# Permutations and Combinations Questions and Answers

Algebra

Permutations and CombinationsConsider the following random sample of data:
2, -9, 3, -10, 5, -7, 9, 1, 4, 87
a) What is the mean of the sample data?
b) If the outlier is removed, what is the mean of the remaining sample data?

Algebra

Permutations and CombinationsIf 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)

Algebra

Permutations and CombinationsWhat 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.

Algebra

Permutations and CombinationsGive 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.

Algebra

Permutations and CombinationsFind 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.

Algebra

Permutations and CombinationsTwo 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.

Algebra

Permutations and CombinationsIf2-√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

Algebra

Permutations and CombinationsA 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

Algebra

Permutations and Combinations2. 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 =

Algebra

Permutations and CombinationsExpress 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

Algebra

Permutations and CombinationsWe 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?

Algebra

Permutations and CombinationsDylan 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

Algebra

Permutations and CombinationsSamantha 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

Algebra

Permutations and Combinations(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.

Algebra

Permutations and CombinationsA 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)

Algebra

Permutations and CombinationsFive 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.)

Algebra

Permutations and CombinationsOn 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.)

Algebra

Permutations and CombinationsWhich 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

Algebra

Permutations and CombinationsWrite 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.

Algebra

Permutations and CombinationsDecide 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.)

Algebra

Permutations and CombinationsFind 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.

Algebra

Permutations and CombinationsThe 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

Algebra

Permutations and CombinationsThe 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

Algebra

Permutations and CombinationsWhat 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

Algebra

Permutations and CombinationsGive an example of a factor module which is a
torque module? Also give an explanation!

Algebra

Permutations and CombinationsWhich 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?

Algebra

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

Algebra

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

Algebra

Permutations and CombinationsHow 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

Algebra

Permutations and CombinationsConsider 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

Algebra

Permutations and CombinationsThe 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.

Algebra

Permutations and Combinations3/4
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

Algebra

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

Algebra

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

Algebra

Permutations and CombinationsWill 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?

Algebra

Permutations and CombinationsSolve 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

Algebra

Permutations and CombinationsThe 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)

Algebra

Permutations and CombinationsA 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.

Algebra

Permutations and CombinationsA 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?

Algebra

Permutations and CombinationsHow 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

Permutations and CombinationsAlgebra
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.