Emily was checking to see if f(x) and g(x) are inverses of each other. She found that f (g(x))
(gof)(x) = +1. She concluded that f(x) and g(x) are inverses.
Was she correct? Choose the BEST answer.
- O Yes, because both f(g(x)) equals x.
O Yes, because she found f(g(x)) and g(f(x)).
O No, because f(g(x)) does not equal g(f(x)).
O No, because f(g(x)) and g(f(x)) do not both equal x.
= and

Answer: (8,1)

Step-by-step explanation:

Line AB has a length of (14-4) = 10 units.  2/5 of that length is (2/5)*(10) = 4.  The new point would be (8,1).

Christian's party had 15 attendees, The cost of renting a private room at a restaurant is $400, and there is an additional charge of $25 for each person who attends.

The total cost for Christian's party at the restaurant was $775. To determine the number of people who attended the party, we subtract the cost of renting the room from the total cost and then divide the remaining amount by the per-person charge. Christian's party had 14 attendees.

Let's assume the number of attendees at Christian's party is denoted by 'x'. The total cost of the party is the sum of the cost of renting the room and the cost per person multiplied by the number of attendees:

Total cost = Cost of renting room + (Cost per person * Number of attendees)

We are given that the cost of renting the room is $400 and the total cost is $775. Therefore, we can write the equation as:

$775 = $400 + ($25 * x)

To determine the number of attendees, we rearrange the equation:

$375 = $25 * x

Dividing both sides of the equation by $25:

15 = x

Therefore, Christian's party had 15 attendees.

To learn more about total cost click here : brainly.com/question/30355738

#SPJ11

Answer:

576

Step-by-step explanation:

5 + 3 = 8

5 - 2 = 3

8 x 3 = 24

24 to the second power is 576

Answer:

27x+5

Step-by-step explanation:

5+3x(5-2)^2

5+3x(3)^2

5+3x*9

5+27x

27x+5

The given series 23−36+49−512+615−−− converges.

Given series is 23, −36, 49, −512, 615 ...

We can write the given series as ∑[infinity]n=1 an, where:

an = (-1)n+1 * n2

In order to test the convergence or divergence of the given series, we can use the Alternating series test.

Using Alternating Series Test:

If an alternating series satisfies the following three conditions, then the series converges:

Condition 1: The series must be alternating.

Condition 2: The absolute value of each term in the series must be decreasing.

Condition 3: The absolute value of each term in the series must approach zero.

In the given series, we observe that each term in the series is positive and the terms are decreasing. Thus, it satisfies the Condition 2 and Condition 3.

Now, let us take the partial sums of the given series,

s1=23

s2=23-36=-13

s3=23-36+49=36

s4=23-36+49-512=-476

s5=23-36+49-512+615=139

Here, we see that the sign of the sum is alternatively changing and we can infer that the series is an alternating series. Since this series satisfies all the 3 conditions of the alternating series test, it is convergent.

Hence, the given series converges.

To learn more about convergent series visit : https://brainly.com/question/15415793

#SPJ11

Answer: You can search it up...

Step-by-step explanation: Have a nice day!

Answer:

- 2

Step-by-step explanation:

Step 1:

- 7b - 3 = - 3b + 5           Equation

Step 2:

- 3 = 4b + 5        Add 7b on both sides

Step 3:

- 8 = 4b         Subtract 5 on both sides

Step 4:

b = - 8 ÷ 4        Divide

Answer:

b = - 2

Hope This Helps :)

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

To know more about Greek visit:

brainly.com/question/30200246

#SPJ11

The number is 320 and 80 % of the number is 256

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the equation A is

65% of a number is 208 and 15% of the same number is 48

So , 65% of n = 208   be equation (1)

15% of n = 48   be equation (2)

Now , on simplifying the equations , we get

( 15 / 100 ) x n = 48

15n/100 = 48

Multiply both sides by 100 . we get

15n = 4800

Divide by 15 on both sides of the equation , we get

n = 320

The number n can also be determined by

( 65% - 15% ) of n = 208 - 58

50 % of n = 160

So , 100 % on n = 160 x 2

n = 320

Therefore , the number n is 320

Now , the 80 % of the number n is A = 80/100 x 320

A = 320 x 0.8

A = 256

Therefore , the value of A is 256

Hence , The number is 320 and 80 % of the number is 256

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Answer:

1/2, or 0.5

Step-by-step explanation:

Answer:

1, 3, 4 is the answer

Step-by-step explanation:

just did it on edge

The solution for p(-2) in the function when the function p(n) = 2n is -2

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

p(n)=2n

To make the equation legible, we need to rewrite it

So, we have the following representation

p(n) = 2n

Also from the question, we have

p(-1)

This means that the value of n is -1, and we calculate p(n) when n = -1

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

p(-1) =  2 * -1

So, we have the following equation

p(-1) =  2 * -1

There is no constant to add or subtract to both sides of the equation

So, we have the following representation

p(-1) =  -2

Hence, the solution is -2

Read more about functions at

brainly.com/question/28277110

#SPJ1

Answer:

6x + 3

Step-by-step explanation:

3(2x + 1)

=3*2x + 3*1

=6x + 3

Answer:

Hi there, this should be the correct answer!

x = -1 - 1/2y

y = -2 - 2x

Step-by-step explanation:

Work I did, hope this helps:

y + 4 = -2x + 2

y + 2x = -2

2x = -2 - y

x = -1 - 1/2y

y = -2 -2x

Hope this helped!

Answer:

(I'm assuming you find how many miles in a minute.) 0.013 miles.

Step-by-step explanation:

So in order to find the amount of miles in a minute you are going to divide it.

10/3 divided by 85/3 = 0.013 miles in a minute.

The speed is equivalent to 2/17 miles/minutes.

Given is the statement -

28 1/3 minutes to run 3 1/3 miles

We can calculate the speed as -

s = x/t

s = 3\(\frac{1}{3}\) / 28\(\frac{1}{3}\)

s = (10/3)/(85/3)

s = 10/3 x 3/85

s = 10/85

s = 2/17

Therefore, the speed is equivalent to 2/17 miles/minutes.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

Answer:

Hard

Step-by-step explanation:

I don't know sorry

Answer:

8x20+22

160+22

182.

48x4= 192 (closest to 182) since you can’t have a remainder of kids.

(I’m in 6th grade so I hope I helped and didn’t get it wrong)

So the answer is 4 or 5 busses.

For your first answer 2=x+5/17 your second answer is 29. This is because "x" is the number that you need to bake which is 29. Therefore, 31/17=2

If bx = by in the cross product or vector product, the unit-vector notation of the resulting vector would be (0, 0, 1) or simply k-hat.

In the cross product or vector product of two vectors, the resulting vector is perpendicular to both of the original vectors. The direction of the resulting vector is determined by the right-hand rule, where the thumb represents the direction of the cross product.

If bx = by, it means that the x-component of the first vector is equal to the y-component of the second vector. In this case, the resulting vector will have an x-component and y-component of zero.

Since the resulting vector must be perpendicular to both vectors, its z-component must be non-zero. Therefore, the unit-vector notation of the resulting vector would be (0, 0, 1), where the z-component (k-component) is 1.

If bx = by in the cross product, the resulting vector in unit-vector notation would be (0, 0, 1) or simply k-hat. This indicates that the resulting vector has zero components in the x and y directions and a non-zero component in the z direction.

To know more about vector , visit;

https://brainly.com/question/24256726

#SPJ11

Answer:

B 136.8 cm²

Step-by-step explanation:

Add the diameters of the three smaller circles to find the diameter of the largest circle.

D = 3 cm + 2.5 cm + 1.1 cm = 6.6 cm

area = πr²

area = 3.14 × (6.6 cm)²

area = 136.8 cm²

Answer:

$10,000.

Step-by-step explanation:

You divide by 95% ( = 0.95)

So it is 9500 / 0.95.

= 10000

the estimate of the slope parameter of the regression is approximately -0.11 (rounded to two decimal places).To determine the slope estimate of the linear least squares regression, we can use the formula:

b = Σ((xi - x)(yi -y )) / Σ((xi -x )^2)

Where:
b = slope estimate
xi = x-valuimax of the data point
x = mean of the x-values
yi = y-value of the data point
y = mean of the y-values

First, we need to calculate the means of the x-values and y-values:

x= (0 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 8 = 5.125
y  = (3 + 4.2 + 3.7 + 4.3 + 4.2 + 4.5 + 4.6 + 5.1) / 8 = 4.35

Next, we can calculate the numerator and denominator of the slope estimate formula:

Numerator:
Σ((xi - x)(yi - y )) = (0 - 5.125)(3 - 4.35) + (3 - 5.125)(4.2 - 4.35) + ... + (9 - 5.125)(5.1 - 4.35) = -5.83

Denominator:
Σ((xi - x )^2) = (0 - 5.125)^2 + (3 - 5.125)^2 + ... + (9 - 5.125)^2 = 52.375

Finally, we can calculate the slope estimate:

b = -5.83 / 52.375 ≈ -0.11

Therefore, the estimate of the slope parameter of the regression is approximately -0.11 (rounded to two decimal places).

 To learn more about slope click here:brainly.com/question/3605446

#SPJ11

Answer:

C. P = 30

Step-by-step explanation:

Parallelogram opposite (or parallel) sides are equal,

so:

2x = x + 2

5y - 9 = 2y + 3

For x:

2x = x + 2

2x - x = 2

x = 2

For y:

5y - 9 = 2y + 3

5y - 2y = 3 + 9

3y = 12

y = 4

the smallest sides are equal 2x and x + 2 => 2 * 2 = 4

the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11

P = 2 * (a + b)

P = 2 * (4 + 11)

P = 2 * 15

P = 30

well, we know the first $25,000 is taxed at 8%, wait a second!!!!! Chris didn't make 25,000 bucks, he only made $17,000, so he'd be in the range of $0 - $25,000 because $17,000 is in that range, that means he owes 8% of 17,000

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 17000}}{\left( \cfrac{8}{100} \right)17000}\implies 1360\)

The amount Chris owes in tax is $1360.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The first $25,000 is taxed at 8%.

This means,

Amount from 0 to $25000 is taxed at 8%.

Now,

Chris earned = $17,000

Tax amount.

= 8% of 17,000

= 8/100 x 17,000

= 8 x 170

= $1360

Thus,

The tax amount is $1360.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

Linear Approximation:

L(x) ≈ 3 - 3x

A linear approximation is an estimation of a function using a tangent line at a specific point. In this case, we are given the function g(x) = 3/(1 + x) and we need to find its linear approximation, L(x), at a = 0.

To obtain the linear approximation, we first find the derivative of g(x) with respect to x. Taking the derivative of g(x) using the quotient rule, we get:

g'(x) = (-3)/(1 + x)²

Next, we evaluate g'(x) at x = 0 to find the slope of the tangent line at that point:

g'(0) = (-3)/(1 + 0)² = -3

The linear approximation, L(x), is given by the equation of the tangent line, which has the form y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values we have:

L(x) = -3x + b

To find the y-intercept, we substitute x = 0 into the original function:

g(0) = 3/(1 + 0) = 3

Since the y-intercept of the tangent line matches the y-value of the function at that point, we have b = 3. Thus, the linear approximation is:

L(x) ≈ 3 - 3x

Learn more about: Linear Approximation:

brainly.com/question/30403460

#SPJ11

Answer: 5.5 years

Step-by-step explanation:

Half life, T = 0.693/ decay constant

⇒ decay constant = 0.693/10.76 = 6.4405 × 10^(-2)

Now, ㏑(0.7) = - 6.4405 × 10^(-2) × t

⇒t = ㏑(0.7)/(-6.4405 × 10^(-2))

⇒t = 5.53 y

The height of the cylinder is 4 feet.

The volume of a cylinder can be found as follows;

volume of a cylinder = base area × height

Therefore,

base area = πr²

volume of the cylinder = 48π ft³

base area = 12π ft²

Therefore, let's find the height of the cylinder as follows:

48π = 12π × h

divide both sides of the equation by 12π

h = 48π / 12π

h = 4 ft

Therefore,

height of the cylinder  = 4 feet

learn more on volume here: https://brainly.com/question/28512386

#SPJ1

Answer:

x = 120°

Step-by-step explanation:

We are given;

sec²x + 4secx = -4

Rearranging gives;

sec²x + 4secx + 4 = 0

Factorizing the left hand side gives;

(sec x + 2)(sec x + 2) = 0

This means that;

(sec x + 2) = 0

From trigonometry, we know that sec x = 1/cos x

Thus;

(1/cos x) + 2 = 0

1/cos x = -2

cos x = -1/2

cos x = -0.5

x = cos^(-1) -0.5

x = 120°

If a logical vector z has at least one entry TRUE, the function all(!z) will always be false.

If a logical vector contains only TRUE items, the all() method returns FALSE; otherwise, it returns TRUE.

The any() function, on the other hand, gives a result of TRUE if a logical vector has at least one element that is TRUE and FALSE otherwise.

any(z) will always be TRUE if z contains at least one TRUE element since there is at least one TRUE element. On the other hand, depending on whether all of the components of z are TRUE, all(z) may or may not be TRUE.

any(!z) will always return FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.

Additionally, all(!z) will always return FALSE if any element is FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.

Learn more about propositional logic in discrete mathematics here:

https://brainly.com/question/1103576

#SPJ4

The z-score for an individual midge that spends 12. 7 days in its larval stage is -0.636

Given,

The mean number of days that the midge Chaoborus spends in its larval stage = 14.1 days

Standard deviation = 2.2 days

We have to find the z-score for an individual midge that spends 12. 7 days in its larval stage;

Now,

z score = (x - μ) / σ

Here,

x = 12.7

Mean, μ = 14.1

Standard deviation, σ = 2.2

Then,

z score = (x - μ) / σ = (12.7 - 14.1) / 2.2 = -0.636

That is,

The z-score for an individual midge that spends 12. 7 days in its larval stage is -0.636

Learn more about z score here;

https://brainly.com/question/14695092

#SPJ4