Permutations and Combinations Questions and Answers

Suppose we want to choose 7 colors, without replacement, from 11 distinct colors. (a) How many ways can this be done, if the order of the choices matters? 1 (b) How many ways can this be done, if the order of the choices does not matter?

What is the degree of the given polynomial? -3x² + 4x² - 2x6 - 2 A/

The lengths of the sides of a triangle are2x - 1, 4x - 3, & 5x + 2 Express the perimeter of the triangle in terms of x. 11x-2 11x-6 11x² +6 40x + 6

List all numbers from the given set that are: a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. a. List all the natural numbers from the given set. (Use commas to separate answers. Type each number as it appears.) b. List all the whole numbers from the given set. (Use commas to separate answers. Type each number as it appears.) c. List all the integers from the given set. (Use commas to separate answers. Type each number as it appears.) d. List all the rational numbers from the given set. (Use commas to separate answers. Type each number as it appears.) e. List all the irrational numbers from the given set. (Use cornmas to separate answers. Type each number as it appears.) 1. List all the real numbers from the given set.

What is the fourth term of (x - 2y)? 4 560x5y³ -560x5y³ 448x5y³ -448x5y³

A group of 9 students from the same middle school have been asked to record how much time they spent this morning traveling from home to school. Here are the results (in minutes). 5, 15, 16, 12, 7, 10, 5, 7, 16 Send data to calculator Find the median travel time for that group of students, DO 15

LR2: A pattern of numbers has a multiplier of -3 and has a value of 9 at position 2. Determine what position will have a value of -279? (2 Points)

The following list contains the number of movies that a group of 8 students saw in theaters in the past 12 months. 7, 8, 10, 4, 18, 11, 19, 15. Send data to calculator Find the median number of movies that the students saw.

Deandre must choose a shirt and a pair of pants for today's outfit. He has 3 shirts and 3 pairs of pants to choose from. How many different outfits can he make?

If p is true, q is true, and r is true, find the truth value of the statement below. -[(p-q)^(p-¹)] Select the truth value of [(p-q)^(p-1)]. O True O False

SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES GET THE VARIABLES TO ONE SIDE AND THE NUMBERS TO THE OTHER SIDE. 7x - 3 = 5x + 9

2. Prove the following: a) cot + tan 0 = 2csc 20 (4 + 2 marks) b) csc 20 = (sec 0) (csc 0)

Solve. 3x+6 3 2 X-4 7 X-2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O B. The solution set is {x|x is a real number and x # }. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OC. There is no solution.

For the function f(x) = 6 cotx determine its stretching factor and phase shift, and then graph it for two periods. Using your answers for the stretching factor and phase shift, select the correct graph of the function f(x) = 6 cotx.

Which equations arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers? (123, 2347) 1-10-3-3 1-37-10-3-123 1-37-2347-706-123

If men's heights are from a Normal distribution with a mean of 70 inches and a standard deviation of 2.5 inches... 17) what percent of men are between 68 inches and 74 inches tall? 18) what percent are shorter than 72 inches tall? 19) what percent are over 67 inches tall?

Explain how we get the S² by equivalent relation.

Given the normally distributed variable X with mean 20 and standard deviation 2.5, find (a) P(X<14); (b) the value of k such that P(X<k) = 0.1894; (c) the value of k such that P(X> k) = 0.2327; (d) P(17<X<22).

An aerial tram takes passengers from an elevation of 6319 ft to an elevation of 10,459 ft up the slope of a mountain. If the tram runs on a cable measuring 12,273 ft in length, what is the angle of incline of the tram to the nearest tenth of a degree?

These two hexagons are similar. Find the area of the smaller one.

In which of the following spans in R³ lies the vector [5,-1, -2]? span{ [0, 1, 0], [0, 1, 1]} span{[1, 0, 0], [0, 0, 1]} span{[7,-4,0], [-2,3,-2]} span{[0, 1, 0], [0, 1, 1],[1,1, 1]}

Determine whether S= ((7, 6, 3), (0, 6, 3), (0, 0, 3)) is a basis for R³. If it is, write (28, 18, 21) as a linear combination of the vectors in u= a. S is a basis for R³ and b. S is a basis for R³ and c. S is a basis for R³ and d. S is a basis for R³ and u=4(7,6, 3)-(0, 6, 3)-4(0, 0, 3)=(28, 18, 21). e. S is not a basis for R³. =-4(7, 6, 3) + (0, 6, 3)+4(0, 0, 3)=(28, 18, 21). = 4(7, 6, 3)-(0, 6, 3) +4(0, 0, 3)=(28, 18, 21). =-4(7,6, 3) + (0, 6, 3)-4(0, 0, 3)=(28, 18, 21).

A company is deciding to set up operations in one of two locations. It is estimated that site A will net $57000 if successful (probability 0.22) and lose $4900 if not (probability 0.78); site B will net $117000 if successful (probability 0.12) and lose $5300 if not (probability 0.88). (a) What is the expected return for Site A? (b) What is the expected return for Site B?

Find the value of n(An B) if n(A)=9, n(B) = 12, and n(AUB) = 17. n(An B)= (Type a whole number.)

[10 pts] Rohan is an extremely lucky individual each time he enters a giveaway for free concert tickets, he has a 3/4 probability of winning. If Rohan enters three giveaways for free concert tickets, what is the prob- ability that he wins in at least two of them?

1. [10 pts] Rohan is an extremely lucky individual - each time he enters a giveaway for free concert tickets, he has a 3/4 probability of winning. If Rohan enters three giveaways for free concert tickets, what is the prob- ability that he wins in at least two of them?

Weston completed a hypothesis test and found that he could not reject the null hypothesis. Which of the following is a valid reason for his conclusion? The z-statistic is less than 0. The z-statistic lies in the critical region. The z-statistic is greater than 0. The z-statistic lies outside the critical region.

Which of the following statements is correct? Population parameters are used to make inferences about sample statistics. Population statistics are used to make inferences about sample parameters. Sample parameters are used to make inferences about population statistics. Sample statistics are used to make inferences about population parameters.

4x + 6y = 24 2x + y = 8 The system of equations has exactly one (x, y) pair for its solution. If we double each side of the second equation, 2x + y = 8 we have 4x + 2y = 16 is also a solution to this new equation. Explain why the same (x, y) pair that is the solution to the system If needed, you can support your explanation with hanger diagrams, or by inventing a situation that the equations represent. If we add the two equations in the original system, we have 6x + 7y = 32 Again, you can support your explanation with diagrams or a situation, if needed. Explain why the same (x, y) pair is also a solution to this equation.

Jason and Yolanda both drew a simple random sample from a non-normally distributed population of 25,000. Jason's sample consisted of 0.24% of the population, while Yolanda's sample consisted of 0.32% of the population. Whose sample can be used to make inferences about the population? neither Jason's sample nor Yolanda's sample only Jason's sample only Yolanda's sample both Jason's sample and Yolanda's sample

Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that at most 4 students have taken chemistry? Round the answer to the nearest thousandth. 0.008 0.438 0.562 0.665

Which of the following z-values, standard deviations, and sample sizes produce a margin of error of 0.95? z = 2.14; s = 4; n = 9 z = 2.14; s = 4; n = 81 z = 2.14; s = 16; n = 9 z = 2.14; s = 16; n = 81

Johnni guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that she got exactly 3 questions correct? Round the answer to the nearest thousandth. 0.004 0.208 0.422 0.792

Write down the chromatic polynomials of (i) the complete graph K6; (ii) the complete bipartite graph K1.5. In how many ways can these graphs be coloured with 7 colours?

If θ = 5π/4 sin(θ) = cos(θ) = then Give exact values. No decimals allowed!

The Monterey-San José Speedy Student Shuttle Service, or MSSSSS, runs regular buses between Monterey and San José, with full price tickets going for $23 each and discount tickets going for $19 each. In 2021, they sold a total of 57,636 tickets (including both full price and discount) and made a total of $1.210.392 in revenue. How many full price tickets did MSSSSS sell in 2021?

Express the following as a single logarithm. log 5 + log 2

A researcher collated data on Americans' leisure time activities. She found the mean number of hours spent watching television each weekday to be 2.7 hours with a standard deviation of 0.4 hours. Jonathan believes that his football team buddies watch less television than the average American. He gathered data from 15 football teammates and found the mean to be 2.3. Which of the following shows the correct z-statistic for this situation? -3.87 -0.26 3.23 5.22

3 spheres of radius 1m are placed horizontally into a cylinder and fit perfectly. what fraction of the total cylinder is occupied by the spheres?

How do the functions in the table compare? Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start. Since the maximum value in the able for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.

Use the slope-intercept form to graph the equation 4x - 5y = 20.

Van guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got exactly 1 question correct? Round the answer to the nearest thousandth. 0.033 0.267 0.461 0.733

Find the quotient using long division. 7x² + 16x + 4 x + 2

3. (Equations of lines, fractions) One of the places in College Algebra where we have had to work with fractions is when we are writing equations of lines. Remember that you should use improper fractions rather than mixed numbers. Write the equation of the line passing through the point (-7,2) that is perpendicular to the line 3x - 4y = 16.

a) b) Simplify the following expression. Write the answer with only positive exponents. x-4y3 2xy², -3 Solve the following equations: log (x + 3) = 1- log x (2) (2)

Question 2. Let G be a finite Abelian group and suppose there exists an a € G such that lg| ≤ la for all g € G. Prove that g| divides al for all g € G.

Solve the system of linear equations by graphing [y=x-3 y=5x+1 MEER I enlarge graph Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA The solution of the system is (Type an ordered pair.) OB. There are infinitely many solutions: ((x,y)ly=x-3) or ((x,y)ly = 5x + 1}. OC. There is no solution; or Ø.

1 Use the slope-intercept form to graph the equation y = x + 1. SCOOB Use the graphing tool to graph the line. Use the slope and y-intercept when drawing the line. Click to enlarge graph -10. 10 18 6 2 10 Ay ↑ 10 Q

Solve the system of linear equations by graphing. y-3x = -1 -9x+3y = -3 enlarge graph Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution of the system is (Type an ordered pair.) OB. There are infinitely many solutions; ((x,y)ly-3x = -1) or ((x,y)|- 9x + 3y = -3}. OC. There is no solution; or Ø. 10 10 Ay 8 6 H 18- N 10 OU

Fill in the blanks. If x is any nonzero real number, then xº = If x is any nonzero real number, then x¯n -n Need Help? Read It =