Permutations and Combinations Questions and Answers
Algebra
Permutations and CombinationsWhat is the degree of the given polynomial?
-3x² + 4x² - 2x6 - 2
A/
Algebra
Permutations and CombinationsThe 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
Algebra
Permutations and CombinationsList 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.
Algebra
Permutations and CombinationsWhat is the fourth term of (x - 2y)?
4
560x5y³
-560x5y³
448x5y³
-448x5y³
Algebra
Permutations and CombinationsA 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
Algebra
Permutations and CombinationsLR2: 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)
Algebra
Permutations and CombinationsThe 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.
Algebra
Permutations and CombinationsDeandre 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?
Algebra
Permutations and CombinationsIf 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
Algebra
Permutations and CombinationsSOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES
GET THE VARIABLES TO ONE SIDE AND THE NUMBERS TO THE OTHER SIDE.
7x - 3 = 5x + 9
Algebra
Permutations and Combinations2. Prove the following:
a) cot + tan 0 = 2csc 20
(4 + 2 marks)
b) csc 20 = (sec 0) (csc 0)
Algebra
Permutations and CombinationsSolve.
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.
Algebra
Permutations and CombinationsFor 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.
Algebra
Permutations and CombinationsWhich 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
Algebra
Permutations and CombinationsIf 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?
Algebra
Permutations and CombinationsGiven 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).
Algebra
Permutations and CombinationsAn 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?
Algebra
Permutations and CombinationsThese two hexagons are similar. Find the area of the smaller one.
Algebra
Permutations and CombinationsIn 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]}
Algebra
Permutations and CombinationsDetermine 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).
Algebra
Permutations and CombinationsA 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?
Algebra
Permutations and CombinationsFind the value of n(An B) if n(A)=9, n(B) = 12, and n(AUB) = 17.
n(An B)= (Type a whole number.)
Algebra
Permutations and Combinations[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?
Algebra
Permutations and Combinations1. [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?
Algebra
Permutations and CombinationsWeston 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.
Algebra
Permutations and CombinationsWhich 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.
Algebra
Permutations and Combinations4x + 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.
Algebra
Permutations and CombinationsJason 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
Algebra
Permutations and CombinationsMrs. 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
Algebra
Permutations and CombinationsWhich 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
Algebra
Permutations and CombinationsJohnni 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
Algebra
Permutations and CombinationsWrite 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?
Algebra
Permutations and CombinationsIf θ =
5π/4
sin(θ) =
cos(θ) =
then
Give exact values. No decimals allowed!
Algebra
Permutations and CombinationsThe 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?
Algebra
Permutations and CombinationsA 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
Algebra
Permutations and Combinations3 spheres of radius 1m are placed horizontally into a cylinder and fit perfectly. what fraction of the total cylinder is occupied by the spheres?
Algebra
Permutations and CombinationsHow 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.
Algebra
Permutations and CombinationsUse the slope-intercept form to graph the equation 4x - 5y = 20.
Algebra
Permutations and CombinationsVan 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
Algebra
Permutations and Combinations3. (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.
Algebra
Permutations and Combinationsa)
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)
Algebra
Permutations and CombinationsQuestion 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.
Algebra
Permutations and CombinationsSolve 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.
Algebra
Permutations and Combinations1
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
Algebra
Permutations and CombinationsSolve 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
Algebra
Permutations and CombinationsFill 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
=
Algebra
Permutations and CombinationsSolve the system of equations by graphing.
x+y=8
x-y=6
Use the graphing tool to graph the system.
Select the correct choice below and fill in any answer boxes present in your choice.
OA. The solution of the system is
(Type an ordered pair.)
OB. There are infinitely many solutions.
OC. There is no solution.