Permutations and Combinations Questions and Answers

manufacturer of skis produces two types downhill and cross country The times required for manufacturing and finishing each ski are given in the table The maximum total weekly hours availabl or manufacturing and finishing the skis are 108 hours and 72 hours respectively The profits per ski are 60 for downhill and 90 for cross country Determine how many of each kind of ski should De produced to achieve a maximum profit Manufacturing time per ski Finishing time per ski Downhill 3 hours 1 5 hours Cross country 1 5 hours 1 5 hours CITO To achieve maximum profit the manufacturer should produce downhill skis and cross country skis

Use the above property to solve the following 1 3 34 2 4 If a a then n m 2 42 165 3 42 3 8 22 2 3 2 x 37 3x 2x 1 3X 6 3x 2x 6 4 32 2x x 3 x 6

For a vector space V a basis B b b and the coordinate mapping x X show that the coordinate mapping is one to one Hint Suppose u w g for some u and win V and show that u w

Part 1 of 2 The decision to round up or down to a given place value is determined by the digit to the right of the given place value 9438 Hundreds place Part 1 2 Part 2 of 2 This is the digit to the right of the hundreds place

5 out of 16 students will ride in a car instead of a van. Combination; 4,368 Permutation; 524,160 Permutation; 3,622 Combination; 1,092

True or False: Your finance charge is $6.61 if you have an unpaid balance of $287.45 and the annual interest rate charge is 2.3% of the unpaid balance. True False

You deposit $400 in an account earning 3% interest compounded annually. How much will you have in the account in 10 years?

The length and width of a rectangular field are 500 m and 69 m. Find Its area in hectares (10,000 square meters = 1 hectare). 6.52 3.45 7.52

The mean time for a group of runners on the 200 meter dash was 27 seconds with a standard deviation of 1.2. What percent of the runners had time that was less than 25.8 seconds?

Josie is making baked goods for her cheer squad's bake sale. She is selling cookies for $1.50 and brownies for $2.25. She wants to make at least $40 from her baked goods but only has enough batter to make 10 brownies

On July 1, Mr. Taylor owed $6,000. On the 1st of each of the following months, he repaid $400. List the amount owed by Mr. Taylor on the 2nd of each month starting with July 2. Explain why the amount owed each month forms an arithmetic sequence. Li is developing a fitness program that includes doing push-ups each day. On each day of the first week he did 20 push-ups. Each subsequent week, he increased his daily push-ups by 5. During which week did he do 60 push-ups a day? a. Use a formula to find the answer to the question. b. Write the arithmetic sequence to answer the question. c. Which method do you think is better? Explain you answer.

Samantha sold 34 bags of popcorn for a fundraiser. If the mean number of bags sold was 38 with a standard deviation of 2.5, find Samantha's z-score.

A survey of 20 colleges found that seniors graduated with an average $28,950 in debt from student loans. The debt was normally distributed with a standard deviation of $3200. Find the probability that a senior graduated owing more than $15,000.

Caroline is going to invest in an account paying an interest rate of 5.2% compounded continuously. How much would Caroline need to invest, to the nearest dollar, for the value of the account to reach $940 in 6 years?

Dominic invested $8,600 in an account paying an interest rate of 2.2% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $9,600?

There are 10 applicants for two different jobs (computer programmer and software tester). This is an example of a [Select] There are two different jobs of ways to assign these 10 applicants to the

There are 25 applicants for four jobs; Computer Programmer, Software Tester, Manager, and Systems Engineer. This is an example of of a computer programmer, software tester, manager, and systems engineer. ways to choose an applicant for the positions

A group of 25 people is going to run a race. The top three runners earn gold, silver, and bronze medals. This is an example of of ways to choose the gold, silver, and bronze

The student body of 135 students wants to elect two representatives.

Of the 30 players trying out for the school basketball team, 12 are more than 6 feet tall and 18 have good aim. There are 8 players over 6 feet tall that have good aim Fill in the Venn diagram for the scenario. What is the probability that the coach would randomly pick a player over 6 feet tall or a player with a good aim?

Sanji throws an 8-sided solid with faces numbered 1 through 8. Which of the following statements is true? Select all that apply. P(number less than 8) = 1 P(factor of 24) P(the number 9) = 0 P(even number) P(multiple of 3) = 1 P(odd number)

There are thirteen songs on your playlist. Seven of them are country and six are pop. With random shuffle and no repetition, you listen to seven songs. What is the probability that you listened to all country songs?

Ashley and Dan are planning trips to eight countries this year. There are 12 countries they would like to visit. They are deciding which countries they will skip this year.

The table shows the outcomes of rolling two number cubes at the same time and inding the product of the two numbers. Use the table for 4 and 5. 4. What is the theoretical probability of rolling a product greater than 10? 5. If Abby rolls two number cubes a hundred times, about how many times would she expect a product greater than 10?

Jimmy has homework assignments in seven subjects. He only has time to do four of them. This is an example of

Gambling. Roulette is a game of chance. It uses a spinning wheel with numbered pockets as shown below. The wheel is spun one way and a ball is sent round the other way. Find the probability of each event.

Consider the random experiment where the numbers 1-35 are written on separate tickets and placed in a jar and 1 ticket is drawn from the jar. Find the probability. P(not divisible by 7) = Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3,

Select the formula for the area of each figure. 1. A = bh 2. A = 3. A = rhombus 4. A = 5. A = x² 6. A = 1d₁d₂

Which angles are complimentary? ZDFE and LBFA ZBFC and CFD ZAFB and LBFC ZAFB and ZBFE

Let p represent Two angles are vertical angles. Let q represent The angles are congruent. What is the symbolic representation of the following statement? If two angles are congruent, then the angles are vertical angles.

Find the probability for the random experiment of 1 roll of 2 dice. Express the result as a fraction and as a decimal rounded to the nearest thousandth. (The illustration in Section 6.1 Study Set problem 19 may be helpful.) See Example 4. What is the probability if rolling hard 6 (two 3s) or hard 8 (two 4s)?

Graph the linear equation. f(x) = -2x+6 Use the graphing tool to graph the linear equation. Click to enlarge graph -10 R -64 10 16 AY 10

True or false: The chromatic number of a graph is always bigger than the number of vertices of the graph. None of these is correct. True because of Euler's Theorem. True because of Fermat's Last Theorem. O True because of Dijkstra's algorithm. True because of the Euler circuit. O False because chromatic numbers are a type of prime number and don't have anything to do with graphs. False because most graphs do not have a chromatic number. False because the chromatic number of any connected graph is 0.

For each year t, the population of a certain type of wasps in forest A is represented by A(t) = 100(1.024)t. In forest B, the population of the same type of wasps is represented by B(t) = 112(1.023)t. 1) Which forest's population of wasps is growing at a faster rate? Enter A for forest A, and B for forest B. 2) Which forest had a greater number of wasps initially, A or B? A 4) How many wasps? 3) Assuming the growth models continue to represent the population of wasps in each forest, which forest will have a greater number of wasps in 20 years, A or B? Round your answer to the nearest integer. A/ A/ A/

2. In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together? A. 9800 B. 120960 C. 100020 D. 140020

Day 9 SB SOL AII.10,12 Exit Ticket 1. A committee of 5 teachers and 2 students is to be formed to judge science projects. If there are 9 teachers and 5 students to choose from, how many different committees could be formed? Class W5 Name Uriah Garland

Caroline is going to invest $66,000 and leave it in an account for 9 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Caroline to end up with $108,000?

(16 points) Let T: P3 → P3 be the linear transformation such that T(2x²) = 4x² + 4x, T(-0.5x - 5) = 2x² + 3x + 2, Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers.

To completely factor 2x6y - 16x5y - 4x4y, what is the greatest common factor that will be taken out first? 4x¹y 2xy 02y 2x¹y

What is the complete factorization of 8 - 2x4 +1? (x² − 1)² © (x² + 1)² (x + 1)² (x − 1)² (x¹ + 1) (x² − 1) (x² + 1)² (x² − 1)²

Composing two functions is always the same operation as Omultiplication division addition Onone of the above

Let f(x) = x² + 1 and g(x) = √3x - 1, find (gof)(x). 4 √3x²+2 18x²-3 √3x² 3x

If f(x) passes through the point (5, 6n), which of the following points does its inverse function f¹(x) pass through? (6n, k) (-4, -6n) 1 ( ² /, /n) k? (-6n, -k)

How many terms are in the expansion of (3x + 2y) ³? 8 9 07 16

Suppose we want to choose 6 objects, without replacement, from 13 distinct objects. (a) How many ways can this be done, if the order of the choices is not taken into consideration? 0 (b) How many ways can this be done, if the order of the choices is taken into consideration? 0

If the following polynomial is written in standard form, what would be the leading coefficient? -3x² + 4x² - 2x6 - 2

f(x) = √x+3, g(x) = 8x³ - 3, & h(x)=2x-1, what is the value of f(h(-1))? -2 2 5

Find the inverse of the function. x f(x) = -5 4 4 X Of(x) = ² + 20 f(x) = 4x + 5 O f(x) = 4x + 20 f(x) = 4x - 20

Suppose we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair. (a) How many ways can this be done, if the order of the choices is taken into consideration? 0 (b) How many ways can this be done, if the order of the choices is not taken into consideration? 5

Suppose we want to choose 4 letters, without replacement, from 16 distinct letters. (a) If the order of the choices is not relevant, how many ways can this be done? (b) If the order of the choices is relevant, how many ways can this be done?