Permutations and Combinations Questions and Answers

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

A family has five children. The probability of having a girl is 1/2. What is the probability of having at least 3 boys? Round the answer to four decimal places as needed A. 0.3125 B. 0.1563 C. 0.4688 D. 0.5000

Some participants in a focus group watched two proposed new TV shows and rated each show on a 0 to 5 scale. For show A, the mean rating was 3.6 and the MAD was 0.7. For show B, the mean rat- ing was 3.4 and the MAD was 0.9. Discuss what these numbers tell us.

Annette buys a wardrobe of 3 skirts, 3 pants, 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.)

The Lorenz curve for a country is given by y = 25.415. Calculate the country's Gini Coefficient.

A cable company is laying optic fibre starting from point A and cables 16 km west to point B, then turns North and cables 8 km to point C. What is the bearing and distance from point A to where the company finished cabling at point C?

Suppose medical records indicate that the length of newborn babies (in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6. Find the probability that a given infant is between 17.4 and 22.6 inches long.

At a math center in a class, there is a bag filled with 30 red blocks and 20 blue blocks. Each child in the class of 25 will complete the following activity at the math center: Pick a block out of the bag without looking, record the block's color, and put the block back into the bag. Each child will do this 10 times in a row. Then the child will write the number of blue blocks picked on a sticky note. Describe a good way to display the data of the whole class. Show roughly what you expect the display you suggest to look like, and say why.

If 13600 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent. (a) Annual: $ (b) Semiannual: $ (c) Monthly: $ (d) Daily: $

Your shirt drawer contains 8 different colored shirts that you will wear over the next 8 days. What is the probability that you will randomly choose the orange shirt to wear today and the red shirt to wear tomorrow?

(8 pts) Use the functions s and h, defined below, to answer the following questions. s(x)=√x-3 h(x) = x² +6 a) Find (s+h)(7) = s(7) + h(7):_ b) Find h(s(19)):__ c) Write an expression for h(s(x)) = (hs)(x). Simplify your answer as much as possible by writing your answer without radicals.

This test is worth 23 points. To pass, you need to earn 14 of them. Identify the absolute value inequality that describes the points required to pass. Let p represent the actual points earned on the test. |p| <9 |18.5-pl<4.5 |23-14|<P O 23-4.5 |p| > 18.5

What is the slope of the line x = -7? Select one: a. zero b. -7 c. 1 d. undefined

Find the order of the element x = (4, 9, 18) in Z16X Z24 x Z36.

Make a scatter plot for the following set of points. Describe the correlation. {(1,1), (1.5, 1.5), (2, 1), (2.5,1.5), (3,2), (3.5, 3), (4,3), (5,3), (5.5, 3.5), (6,4)} Select one: O a. no correlation O b. weak positive O c. strong negative O d. strong positive O e. weak negative

Solve the equation using logarithm: 33x-6= 98-10

y varies directly with x. If y = 15 when x = 6, find x when y = 10.

Find the equation of the circle in standard form with center at (2, 1) and a point on a circle with coordinates (-2, 5). (2 marks) Note: Place your answer in the box provided. Type your answer properly.

What is the slope of the line 3x + 12y = 24? Select one: a. 4 b. -1/4 c. 2 d. 1/4 e. 12

You are making an information item. You can use tag board, box, paper or paper plate. To write on the item you can use markers, crayons, pen, pencil, chalk or all of the items. For resources you can use a book, friend, what you have learned, the internet or all of the items. How many different combinations information items are possible? Select one: a. 100 b. 42 C. 120 d. 68 e. 15

There is a 85% probability that you can drive the car. There is a 60% chance that you be able to drive the car alone and go to a basketball game. What is the probability that you will be able to drive to the basketball alone given that you can drive the car? Select one: a. 88% b. 65% c. 82% d. 71%

Which values of x, when substituted into the function y = x-4/2x² +8x would make it undefined? (1) x=2 and 8 (2) x = -4 and 8 (3) x = -4 and 4 (4) x = -4 and 0

How many zeros can a quartic function have? a) only one b) only four c) zero, two or four d) zero, one, two, three or four

For Event A and Event B, P(A) = 3/4 P(B)= 3/5 and P(A and B)= 9/20 dependent? independent

Write 7 log-logy - 2 log z as a single logarithm with coefficient 1. Provide your answer below:

Solve the equation: log₂ (x + 2) + log₂ (1-x) = 1+ log₂ (x + 1). Select all applicable answers. Select all that apply: 0 9 -3 No Solution

Write "the set of all natural numbers N less than 6" in two different ways. What is the set of all natural numbers N less than 6? Choose the correct answer below. A. {0, 1, 2, 3, 4, 5} B. {1, 2, 3, 4, 5} C. (0, 1, 2, 3, 4, 5, 6} D. {1, 2, 3, 4, 5, 6}

Prove that, for any two vectors a and bin R³: la x b₁² + (a - b)² = |a₁²161²

Solve e³ (3²-1) -e = 0 using the one-to-one property of exponential functions.

Great Job! You completed the Major Circuit! Here are your stats from each fight. 1st fight: 62 points 2nd fight: 52 points 3rd fight: 63 points TB Round 1: 63 points TB Round 2: 48 points TB Round 3: 55 points Can you find the mean, median, range and mean absolute deviation (MAD) for the four fights using ALL SIX scores? Press "Submit" to check your work. Mean 57.1 Median 55 Range 15 MAD

Find the inverse: f(x) = log3 (x + 1)-2. Present the answer using function notation. Provide your answer below:

Castings are finished on a belt grinder. Twenty-five castings are finished per hour, and the grinder belt lasts 18 hours. If a higher-grade belt will last 30 hours, how many more castings can be finished on one grinder belt, using the higher-grade belt?

One coin is flipped and then one die is rolled. What is the probability of getting a tail on the coin and a number less than 5 on the die?

Select the correct answer from each drop-down menu. Ben and Carmella want to go to a basketball game. Carmella proposes they use a bag of 90 lettered tiles to decide who will pay for the tickets. Of the tiles, 35 are vowels and the rest are consonants. She will blindfold Ben and ask to him randomly choose a tile. If Ben picks a vowel, Carmella will pay for the tickets. If Ben picks a consonant, he will pay for the tickets. Carmella distributes the 90 tiles into two boxes that are located to the left and to right of Ben. She tells Ben that there are a total of 43 lettered tiles in the box on his left, and 43 of the tiles in the box on his right are consonant tiles. Carmella gives Ben three options of how to select his tile. • Method 1: choose randomly from the box on his right • Method 2: choose randomly from the box on his left • Method 3: mix the letter tiles back together, and choose randomly from the entire set of tiles Use this information to complete the statement. The probability that Carmella will pay for the tickets is greatest, approximately ✓%, if Ben selects his tile using method

Select a right triangle corresponding to the trigonometric function of the acute angle 8. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of Θ. tan Θ=7/24

The ogive shown below is the distribution of monthly returns for a group of aggressive (or high growth) mutual funds over a period of 25 years from 1975 to 1999. (Recall that an ogive, or cumulative relative frequency graph, shows the percent of cases at or below a certain value. Thus, this graph always begins at 0% and ends at 100%.) Complete parts a through c to the right. a) Estimate the median. The median is 6%. (Round to the nearest whole number as needec b) Estimate the quartiles. The lower quartile is 3%. (Round to the nearest whole number as needed The upper quartile is 10%. (Round to the nearest whole number as needed c) Estimate the range and the IQR. The range is 27%. (Round to the nearest whole number as needed The IQR is 7%. (Round to the nearest whole number as needed

There are 5 dessert courses in a restaurant. They will be presented two at a time in an order. How many different arrangements are there?

If f(0)=3 tan 8-sin 20, find f Do not use a calculator and express each exact value as a single fraction. (Type an integer or a simplified fraction. Type an exact answer, using radicals as needed. Rationalize the denominator.)

Given: (x is number of items) Demand function: d(x) =3125/√x Supply function: s(x) = 5√x Find the equilibrium quantity: Find the consumers surplus at the equilibrium quantity: $

Use Al Homer Simpson receives an annual salary of $110 760.00, is paid biweekly, and works 40 regular hours per week. Overtime is paid at time-and-a-half regular pay. How many hours overtime (to the nearest integer) did Homer work during a pay period for which his gross pay was $5 005.50?

Use linear regression to find a function that fits the following points. (-2,-4), (8,1) y = [___] /[____ ]x + [_____]

Use Al Homer Simpson receives an annual salary of $110760.00, is paid biweekly, and works 40 regular hours per week. Overtime is paid at time-and-a-half regular pay. How many hours overtime (to the nearest integer) did Homer work during a pay period for which his gross pay was $5005.50? Do not include any units in your answers.

How many different ways can 7 different kinds of jellybeans be lined up in a row of 3?

Forty five percent of US adults have very little confidence in newspapers. 7 people are randomly selected. a. What is the probability that exactly 4 people will have very little confidence in newspapers? b. What is the probability that more than 5 people will have very little confidence in newspapers. c. What is the probability that at least 1 will have very little confidence in newspapers?

Find the mode of the following set of numbers: 23, 21, 25, 34, 21, 37. (A) 21 (B) 24 (C) 26

You owe $644.90 on your credit card. Your average daily balance is $376.11, the billing cycle is 38 days, and the interest rate on the credit card is 19%. What is your interest charge? $7.44 $6.95 $4.74 $7.84

B In a large clinical trial, 392,551 children were randomly assigned to two groups. The treatment group consisted of 197,704 children given a vaccine for a certain disease, and 40 of those children developed the disease. The other 194,847 children were given a placebo, and 155 of those children developed the disease. Consider Be the vaccine treatment group to be the first sample. Identify the values of n. Pl... 262, P, and a EC GE a n- ext- (Type an Integer or a decimal rounded to elight decimal places as needed) G- le (Type an integer or a decimal rounded to eight decimal places as needed) udy oral ces esou 2 =D (Type an integer or a decimal rounded to eight decimal places as needed) urch bols em (Type an integer or a decimal rounded to eight decimal places as needed) p= (Type an integer or a decimal rounded to eight decimal places as needed.) (Type an integer or a decimal rounded to eight decimal places as needed.) Next

The distance of Josh throwing a javelin are normally distributed. What is the percentage of these distances that are within 2 standard deviation of the mean? (make sure to include % sign in answer.)

Your parents bought your little brother a sandbox in the shape of a rectangular prism for his birthday. The dimensions are a length of 24 inches, height of 8 inches, and a width of 16 inches. Your parents only want to fill the sandbox up to 75% capacity to stop it from spilling out. How much sand do your parents need to buy? What is the total volume of the sandbox? How much sand would your parents need to buy? (75% of the total volume)

A town has a population of 12000 and grows at 5% every year. What will be the population after 12 years, to the nearest whole number?