Math Questions

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 algebra to find the point at which the line g(x)= -4/5x+19/60 f(x)= 8/3x+469/36 Write the values of x and y as reduced fractions or integers. x= y=

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.)

Consider circle O, in which arc XY measures 16π cm. The length of a radius of the circle is 32 cm. What is the circumference of the circle? π units What is the ratio of the arc length to the circumference? What is the measure of central angle XOY? 45° 90° 135°

Suppose the dimensions of your dining room are 12 feet by 14 feet. You purchase a rectangular table that is 7 feet by 9 feet. After you put the table in the dining room, how much space is left in the dining room (in square feet)?

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?

For f(x) = 5x -2 and g(x) = 3x^2 - 4. find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(-2); d. (gof)(-2) a. (fog)(x) = (Simplify your answer.) b. (gof)(x) = (Simplify your answer.) c. (fog)(-2) = (Simplify your answer.) d. (gof)(-2) = (Simplify your answer.)

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%?

Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither. f(x)=x²+x+1 Determine whether the function is even, odd, or neither. Choose the correct answer below. neither odd even Determine whether the graph of the function is symmetric with respect to the y-axis, the origin, or neither. Select all that apply. origin y-axis neither

If set A contains four distinct numbers and set B contains seven distinct letters, how many elements are in (A ∪ B)? Enter

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.)

Kelsey is knitting baby items to sell at a craft fair. She has a total of 1,620 yards of yarn to use for the items. A pair of mittens uses 81 yards of yarn and a hat uses 162 yards. She wants to knit a minimum of 12 items for the fair. If the solution region represents the number of pairs of mittens and hats that Kelsey can knit, determine which graph represents the solution set to the system of inequalities representing this situation.

The expression f(x+h)-f(x)/h for h#0 is called the difference quotient. Find and simplify the difference quotient for the following function. f(x)=3x² +5x+6

Find the slope of the line that passes through (10, -8) and (1, 12). 4/9 -20/9 9/4 20/9

A card is drawn from a standard, well-shuffled deck of 52 cards. What is the probability that it is a face card (J, Q, or K)?

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.

Write the equation in point-slope form of the line that passes through the given point and has the given slope: (-2,-1); m= -3 A. y-1=3(2-1) B. y+2=-3(x+1) C. y+1 = -3 (x-2) D. y+1 = -3(x+2)

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?

In how many ways can first, second, and third prizes be awarded in a contest with 130 contestants?

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

Use implicit differentiation to find y'. Then evaluate y' at (-1,1). x^5 + y^5 = lny

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 the axis of symmetry for the parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose y-coordinate is the same as the given point. f(x) = 2(x+3)²-3; (-2,-1) The axis of symmetry is (Type an equation. Simplify your answer)

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.

Find and simplify each of the following for f(x) = 8x - 9. (A) f(x + h) (B) f(x+h)-f(x) (C)f(x+h)-f(x)/h

In a class there are 14 students: 4 are 5' 6", 2 are 5'8", 2 are 5'10", 3 are 6', and 3 are 6' 2". A student is chosen at random. What is the student's expected height in inches? Round to the nearest tenth of an inch.

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.

You own 22 CDs. You want to randomly arrange 9 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? The probability that the CDs are in alphabetical order is

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.

In a lottery game, a player picks six numbers from 1 to 20. If the player matches all six numbers, they win 50,000 dollars. Otherwise, they lose $1.

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?

One line passes through the points (-8,1) and (4,4). Another line passes through points (-9, -7) and (9.-3). Are the lines parallel, perpendicular, or neither? Choose 1 answer: Parallel Perpendicular Neither

The function f(x) = x + 19 is one-to-one. Find an equation for f1(x), the inverse function.

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