Let h(x) = (fog)(x) = (x - 2)^4. Find f(x) given g(x) = x - 2.


f(x) =

To determine the variance of a sample we can use the following formula:

where

is the mean of the dataset.

The standard deviation is the square root of the variance.

Recall that the mean of a dataset is the sum of the number divided by the number of numbers, therefore, the mean of the given dataset is:

Substituting the above result in the formula for the variance, we get:

Therefore, the standard deviation is:

Answer:

Variance:

Standard deviation:

We are given the equation;

Collect like terms

To check this, we insert the x value into the original equation, if it gives both sides equal, it is correct.

Therefore, the answer is -7

Solution:

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Write the given values

STEP 3: Substitute the values and simplify

We solve the bracket first:

We solve the division operator next:

We do the addition and subtraction simultaneously to have:

Hence, the result of the simplification gives 3

Answer:

last answer is right

( but x can be any number not just x>=0 )

Notation:

μ = mean

σ = standard deviation

Exam A:

The score of the exam is 64, so we calculate the z-score given that scores on the exam are normally distributed. The formula of the z-score is:

Now, for X = 64:

Exam B:

Now, we need to find a z-score equal to that of the score on Exam A. This z-score is -1.8, and the score on exam B should be:

The score on exam B should be 528 in order to do equivalently well as he did on Exam A

The given trinagle is a right angle triangle. let the missing side be x. To find x, we would apply the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

From the triangle,

hypotenuse = 14

one leg = 9

other leg = x

Thus, we have

To the nearest tenth, the length of the third side is 10.7

We have the following:

now, we must give values to x, to be able to graph

The grahp is:

Answer:

15400

Step-by-step explanation:

Hope it helps and I hope you have a nice day!!! :)

BRAINIEST is appreciated it would really help!!!

we have that

The temperature T in degrees Celsius (°C) is equal to the temperature T in Kelvin (K) minus 273.15

so

°C=K-273.15

For T=55°C

substitute

55=k-273.15

solve for k

k=55+273.15

The coordinates of endpoint J which has the midpoint M(–17, 16.5) and endpoint K(–12, 4) is (-22,29)

Mid point:

Midpoint means the point that is in the middle of the line joining two points.

Given two points A (x)1, (y)1 and B (x)2, (y)2, the midpoint between A and B is given by,

M(x)3, (y)3 = [(x)1 + (x)2]/2, [(y)1 + (y)2]/2

where, M is the midpoint between A and B, and (x)3, (y)3 are its coordinates.

Given,

JK has midpoint M(–17, 16.5) and endpoint K(–12, 4).

Here we need to find the coordinates of endpoint J.

We know that formula of mid point through the given definition,

So let us consider

(x1, y1) = (a, b)

(x2, y2) = (-12,4)

Now we have to apply the values on the formula in order to solve it,

Therefore,

(-17, 16.5) = (a + (-12))/2 , (b + 4)/2

Compare the values individually, then we get,

-17 = (a - 12) / 2

-17 x 2 = a - 12

- 34 = a - 12

a = -34 + 12

a = -22

Similarly, when we take the second part,

16.5 = (b+4)/2

16.5 x 2 = b + 4

33 = b+ 4

b = 33 - 4

b = 29

Therefore, the coordinate end points of J is (-22, 29).

To know more about Mid point here.

https://brainly.com/question/11302835

#SPJ1

The next transaction statement can be described through option A) Thirty dollars was withdrawn if the next transaction on his statement shows –$30.

The term "Transaction Statement" refers to a statement that the lender may from time-to-time issue to any borrower, at the borrower's reasonable request or at the lender's option, listing the loans made, the inventory and accounts receivable they financed, as well as the terms and conditions of repayment.

A transaction can be said as a unit of work that is thus performed against a database. These transactions are units or mostly sequences of work that are accomplished in a logical order.

You can find your most recent statement via your bank branch because most banks allow you to generate statements through your online banking platform.

To know more about transactions, visit:

https://brainly.com/question/28390340

#SPJ9

Complete Question

When Levi deposited $40 into his savings account, his bank statement showed the transaction as $40.

If the next transaction on his statement shows –$30, which of these describes the transaction?

A) Thirty dollars was withdrawn

B) Money was neither deposited nor withdrawn

C) $30 was deposited

D) Seventy dollars was deposited

Answer:

The TV is 3 inches tall.

Explanation:

Given that the width of the TV is

And the TV is 5 inch TV, which means its diagonal is;

The height of the TV can be calculated using the Pythagoras Theorem;

substituting the diagonal and the width;

Therefore, the TV is 3 inches tall.

Mathematics is a branch of science that deals with numbers, quantities and shapes. It includes arithmetic, geometric, algebra, calculus and many more. It also refers to the study of relationship between numbers or items.

One example is counting numbers which we are using almost everyday in our life.

1, 2, 3, 4 and so on.

Answer:

Step-by-step explanation:

To solve the equation for x, isolate it on one side of the equation.

Subtract by 8 from both sides.

6x+8-8=50-8

Solve.

50-8=42

6x=42

Divide by 6 from both sides.

6x/6=42/6

Solve.

Divide.

42/6=7

[tex]\Rightarrow \boxed{\sf{x=7}}[/tex]

Therefore, the solution is x=7, which is the correct answer.

I hope this helps, let me know if you have any questions.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6x + 8 = 50}[/tex]

[tex]\large\text{SUBTRACT \boxed{\textsf 8} to BOTH SIDES}[/tex]

[tex]\mathsf{6x + 8 - 8 = 50 - 8}[/tex]

[tex]\large\text{CANCEL out: \boxed{\mathsf{8 - 8}} because it gives you 0}[/tex]

[tex]\large\text{KEEP: \boxed{\mathsf{50 - 8}} because it help solve for the x-value}[/tex]

[tex]\mathsf{6x = 50 - 8}[/tex]

[tex]\large\text{New equation: } \mathsf{6x = 42}[/tex]

[tex]\large\text{DIVIDE \boxed{\mathsf{6}} to BOTH SIDES sides}[/tex]

[tex]\mathsf{\dfrac{6x}{6} = \dfrac{42}{6}}[/tex]

[tex]\large\text{CANCEL out: \boxed{\mathsf{\dfrac{6}{6}}} because it gives you 1}[/tex]

[tex]\large\text{KEEP: \boxed{\mathsf{\dfrac{42}{6}}} because it gives you the x-value}[/tex]

[tex]\mathsf{x = \dfrac{42}{6}}[/tex]

[tex]\mathsf{x = 7}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 7}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: False?

Step-by-step explanation:

Answer:

It is closer to [tex]1[/tex] than [tex]0[/tex], so the statement is True.

Step-by-step explanation:

Step 1: Finding the decimal form of [tex]\frac{8}{11}[/tex]

Upon simplification on a calculator, we can see that the exact value of [tex]\frac{8}{11}[/tex] is:

[tex]0.7272727273[/tex]

Let's round this to [tex]0.73[/tex] for an easier time.

Step 2: Identifying the value's difference from 1 and 0

We have found the value of the fraction to be [tex]0.73[/tex].

If we subtract the value from [tex]1[/tex], we get:

[tex]1-0.73\\=0.27[/tex]

If we find the difference between it and [tex]0[/tex], we get:

[tex]0.73-0\\=0.73[/tex]

As we can see, the value is [tex]0.27[/tex] units away from [tex]1[/tex], but is [tex]0.73[/tex] units away from [tex]0[/tex].

We can clearly see that it is closer to [tex]1[/tex], so the statement is True.

Answer:

Step-by-step explanation:

y = 4 - 2x

The value of angle EFG is 50°.

An angle results from the intersection of two straight lines or rays at a single terminal.

Angles' Components

Vertex: The intersection of two lines or sides at an angle is called a vertex.

Arms: The angle's two sides linked at a single end.

Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line.

∵ exterior angle = sum of opposite interior angles

∴ 7x+18 = (6x-10) + 38

7x + 18 = 6x +28

x = 10°

∴∠EFG = 6*10-10

  ∠EFG = 50°

Option (B) is correct answer.

To know more about angle please visit:

https://brainly.com/question/28451077

#SPJ13

We have the following:

We have that 4 is equal to 64/16

Thefore:

The bar is found in 2 and 15 more lines, each line is 1/16

the length of the shadow is 30m

hypotenuse = 50m

height of tree = 40 m

To solve the question, we will use an illustration:

To get the length of the shadow, we will apply pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

hypotenuse = 50m, opposite = 40m

50² = 40² + shadow²

2500 = 1600 + shadow²

2500 - 1600 = shadow²

900 = shadow²

square root both sides:

Hence, the length of the shadow is 30m

To answer this question, we need to subtract 0.435 to both sides of the equation as follows:

Therefore, the solution for x in this equation is x = 0.485 (last option).

Answer

Explanation

The variable given is x

Five times the variable is 5x

When 4 is added, the expression becomes 5x + 4, which gives the Left Hand Side of the equation.

For the Right Hand Side, four times the number is 4x

7 more than 4x is 4x + 7

Since the result on the Left Hand Side = Right Hand Side, then the required equation is

Now, to find the number x, we shall solve the above equation as follows

Given the function:

To graph the function, we will identify the maximum and the minimum points

As we can see, the coefficient of the function = 1

So, the maximum will be at f = 1

And the minimum will be at f = -1

The period of the function will be as follows:

So, beginning from the point (0, 0) then rise till we reach the maximum at ((1, 0) then complete the sine wave

The graph of the function will be as shown in the following picture:

Answer:

Alternative C - All real numbers.

Step-by-step explanation:

The domain of an function is the set of all possible numbers which x can assume.

As we can see, we have no restrictions for x.

So, the domain is all real numbers.

Answer: Alternative C - all real numbers.

The investment will be worth $7,401.22 after 10 years

Here, we want to calculate the amount the investment will be worth after 10 years

Mathematically, to get this, we will use the compound interest formula;

where A is the amount after 10 years

P is the amount invested which is $5,000

r is the interest rate which is 4%, same as 4/100 = 0.04

n is the number of terms yearly the investment will be compounded. Since the interest rate is annual, then the number of times it will be compounded yearly is 1

t is the number of years which is 10 in this case

Substituting these values, we have;

A = $13,366.37

A = P + I where

P (principal) = $10,000.00

I (interest) = $3,366.37

Answer:

d

Step-by-step explanation:

The number of years must be non-negative. This eliminates all of the options except for d.

The triangle can be drawn as shown below:

The Cosine Rule can be applied in this case. It is given to be:

From the question, we have the following measures:

Therefore, we can substitute and solve as shown below:

Therefore, the measure of angle C will be gotten to be:

The measure of angle C is 44.4°.

To solve this problem it is necessary to simplify the expression.

Step 1. Write the equation as a sum of homogeneous fractions:

Step 2. Simplify the obtained expressions:

Step 3. Rewrite the expression using the simplified terms:

Solution:

In geometry, a line segment is a part of a line that is bounded by two distinct endpoints and contains every point on the line that is between its endpoints. The angle of rotational symmetry or angle of rotation is the smallest angle for which the figure can be rotated to coincide with itself.

A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. The fixed point is called the center of rotation

Rotation of a line does not change the length of the line segments

Reflection does not preserve orientation.

Dilation (scaling), rotation, and translation (shift) do preserve it.

Hence,

The final answer is the THIRD OPTION

To solve the exercise, we can first find the slope of the line that passes through the given points using the following formula:

So, in this case, we have:

Now, we can use the point-slope formula, and we solve for y:

Therefore, the equation of the line that passes through the points (-2, -1) and (-4, -3) in its slope-intercept form is: