For f(x) = x + 4 and g(x) = 5x + 3, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(1); d. (gof)(1)

There are p × (p − 1) × (p − 2) ×... × (p − n + 1) one-to-one functions from x to y and There are 2^(n^2 - n) reflexive relations on x.

(a) Calculation of the number of one-to-one functions from x to y :

Given, x and y are finite sets, with |x|= n, |y |= p.

A function is one-to-one if it maps distinct elements of x into distinct elements of y.

The first element of x can be mapped in p ways, the second element of x can be mapped in p − 1 ways (since we already used one element), and so on, until the nth element of x is mapped.

The number of one-to-one functions from x to y is, therefore,p × (p − 1) × (p − 2) ×... × (p − n + 1).

Hence, there are p × (p − 1) × (p − 2) ×... × (p − n + 1) one-to-one functions from x to y.

(b) Calculation of the number of reflexive relations on x:

A relation R on a set X is said to be reflexive if (a, a) ∈ R for every a ∈ X.

In our case, the relation R is a reflexive relation on x.

So we are looking for the number of reflexive relations on x.

We will think of R as a subset of the Cartesian product X × X.

We first select n elements of X and put each of them in relation with itself. That is, we include the pair (a, a) for each a ∈ X.

We now have (n² − n) pairs to place in any of the remaining elements of X × X.

We can choose any number of the remaining pairs, from zero to n² − n, and place them in the remaining positions.

So, the number of reflexive relations on x is equal to 2^(n^2 - n).

Therefore, there are 2^(n^2 - n) reflexive relations on x.

Answer: (a) p × (p − 1) × (p − 2) ×... × (p − n + 1)

             (b) 2^(n^2 - n).

Learn more about one-to-one functions from the given link;

https://brainly.com/question/30563810

#SPJ11

The expression represents the height of a tree that begins at 6.7 feet and increases by 2.6 feet per year will be h=6.7+2.7t.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given that, the expression that represents the height of a tree begins at 6.7 feet and increases by 2.6 feet per year.  

Expression is the combination of constants and variables with mathematical operators.

Suppose t represents the number of years and h represents the height of a tree,

The obtained expression for the given condition,

h=6.7+2.7t

Thus, the expression represents the height of a tree that begins at 6.7 feet and increases by 2.6 feet per year will be h=6.7+2.7t.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

Answer:

Step-by-step explanation:

An=3*n

Answer:

n=3m

Step-by-step explanation:

n represent the number of movies he will watch

m shows the amoutn of month

Answer:

there will be 2.38 ounces in one bag of the trail mix

Answer:

2.15 ounces

Step-by-step explanation:

The total ounces of nuts in the bag is calculated as:

20 ounces of walnuts + 11.1 ounces of almonds + 24.8 ounces of cashews = 55.9 ounces.

From the question we are told that these amounts make 26 bags.

The number of ounces that are in each bag is calculated as:

26 bags = 55.9 ounces

1 bag = x ounces

Cross Multiply

26 bags × x ounces = 1 bag × 55.9 ounces

x ounces = 1 bag × 55.9 ounces/26 bags

x ounces = 2.15 ounces

Therefore, there are 1.94 ounces in each bag

Answer:

I think this is if it is right then help me plz this is false ..

Answer:

The formula for solving surface area is LxWxH (LengthxWidthxHeight)

And the formula for solving area is LxW (LenghtxWidth)

Step-by-step explanation:

I hope this helps. I didnt really see any pictures for this.

Answer: 1. 60 square centimeters and the volume was 24 cm3

2. Yes, because if you have length, width and height, that's really all the information you need to find out the area, volume, perimeter, surface area, ect!

Step-by-step explanation: Hope this helps! :)

(I had the same question btw)

Answer:

B. {(-3, 4), (-8,0), (3, -8), (-3, -4)}

Step-by-step explanation:

B. is not a function because the x's repeat in this one.

If the x's repeat then it is not a function.

{(-3, 4), (-8,0), (3, -8), (-3, -4)}

The -3 repeats so it is not a function.

Y can repeat, but x cannot.

Hope this helps ya!!

Answer:

You would say miles per hour.

Answer:

x = -2

Step-by-step explanation:

3/2 (x-5) - 3/2 = 9x/2

3x/2 - 15/2 - 3/2 = 9x/2 ... alldenominator

are 2 so we can multiply all term by 2

2(3x/2 - 15/2 - 3/2 = 9x/2)

3x - 15 - 3 = 9x ... simplify it

3x - 12 = 9x

-12 = 9x - 3x ... take 3x to the left

-12 = 6x ... simplify

6x/6 = -12/6 ... dividing both side by 6

x = -2 ... simplify and solve x

(35x) + (-56) this is an equivalent equation.

Answer:

7x(-4x+5)

Multiplying: -56+35x

Step-by-step explanation:

\(\mathrm{Factor\:assuming\:x\ge-\\\infty}\\\:a^{b+c}=a^ba^c\\x^2 = xx\\-28xx+35x\\-7 \times 4xx + 7 \times 5x\\=7x\left(-4x+5\right)\)

The only reason I had to assume x was any negative number was so that the absolute value did not matter in this instance, therefore making x become a negative number.

The other result, however, came from this:

\(-28\cdot \:2=-56\\=-56+35x\)

Inform me of any concerns. Hope this helps.

Answer:

if it says greatest change then its 6:30 to 7:00

Step-by-step explanation:

Answer:

6:30-7:00

Step-by-step explanation:

The  distance between the shortstop and the pitcher calculated as per the given data is 63.6.

Distance between two consecutive bases = 90 feet

Halfway distance between them will be = 45 feets

therefore, halfway distance between first base and second base = 45 feet

and that between second base and third base = 45 feet

So the distance between the  shortstop and the pitcher using pythagoras theorem

= >SP² = PQ² + QS²

           = 45²  + 45²

            =4050

SP = 63.6

Therefore , the required distance is 63.36feets.

The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle

In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. We can derive the base, perpendicular, and hypotenuse formulas using this theorem.

To learn more about hypotenuse

https://brainly.com/question/14298539

#SPJ4

Let a represent the volume of solution A. If it contains 2% of alcohol, then the amount of alcohol that A contains is 2/100 * a = 0.02a

If A = 200, then the amount of alcohol in A is 0.02 * 200 = 4

Let b represent the volume of solution B. If it contains 7% of alcohol, then the amount of alcohol that B contains is 7/100 * a = 0.07b

The total volume of solution A and B is (a + b)

If the volume of A = 200, then the total volume or resulting mixture is 200 + b

If the mixture contains 5% alcohol, the the amount of alcohol in the mixture is

5/100 * (200 + b)

0.05(200 + b)

By equating the concentrations, we have

4 + 0.07b = 0.05(200 + b)

4 + 0.07b = 10 + 0.05b

0.07b - 0.05b = 10 - 4

0.02b = 6

b = 6/0.02

b = 300

She needs to use 300 milliliters of solution B

Answer:

I saw people trolling your answer here is the answer! I am sorry what people are doing to you!

There is a rectangle and a cylinder

5ft cost 4.50

Area is 643

Now

643x4.5

Answer:

Around 2893.5

average rate of change = -1

Average rate of change formula:

The range is from 1 to 3.

b= 3, a = 1

From the given function, x is greater than 1 when f(x) = -x + 2

when x = 3

f(3) = -3 + 2 = -1

when x = 1

f(1) = -1 + 2 = 1

There are 18 black disks in the bag given that the probability of selecting two disks of the same color is equal to the probability of selecting two disks of different colors.

Let's assume there are x black disks in the bag. So there are 36-x white disks.

The probability of selecting two black disks is (x/36)*((x-1)/35).

The probability of selecting two white disks is ((36-x)/36)*((35-x)/35).

And the probability of selecting one black and one white disk is (x/36)*((36-x)/35).

Since the probability of selecting two disks of the same color is equal to the probability of selecting two disks of different colors, we can set these probabilities equal to each other:

(x/36)((x-1)/35) = (36-x)/36)((35-x)/35)

Expanding both sides and simplifying, we get,

\(x^2\) - x = 36x - \(x^2\)

2\(x^2\) = 36x

\(x^2\) = 18x

x = 0 or x = 18

Since there must be at least some black disks in the bag, we can conclude that there are 18 black disks in the bag.

Read more about Probability:

brainly.com/question/24756209

#SPJ4

Degree of the expressions are,

a) 2

b) 1

c) 1

d) 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

All the expressions are,

a) 5 - p + px - p²

b) 3f - 6

c) - 2a

d) 3y² + 5xy - 27x² + 2

Now, We know that;

The degree of an algebraic expression in more than one variable is the highest sum of the powers of the variables.

Hence, The degree of the expressions are,

a) 5 - p + px - p²

Degree = 2

b) 3f - 6

Degree = 1

c) - 2a

Degree = 1

d) 3y² + 5xy - 27x² + 2

Degree = 2

Thus, Degree of the expressions are,

a) 2

b) 1

c) 1

d) 2

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ9

Answer:

\( {x}^{2} - 12x + 23 = 0\)

\( {x}^{2} - 12x = - 23\)

\( {x}^{2} - 12x + 36 = 13\)

\( {(x - 6)}^{2} = 13\)

x - 6 = +√13

x = 6 + √13

A) 35. 8 million; thirty-five million eight hundred thousand, or thirty-five million eight hundred thousand dollars ,(b)115. 2 thousand; one hundred and fifteen thousand two hundred.(c) 97.8 million eight hundred thousand; 97.8 million eight hundred thousand. or 978 million.

What significance do numbers have?

We need good numeracy skills as parents to assist our children to develop, as patients to grasp healthcare information, and so as politicians to make sense of numbers and economic news. Selections in life were frequently based upon numerical data; in order to arrive at optimal decisions, we must be good at maths.

How are numbers used in everyday life?

Numbers are utilized in a variety of mathematical operations such as summation, subtraction, multiplication, division, percentage, and so on, that we employ in the everyday companies and exchanges. Quantities are numerical symbols representing integers that may be used for numbering, estimating, and doing other arithmetic operations.

To know more about integers click here

brainly.com/question/10930045

#SPJ4

The future value of the deposits at the end of 5 years is approximately $6,138.74.

To calculate the future value of the deposits, we can use the formula for compound interest:

FV = P(1 + r/n)^(nt)

Where: FV is the future value

P is the principal amount (initial deposit)

r is the annual interest rate (3% in this case)

n is the number of times interest is compounded per year (quarterly in this case)

t is the number of years

In this case, the principal amount is $1,000, the annual interest rate is 3% (or 0.03), the number of times interest is compounded per year is 4 (quarterly), and the number of years is 5.

Plugging in these values into the formula, we get: FV = $1,000(1 + 0.03/4)^(4*5)

Calculating this, the future value of the deposits at the end of 5 years is approximately $6,138.74.

Learn more about interest rate at

https://brainly.com/question/32122915

#SPJ11

Answer:

Step-by-step explanation:

According to the table, each value of y (dependent variable) is twice the corresponding value of x (independent variable).

This can be shown as

Correct choice is 2 times

The relationship between the continuity of a function and its derivative can be described as follows: differentiability implies continuity, but continuity does not always imply differentiability. Additionally, differentiability on an interval implies continuity on that interval, and differentiability at an endpoint implies continuity at that endpoint.

The continuity of a function and the derivative of the function are closely related concepts in calculus. Here are some connections that can be made between the two:

1. Differentiability implies continuity: If a function is differentiable at a point, then it must be continuous at that point. In other words, if a function has a derivative at a point, it must also be defined and continuous at that point. This means that the function does not have any jumps, holes, or vertical asymptotes at that point.

2. Continuity does not imply differentiability: Although differentiability implies continuity, the converse is not always true. A function can be continuous at a point but fail to have a derivative at that point. For example, the absolute value function |x| is continuous everywhere but does not have a derivative at x = 0.

3. Relationship between continuity and differentiability on an interval: If a function is differentiable on an interval, then it must be continuous on that interval. However, a function can be continuous on an interval without being differentiable at every point within the interval. For example, the function f(x) = |x| is continuous on the interval [-1, 1], but it is not differentiable at x = 0 within that interval.

4. Relationship between continuity and differentiability at the endpoints: If a function is differentiable on an open interval that includes its endpoint, then the function must be continuous at the endpoint. For example, if a function f(x) is differentiable on the interval (a, b) and has a derivative at the point a, then f(x) must be continuous at x = a.

In summary, the relationship between the continuity of a function and its derivative can be described as follows: differentiability implies continuity, but continuity does not always imply differentiability. Additionally, differentiability on an interval implies continuity on that interval, and differentiability at an endpoint implies continuity at that endpoint.

To learn more about "Derivative of a function":

https://brainly.com/question/12047216

To learn more about "Continuity of a function":

https://brainly.com/question/30089593

#SPJ11

Answer:

3

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

Answer:

0.14

Step-by-step explanation:

1/7 = 0.1428571429.......

round to two decimal places so se look at the 4 which is the second decimal place, and then we see that the number to the right of it is less than 5 and therefore we round down to 4 and not 5.

:) hope this helps, please mark as brainliest!

The value of  \(\bold{\dfrac{1}{7}}\) as a decimal is 0.14.

As we know the value of  \(\dfrac{1}{7}= \overline{0.142857}\), where the line over the 0.142857 represent that the number is repeated decimal or recurring decimal.

But we the value of \(\bold{\dfrac{1}{7}}\) upto 2 decimal only. As the number after 4 in 0.142857 is 2 which is smaller than 5, we can round off the number as 0.14 only.

Hence, the value of  \(\bold{\dfrac{1}{7}}\) as a decimal is 0.14.

To know more visit:

https://brainly.com/question/4893336

Answer:

x = 7

Step-by-step explanation:

3x²+5=152

3x²=147

x²=147/3

x² = 49

x = 7

Answer:

x =±7

Step-by-step explanation:

3x²+5=152

To find x, subtract 5 from each side

3x²+5-5=152-5

3x²=147

Divide each side by 3

3x²/3=147/3

x²=49

Take the square root of each side

\(\sqrt{x^{2} }=\sqrt{49}\)

x =±7

The relation that shows y as a function of x is an equation.

An equation is a mathematical statement that two or more algebraic expressions share equality or equivalence.

Equations are depicted using the equation symbol (=), unlike mathematical expressions, which combine variables, numbers, constants, and values with mathematical operands but without the symbol of equality.

Thus, the relation, y is the dependent variable while x is the independent variable.

Learn more about equations at https://brainly.com/question/2972832.

#SPJ1

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

learn more about Chi-Square here: brainly.com/question/24976455

#SPJ11

Answer:

No solutions

Step-by-step explanation:

3(2y + 4) = 7y + 4 - y

~Simplify both sides

6y + 12 = 6y + 4

~Subtract 12 to both sides

6y = 6y - 8

~Subtract 6y to both sides

0 = 8

Best of Luck!