Permutations and Combinations Questions and Answers

Solve the equation for x. -2(6x-7)+6= -12x+20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. x= (Type an integer or a fraction. Simplify your answer.) OB. The solution is all real numbers. OC. There is no solution.

Solve the formula for the variable h. f=3gh h=0

Solve the following inequality. - 4(x-1) < -11 (Simplify your answer. Type an integer or a fraction.)

You want to determine how many minutes are in one day. 1 day [?] Which choice goes in the green box? A. 24 hour B. 60 minutes C. 1 day

Solve the system of equations by the addition method. x-2y=1 -x+6y=3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions; {(x,y) |x-2y=1} or {(x,y)-x+6y=3}- C. There is no solution; {} or Ø.

If f(x)=2x + 6 and g(x) =1/x+5 a) (fog)(x) find the functions (a, b) and their domains. b) (gof)(x)

Use the commutative property to rewrite the following expression. x+16 x+16=

Determine the domain of each of the following. Show all work and write the solution in interval notation b. f(x)=log (6-2x) c. f(x)=log (3x)² a. f(x)=4log, (3x-6)

Solve the equation. 0.1-0.02(x + 1) = -0.01(1-x) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x = (Simplify your answer.) B. The solution is all real numbers. Oc. There is no solution.

Solve the equation for y. 4x + y = 7 y=

An experiment consists of rolling 2 fair dice and adding the dots on the two sides facing up. What is the probability that the sum is 5 or 11?

A S'mores recipe is given below Use it to help answer the question. S'More - 1 serving 2 graham cracker squares 1 mini chocolate bar 1 marshmallow

Kent can paint a room in 6 hours, but Kendra needs 4 hours to paint the same room. How many hours does it take them to paint the room if they work together? Round to the nearest tenth.

A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 9% per year and the rest in an account that pays 10% per year. If the interest earned in the first year is $666, how much did she invest in each account?

Suppose that the functions f and g are defined as follows. f(x) = 9/x g(x) = 4/x+1 Find g/f. Then, give its domain using an interval or union of intervals.

Given g(x) = and f(x) = x². (fog)(x) will result in an even function. a) Always True b) Sometimes True c) Never True

Consider the function y = 3 cos(2x) What is the period? Graph the given function. Identify and LABEL the 5 key points.

A liquid that occupies a volume of 2.68 L has a mass of 2.40 kg. What is the density of the liquid in kg/L? density=[?] kg/L

Write an equation (a) in standard form and (b) in slope-intercept form for the line described. through (6,5), parallel to y = -9

Stutz Department Store will buy 10 pairs of sunglasses if the price is $80 per pair and 30 pairs if the price is $30. The supplier of the sunglasses is willing to provide 35 pairs if the price is $85 per pair but only 5 pairs if the price is $25. Assuming that the supply and demand functions for the sunglasses are linear, find the market equilibrium point.

The perimeter of a rectangle is 64 cm. The length is 7 less than 2 times the width. What is the width? [?] cm

Brian is 15 years old and Jeremy is 22 years old. In how many years will Jeremy be 7 years older than three times Brian's age now?

The length of a rectangle is 3 more than 5 times its width. Find the perimeter of this rectangle if its area is 92 m². [?]m

The mean score for the treatment group is 7.1 (standard deviation of 1.0) and the mean score for control group is 8.4 (standard deviation 2.2). Calculate the effect size to determine the magnitude of the difference between the two groups.

Determine the simple interest earned on $22,500 after 15 years if the APR is 15 %.

A couple deposits $24,000 into an account earning 3 % annual interest for 30 years. Calculate the future value of the investment if the interest is compounded quarterly. Round your answer to the nearest cent. Formulas

Find the area of the triangle ABC. a=12.4 m b=5.3 m C=15.4° What is the area of the triangle?

Change the word phrase to an algebraic expression. Use x as the variable to represent the number. 46 subtracted from a number The algebraic expression is (Type an expression using x as the variable. Do not simplify.)

Translate the phrase and then simplify. Subtract 19 from - 22.

Suppose we want to choose 6 letters, without replacement, from 15 distinct letters. (a) If the order of the choices is not taken into consideration, how many ways can this be done?

A note is due in 7 years, with interest of 10% compounded semiannually. The face value of the note is $39,000. Find the maturity value of the note and find the minimum sale price of the note if money can be deposited at 4% compounded quarterly. $55.105.98, $41,706.17 $77.217.33, $44.351.63 $148,102.44. $58.440.78 $77.217.27, $58,44116

Solve the equation by the square root property. 2x² +2=8

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6100 dollars. If she earns a total of 99100 dollars per year, what is her monthly salary in dollars?

Elisha is a photographer and charges a set fee to photograph weddings. This is an example of _ income. a. capital gains b. earned c. hourly d. passive

Factor the following polynomial completely. 3x³-4x² -75x+100

Earned income and capital gains (or "portfolio income") are acquired in different ways. Which statement describes how they are different? a. Earned income and capital gains are both based on the number of hours you work. b. Earned income is payment for employment, while capital gains are produced by your investments. c. Capital gains are received if you manage the company, but earned income is received if you are an employee of the company. Earned income is when you make the investment directly, but capital gains are when someone else has managed your investments. d. Please select the best answer from the choices provided

Agency Issue. Discuss which of the following forms of compensation is most likely to align the interests of manager and shareholders: A. A fixed salary. B. A salary linked to company profits. C. A salary that is paid partly in the form of the company's shares.

Financial Decisions. What is the differences between capital budgeting decisions and capital structure decisions?

Corporate Financing. How can small, private firm finance its capital investments? Give two or three examples of financing sources.,

One number is 10 greater than another. The product of the numbers is 24. Find the numbers. One pair of numbers, both of which are positive, is

Give exact and approximate solutions. x² +7x-5=0 The exact solutions are x= (Simplify your answer, including any radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Finance. Suppose that $7,900 is invested at 5.2% annual interest rate, compounded monthly. How much money will be in the account in (A) 4 months? (B) 13 years?

A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses. 16, 18, 6, 8, 8, 18 Send data to calculator Find the mean number of hours for these students. If necessary, round your answer to the nearest tenth.

Solve: 32-82 13. Express your answer in interval notation. The solution is € indicate a union of intervals, and "oo" to express ∞) (Express your answer in interval notation. Use U to

Country Day's Scholarship fund receives a gift of $188269.662790859. The money is invested in stocks, bonds and CO's CD's pay 5.25% interest, bonds pay 2.7% interest, and stocks pay 8.8% interest Country day invests $23353.2395363578 more in bonds than in CO's. If the annual income from the investments is $9890.07593506916, how much was invested in each vehicle?

Consider a dataset with 50 observations of men's heights. The five-number summary of these heights is [62, 69, 71, 73, 78]. Using the 1.5 IQR Rule, determine the cut-off values for what heights would be considered outliers. Low outliers are < 62, high outliers > 78. O Low outliers are < 63, high outliers > 9. Low outliers are < 65, high outliers > 77. Low outliers are < 69, high outliers > 73.

Annette buys a wardrobe of 3 skirts, 3 pants, 5 shirts, and 3 sweaters, all of which are coordinated so that she can mix and match them any way she likes. How many different outfits can Annette cre- ate from this wardrobe? (Every day Annette wears either a skirt or pants, a shirt, and a sweater.)

Solve the equation. Enter the solution set in the blank. (Do not insert any additional spaces when entering the answer.) 6x (x-4)= 3(2x - 1)

In a certain lottery, you must correctly select 4 numbers (in any order) out of 31 to win You purchase one lottery Sicket. What is the probability that you will win?

Find the quotient and remainder (if any) (a) ( − 5x³ + 30x + 25) ÷ (5x + 5) The quotient is The remainder is (b) (-2x³ + x² + 10x − 18) ÷ (x − 3) 2 The quotient is The remainder is