Math Questions

Find the constant of variation & for the inverse variation. Then write an equation for the inverse variation. y= 2.5 when x = 9 3.6 k=3.6: y=- k = 22.5; xy = 22.5 k = 22.5; y = 22.5× k= 3.6; xy = 3.6

Identify the type of sampling used. At a local technical school, five auto repair classes are randomly selected and all of the students from each class are interviewed. What sampling technique is used? A. systematic B. convenience C. simple random D. cluster E. stratified

A student in the sophomore class has an equal chance of being in room 1, 2, 3, 4, or 5 for any of her six classes. What is the probability that she will be in room 3 for at least one class? 0.80 0.74 0.26 0.14

Use a graph or table of values near x =π/2 to estimate the value of this limit: lim x - 72 cos(7x)/x-π/2 i

Explain the Error Jane and Jill were simplifying the expression (2x² + x) + 2(x² + x) and obtained different answers. Who is correct and why?

Create a frequency chart of the data below using 2 - 4 as your first interval: 5, 3, 8, 4, 2, 5, 6, 2, 7, 4, 9, 10, 3 What's the frequency for data values 5 - 7? A. 4 C. 3 B. 6 D. none of the above

The graph of the cosine function has been vertically compressed by a factor of reflected in the y-axis, has a period of 720°, has been shifted left 60°, and has been shifted up 5. Write the equation of this function.

Bonus: Rangeview High School has 1,160 students and is growing by 22 students each year. Hinkley High School has 1,900 students and is shrinking by 15 students each year. When will RHS and HHS have the same number of students? You MUST write two equations and solve them for FULL credit! Don't forget to put a label on your answer!

Graph the system of inequalities. Then find the coordinates of the vertex. y<x y>4-x Use the graphing tool on the right to graph the system of inequalities. What are the coordinates of the vertex?

A rectangular painting measures 14 inches by 16 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 92 inches. Determine the width of the frame. The width of the frame is inch(es).

Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation Slope = 5, passing through (-6,6) Type the point-slope form of the equation of the line. (Simplify your answer. Use integers or fractions for any numbers in the equation.) Type the slope-intercept form of the equation of the line. (Use integers or simplified fractions for any numbers in the equation.)

Which equation represents the line that passes through the points (-1,-2) and (3,10)? y = 3x + 1 y = 3x - 1 y=4x-2 y = 4x+2

Compute the total and annual returns on the described investment. Four years after buying 100 shares of XYZ stock for $70 per share, you sell the stock for $10,900. The total return is 55.7 %. (Do not round until the final answer. Then round to one decimal place as needed.) The annual return is %. (Do not round until the final answer. Then round to one decimal place as needed.)

A water tank that holds 60 L of water can be emptied in 24 min. How long will it take to empty a water tank that holds 280 L of water? A. 82 min B. 96 min C. 112 min D. 128 min

Surveyors counted the number of trees is a popular city park. There were 62 spruce trees, 44 firs, 12 oaks, and 2 maples. What is the theoretical probability that a randomly selected tree is an oak? (Write your answers as a reduced fraction using the / symbol as your fraction bar.)

You write the numbers 1-10 on slips of paper and throw them into a hat. If you pull out a 7 first and do not replace it, the probability of pulling out an 8 is 1/10 1/8 1/9 1/5

What are the critical numbers of the function f(x) = x³ - 1¹7x² - 56x - 2? Note: For answers with multiple numbers, separate using commas and enter in ascending order. Write values in decimals and round to the nearest hundredth.

Which number represents the probability of an event that is very likely to occur? A 0.12 B 1.3 C 0.89 D 0.09

What's the circumference of a circle with a radius of 5 inches? Use 3.14 for I.

If the rate of inflation is 2.8% per year, the future price p (t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)=3000 (1.028) Find the price of the item 6 years from today and 10 years from today. Round your answers to the nearest dollar as necessary. Price 6 years from today: Price 10 years from today: $

A bag contains 5 red and 5 white tokens. Tokens are randomly selected and removed one at a time until the bag is empty. Find the probability that the red tokens are drawn consecutively. In how many different ways can the tokens be drawn? ___ The probability that the red tokens are drawn consecutively is ___

How many ways can twelve numbers be arranged around a circle?

In how many ways can the expression a5b5c5 be rewritten as a product without exponents? The number of ways a5b5c5 can be written without exponents is ___

How many ways can five people can be seated around a circular table if Dave is always immediately to the right of Pete?

The combination to a lock consists of a sequence of three numbers in the range 0-42. a) How many combinations are possible in which no two consecutive numbers can be the same? b) How many combinations are possible in which all three numbers are different? c) What is the probability that the combination of a randomly-chosen lock consists of three different numbers? d) What is the probability that the combination of a randomly-chosen lock contains at least one repeated number? a) If no two consecutive numbers can be the same, write the expression (consisting of a product of numbers) that represents the number of possible combinations. ___ (Do not simplify.) Thus, if no two consecutive numbers can be the same, the number of combinations is ___ (Simplify your answer.) b) If all three numbers are different, the number of combinations is ___ (Simplify your answer.) c) The probability that the combination of a randomly-chosen lock consists of three different numbers is. ___ (Round to two decimal places as needed.) d) The probability that the combination of a randomly-chosen lock contains a repeated number is ___ (Round to two decimal places as needed.)

a) How many plates are possible when letters and numbers can repeat? Set up the expression that can be used to calculate the number of plates that are possible when letters and numbers can repeat. The expression is. ___ (Do not simplify.) The number of plates possible when letters and numbers can repeat is. ___ (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.) b) How many plates would be possible if letters could repeat but numbers could not? ___ (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.). c) How many plates would be possible if letters could not repeat but numbers could? ___ (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.) d) How many plates would be possible if neither letters nor numbers could repeat? ___ (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.) e) What is the probability that a randomly generated plate has no repeating letters or numbers? ___ (Type an integer or decimal rounded to three decimal places as needed.)

Radio stations in a certain country use a sequence of 4 or 5 letters as their station identification call letters. The first letter must be W, P, A, or Q. Assume there are no restrictions on the remaining letters, and repetition is allowed. a) How many 4-letter station identifications are possible? b) How many 5-letter station identifications are possible? c) How many total station identifications are possible? d) The identification for a randomly-chosen radio station is 4 letters in length. What is the probability that all four letters are different? a) Set up the expression that would be used to calculate the number of possible 4-letter station identifications. The expression is ___ (Do not simplify.) There are ___ possible 4-letter station identifications. (Simplify your answer.) b) There are ___ possible 5-letter station identifications. (Simplify your answer.) c) The total number of possible station identifications is ___ (Simplify your answer.) d) If the identification for a randomly-chosen radio station is 4 letters in length, then the probability that all four letters are different is ___ (Round to three decimal places as needed.)

Glenn and Kim are members of a comedy troupe that has 11 members in all. How many ways can the 11 members line up if Glenn and Kim must stand side by side? Give the expression that can be used to calculate the number of ways the members of the troupe can line up. Choose the correct answer below. O A.11!*2 O B.9!*10 O C.9!*2 O D.9! O E.11!*10 O F.11!*10*2 O G.9!*10*2 O H.11! The number of ways that the troupe can line up is. (Simplify your answer.)

A person standing close to the edge on top of a 80-foot building throws a ball vertically upward. The quadratic function h(t) 16t^,2 +64t+ 80 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown. a) What is the maximum height of the ball? feet b) How many seconds does it take until the ball hits the ground? seconds

Find all solutions of the equation. Express the solutions in radians in the form a + 2π, where a is in [0,2π). sin x = -√3 / 2

Consider the Quadratic function f(x) = x²-3x - 40. Its vertex is Its largest x-intercept is x = Its y-intercept is y =

The original 24 medige length x of a cube decreases at the rate of 3 m/min. a. When x=3 m, at what rate does the cube's surface area change? b. When x=3m, at what rate does the cube's volume change? a. Whenx=3m, the surface area is changing at a rate of (Type an integer or a decimal)

Raise the number to the indicated power and express in trigonometric notation. [3(cos 27+ i sin 27)] 4 81(4cos 27+ i 4sin 2π) 03(cos/271 + 1 sin = 17) 81(cos 87 + i sin 87) 3(cos 27+ i sin 27)

Which revolution will generate a cylinder? None of the other answers are correct Rotate a circle 360° about one of its diameters. Rotate a rectangle 360° about one of its diagonals. Rotate a circle 360° about one of its tangent lines. Rotate a rectangle 360° about one of its sides.

Simplify the expression y² + 4y / y²-16 and give your answer in the form of f(y) / g(y) Your answer for the function f(y) is : Your answer for the function g(y) is :

23, 20, 24, 19, 27, 20, 31 What is the mode? B. 31 D. 27 A. 20 C. 23.4

A man has 4 shirts and 3 ties. How many different shirt and tie arrangements can he wear?

Find the slope using the formula: 2-y1 / x2-x1 Plug in your slope and ONE of your coordinates (doesn't matter which) into the intercept form: y = mx +b Solve for b (your y-intercept) Write your formula into slope intercept form: y = mx + b

Brendon Walsh wants to borrow $30,000 from the bank. The interest rate is 6% and the term is for 5 years. What is the yearly payment amount? $1,800 $7800 $18,000 $3600

For Pam, the probability of getting diabetes (event A) is 0.35, and the probability of having thyroid problems (event B) is 0.28. The probability of getting both is 0.098. Are events A and B dependent or independent? Show your work.

A town that had 4000 people at the beginning of the year 2000 has been decreasing by 3.1% per year. (a) What is the 1-year percent change in the city's population? (b) Whenever 1 year passes, the population becomes what percent of its previous value? (That is, the "new" population is what percent of the "old" population whenever 1 year passes?) (c) What is the 1-year growth factor for the population of the city? (d) Write a function g that determines the population of the city (in number of people) in terms of the number of years t since the beginning of 2000. g(t)=

What is the simplest form of ∛24 ? 8 None of the choices are correct. 3∛2 2∛3 12

At 12:00 P.M. the volume of water in a tank started changing steadily over time. The volume V measured in gallons, ₺ minutes after the water volume started to change is given by the equation V = 9200 - 4.6t . The equation tells us that the volume of water in the tank was initially __ gallons, and that the volume is __

Given two functions f(x) = √1 - x) / 2 and g(x) = √1 + x) / 2 If x = 2√2)/ 3, find f(x) = g(x) = f(x) / g(x) =

Compute the first-order central difference approximation of O(h^4) at x=0.5 using a step size of h=0.25 for the following function f(x) =(a +b +c)x^3 + (b +c +d)x –(a +c +d) Compare your result with the analytical solution. a=1, b=7, c=2 , d =4

Samples of size n = 900 are randomly selected from the population of numbers (O through 9) produced by a random-number generator, and the proportion of numbers 2 5 is found for each sample. What is the distribution of the sample proportions? skewed to the right normal (approximately) skewed to the left not enough information provided

Given a sample size n, how will the distribution of the sample mean behave? unable to discern from this information like the original distribution like the normal distribution like the uniform distribution

Factor the following, where n is a positive integer. 6²ⁿ - 2bⁿ +1

Samples of size n = 90 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the variance is found for each sample. What is the distribution of the sample variances? skewed to the left normal (approximately) skewed to the right not enough information provided

Find the values of the trigonometric functions of from the information given. tan (θ)=12/5, θ in Quadrant III sin(θ) = cos(θ) = csc(θ) = sec(θ) = cot(θ) =