Math Questions

There are 14 members of the scholastic bowl team, 8 of whom are boys and 6 of whom are girls. The coach wants to play 3 boys and 1 girl in the next round. How many different teams of 3 boys and 1 girl could be formed to play the next round?

A growing deer population increases by 3 animals per year. If the current population is 47 animals, what will it be in 6 years? In 6 years the population will be _____ animals.

In an arithmetic sequence a₁₃ = 2 and a₂₅ = 12. Determine a₁. a₁=

Find the first four terms of the arithmetic sequence. a₁ = -5, d= -9 What is the first term? a₁ = ▢

Graph the feasible region for the following system of inequalities. Tell whether the region is bounded or unbounded. x + y ≤ 4 x - y ≥ 5

A political party is planning a ninety-minute television show. The show will have at least 9 minutes of direct requests for money from viewers. Three of the party's politicians will be on the show-a senator, a congresswoman, and a governor. The senator, a party "elder statesman," demands that he be on screen for at least twice as long as the governor. The total time taken by the senator and the governor must be at least twice the time taken by the congresswoman. Based on a pre-show survey, it is believed that 39, 44, and 49 (in thousands) viewers will watch the program for each minute the senator, congresswoman, and governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers. Find the maximum number of viewers. The quantity to be maximized, z, is the number of viewers in thousands. Let x₁ be the total number of minutes allotted to the senator, x₂ be the total number of minutes allotted to the congresswoman, and x3 be the total number of minutes allotted to the governor. What is the objective function? The senator should be allotted minutes. (Simplify your answer.) The congresswoman should be allotted minutes. (Simplify your answer.) The governor should be allotted minutes. (Simplify your answer.) The maximum number of viewers is (Simplify your answer.)

Let f(x)=x²-9 and g(x) = 6 -x. Perform the composition or operation indicated. (fg)(-1)

Type the correct answer in each box Use numerals instead of words. If necessary, use / for the fraction bar(s). Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button. The sample size for this compound event is Suppose one square-shaped button is added to the container. If Lucas repeats the same picking process, then the sample size would be

(b) Find the coordinates of the vertex. (c) Find the intercept(s). For both the x- and y-intercept(s), make sure to do the following. If there is more than one, separate them with commas. .If there are none, select "None". x-intercept(s): y-intercept(s): (d) Find the equation of the axis of symmetry. equation of axis of symmetry:

Given sinθ= -5/13 and π<θ<3π/2, what is the exact solution of sin 2θ?

The amount of daylight in a town can be modelled by the sinusoidal function d(t)= 4.37 cos 0.017t + 12.52 where d(t) represents the hours of daylight and t represents the number of days since June 20, 2012. How many hours of daylight should be expected on June 20, 2013? a) 16.80 hr c) 16.84 hr b) 16.88 hr d) 16.92 hr

Given the equation y = 2 sin(3(x + 6)) + 7 The amplitude is: The period is: The horizontal shift is: The midline is: y =

Find the exact value of tan (11π/4) using the unit circle. zero 1 -1 2

Suppose that, in a certain population, 25% of adults are regular smokers. Of the smokers, 18.3% develop emphysema, while of the nonsmokers, 0.9% develop emphysema. An adult from this population is randomly chosen. a) Find the probability that this person is a smoker, given that the person develops emphysema. b) Find the probability that this person is not a smoker, given that the person does not develop emphysema. a) The probability that this person is a smoker, given that the person develops emphysema, is (Do not round until the final answer. Then round to four decimal places as needed.) b) The probability that this person is not a smoker, given that the person does not develop emphysema, is (Do not round until the final answer. Then round to four decimal places as needed.)

The probabilities of events E, F, and E⋂F are given below. Find (a) P(EIF), (b) P(FIE), (c) P (EIF'), and (d) P (FIE'). P(E) = 0.5, P(F) = 0.6, P(E⋂F) = 0.5 a. P(EIF) = (Type an integer or decimal rounded to two decimal places as needed.) b. P(FIE) = (Type an integer or decimal rounded to two decimal places as needed.) c. P (EIF') = (Type an integer or decimal rounded to two decimal places as needed.) d. P (FIE') = (Type an integer or decimal rounded to two decimal places as needed.)

Sample space S is partitioned into E₁, E₂, and E₃ such that P(E₁)= 1/6 and P(E₂)= 1/8 a) Find P(E₃). b) Find the odds in favor of and the odds against E₃ occurring. a) P(E₃) = (Simplify your answer.) b) The odds in favor of E₃ occurring, in lowest terms, are (Simplify your answer. Type whole numbers.) The odds against E₃, in lowest terms, are (Simplify your answer. Type whole numbers.)

Two fair 6-sided dice are rolled. Let A = the event that the dice add to 8, and let B = the event that the dice add to an even number. Find P(A|B) and P(A|B'). P(A|B)= (Simplify your answer.) P(A|B') = (Simplify your answer.)

Which of the following shows the graph of y = cot (1/2*x) + 1?

In a batch of 21 pedometers, 3 are believed to be defective. A quality-control engineer randomly selects 6 units to test. Let random variable X= the number of defective units that are among the 6 units tested. a. Find the probability mass function f(x)=P(X=x), and sketch its histogram. b. Find P(X= 1). What does this number represent? c. Find P(X≥ 1). What does this number represent? Using the hypergeometric probability distribution model, set up an expression that can be used to find a single ordered pair in the probability mass function f(x)=P(X=x). f(x)=P(X=x)= (Simplify your answers.) a. Find the probability mass function f(x)=P(X=x). f(x) = (Type an ordered pair. Use a comma to separate answers as needed. Round to five decimal places as needed.) Let x = the number of defective pedometers among the 6 units tested, and let y=f(x). Choose the correct histogram below.

Nico's Nuts buys a blend of peanuts and cashews from 2 vendors, with 65% coming from Brasstown farms and the rest from Rabun farms. The blend from Brasstown is 80% peanuts and 20% cashews, and the blend from Rabun is 56% peanuts and 44% cashews. All nuts are mixed by Nico's before packaging. A random nut is chosen from the mixture. a) Find the probability that the nut came from Brasstown, given that it is a peanut. b) Find the probability that the nut came from Rabun, given that it is a cashew. a) The probability that the nut came from Brasstown, given that it is a peanut, is (Do not round until the final answer. Then round to four decimal places as needed.) b) The probability that the nut came from Rabun, given that it is a cashew, is (Do not round until the final answer. Then round to four decimal places as needed.)

Find the slope, y-intercept. Then use the slope and the y-intercept to find a second point for graphing the line. x+y=2 Slope = y-intercept:

Solve by any method. 6x - 8y = -0.6 3x + 2y = 0.9

There were 636 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed. Find the number of students who passed and the number who failed. Number of students who passed Number of students who failed

The function fx)=80,000+0.2x/ x yields the average cost in dollars for a company to produce x copies of a comic book. Which statement best fits the situation modeled by the function? The company earns 20% of the issue price as profit from each copy sold. The company earns 20 cents as profit from each copy sold. The company spends 20% of the issue price on materials to produce each copy The company spends 20 cents on materials to produce each copy.

How much should you invest at 2.5% simple interest in order to earn $85 interest in 4 months?

Find fx and fy for f(x,y) = y In (3x+8y).

The relationship between water content (w%) and number of blows (N) in soils, as obtained from Casagrande's liquid limit device, is given by w = 20-log10 N The liquid limit of soil is (a) 15.6% (b) 16.6% (c) 17.6% (d) 18.6%

Suppose one would like to construct a 93% confidence interval for a sample mean, when the population. standard deviation is known. Determine the z-value that would be used to construct such a confidence interval. Round the solution to two decimal places.

Suppose 0 ≤θ≤ π/2. Solve the equation: 2 cos(3θ) + cos(3θ) - 2 = 0 for θ. Give your answer rounded to 2 places after the decimal point.

Find the exact value of the expression: cos(165°) The final solution needs to be simplified for full credit.

Suppose you want to have $800,000 for retirement in 20 years. Your account earns 10% interest. a) How much would you need to deposit in the account each month? b) How much interest will you earn?

Write the equation in standard form and enter it below. Do not enter blank spaces in your answer. y=3/4 x+2 Standard form of equation:

Let f(x) = 3x² - 8x + 5 and g(x) = x² + 16. Find ƒ + g, ƒ − g, f · g, and Simplify your answers. 1. f + g = 2. f-g= 3. f . g = 4. f/g =

Write 2 tan 17°/1 - tan² 17° as a trigonometric function of one number. You do NOT need to type in the degree symbol.

For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. f(x) = 4, [2.25, 2.50] A. μ=2.375; σ²=0.0052; σ = 0.072 B. μ= 2.500; σ² = 0.0048; σ = 0.069 C. μ=2.500; σ² = 0.0049; σ = 0.070 D. μ=2.375; σ² = 0.021; σ = 0.144

The function P(t) = 37.25e0.0096t. approximates the population, in millions, of California t years since 2010. Assuming this trend continues, approximate the number of years it will take California's population to reach 50 million. Round your answer to two decimal places.

If the point (5,-2) is on the graph of a function that is shifted to the right by 3, what point is on the new graph? (5, 1) (8.1) (8,-2) (2,-2)

Using y(t) = 110ekt, and the fact that y(30)= 75, we can solve for k. y(t) = 110ekt y(30) =110ek. =110ek Thus, we have the following equation. k =

given cot 38= 4/3 and csc 33= 13/12 find sin 66

Ne Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x)=kx, 4≤x≤7 What is the value of k? k= (Simplify your answer.) What is the probability density function? f(x)=

Use Gaussian elimination to solve. The Burkes pay their babysitter $5 per hour before 11 P.M. and $7.50 after 11 P.M. One evening they went out for 5 hr and paid the sitter $35.00. What time did they come home? They came home at A.M.

Tell the maximum number of zeros that the polynomial function may have. Then use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the polynomial function may have. Do not attempt to find the zeros. f(x) = -x8-9x6-x+6 What is the maximum number of zeros that this polynomial function can have? How many positive real zeros can the function have? (Use a comma to separate answers as needed.) How many negative real zeros can the function have? (Use a comma to separate answers as needed.)

Expand the logarithm as much as possible by rewriting it as a sum, difference, or product of logarithms. log4(x/z / w)

Rewrite the expression as an equivalent ratio of logs using the indicated base. log13 (57.25) to base 10

Does the following argument illustrate the Law of Syllogism? Given: If the power is cut, then the refrigerator will not work. If the refrigerator will not work, then the food will spoil. Conclude: If the power is cut, then the food will spoil. yes no

(a) Find the magnitude of an earthquake that has an intensity that is 73.7 (that is the amplitude of the seismograph reading is 73.7 cm). [Round your answer to one decimal (b) An earthquake was measured to have a magnitude of 5,4 on the Richter scale. Find the intensity of the earthquake. (Round your answer to one decimat place)

Match the solution region of each system of linear inequalities with one of the four regions shown in the figure. 9. x+2y ≤ 8 x-2y ≥ 0 10. x+2y ≥ 8 x-2y ≤ 0 11. x+2y ≥ 8 x-2y ≥ 0 12. x+2y ≤ 8 x-2y ≤ 0 Drag each of the regions given above and shown in the figure into the appropriate system of linear inequalities below to complete questions.9 through 12.

Solve each equation a) Solve x2/3 - 5x¹/3 +6=0 b) Solve p4-3p2-4 = 0 c) Solve x² - 4x-1-5 = 0

You need a 25% alcohol solution. On hand, you have a 225 mL of a 20% alcohol mixture. You also have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired solution? You will need ml of the 70% solution

The parametric equations x = t +2 and y = t² + 3t represent a plane curve. Which of the following rectangular equations represents the plane curve? y=x² - 4x + 7 y=x²-x-2 y=x² + 3x y=x² +7x+10