Permutations and Combinations Questions and Answers

If light travels at a speed of 3 x 10⁸ m/s, and remembering the formula distance = speed x time. (or d = v*t), calculate the distance traveled by light in 2 milliseconds (i.e. in t = 2 x 10-³ seconds)

What happens to the input when you plug it in? Find expressions for the composite functions (MG) (t) and (Go M)(r). Explain in words what happens to your input when you plug it in to these composite functions. We call G and M inverses.

Give the version of the Parallel Postulate as used in Euclidean geometry, beginning the statement with, "Given a line and a point P not on,..." Now show how to change this statement in two different ways, giving rise to two different forms of non-Euclidean geometry.

Describe the transformation of the parent function y = 2*.

Find all solutions to sin (x + 4) + sin(x-4)=0 on [0, 2π). Enter the answer in terms of , as needed. Do not enter a decimal approximation.

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. Find sin B when b = 5 and c = = 6.

If2-√3 is a root of a polynomial with integer coefficients, which of the following is another root? 2√3 3-√2 2+√3 √3-2

A garden has width /13 and length 7/13. What is the perimeter of the garden in simplest radical form? Select one: O a. 16√13 O b. 91 O c. 8√13 Od. 14v13

When x⁴ - 16 is factored completely, one of the factors will be

Write a rate in simplest form for earning $171 in 18 hours.

2. Use the Law of Cosines to determine the indicated angle O. (Assume a = 136.5, b = 59.2, and c = 160.5. Round your answer to the nearest degree.) 0 =

Express the proposition as an English sentence and determine whether it is true or false, where p and q are the propositions p: "9.9=81" q: "8.10<7.11 The contrapositive of p →q A. If 8.10 is not less than 7. 11, then 9.9 is not equal to 81; false B. If 8.10 is not less than 7. 11, then 9.9 is equal to 81; false C. If 8.10 is less than 7.11, then 9.9 is equal to 81; false D. If 8.10 is less than 7.11, then 9.9 is not equal to 81; false

We distribute 30 indistinguishable toy cars to 3 people (say, A, B, and C). How distinguishable many ways can we do this so that no people get precisely 10 toy cars?

Dylan has 7 soccer trophies. He can only fit 4 trophies in a row on his display shelf. In how many different ways can Dylan arrange the trophies on the shelf? Select on O 28 O 840 O 35 O 210

Samantha is arranging the letters in the word "MUSICAL." How many different 7-letter arrangements can she make if she must use all seven letters each time? Select one: O 5040 O 7 O823,543 O28

(a) How many black playing cards must be drawn from a single deck of cards to be sure that at least two are the same suit? (b) How many black playing cards must be drawn from a single deck of cards to be sure that at least twelve are spades or at least twelve are clubs? (a) There must be at least _____ black playing cards drawn from a single deck of cards to ensure there are at least 2 of the same suit. (b) There must be at least ________ black playing cards drawn from a single deck of cards to ensure there are at least twelve spades or twelve clubs.

A hole is cut through the center of a thick sheet of metal. The metal is 8.5mm thick,10cm long and 13cm wide. The hole was 4cm wide. Find the weight of the metal. (in grams)

Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to bedrawn at random and monetary prizes awarded as follows: 1 prize of $500, 3 prizes of $200, 5 prizes of $30, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket? Let X be the random variable for the amount won on a single raffle ticket. E(X)=dollars (Round to the nearest cent as needed.)

On three rolls of a single die, you will lose $14 if a 3 turns up at least once, and you will win $8 otherwise. What is the expected value of the game? Let X be the random variable for the amount won on a single play of this game. E(X)= dollars (Type an integer or a decimal rounded to the nearest cent as needed.)

Which of the following situations can be modeled with a periodic function? the height of a football after it has been thrown the height of a person riding on an escalator the height of a building after it has been constructed the height of a pebble stuck in the tread of a tire

Write an algebraic equation to represent the given information. Let x be the first number and y be the second number The first number is 2 less than twice the second number.

Decide which of the two given prices is the better deal and explain why. You can buy shampoo in a 5-ounce bottle for $2.49 or in a 15-ounce bottle for $9.79. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The 15-ounce bottle is the better deal because the cost per ounce is per ounce while the 5-ounce bottle is $ per ounce B. The 5-ounce bottle is the better deal because the cost per ounce is $ per ounce while the 15-ounce bottle is $ per ounce. (Round to the nearest cent as needed.)

Find the indicated root. √169 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. √169 is a real number. √169 = (Type an integer or a simplified fraction.) B. √169 is not a real number.

Subtract as indicated. - 3/-(- 5 4 15

The equation d=11cos 5 models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance. O 0.625 seconds O 0.8 seconds O1.25 seconds O 1.6 seconds

The scores of the top ten finishers in a recent LPGA Valley of the Stars Tournament are listed below. What is the mean score. 71 67 67 72 76 72 73 68 72 72

What is the antenna gain of an airport surveillance radar with a peak power (Pt) of 1.4 MW at a range of 25 NM with the following characteristics: Horizontal beamwidth: 1.4° Vertical beamwidth: 5° O 7906.25 O 5906.25 O 6906.25 4906.25

Give an example of a factor module which is a torque module? Also give an explanation!

Which of the following is the value of a when the function f(x) = 3xl is written in the standard form of an absolute value function?

Complete the sentence below. For a circle, the is the distance from the center to any point on the circle.

Given the points (-7, 8) and (5, -7) find the slope. Round to at least 3 decimal values if needed. m =

How many different license plates are possible if each contains 3 letters (out of the alphabet's 26 letters) followed by 6 digits (from 0 to 9)? There are different possible license plates

Consider the linear transformation Tao + a₁x + a₂x²) = (a₁-a₂) + (a₁ + a₁ + a₂ If u =2-x+3x², B = {1+ x², 1 + x, 1} and C= {1-x, -x}, what is [T](P A B C D 4-4x 4-8x 4 + 4x 8-4x

The height h of a projectile launched from ground level is a function of the time t it is in the air. The height in feet for t seconds is given by the function h(t) = -16t2 domain of the function? (Enter your answer using interval notation.) What does the domain mean in the context of the problem? After the projectile is launched from ground level it takes seconds for the projectile to return to the ground.

3/4 The expression 0.036m 10¹? Select one: O a. 1660 O b. 636 O c. 1460 O d. 16,600 is used in the study of fluids. Which best represents the value of the expression for m = 46 x

wRite the following in terms of Permutation OR Combination and Evaluate: 16 ! 9ļ

If P(x)=x²+x+2 and Q(x) = 8x² - 2, find P(6). P(6)= (Type an integer or a fraction.)

Will can afford $225.00 monthly car payments on a 4 year loan. His bank is offering a 7% interest rate on new car loans for 48 months. What is the largest loan he can afford?

Solve the equation 8x³+2x=21, Restrict your attention to the horizontal span of 0 to 5. Round your answer to two decimal places if necessary. A) 3.24 B 1.15 C) 2.77 D 1.32

The current student population of Atlanta is 2400. If the population decreases at a rate of 16.4% each year. What will the student population be in 5 years? Write an exponential growth model for the future population P(x) where x is in years: What will the population be in 5 years? (Round to nearest student)

A plane is increasing its elevation at a constant rate of 77%. It does this for a distance of 2480 feet, how much does its elevation increase? Note: You can type the trig in the answer box for all these problems. For example if the answer is 50cos(10), you can just type that into the answer box. To get inverse trig functions type arcsin, arccos or arctan.

A football team scored 222 points during a 3-game series from touchdowns (6pts each),extra points (1pt each), field goals (3pts each), safeties (2pts each), and two-point conversions (2pts each). After the games, the coach reflected on the fact that half their touchdowns resulted in 2pt conversions, the other in extra points from their kicker. The assistant coach remarked that they made two less field goals than touch downs and that they had half as many safeties as field goals. How many touchdowns, extra points, field goals, safeties, and two-point conversions did they make?

How many distict prime factors does 2031120 have? a prime factor of 2031120. What is its power in the prime factorization of Clearly, 2 is of 2031120?

Algebra A cube is called colored if each of its faces is colored by one of three given colors. Two colorings are considered to be the same if there is a rotation of the cube carrying one coloring to the other. Prove that there exist exactly 57 different colorings of the cube.