how many one-to-one functions are there from a set with five elements to sets with the following number of ele- ments? a) 4 b) 5 c) 6 d) 7
Answers
a) Number of one-to-one functions are equal to the zero, because n< m.
b) Number of one-to-one functions are equal to the ⁵P₅ = 120.
c) Number of one-to-one functions are equal to the ⁶P₅ = 720.
c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.
One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then
Number of one-to-one functions from set A to Set B = P(n,m) or ⁿPₘ , n≥ m and number of one-to-one functions from set A to Set B = 0 , n< m.Now, we have a domain set with five elements, m = 5
a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.
b) number of elements in another set,n= 5
So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)
= 5!/0! = 120
c) Number of elements in another set, n= 6
So, Number of one-to-one functions= ⁶P₅
= 6!/(6 - 5)!
= 6!/1! = 720
d) Number of elements in another set, n
= 7
So, Number of one-to-one functions
= ⁷P₅ = 7!(7 - 5)!
= 7!/2! = 2250
Hence, required value is 2250.
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Related Questions
Please help!!! I will give 20 points to the correct answer !! Thanks so much
Answers
How many roots do the functions have in common f(x)=x^2+x-6
Answers
To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.
For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:
x^2 + x - 6 = 0
To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:
(x + 3)(x - 2) = 0
Setting each factor equal to zero:
x + 3 = 0 or x - 2 = 0
Solving for x in each equation:
x = -3 or x = 2
Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.
To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.
Sonya made a resolution to walk 2.5 kilometers a day. On Tuesday she walked 4 times around the running track at the local high school. The chart shows the length of a standard-sized pool and the distance around a standard-sized running track.
PLEASE HELP
How many additional kilometers does Sonya need to walk on Tuesday? Round your answer to the nearest tenth if necessary.
Sonya has to walk an additional 0.5 kilometers on Tuesday.
Sonya has to walk an additional 0.9 kilometers on Tuesday.
Sonya has to walk an additional 2.3 kilometers on Tuesday.
Sonya has to walk an additional 4.1 kilometers on Tuesday.
Answers
Answer:i think its B
Step-by-step explanation: well if she ran 0.4 on that day and her goal was
2.5 you would subtract the two and get 0.9.
Answer:B
Step-by-step explanation:
I got it right on my test
WILL GIVE BRAINLEST PLZZZ HELPP MEEEE
Answers
Answer: its C
Step-by-step explanation:
A random variable X is generated as follows. We flip a coin. With probability p , the result is Heads, and then X is generated according to a PDF f X|H which is uniform on [0,1] . With probability 1−p the result is Tails, and then X is generated according to a PDF f X|T of the form
f X|T (x)=2x,if x∈[0,1]. (The PDF is zero everywhere else.)
1. What is the (unconditional) PDF f X (x) of X ? For 0≤x≤1 : f X (x)=
2. Calculate E[X] .
Answers
Answer:
Following are the solution to the given points:
Step-by-step explanation:
For point a:
\(fx|H(x) = 1;0< x<1\\\\fX|T(x) = 2x; 0\leq x \leq 1\\\\fx(x) = P(H \bigcap X = x) +P(T \bigcap X=x)\\\\\)
\(=P(H)fX|H(x)+P(T)fX|T(x)\\\\= p(1) + (1-p)2x\\\\= p(1 -2x)+2x\\\\\)
Using the PDF of the X value
\(fX(x) =2x +p(1 - 2x); \ 0\leq x\leq 1\)
0 ; otherwise
For point b:
\(E(X)=\int^{1}_{0} \ x fX (x)\ dx=\int^{1}_{0} \ x(2x+p(1-2x))\ dx\\\\=\int^{1}_{0} \ (2x^2+(x-2x^2)p) dx\\\\\)
\(= 2(\frac{x^3}{3}) + (\frac{x^2}{2}-2(\frac{x^3}{3}) \begin{vmatrix} x=1\\ x=0\end{vmatrix} \\\\\)
\(= \frac{2}{3} + (\frac{1}{2} - \frac{2}{3})p\\\\= \frac{2}{3} -\frac{p}{6}\\\\= \frac{(4 - p)}{6}\)
Find the derivation of the following functions with they corresponding variables
Answers
Answer:
d(f(t))/dt = –56/(t^8) – (5/6)/t^(7/6) + 12t^3 – 2t + (1/3)t^(2/3))
Step-by-step explanation:
To find the derivative of f(t), we have to find the derivative of each component of the function to make it easier.
d(8/(t^7))/dt = d(8xt^-7)/dt = –7 x 8 x t^-8 = –56t^-8 = -56/(t^8)
d(5/(t^(1/6)))/dt = –(1/6) x 5 x t^(-7/6) = –(5/6)/t^(7/6)
d(3t^4)/dt = 4 x 3 x t^3 = 12t^3
d(t²)/dt = 2t
d(t^⅓)/dt = ⅓t^(-2/3) = (1/3)t^(2/3))
d(12)/dt = 0.
Therefore,
d(f(t))/dt = –56/(t^8) – (5/6)/t^(7/6) + 12t^3 – 2t + (1/3)t^(2/3))
Find the measure of angle A
Pls help
Answers
Step-by-step explanation:
x+85+x+44+63=180(sum of angles of a triangle)
or,2x+192=180
or,2x=180-192
or,x=-12
Angle A=x+44
=-12+44
=32°
Give brainliest plse .
Free Brainliest
There are 7 red, 6 blue, 12 green and 9 yellow marbles in a bag. What is the probability of not selecting a red or yellow marble?
Answers
Answer:
there are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
Step-by-step explanation:
Answer:
I believe its 52.94% (53 rounded)
Step-by-step explanation: First add all the numbers to see the total amount of marbles (34) Second is add the marbles that are NOT red or yellow (18).Then the final step is divide 18/34
Hope this helps and have a great day
What the meaning of statement this?
Answers
The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.
Axiom of RegularityThe set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.
The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.
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Find greatest common factor for each group,factor completely and find real roots
Answers
SOLUTION
Write out the polynomial given
The first group of the expresion is
\(\begin{gathered} 3x^3+4x^2 \\ \text{Then the GCE is } \\ x^2(\frac{3x^3}{x^2}+\frac{4x^2}{x^2}) \\ \text{GCE}=x^2 \end{gathered}\)GCE is x²
For the second group, we have
\(\begin{gathered} 75x+100 \\ \text{GCE}=25(\frac{75x}{25}+\frac{100}{25}) \\ \text{GCE}=25 \end{gathered}\)The GCE for the secod group is 25
To factorise completely, we have
\(\begin{gathered} 3x^3+4x^2+75x+100 \\ \\ x^2(\frac{3x^3}{x^2}+\frac{4x^2}{x^2})+25(\frac{75x}{25}+\frac{100}{25}) \end{gathered}\)Then by simplification, we have
\(\begin{gathered} x^2(3x+4)+25(3x+4) \\ \text{Then, we factor completely to get} \\ (3x+4)(x^2+25) \end{gathered}\)Then factors are (3x +4)(x²+ 25)
To find the real root, we equate each of the factors to zero, hence
\(\begin{gathered} (3x+4)(x^2+25)=0 \\ \text{Then} \\ 3x+4=0orx^2+25=0 \\ 3x=-40rx^2=-25 \\ \end{gathered}\)Thus
\(\begin{gathered} \frac{3x}{3}=-\frac{4}{3} \\ x=-\frac{4}{3}\text{ is a real root } \\ or\text{ } \\ x^2=-25 \\ \text{take square root} \\ x=\pm_{}\sqrt[]{-25}\text{ not a real root} \end{gathered}\)Therefore, since the root of -25 is a complex number,
The only real root is x = -4/3
Find the coordinates of the point 3/10
of the way from A to B.
Answers
The coordinates of the point 3/10 of the way from a to b is (-0.3, -6.3)
How to determine the coordinates of the point?The given parameters are:
the coordinates of b is (9,7) the coordinates of a is (-4,-6)The position of the point is given as:
Location = 3/10
Express as ratio
m ; n = 3 : 10 - 3
This gives
m ; n = 3 : 7
The coordinates of the point are then calculated as:
Point = Location * (mx2 + nx1, my2 + ny1)
This gives
Point = 3/10 * (3 * 9 + 7 * -4, 3 * 7 + 7 * -6)
Evaluate
Point = 3/10 * (-1, -21)
This gives
Point = (-0.3, -6.3)
Hence, the coordinates of the point 3/10 of the way from a to b is (-0.3, -6.3)
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Complete question
find the coordinates of the point 3/10 of the way from a to b
the coordinates of b is (9,7)
the coordinates of a is (-4,-6)
The numbers of blocked intrusion attempts on each day during the first two weeks of
the month were-
53, 47, 49, 37, 38, 60, 50, 43, 43, 59, 50, 56, 54, 59
Construct a stem-and-leaf plot and find the quartiles number of blocked intrusion.
Answers
Answer:
quartiles: 43, 56median: 50Step-by-step explanation:
A stem-and-leaf plot is a kind of histogram in which the most significant digit of a data value is taken to be the "stem", and the "leaves" are a list of the least-significant digits of the data values. It is convenient to list the leaves in increasing order, to facilitate determining the quartiles in the data.
__
The 14 data set values can be represented by the plot below. Here, we have elected to use parentheses ( ) to identify the 1st and 3rd quartile values, and a slash / to signify the location of the median.
__
stem | leaves
3 | 7 8
4 | 3 (3) 7 9
5 | 0 / 0 3 4 (6) 9 9
6 | 0
_____
The first and third quartiles are 43 and 56, respectively. The median is 50.
Convert 4
3
5
cups to pints.
2 cups = 1 pint PLEASE HELP!
Answers
Answer:
4 cups=2 pint
3 cups=1.5 pint
5 cups=2.5 pints
Step-by-step explanation:
Because there are 2 cups in each pint, we can divide the number of cups by two to get the number of pints.
4/2=2
3/2=1.5
5/2=2.5
Let me know if you have any questions!
Which ordered pair is a solution to the system of linear equations?
x + 2y = 3
y = −2x − 3
A. (−3, −3)
B. (3, 3)
C. (3, −3)
D. (−3, 3)
Answers
Answer:
D. (−3, 3)
Step-by-step explanation:
x + 2y = 3
y = −2x − 3
We subtitude in for y
x + 2(-2x - 3) = 3
x - 4x - 6 = 3
-3x - 6 = 3
-3x = 9
x = -3
Now we put -3 in for x and solve for y
-3 + 2y = 3
2y = 6
y = 3
So, the answer is D. (−3, 3)
The ESS Ravens bought pizza for $900 to sell at the football game. They kept 10 pizzas to feed the players after the game and sold the rest for $1040. There were 8 slices in each pizza. Their profit was 50 cents a slice.
a) How many pizzas were in the original order?
Answers
Answer: 45
Step-by-step explanation:
The total profit in all was \(1040-900=\$ 140\).
The total profit per pizza was \((0.50)(8)=\$4\).
This means they sold \(\frac{140}{4}=35\) pizzas.
Adding this to the 10 pizzas held back, there were \(35+10=45\) pizzas in the original order.
A movie theater can seat a maximum of 25 people. Let p represent the total number of people. Which inequality represents p, the number of people the theater can seat?
Answers
The inequality that represents p, the number of people the theater can seat is p ≤ 25
Which inequality represents p, the number of people the theater can seat?From the question, we have the following parameters that can be used in our computation:
A movie theater can seat a maximum of 25 people
This means that
Maximum = 25 people
In other words, the movie theatre can allow 25 or less people to attend a movie
In inequality, 25 or less means less than or equal to 25
When represented as an inequality expression, we have
≤ 25
Using the variable p, we have
p ≤ 25
Hence, the inequality is p ≤ 25
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The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 6 credit hours of A, 15 credit hours of B, 31 credit hours of C, and 8 credit hours of D.
a. Compute the student's grade point average. Round your answer to two decimal places.
b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?
Answers
The student's grade point average is 2.32.
The student will not be admitted to the business college.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
(a)
Total grade points earned
= (6 x 4) + (15 x 3) + (31 x 2) + (8 x 1)
= 24 + 45 + 62 + 8
= 139
Total credit hours.
= 6 + 15 + 31 + 8
= 60
Now,
The student's grade point average:
= Total grade points earned / Total credit hours taken
= 139 / 60
= 2.32
(b)
2.32 < 2.5
This means,
The student's grade point average is lower than the required 2.5 GPA for admission to the business college.
Thus,
The student's grade point average is 2.32.
The student will not be admitted to the business college.
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Given 36 − 9, simplify the expression using the Difference of Squares.
Wait, wait. I know what you are saying. 36 − 9 is not exactly a difficult math problem, it is 27. Yes you are correct; however, 36 − 9 is going to serve as a proof that the Difference of Squares is valid regardless of what x and y are.
36 − 9
62 − 32
This looks exactly like the Difference of Squares, x2 − y2. So substitute 6 and 3 in for x and y.
Answers
Answer:
See below
Step-by-step explanation:
Using formula
x^2 - y^2 = (x + y)(x - y)Applying to given expression
36 - 9 = 6^2 - 3^2=(6 + 3)(6 - 3)=9*3=27For the function defined here, find f(0), ƒ(2), and f(4) by using the graph below.
x² - 1
f(x) = {¹
-x+1
if
if
x < 2
x > 2
Answers
The values of the functions are f(0) = 2, f(2) = 0 and f(4) = -2
How to evaluate the piece-wise functionThe graph that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the first curve is a quadratic function,
Also, it has an open circle at x = 1
So, we have:
x² + 2 if x < 1
Next, we have a linear equation with a closed circle at x = 1
So we have:
y = -x + 2 for x ≥ 1
This means that
f(0) = 0^2 + 2 = 0f(2) = -2 + 2 = 0f(4) = -4 + 2 = -2Read more about piecewise functions at:
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In the polyhedron above x=5 mm, y=9 mm, and z=4 mm. The volume of the polyhedron is _____ mm3. Round your answer to the tenths place.
Answers
Answer:
180 mm³
Step-by-step explanation:
The polyhedron is an oblique rectangular prism
Area of the oblique rectangular prism = base area * height
height = z = 4 mm
Base area = L*W
L = y = 9 mm
W = x = 5 mm
Base area = 9*5 = 45 mm²
Area of the oblique rectangular prism = 45*4 = 180 mm³
Hey! I am stuck on this question anyone mind helping me? and tysm for the people who helped me! <3 have a nice day!
Answers
Answer: 166 2/3m
Step-by-step explanation:
Area of a rectangle = length times width
Length: 16 2/3
To find the width, multiply it by 3/5.
w = 16 2/3 · 3/5
w = 10
Then, multiply the length by the width.
a = l · w
a = 16 2/3 · 10
a = 166 2/3m
if 6 people can walk 12 dogs, how many people are needed to walk 24 dogs
Answers
Answer:
12 people are need to walk 24 dogs
Step-by-step explanation:
12/2=6
24/2=12
Answer:
12 people can walk 24 dogs.
Step-by-step explanation:
Given information,
→ 6 people can walk 12 dogs.
→ People required for 24 dogs = ?
Let us assume that,
→ Missing value = p
Forming the equation,
→ 6/12 = p/24
Then the value of p will be,
→ 6/12 = p/24
→ p/24 = 6/12
→ p × 12 = 6 × 24
→ 12p = 144
→ p = 144/12
→ [ p = 12 ]
Hence, the value of p is 12.
Amiya Kettey
Reflection of a Point
Oct 01, 11:38:14 PM
Watch help video
What is the image of (0, -6) after a reflection over the line y = 2?
Submit Answer
Answers
Answer:
(0,10)
Step-by-step explanation:
Answer:
(0,10)
Step-by-step explanation:
See picture
What is the inverse of the function f(x) = x +3?
Answers
Answer:
f⁻¹(x) = x - 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
FunctionsFunction NotationInverse FunctionsStep-by-step explanation:
Step 1: Define
Identify
f(x) = x + 3
Step 2: Find
Swap: x = y + 3[Subtraction Property of Equality] Isolate y: x - 3 = yRewrite: f⁻¹(x) = x - 3The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 280 tickets sold. The winner gets a prize worth $62. Round your answers to the nearest cent.
What is the expected value (to you) of one raffle ticket? $
Calculate the expected value (to you) if you purchase 12 raffle tickets. $
What is the expected value (to the PTO) of one raffle ticket? $
If the PTO sells all 280 raffle tickets, how much money can they expect to raise for the classroom supplies? $
Answers
The expected values of the raffle ticket for you are given as follows:
One ticket: -$3.76.12 tickets: -$45.12.For the PTO, the expected values are given as follows:
One ticket: $3.76.12 tickets: $45.12.What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
For you, the distribution is given as follows:
P(X = 62) = 1/280.P(X = -4) = 279/280.Hence the expected value for one ticket is given as follows:
E(X) = 62/280 - 4 x 279/280
E(X) = -$3.76.
For twelve tickets, the expected value is given as follows:
12 x -3.76 = -$45.12.
For the PTO, we use the inverse signals, as the distribution is the inverse, that is:
P(X = -62) = 1/280.P(X = 4) = 279/280.More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
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I will mark you as BRANLIEST and I will give you 55 points if you answer correctly.
~Solve each system of equations using elimination. SHOW YOUR WORK
1) -4x+3y=-5
4x-5y=3
2) 2x+3y=36
10x-6y=12
Answers
Answer:
1. x = 2 y = 1
2. x = 17 y = 29/3
Step-by-step explanation:
1. Use elimination
-4x+3y=-5
4x-5y=3
x's cancel, so add them
-2y = -2
y = 1
substitute
4x -5(1) = 3
4x - 5 = 3
4x = 8
x = 2
2. Use elimination
2x+3y=36
10x-6y=12
Multiply top equasion by 5
10x+30y = 360
10x-6y = 12
x's cancel so subract
36y = 348
y = 29/3
Substitute
2x+3(2/3)=36
2x+2 = 36
2x = 34
x = 17
What is the vertex of the quadratic function below?
(-4, 0)
There is no y-intercept
(0, -1)
(-2, 3)
Answers
Answer:
(-2, 3)
Step-by-step explanation:
In the triangle below,
y = [ ? ) cm. Round to the
nearest tenth.
15 cm
х
35
90°
y
Enter
Answers
y ≈ 12.3
Good luck
Helppppppppppppppppp
Answers
the expression negative five eighths times k minus 8 plus the expression 2 plus one third times k
7 over 24 times k plus negative 6
negative 4 over 11 times k plus negative 10
negative 7 over 24 times k plus negative 6
negative 23 over 24 times k plus negative 10
Answers
After solving the expression, the value is negative 7 over 24 times k plus negative 6. Therefore, option C is correct.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given statement for the expression,
-(5/8)k - 8 + 2 + (1/3)k
Take LCM as 24 and solve the equation,
(-7k - 144) / 24
= (-7/24)k - 6
Therefore, this concludes that option C is correct.
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