal to x. int(4.4) = 4 int(-5.4)= -6 int(0.6)=

Which statements are true regarding the area of circles and sectors? Check all that apply. The area of a circle depends on the length of the radius. The area of a sector depends on the ratio of the central angle to the entire circle. The area of a sector depends on pi. The area of the entire circle can be used to find the area of a sector. The area of a sector can be used to find the area of a circle.

Sally is at the store and has $690 worth of furniture in her cart. The store is offering a one day sale of 70% off your entire purchase. What is her total at checkout before tax?

Use the price-demand equation p +0.004x = 60, 0≤p≤60. Find the elasticity of demand when p = $24. If the $24 price is decreased by 3%, what is the approximate percentage change in demand? The elasticity of demand when p = 24 is 2/3. (Type an integer or a simplified fraction.) If the price is decreased by 3%, the demand approximately %.

Find the slope of the line passing through the pair of points below. Assume that all variables represent positive real numbers. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (a,b) and (a,b-c) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is B. The slope is undefined. Which of the following describes the line passing through the given points? Vertical Horizontal Rises from left to right Falls from left to right

A mathematical model for world population growth over short intervals is given by P= Poe, where Po is the population at time t = 0, r is the continuous compound rate of growth, t is the time in years, and P is the population at time t. How long will it take the world population to double if it continues to grow at its current continuous compound rate of 1.05% per year?

First find f + g. f- g. f/g and. Then determine the domain for each function. f(x) = 3x-6, g(x)=x+5 (f+g)(x) = (Simplify your answer.)

Answer the following questions about the equation below. x³ - 8x+8 = 0 (a) List all rational roots that are possible according to the Rational Zero Theorem. Choose the correct answer below. A. ±1 B. ±8 C. ±1, ±2, ±4, ±8 D. 1,2,4,8 (b) Use synthetic division to test several possible rational roots in order to identify one actual root. One rational root of the given equation is (Simplify your answer.)

Paul has 520 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

Casey Martin's ISP charged a $35 installation fee, a monthly rental fee of $2.50 for the modem, and a monthly access fee of $39.95 for an unlimited connection. Casey also purchased antivirus and firewall software for $59.99. What will be Casey's total cost to connect to the Internet for the first year?

You want to buy a $222,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan for the rest. a) How much is the loan amount going to be? b) What will your monthly payments be if the interest rate is 5%? c) What will your monthly payments be if the interest rate is 6%?

When purchasing a new Cell Phone Plan you are given two pay options (both included unlimited text). With Plan A, you pay $0.37 per minute. With Plan B, you pay $0.11 per minute plus a flat fee of $7.50. Write an algebraic expression to represent the cost for Plan A if you talk for m minutes. Cost for Plan A: Write an algebraic expression to represent the cost for Plan B if you talk for m minutes. Cost for Plan B: How many minutes you would need to use for Plan B to be less expensive than Plan A? Write an inequality that represents Plan B < Plan A Inequality: Solve the inequality and use your answer to complete the following sentence: Plan B is less expensive than Plan A when you use Select an answer minutes.

Given that f(x)=x²-1 and g(x) = 4x + 4, find (g-f)(6), if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (g-f)(6)= (Simplify your answer.) B. (g-f)(6) does not exist.

For the equation y-3 = 2(x + 4), the line has a slope of 2 and contains what point? A-4, -3) B (3,-4) C(-3,-4) D (-4,3)

Solve and write interval notation for the solution set. Then graph the solution set. x +14 ≤ -1/2 or x + 14 ≥ 1/2 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Find the distance between the pair of points (1.3.9.2) and (-0.7.7.2). If necessary, express the answer in simplified radical form and then round to two decimal places.

Laura asked 10 students how many courses they have taken so far at her college. Here is the list of answers. 12, 9, 13, 6, 2, 19, 15, 4, 21, 15 What is the percentage of these students who have taken fewer than 6 courses?

The price p (in dollars) and demand x for wireless headphones are related by x = 7,000-0.15p2. The current price of $100 is decreasing at a rate $7 per week. Find the associated revenue function R(p) and the rate of change (in dollars per week) of revenue.

What is this called: y-y₁=m(x-x₁) A formula to find the slope of a line B) Standard form C) Point Slope form D) Slope-Intercept form

Find the greatest common factor of the following numbers. 2.3.4^2.5^2.7^3 3^3. 4^3. 5. 11 2^2. 3^3. 4^2. 5^3. 11. 17

a. Use synthetic division to show that 3 is a solution of the polynomial equation below. 13x3-16x²-16x - 159 = 0 b. Use the solution from part (a) to solve this problem. The number of eggs, f(x), in a female moth is a function of her abdominal width, in millimeters, modeled by the equation below. f(x) = 13x³-16x²-16x-7 What is the abdominal width when there are 152 eggs?

Select all of statements that are logically equivalent to the statment: if Donald danced then Frank didn't follow Donald danced and Frank didn't follow Either Donald didn't dance or Frank didn't follow Oif Frank followed then Donald didn't dance It's not true that Donald danced and Frank followed

Find all roots of the polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first root. 4x^4-14x³ +36x²-84x + 72 = 0 The solution set of the equation 4x4-14x3 +36x²-84x + 72=0 is.

Laura and her sister enjoyed a special dinner in a restaurant, and the bill was $78.72. If she leaves $ 13.38 for the server as her tip, what percent tip did she leave? Round your answer to the nearest tenth of a percent.

Divide using synthetic division. x^5-1/x-1

For the function f(x) = -1/3X, construct and simplify the difference quotient f(x+h)-f(x)/h The difference quotient for f(x) =

An accountant needs to withhold 23% of income for taxes if the income is below $30,000, and 31% of income if the income is $30,000 or more. The income amount is in cell A1. Write a spreadsheet expression that would calculate the amount to withhold.

A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 14 characters long, and that each character is either a lowercase letter, (a, b, c, etc.), an uppercase letter (A, B, C, etc.) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.

Hillary is sending out holiday greeting cards. She has gold (G), and red (R) cards, and blue (B), white (W), and grey (G) envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations?

State the law of logic that is illustrated. If you are sixteen years old, then your parents will buy you a cell phone. If your parents buy you a cell phone, then they will buy you an iPhone. If you are sixteen years old, then your parents will buy you an iPhone. A. Law of Detachment B. Law of Syllogism

If A = {5, 6, 7...} and B = {x| 2n +4, n e {2, 3, 4, 5}}, what is the roster for B? Enter a, b, c, d, or e. a. 6, 9, 10, 12 c. 8, 10, 12, 14 b. 2, 4, 6, 8 d. 5, 6, 7, 8 e. none of the above

Which of the following is NOT a real number? Enter a, b, c, d, or e. a. 5√0 b. 5⁰ c. 0^5 d. 0.5 e. 5/0

A point is on a circle if the distance from the center of the circle to the point is equal to the area. circumference. radius. diameter.

Write in slope intercept form: 2x + y = 2 y=2x+2 y=-2x y = -2x + 2 y=-2x - 2

Find the slope of the line that passes through (10, 1) and (5,2) A) 5 B) -1/5 C) -5 D) 1/5

Graph the following function f(x). Estimate the intervals on which the function is increasing or decreasing and any relative maxima or minima. f(x)=x² + 4x-5

Solve and graph the solution set. 1-4x≤2x+25 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is B. There is no solution.

What is the common ratio of the following sequence? 80, 20, 5, ... 1/4 4 -4

Consider the function f(x) = 3x² - 12x-3. a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. C. Identify the function's domain and its range.

Find the midpoint of the line segment whose endpoints (-9,-5), (1,8)

Use synthetic division to divide f(x) = x3 - 2x2 - 23x+60 by x-4. Use the result to find all zeros of f. (x3 - 2x² - 23x +60) = (x-4)= ?

On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The relationship between the elapsed time t, in days, since the beginning of spring, and the number of locusts, L(t), is modeled by the following function: L(t)= 990 (1.47) ^t/4.8 Complete the following sentence about the rate of change in the locust population. The population of locusts gains 47% of its size every ____ days.

At the beginning of an experiment, there are 400 grams of contaminants. Each hour, three-fourths of the contaminants are filtered out. A. Formulate a recursive sequence modeling the number of grams after n hours. B. Use the model to calculate the amount of contaminants after the third hour of the experiment.

A cooler at a picnic contains 100 cans of soda covered by ice. There are 15 cans of cola, 33 cans of orange soda, 21 cans of ginger ale, and 31 cans of root beer. The cans are all the same size and shape. If one can is selected at random from the cooler, determine the probability that the soda selected is root beer.

What is the probability of getting either a king or a queen when drawing a single card from a deck of 52 cards? What is the probability that the card is either a king or a queen?

Which is true regarding secants and chords? Chords intersect the perimeter of a circle at two points. Secants intersect the perimeter of a circle once. Chords intersect the perimeter of a circle at one point. Secants intersect the perimeter of a circle twice. Chords and secants intersect the perimeter of a circle twice. Chords are segments entirely within a circle, while secants are lines or rays that extend through a circle. Chords and secants intersect the perimeter of a circle twice. Chords are lines or rays that extend through a circle, while secants are segments entirely within a circle.

A population of butterflies grow in such a way that each generation is simply 1.5 times the previous generation. There were 350 butterflies in the first generation, how many will there be by the 19th generation?