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13. Prove that the functions are inverses by showing that f(g(x))= x and g(f(x)) = x

f(x) = x^3 + 7 and g(x) = ∛(x-7)

the universal set be U = {1, 2, 3,..., 10}, and let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, and C= {2, 4, 6, 8}. the elements of (A-C) - (An B) ={7,10}

Set is a collection of well-defined objects and it has distinct elements. The set formulas include the union, intersection, complement, and difference of sets. Venn diagrams are popularly used to visualize set formulas to arrive at their proof.

The universal set be U = {1, 2, 3,..., 10}, and let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, and C= {2, 4, 6, 8}.

So, to calculate (A-C)-(A∩B)

FIRST A-C= {1, 4, 7, 10} -  {2, 4, 6, 8}.

A - C = { 1,7,10}

A∩B={1,4,}

(A-C)-(A∩B)= { 1,7,10} -{1,4,} = { 7, 10}

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Answer:

you do it step by step so it can be expressed

Answer: To solve for all values of x in the equation x^2 - 2x - 48 = 0 by completing the square, we can follow these steps:

Bring the x term to one side of the equation by adding 2x to both sides: x^2 - 2x = 48

Divide the coefficient of the x^2 term (which is 1) by 2 and square it to find the value to add to both sides of the equation to complete the square: (1/2)^2 = 1/4. Add 1/4 to both sides of the equation: x^2 - 2x + 1/4 = 48 + 1/4

Take the square root of both sides of the equation: (x - 1)^2 = 192 + 1

Solve for x by taking the square root of both sides of the equation: x - 1 = ± √193

Add 1 to both sides of the equation to find the values of x: x = 1 ± √193

So the solutions of the equation are x = 1 + √193 and x = 1 - √193

It is important to notice that these are the solutions in radical form, so they are not exact values of x.

Step-by-step explanation:

Answer:

C 16 km

Step-by-step explanation:

Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

in our case that is

27² = 21.5² + x²

729 = 462.25 + x²

x² = 266.75

x = sqrt(266.75) = 16.33248297... km ≈ 16 km

The probability that exactly seven claims will be received during a given two-week period=1/64.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject because it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

An insurance company determines that N, the number of claims received in a week, is a random variable with P[N = n] = 1/2n+1, where n > 0 .

Let N1 and N2 represent the number of claims during weeks one and two, respectively,

then since N1 and N2 are independent.

[tex]Pr[N_1+N_2=7]=\sum_{n=0}^7Pr[N1=n]Pr[N2=7-n]\\\\=\sum_{n=0}^7\frac{1}{2^{n+1}}\frac{1}{2^{8-n}}\\\\=\sum_{n=0}^7\frac{1}{2^{9}}\\\\=\frac{8}{2^9}=\frac{1}{64}[/tex]

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Answer:

Choice A

Step-by-step explanation:

1/5 = 9/15

2/3 = 10/15

so 3/5 < 2/3

To determine the key terms refer to in the following conducted study in a local community will be as follows:

a. voted, didn't vote, voted will be variable.

b. a group of voters in the community who voted, randomly selected will be sample.

c. the number of eligible voters who actually plan to vote will be population.

d. the number of eligible voters in the study who actually plan to vote statistic.

e. the attendance of a single voter will be data

f. all eligible voters in the comunity will be parameter.

Any quantity calculated from sample values and taken into consideration for statistical purposes is referred to as a statistic (singular) or sample statistic. A population parameter estimate, a sample description, or a hypothesis evaluation are examples of statistical purposes. Statistics are expressed as the average (or mean) of sample values.

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Answer:

Step-by-step explanation:

5 quart to gallon is 1.25

5 quart to cup is 20

5 Quart to oz is 160

5 Quart to tablespoon is 320

Answer: C

f(x) is continuous at z = 3. a-3 Check the option from the following that best represents this information O A. limit f(x) = 2 O B. lim f(x) = 2 OC.

What is a limit?

A limit is given by the value of function f(x) as x tends to a value.

For this problem, at x = 0, we have that to the left the function goes to positive infinity, while to the right it goes to negative infinity, hence:

1. lim f(x) = ∞

x->0-

2. lim f(x) = -∞

x->0+

At x = 2, the function goes to infinity to the left and to the right, hence:

3. lim f(x) = ∞

x->2

To the left of the graph, the function goes to negative infinity, while to the right it goes to 1, hence:

4. lim f(x) = 1

x-> ∞

5. lim f(x) = -∞

x-> -∞

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Answer: this is a function since there is only one value of y for every value of

Step-by-step explanation:

Jennifier was paid $1.49 for each shirt, $4.99 for each pair of slacks and $7.99 for each sports coat.

Two or more expressions with an Equal sign is called as Equation.

Let x = shirts, y = slacks, z = sports coats.

Set up your systems of equations equations.

3x+2y=$14.45..(1)

6x+2y+z=$26.91...(2)

4x+2z=$21.94...(3)

From equation 2

$14.45+3x+z=$26.91

3x+z=12.46...(4)

Multiply equation 4 with 2

6x+2z=24.92..(5)

6x+2z-4x-2z=24.92-21.94

2x=2.98

Divide both sides by 2

x=$1.49

Now plug in x value in equation 1.

3(1.49)+2y=$14.45

4.47+2y=14.45

2y=9.98

Divide both sides by 2

y=$4.99

4x+2z=$21.94

4(1.49)+2z=21.94

5.96+2z=21.94

2z=21.94-5.96

2z=15.98

Divide both sides by 2

z=$7.99

Hence, Jennifier was paid $1.49 for each shirt, $4.99 for each pair of slacks and $7.99 for each sports coat.

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Answer:

yes u would be on track.

Step-by-step explanation:

yes; 10 miles in 12 days is equivalent to 10 ÷ 2 = 5 miles in 12 ÷ 2 = 6 days.

:o)

Equation of parallel line = y = 3x + 2 and equation of perpendicular line 3y = -x + 16, passing through the point (1,5).

(a) To find an equation of the line that passes through the point (1,5) and is parallel to the line y = 3x - 5, we need to use the slope of the given line. The slope of a line is represented by m and it is equal to the coefficient of x. In this case, the slope of the line y = 3x - 5 is 3.

Therefore, the slope of the line that is parallel to y = 3x - 5 is also 3.

We can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope.

Substituting the given point (1, 5) and the slope of 3, we get:

y - 5 = 3(x - 1)

Simplifying the equation, we get:

y = 3x + 2

So, the equation of the line that passes through the point (1, 5) and is parallel to the line y = 3x - 5 is y = 3x + 2

(b) To find the slope of a line that is perpendicular to the line y = 3x - 5, we need to take the negative reciprocal of the slope. The negative reciprocal of 3 is -1/3. So, the slope of a line that is perpendicular to y = 3x - 5 is -1/3

We can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope.

Substituting the given point (1, 5) and the slope of -1/3, we get:

y - 5 = -1/3(x - 1)

Simplifying the equation, we get:

3(y - 5) = -x + 1

3y = -x + 16

So, the equation of the line that passes through the point (1, 5) and is perpendicular to the line y = 3x - 5 is 3y = -x + 16

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We can only say that X+y=21 is a true statement for any values of X and y that satisfy this equation.

In mathematics, elimination is the process of solving a system of equations by eliminating variables. Elimination involves two steps: first, a variable is chosen to be eliminated and then the coefficients of the variable are used to modify the remaining equations so that they contain only the other variables.

To solve for the unknown variables, we can use the following methods:

Graphing: We can graph the equation on a coordinate plane by plotting the line of the equation. The point of intersection of the line with the x and y-axis represents the solution of the system of equations.

Substitution: We can solve for one variable in terms of the other by isolating one variable and substituting it into the other equation.

Elimination: We can eliminate one variable by adding or subtracting the equations to eliminate one of the variables.

In this case, we don't have any other equation to solve the system, so we can not find a unique solution, we can only say that X+y=21 is a true statement for any values of X and y that satisfy this equation.

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The best estimate we can give for the number of orange balls in the tub is 7, and the number of white balls in the tub is 43.

To calculate this, we take the number of orange balls picked (7) and divide it by the total number of balls picked (25) to get the proportion of orange balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of orange balls in the tub.

7 / 25 = 0.28

0.28 x 50 = 14

Similarly, we take the number of white balls picked (18) and divide it by the total number of balls picked (25) to get the proportion of white balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of white balls in the tub.

18 / 25 = 0.72

0.72 x 50 = 36

This method of calculation makes sense because it uses the data we have (the number of orange and white balls picked) to estimate the overall makeup of the tub. By using the proportion of orange and white balls picked, we can make an educated guess about how many of each color ball are in the tub without seeing it.

However, it's important to note that this best estimate is not necessarily accurate. The real number of orange and white balls in the tub could be different. The method used here is a probability method, it's best estimate based on the sample data. The sample data is based on a random selection of 25 balls, and the number of orange or white balls that would be picked could vary depending on the random draw. The more samples we take, the more accurate our estimate would be.

The solution for f(3) in the function is -7772

From the question, we have the following equation that can be used in our computation:

f(x) = 4 − (x + 3)⁵

Also from the question, we have

f(3)

This means that the value of x is 3, and we calculate f(x) when x = 3

Substitute the known values in the above equation, so, we have the following representation

f(3) = 4 − (3 + 3)⁵

Evaluate

f(3) = −7772

Hence, the solution is −7772

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Complete question

Given f ( x ) = 4 − ( x + 3 )^5, find f(3).

To find the probability that the entire batch will be accepted, we need to find the probability that all 6 CDs selected for testing are not defective. This is known as the probability of a "success" in the binomial distribution, which is (1 - population proportion of defective CDs) raised to the power of the number of CDs selected for testing.

The population proportion of defective CDs is 160/1500 = 0.107. So the probability of a CD being not defective is 1- 0.107 = 0.893. Therefore, the probability of all 6 CDs selected for testing are not defective is (0.893)^6 = 0.827 which is about 83%

Therefore, the probability that the entire batch of 1500 CDs will be accepted if 6 CDs are randomly selected for testing is 0.827 or about 83%.

It's worth noting that this method is based on some assumptions and the actual probability might be different.

The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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Answer: Lim (1 - 1/(n + 1)) ^ (n ^ 2) = 1^infinity = 1

Step-by-step explanation: The expression given is the limit of the sequence (1 - 1/(n + 1)) ^ (n ^ 2) as n approaches infinity.

We can start by looking at the exponent first. The n^2 will grow faster than any polynomial function, making the entire expression go to zero as n approaches infinity.

Now let's look at the base (1 - 1/(n + 1))

As n increases, the value of the base becomes closer and closer to 1, since 1/(n+1) becomes smaller and smaller.

Therefore, the limit of the expression is:

Lim (1 - 1/(n + 1)) ^ (n ^ 2) = 1^infinity = 1

As n goes to infinity, the expression goes to 1

Please note that this is true for the limit, for a specific value of n, the expression will not be 1.

Answer:

The limit of (1 - 1/(n + 1)) ^ (n ^ 2) as n approaches infinity is 0.

As n becomes larger, the term 1/(n + 1) becomes smaller and closer to zero, which means that (1 - 1/(n + 1)) becomes closer and closer to 1. Therefore, the expression (1 - 1/(n + 1)) ^ (n ^ 2) becomes closer and closer to 1^(n^2) = 1. And any number powered by infinity (n^2) will be approaching zero, so the limit of the expression is 0.

Total 18 different paths are there from a to b that go through the point circled in the following lattice

In the given question, we have to find how many different paths are there from a to b that go through the point circled in the following lattice.

The diagram of the lattice is given below:

Therefore, we must first go from A to the encircled point.

We must travel 2 horizontally and 2 vertically to do that.

Now, to get to this point, we have ways = [tex]C_{2}^{4}[/tex] ways

Total ways to go from A to the encircled point = [tex]\frac{4!}{2!(4-2)!}[/tex]

Total ways to go from A to the encircled point = 6 ways

Additionally, we must travel 2 horizontal and 1 vertical units to get from the encircling point to B.

As a result, total ways to go from the encircling point to B = [tex]C^{3}_{1}[/tex]

Total ways to go from the encircling point to B = [tex]\frac{3!}{1!(3-1)!}[/tex]

Total ways to go from the encircling point to B = 3 ways

So, different paths are there from a to b = 6×3

Different paths are there from a to b = 18 ways

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Answer:

3/4

Step-by-step explanation:

since they are similar, they have the exact same angles.

angle Q = angle X

tan(angle) = sin(angle)/cos(angle)

that is the same ratio here as

9/12 = 3/4

QN is the answer to the equation that results from combining the slopes and y-intercepts of the equations MP and QR.

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The inequality graphed on the number line is the one on the fourth option, we will get:

x > -2

On the number line we can see that we have an open circle at x = -2 (that means that x = -2 is not a solution to the inequality) and then a line that extends to the right side of that value.

Then the inequality is just the set of all numbers larger than -2, then we will get:

x > -2

That is the graphed inequality, and thus, the correct option is the last one.

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Volume of the solid obtained by rotating the region bounded by the given curves about the specified line is [tex]\frac{24\pi }{5}[/tex]

Now, According to the question:

The shell method formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.

Take a vertical cross section of the region.  The width of the cross section is dx, and the height is [tex]8x^3.[/tex]

Rotate the cross section about the line x = 2.  The height of the shell is  [tex]8x^3.[/tex] the radius is 2 - x, and the thickness is dx.

Volume of shell = 2π(2-x)([tex]8x^3[/tex])dx = 2π([tex]16x^3 - 8x^4[/tex])dx  

Volume of solid  = [tex]2 \pi \int\limits^1_0 [16x3 - 8x4]dx[/tex]

[tex]= 2\pi (4x^4 - (8/5)x^5)^1_0[/tex]  

= 24π/5

Hence,  Volume of the solid obtained by rotating the region bounded by the given curves about the specified line is [tex]\frac{24\pi }{5}[/tex].

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Answer:

see belwo

Step-by-step explanation:

65

increase 10/min

in 15min it'll increase 150

so 65+150 =215

over t mins it'll be 65+10*t

Answer: 215°

t = minutes after being turned on

If the oven temperature increases by 10 per minute, and the initial temperature is 65, this can be represented as:

65 + 10t

After 15 minutes:

65 + 10(15)

65 + 150

215°

If x = temperature of the oven, the temperature of the oven t minutes after being turned on is:

65 + 10t = x

Answer:

f(-2)=14

Step-by-step explanation:

 f(x)=x^2 +2x - 10 and  f=(-2)

f(-2)=-2^2 +2(-2) - 10

4+0+10

14

f(-2)=14

:)

Easy if writing/typing put P L S and an .

If speaking maybe instead say please

Answer:

One bowl has 1 yellow, 1 red, and 2 green apples. The other bowl has 5 each of boysenberries, strawberries, blueberries, and blackberries.

Step-by-step explanation:

For the given situation of number of visitors checkout out the library and 150 are randomly selected the population and the sample is represented  by :

Option B. The population is all the given adult visitors of the library ; and the sample is the 150 selected visitors.

Total population is represented by  all the adult visitors check out the library.

Number of adult visitors examine by the librarian = 150 randomly selected adult visitors.

Here 150 randomly selected adult visitors represents the sample of the whole population.

Therefore, the population and the sample for the given situation of visiting the library is given by :

Option B. The population is all the given adult visitors of the library ; and the sample is the 150 selected visitors.

The above question is incomplete, the complete question is :

A librarian is interested in the numbers of books that visitors check out from the library. She examines the checkout records of 150

randomly selected adult visitors.

Identify the population and sample for this situation.

A The population is all visitors of the library; the sample is the adult visitors

of the library.

B The population is all adult visitors of the library; the sample is the 150

visitors selected.

C The population is all visitors who check out at least 1 book from the

Library; the sample is the 150 visitors selected.

D The population is the 150 visitors selected; the sample is the 150 visitors

who check out at least 1 book from the library.​

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