Permutations and Combinations Questions and Answers

On the coordinate plane, the segment from B(-14, 11) to C(4, 11) forms one side of a rectangle. The rectangle has an area of 54 square units. Select all of the points that could be a vertex of the rectangle. 1.(-14, 14) 2. (7, 11) 3. (-14,8) 4. (4, 14)

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 the vaccine treatment group to be the first sample. Identify the values of n . . . . . and a 1 EC GERD Ext PA - (Type an integer or a decimal rounded to eight decimal places as needed) idy 9,- leo (Type an integer or a decimal rounded to eight decimal places as needed) Trai n2- ces Sou B2= (Type an integer or a decimal rounded to eight decimal places as needed) arch 02-0 om (Type an integer or a decimal rounded to eight decimal places as needed.) sols (Type an integer or a decimal rounded to eight decimal places as needed.) Q= (Type an integer or a decimal rounded to eight decimal places as needed.) Next

State if the scenario involves a permutation or a combination. Then find the number of possibilities. A team of 15 basketball players needs to choose two players to refill the water cooler.

The cost is expressed by the function y = 18x + 8, where x is the number of km and y is the total cost. Interpret the rate of change and base fare from the function. 1. The rate of change is 18 dollars per km and base fare is 8 dollars. 2. The rate of change is -18 dollars per km and base fare is 8 dollars. 3. The rate of change is 8 dollars per km and base fare is

A movie star's agent earns 8% of the star's monthly income. If the star's monthly income is $55,200, how much will the agent earn? Step 1 of 2: Describe the above situation as a linear equation using "x'' or "y" as variable names to describe the unknowns.

A person invests 1000 dollars in a bank. The bank pays 6.75% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 2500 dollars? A = P{1 + (r/n)^n t }

One third of the trees in an orchard are olive trees. One-quarter of the trees are fig trees. The others are 180 mixed fruit trees. In the first week of the season the owner harvests one-third of the olive trees and one third of the fig trees. How many trees in the orchard still have to be harvested? (A) 348 (B) 108 (C) 276 (D) 432

Find the mean, median, and mode of the data i. Mean: ii. Median: iii. Mode: iv. Which measure of central tendency best describes the data? Explain your answer. b. How much would a 10th dog have to weight for the average weight in part (a) to be 250 pounds? Explain how you determined your answer Next Slide

You are playing a game where you are rolling a fair 6-sided number cube. It costs $1.00 for every roll. If you roll an even number, you win $3.00. If you roll an odd number, you win nothing. Which of the following is the expected value of this game? (A) expected value = -$0.50 (B) expected value = $0.50 (C) expected value = $1.00 (D) expected value = -$1.00

A candle manufacturer found that their long last candles melted according to the formula h = -2t + 12, where h is the height of the candle, in cm, after t hours. How long will it take the candle to burn to a height of 7 cm? 1. 3 2. 2 3. 2.5

In the city of N, the road system is set up like a Cartesian plane. Point B is 7 blocks east and 18 blocks north from point A. Point C is 18 blocks west and 9 blocks south from point A. Find the distances between each pair of points. Find the distance between A and B Find the distance between A and C Find the distance between B and C (Round to the nearest hundredth as needed)

If X and Y are jointly unity mean and unity variance Gaussian random variables, find the pdf of Z=(X²+Y²)¹/²

Use the ALEKS calculator to evaluate each expression. Round your answers to the nearest thousandth. Do not round any intermediate computations. In √11 = log 21.1 =

Rationalize the numerator. √(17/3) √(17/3) = ____

Simplify the following rational function, assuming the denominator is nonzero. f(x)= x² + 10x +24/x² +13x +42 Give your answer as a simplified rational expression. Do not include "f(x) =" or the domain restrictions in your answer.

A restaurant chain's owners are trying to decide if they want to open up a franchise in your town. To help them decide, they want to find out how often people in your town go out to eat. A researcher interviews people leaving a local restaurant. Is there a bias in this sampling method? Explain.

A simple graph G on n vertices (n ≥2) is drawn in the plane. Prove that if every edge crosses at most one another edge, then the number of edges in G does not exceed 4n - 8.

FINDING A PROBABILITY A movie complex is showing three action films and three comedy films. You randomly select two different films to watch. Find the probability that you select a comedy to watch second given that you randomly selected a comedy to watch first.

In a class of 20 students, 13-play soccer, 8-play tennis and 2-play neither. Find how many students Play soccer or tennis Play both soccer and tennis Play only soccer. A student is selected at random from this class. Find probability that the student plays only soccer. Two students are selected at random from this class the probability that both of them play only soccer.

Algebra Suppose that you will be using homemade chicken stock for the navy bean soup, and you have determined that you can make your stock for $8.3per gallon. What will be the total cost for chicken stock in the navy bean soup recipe if the EP unit cost is $1.25 per gallon? Round your answer to the nearest cent.

Find the missing length of the following SPECIAL, right triangles. Leave your answer as a whole number form.

At a gas station, 84% of customers buy gasoline, 9% of customers buy gasoline and a beverage, and 5% of customers buy gasoline and a snack. a. What is the probability that a customer who buys gasoline also buys a beverage? Express your first answer as a simplified fraction, and round your percent answer to the nearest tenth. b. What is the probability that a customer who buys gasoline also buys a snack? Express your first answer as a simplified fraction, and round your percent answer to the nearest tenth.

△ABC is acute-angled. (a) Explain why there is a square PQRS with Pon AB, Q and Ron BC, and Son AC. (The intention here is that you explain in words why such a square must exist rather than by using algebra.) (b) If AB = 35, AC = 56 and BC = 49, determine the side length of square PQRS. It may be helpful to know that the area of △ABC is 490√3.

The Whispering Winds Company accumulates the following adjustment data at December 31. Revenue of $1,078 collected in advance has been recognized. Salaries of $780 are unpaid. Prepaid rent totaling $392 has expired. Supplies of $605 have been used. Revenue recognized but unbilled totals $675. Utility expenses of $318 are unpaid. Interest of $300 has accrued on a note payable. Assume net income before the adjustments listed above was $22,500. What is the adjusted net income?

A pictograph is a __________ representation of data made with pictures picture of a graph graph that is misleading representation of pictures made with graphs

Two data sets have the same median, the same interquartile range, and the same range. Is it possible for the box-and-whisker plots of the data sets to be different? Justify your answer.

A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 6.0 and 6.9. • about 13.5% •about 34% • about 68% • about 16%

What is the average rate of change of the function graphed above on the interval x = 2 to x = 4? (A) 2 (B) 3 (C) 4 (D) 5

Find the final amount in the following retirement account, in which the rate of return on the account and the regular contribution change over time. $1200 per quarter invested at 5.3%, compounded quarterly, for 13 years; then $1900 per quarter invested at 6.4%, compounded quarterly, for 16 years.

If Carl wants to buy a $23,999 truck and put a 15% down payment on it, how much money should he save for a down payment? $2,399.46 $3,999.58 $ 3,599.85

To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. (Assume points A and B are exactly along the shoreline, and that a = 2.92 miles and b = 3.16 miles. Round your answer two decimal places.)

The logistic growth model P(t)= 3000/1+34.64 e -0.4741 represents the population (in grams) of a bacterium after t hours. Answer parts (a) throught (f). (a) Determine the carrying capacity of the environment. The carrying capacity of the environment is g. (b) What is the growth rate of the bacteria? The growth rate is% per hour. (Type an integer or a decimal.) (c) Determine the initial population size. Initially, the population was g. (Round to the nearest whole number as needed.) (d) What is the population after 6 hours? After 6 hours, the population is g. (Do not round until the final answer. Then round to the nearest tenth as needed.) (e) When will the population be 700 g? It will take approximately hour(s) for the population to reach 700 g.

Debra is the coach of a junior ultimate team. Based on the team's record, it has a 70% chance of winning on calm days and a 50% chance of winning on windy days. Tomorrow, there is a 30% chance of high winds. There are no ties in ultimate. What is the probability that Debra's team will win tomorrow? a. 0.35 b. 0.64 c. 0.49 d. 0.15

Write (3a³)² without exponents. (30²)² =

Solve for g. r=3g +3u The solution is g = (Use integers or fractions for any numbers in the expression. Simplify your answer.)

Which combination of True and False is correct? 1) In making a forward pass through a network, three activities are immediate predecessors for activity T. The early start time for activity T is the largest EF for the three activities that are immediate predecessors for activity T. 2) In critical path scheduling, slack is computed as the difference between finish and start times. Select one: a. 1) True and 2) True b. 1) False and 2) False c) True and 2) False d 1) False and 2) True

This equation shows how the amount of money left to raise is related to the number of cakes that Anita has sold. d = -4c+6 The variable c represents the number of cakes that Anita has sold, and the variable d represents the amount of money that still needs to be raised. After Anita sells 1 cake, how much money will she still have to raise?

Jenny is planning to bake cookies. With only 1/3 cup of sugar, she can bake 12 cookies. The table below shows how many cookies Jenny can bake with a given amount of sugar. What does the slope represent? Cups of Sugar 1/3 2/3 2 3(1/3) Cookies Made 12 24 72 120 A) For every one cup of sugar, Jenny can bake 36 cookies. B) For every cookie baked, the cost is $0.03. C) For every 70 cookies baked, one cup of sugar was needed. D) For every twelve dozen cookies made, one cup of sugar is needed

You take out a 70-day single-payment loan for $570 with an interest rate of 16%. What is the amount of the interest? •$19.94 •$19.74 •$17,49 •$18.44

There is a bag with 600 cubes in it. Some of the cubes are red and some are black. You reach into the bag 30 times, each time picking a random cube, recording its color, and putting the cube back in the bag. You picked 17 black cubes and 13 red cubes. With this information what is the best estimate you can make for how many red cubes and how many black cubes are in the bag? Describe how to calculate this best estimate and explain why your method of calculation makes sense.

The times per workout an athlete uses a stair climber are normally distributed with a mean of 20 minutes and a standard deviation of 5 minutes. What percentage of athletes use the stair climber for less than 18 minutes? (A) 20.33% (B) 34.46% (C) 48.41% (D) 65.54%

Find the range of the function given the domain: f(x) = 5 - 4x; domain = (-1,0,1) 1. (1,5,3) 2. (9,5,1) 3. (9,5,3) 4. (1,5,5)

Karen plans to join a gym but wants to compare rates. She finds State Gym which charges a $30 initial sign-up fee plus $35 per month to be a member. How much will she pay for 5 months if she chooses to be a member of this gym.

At an auto care shop, 70% of customers get an oil change for their car. Only 45% of customers get an oil change for their car and get their car tires rotated. What is the probability that a customer who gets an oil change for their car also gets their car tires rotated? Round your answer to the nearest tenth of a percent. The probability is about____________%.

SOLVE 2x² + 5x - 12-0 a) (-1.25.-15.125) b) -4,1.5 c) 2,6 d) (-4,0)

MODELING REAL LIFE At a school, 43% of students attend the homecoming football game, 48% of students attend the homecoming dance, and 23% of students attend the game and the dance. (A) What is the probability that a student who attends the football game also attends the dance? Express your first answer as a simplified fraction, and round your percent answer to the nearest tenth. (B) What is the probability that a student who attends the dance also attends the football game? Express your first answer as simplified fraction, and round your percent answer to the nearest tenth.

For the function f(X) =(2/3) x+3, answer each of the questions below. (1) What is Ax and Ay given by the Δx slope of the function? (2) Increase the input value you chose by the Δx from the slope. Increase the output value you calculated by the Δy from the slope. What is the new ordered pair?

Scores on an exam are normally distributed with a mean of 76 and a standard deviation of 10. In a group of 230 tests, how many students score within one standard deviation of the mean? about 78 students about 187 students about 115 students about 156 students

Shade 7 more squares so that the symmetric pattern has four lines of symmetry.

In the 2009-2010 school year in country A, there were 112,000 foreign students from country B. This number is 21% more than the number of students from country C. How many foreign students were from country C? There were about ______ students from country C. (Simplify your answer. Round to the nearest thousands as needed.)