Math Questions

What would be the best first step in solving this system? y = x² + 3x - 4 2x+y = 17 A. Substitute for x in the first equation. B. Isolate x in the second equation. C. Substitute for y in the second equation. D. Isolate x2 in the first equation.

Given the following information: P(A) = 0.37 P(B) = 0.19 P(A and B) = 0.1 P(B given A) = 0.27 What is the probability of A or B? Round your answer to the nearest hundredth as needed. P(A or B) =

Use the four-step process to find f'(x) and then find f′(1), f'(2), and f'(3). f(x) = 9 + 5/x

What is the probability of rolling a dice and getting a 7? A. 1/6 B. 1/7 C. 0, it is impossible to roll a 7 on a dice because the dice does not have 7 on any of its sides

There are 6 red socks and 8 black socks in a drawer. Without looking, you pick out 2 socks to wear. What is the probability of picking red, black? A. 15/91 B. 14/27 C. 24/91

Solve 4 x + 6 = 32. A. x = 14 and x = -2 B. x= -14 and x = −2 C. x= -14 and x = 2 D. x = 14 and x = -14

If P (3,2), find the image of P under the following rotation. 180° counterclockwise about the origin

A spinner has the colors red, blue, and green on it. Maria spins it 30 times, and it lands on red 12 times. What is the experimental probability of spinning a red? A. 4/15 B. 2/5 C. 1/3

Solve - 6 + 8 = 15. A. x= 13 and x = -1 B. x= 13 and x = -13 C. x= -13 and x = -1 D. x= -13 and x = 1

What is the result when this equation is solved for y? 4x² + 10x - 2y = 6 A. y = -2x² - 5x+3 B. y = 4x² + 10x - 6 C. y = 2x² + 5x - 3 D. y=-4x² - 10x+6

An equation for the line L is: y = 3 + 5/4 (x - 12) The angle L makes with the x-axis is:

Given a function f(x) with f(− 8) = 1 and f(9) ,m= 2: There must be a number c with -8 < c < 9 and f(c) = 1.4. There might be a number c with 8 < c < 9 and f(c) = 1.4. There cannot be a number c with -8 < c < 9 and f(c) = 1.4.

Select the correct answer. Which of the following functions is the inverse of this function? f (x) = x + 2 / 7 A. p(x)=7x - 2 B. q(x) = -x + 2 / 7 C. r (x) = 7 / x+2 D. s(x)=2x + 7

The following student work is incorrect. The directions say to factor complete. Identify the step that there is an error and explain the error. Step 1: 4x³+36x Step 2: 4x (x² + 9) Step 3: 4x (x + 3) (x + 3) The error is in step 2 because the GCF was not factored out correctly The error is in step 2 because the GCF is not correct The error is in step 3. x² + 9 is prime and cannot be factored.

Without actually performing the calculations indicated, choose to how many significant digits the answer to the calculation should be expressed. A. (0.196) (0.08215) (295) / 1.1 b. (4.215 +3.991+2.442) / 0.42 c. (6.219 +5.98) / 3.1159

Joe's New Car dealership lists the following prices for this year's models. $10,469, $12,895, $15,499, $17,999, $18,595, $21,245, $10,395, $14,985 What is the range in prices? A $15,260 B $15,242 C $10,850 D $10,776

If P = (-1,-1), find the image of P under the following rotation. 180° counterclockwise about the origin

Tami rolled a die 20 times. 14 times it landed on an even number; 6 times it landed on an odd number. What is her experimental probability of it landing on an odd number? A. 1/2 B. 7/10 C. 3/10

Find all real numbers a such that a² = a-2. Explain why this does not violate the exponential function property which states a* = a' if and only if x = y.

Jada saw a music video that her favorite artist recently posted online. The equation v(t) = 320.4^t represents the number of views of the video, t days since Jada saw the video. 1. Find v(-2). 2. What does u(-2) represent in this situation?

f(x) = 4x² + 3x - 2 g(x) = 6x³ – 3x² - 4 Find (f + g)(x). A. (f+g)(x) = 10x³ - 6 B. (f+g)(x) = 6x³ + 7x² + 3x + 2 C. (f+g)(x) = 6x³ + 4x² 6 D. (f+g)(x) = 6x³ + x² + 3x 6

What is the equation of the line with an x-intercept of -1 and a y-intercept of 2? y=2x-2 y = 2x + 2 y=-2x+2

Solve 14x7y= 21 for y. A. y = 14x + 3 B. y = 2x - 21 C. y = 2x - 3 D. y = -14x + 21

To earn full credit for this question, use your own sheet of paper to solve the problem, showing all steps of your work. The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. 17, 20, 23, 27, 36, 29, 32, 36 Find the 5-number summary, check for any outliers using fences, and create a boxplot.

Let u=-51+2j and v=-51-5j. Decompose u into two vectors u, and u₂, where u, is parallel to v and u, is orthogonal to v. Write your answers in the form ai+bj.

Suppose that a guitar company estimates that its monthly cost is C(x) = 400x² + 600x and its monthly revenue is R(x) = -0.4x³ + 600x²200x + 500, where x is in thousands of guitars sold. The profit is the difference between the revenue and the cost. What is the profit function, P(x)? A. P(x) = 0.4x³ + 200x² 800x +500 B. P(x) = -0.4x³ + 1000x² + 400x +500 c. P(x) = 0.4x³ 200x² +800x 500 D. P(x) = 0.4x³ + 200x² 800x + 500

Use implicit differentiation to find y' and then evaluate y' at the point (3,5). y - 3x² +2=0

Solve |x- 4 + 6 = 15. A. x= 13 and x = -13 B. x = 13 and x = -5 C. x= -13 and x = 5 D. x= -13 and x = -5

A 60 ft. long swimming pool is to be constructed. The pool will be 3 ft. deep at one end and 12 ft. deep at the other. To the nearest degree, what will be the measure of the acute angle the bottom of the pool makes with the wall at the deep end? 78° 83° 81° 80° 84°

The Thompson family took a $300,000 mortgage loan, with no down payment, at an annual rate of 3.6% compounded monthly for 30 years. Calculate the family's monthly payment. Round the answer to the nearest hundredth.

Which expression is the simplest form of 5(2x-3) - 3(x+4) / 9 A. 7x-27 /9 B. 13x - 27/9 C. 7X - 3 / 9 D. 7x - 3

There are 12 marbles in a box. 8 are purple, and 4 are green. What is the probability of picking a purple marble and then another purple marble, without replacing the first marble? A. 14/33 B. 1/11 C. 8/33

We created this inequality to represent how Amy can meet her revenue goals: -100x² +15,750x + 212,500 ≥ 243,600 In this activity, you'll solve this inequality to find the minimum ticket price Amy should charge to meet her minimum revenue goal.

Find an ordered pair (x, y) that is a solution to the equation. 4x+y=5

Which one of the following describes the solution set of |x + 7| <3? The interval from -co to 4 together with the interval from 10 to ∞ The interval from 4 to 10. The interval from -10 to -4. The interval from -∞ to -10 together with the interval from -4 to ∞. The interval from -4 to 10.

Which of the following statements is true of a reflection? Select all that apply. It is an isometry. It slides a plane. The transformation is done over a line of reflection. It flips a plane about a fixed line. It changes the size of the figure being reflected.

A 61/4-inch circular power saw rotates at 4,800 revolutions per minute. (Round your answers to two decimal places.) 4 (a) Find the angular speed of the saw blade in radians per minute. rad/min (b) Find the linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut. ft/min

The drug concentration in the bloodstream t hours after injection is given approximately by C(t) = 4.95 e ¹,0sts5, where C(t) is the concentration in milligrams per milliliter. (A) What is the rate of change of concentration after 1 hour? After 5 hours? (B) Graph C.

Noah creates a scatter plot showing the relationship between number of free throws made in a basketball game and the number of points scored. The correlation coefficient for the line of best fit is 0.76. Are the two variables correlated? Explain your reasoning. b. Do either of the variables cause the other to change? Explain your reasoning.

There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If the total number of swans and ducks in the pond is 12, find the number of ducks. 16 9 3 4

How many solutions are there to the equation below? 8(x-3) = 8x-24 A. Infinitely many solutions B. No solution C. One solution

A store is offering 25% off all shoes. Declan purchases shoes and clothes. The expression representing his total cost (including 8% tax) is c+(1-0.25)s+0.08[e+ (1-0.25) s). Which term represents the cost of the shoes after the discount? A. (1-0.25) B. 0.08[c+ (1-0.25) s] C. le+ (1-0.25) s] D. (1-0.25)s

A pyramid is 24 ft tall. A scaled model has a height of 2 ft and is 1 foot wide at the base. Identify the scale factor that was used to create the model. A. 1/12 C. 12 B. 1/24 D. 22

The equation y = -143x³ + 1810x² - 187x+2231 where x represents the time in years since January 1, 1983 is a mathematical model for the number of AIDS cases, y, in some population between the years 1983 and 1991. According to this model, how long after January 1, 1983 was the number of AIDS cases in this population 26,488? Round your answer to one decimal place. 4.4 years 04.3 years 4.6 years 04.7 years 05.1 years

What is the probability of rolling a die, having it land on 7, and then flipping a coin and having it land on heads? A. 1/12 B. 1/2 C. 0

Triangle ABC is translated onto its image, triangle A'B'C'. Use the given vertices of the triangles to answer parts A and B. A(-6, 0) B(-1, 0) C(-5, 3) A'(-2, 4) B'(3, 4) C'(-1, 7) Part A: Use the distance formula to prove that the translation was an isometric transformation. Include all of your work in your final answer. Part B: Use complete sentences to describe the translation that maps triangle ABC onto its image.

Solve 4ax + 5ax = 6ax +9 for x. Assume a ≠ 0. A. x = 3/a B. x = 2a C. x = 1/2a D. x= 3a

Solve |2x - 7 ≥ 11. A. x≤-2 or x ≥ 7 B. x≤-2 or x ≥ 8 C. x≤-2 or x ≥ 9 D. x≤ 3 or x ≥ 6

Select the correct answer. What is the simplest form of4m-17/m^2-16 + 3m-11/m^2-16, assuming no denominator equals zero? A. 7/m+4 B. 7m/m+4 C. 7/m-4 D. 7m-6/m^2-16

Given: x + y = 6. If x € (-15, -6, -1), then which of the following sets of ordered pairs are solutions? ((-15, 21), (-6, 12), (-1, -7)) ((-15, 21), (-6, 12), (-1, 7)) ((-15, -21), (-6, -12), (-1, -7))