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The total area of the regular pentagon prism is 485 square units

The given parameters are:

Base area = 50

Height = 11

Base = 7

Start by calculating the total area of the 5 sides using

Sides = n * Height * Base

Sides = 5 * 11 * 7

Sides = 385

The total surface area is

Total = 2 * Base area + Sides

This gives

Total = 2 * 50 + 385

Evaluate

Total = 485

Hence, the total area of the regular pentagon prism is 485 square units

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The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

In this problem we have the following relationship bewteen the two quadratic equations: g(x) = f(k · x), which means that for all y the following relationship between f(x) and g(x):

[tex]k = \frac{x_{g}}{x_{f}}[/tex]

Let suppose that y = 3, then [tex]x_{f} = - 5.5[/tex] and [tex]x_{g} = - 1.8[/tex], then the value k is:

k = (- 5.5)/(- 1.8)

k = 3.056

The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

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Step-by-step explanation:

Part A: [tex]u^6[/tex] can be written as the square of u³, or [tex](u^3)^2[/tex]. Similarly, [tex]v^6=(v^3)^2[/tex]. Hence, we can write this as a difference of two squares by writing it as

[tex](u^3)^2-(v^3)^2[/tex]

Part B:

We can first factor a difference of two squares a² - b² into (a+b)(a-b). Here, a would be u³ and b would be v³.

[tex](u^3+v^3)(u^3-v^3)[/tex]

We can factor this further by the use of two special formulas to factor a sum of two cubes and a difference of two cubes. These formulas are as follows:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

Since u³ + v³ is a sum of two cubes, let's rewrite it.

[tex]u^3+v^3=(u+v)(u^2-uv+v^2)[/tex]

Since u³ - v³ is a difference of two cubes, we can rewrite it as well.

[tex]u^3-v^3=(u-v)(u^2+uv+v^2)[/tex]

Now, let's multiply them together again to get the final factored form.

[tex]u^6-v^6=(u+v)(u^2-uv+v^2)(u-v)(u^2+uv+v^2)[/tex]

Part C:

If we want to factor [tex]x^6-1[/tex] completely, we can just see that x to the sixth power is just [tex]x^6[/tex] and 1 to the sixth power is just 1. Hence, x can substitute for u and 1 can substitute for v.

[tex]x^6-1=(x+1)(x^2-x(1)+1^2)(x-1)(x^2+x(1)+1^2)\\x^6-1=(x+1)(x^2-x+1)(x-1)(x^2+x+1)[/tex]

We can repeat this for [tex]x^6-64[/tex], as 64 is just 2 to the sixth power.

[tex]x^6-64=(x+2)(x^2-x(2)+2^2)(x-2)(x^2+x(2)+2^2)\\x^6-64=(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)[/tex]

-16t^2 represent the position on the graph on the negative side.

According to the statement

we have given equation is h(t)=5+100t-16t^2 -(1)

And we have to find representation of -16t^2

we know that the equation number (1) represent the Quadratic Equation

And in this we have to solve the Quadratic Equation and find the representation of the given terms. then

h(t)=5+100t-16t^2

5+100t-16t^2 = 0

16t^2 -100t-5 = 0

In this equation 16t^2 represent the equation on the graph.

It means that it shows the position on the graph.

Overall, -16t^2 represent the position on the graph on the negative side.

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Option C. The function that has the table here has  exactly one x-intercept.

As the signs of the functions are changing, we can see that there is a crossing to the x axis.

This tells us that the zero value that we see is the x intercept and there is no other x intercept in the question.

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Answer:

x = 19.1

Step-by-step explanation:

Because this is a right triangle, we can use trigonometry.

Thus, we must use either sine (opposite / hypotenuse), cosine (adjacent / hypotenuse), or tangent (opposite / adjacent).

If we use 33 as the reference angle, the side measuring 16 is the adjacent side and x is the hypotenuse.

Thus, we can use cosine:

[tex]cos 33=\frac{16}{x} \\x*cos33=16\\x=19.0778=19.1[/tex]

There are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.

Given a word of 4 letters of the word "SOLVE".

We are required to find the number of ways the four letters of the word SOLVE if no letter can be used more than once.

Permutation is an arrangement of objects in a definite order of things.

Factorial of a number is the product of it and its lesser numbers upto 1.

Number of letters=4

Number of ways=4!

=4*3*2*1

=24 ways

Hence there are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.

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Answer:

Answer

Answer in decimal

11.8998

The 95th percentile for the average number of residents within five miles of each store is 20219.86.

Given mean of 19000 , sample size of 75 stores and standard deviation of 7600.

We have to find the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores.

We have to first find the margin of error to calculate the upper level of confidence interval.

Margin of error is the difference between the real values and calculated values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the critical value of z at given confidence level.

σ is standard deviation

n is the sample size.

z value at 95% confidence level is 1.39. (one tailed)

Put the values in the formula to get margin of error.

Margin of error=1.39*7600/[tex]\sqrt{75}[/tex]

=10564/8.66

=1219.86

Upper level=19000+1219.86

=20219.86

Hence the 95th percentile is 20219.86 for the average number of residents within five miles of each store in a sample of 75 stores.

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The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team

The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team.

The reason option B is the most biased is because members of a basketball team are typically taller than other people. We know that taller people generally have larger feet, and larger shoe sizes, than shorter people. Thus, choosing only people from this area would lead to a biased sample.

The missing options are;

A) every tenth boy on the school’s phone list

B) every member of the boys’ basketball team

C) every boy in a randomly selected ninth-, tenth-, eleventh-, and twelfth-grade gym class

D) every fifth boy who walks through the front doors of the school in the morning

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Answer:

B)

Step-by-step explanation:

Answer:

Option C more peaked and more widely spread.

Step-by-step explanation:

15 + 35 + 18 + 30 + 25 + 21 + 32 + 16

80 + 78 + 34

192/8 = 24

24 + 22 + 27 + 28

46 + 55 = 101/4 = 25.2

A. 6x²-2x+5, is the quotient of the polynomial.

The value of z-score for a score that is three standard deviations above the mean is 3.

In this question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Let x be the score

let μ be the mean and

let σ be the standard deviations

Now, x =  μ + 3σ

The formula of z-score is

[tex]z_{score} = \frac{x-\mu}{\sigma}[/tex]

⇒ [tex]z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}[/tex]

⇒ [tex]z_{score} = \frac{ 3\sigma }{\sigma}[/tex]

⇒ [tex]z_{score} = 3[/tex]

Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.

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Based on the data set, B. Better measure of center: median. C. Better measure of spread: interquartile range (IQR).

The measure of center should be the median because the mean will be affected by the outliers on the left side.

The IQR will be the best measure of spread because the standard deviation is also affected by the outliers.

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The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).

In this question we have a graph of a quadratic equation translated to another place of a Cartesian plane, whose form coincides with the vertex form of the equation of the parabola, whose form is:

g(x) = C · (x - h)² - k     (1)

Where:

By direct comparison we notice that (h, k) = (5, 1) and C = 1. Now we proceed to check if the points (x, y) = (2, 10) and (x, y) = (8, 10) belong to the parabola.

x = 2

g(2) = (2 - 5)² + 1

g(2) = 10

x = 8

g(8) = (8 - 5)² + 1

g(8) = 10

The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).

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Answer: B

Step-by-step explanation:

looked at the points from the dude above, or below, anyway i hope this helps

Both functions decrease at (-1, 2)

The complete question is added as an attachment

The polynomial function f(x) is represented by the graph.

From the graph, the polynomial function decreases at (-2, 2)

The absolute function is given as;

f(x) = =5|x + 1| + 10

The vertex of the above function is

Vertex = (-1, 10)

Because a is negative (a= -5), the vertex is a maximum.

This means that the function decreases at (-1, ∞)

So, we have

(-2, 2) and (-1, ∞)

Combine both intervals

(-1, 2)

This means that both functions decrease at (-1, 2)

See attachment 2 for the number line that represents the interval where both functions are decreasing

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Hello,

[tex] \frac{5}{4 - m} = \frac{ - 3}{2 + m} [/tex]

[tex]5(2 + m) = - 3(4 - m)[/tex]

[tex]10 + 5m = - 12 + 3m[/tex]

[tex]5m - 3m = - 12 - 10[/tex]

[tex]2m = - 22[/tex]

[tex]m = \frac{ - 22}{2} [/tex]

[tex]m = - 11[/tex]

→ Answer B

Variable m cannot be equal to any of the values −2,4 as division by zero is undefined. Multiply both sides of the equation by (m − 4)(m + 2), the lowest common denominator of 4−m,m + 2.

To find the opposite of 2+m, find the opposite of each term.

Use the distributive property to multiply −2−m by 5.

Use the distributive property to multiply m−4 by −3.

Add 3m to both sides.

Combine −5m and 3m to get −2m.

Add 10 to both sides.

Add 12 and 10 to get 2.

Divide both sides by −2.

Divide 22 by −2 to get −11.

Therefore, the correct option is "B".

Answer:

[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

- 6 ÷ 3 = 12 ÷ - 6 = - 24 ÷ 12 = 48 ÷ - 24 = - 2

this indicates the sequence is arithmetic with explicit rule

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 3 and r = - 2 , then

[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]

Answer:

[tex]\sf \dfrac{-3}{2}(-2)^n[/tex]

Step-by-step explanation:

Explicit formulas are used to represent all the terms of the geometric sequence with a single formula.

  [tex]\sf \boxed{\bf t_n = ar^{n-1}}[/tex]

a is the first term.

r is the common ratio.

r = second term ÷ first term.

   3 , - 6 , 12, - 24, 48 ,........

a = 3

r = -6 ÷ 3 = -2

         [tex]\sf t_n = 3*(-2)^{(n-1)}\\\\[/tex]

             [tex]\sf = 3*(-2)^{n}*(-2)^{-1}\\\\ =3*(-2)^n*\dfrac{-1}{2}\\\\= \dfrac{-3}{2}(-2)^n[/tex]

Check:

[tex]\sf t_1 =\dfrac{-3}{2}*(-2)^1=\dfrac{-3}{2}*(-2) = 3\\\\\\t-2 = \dfrac{-3}{2}*(-2)^2 = \dfrac{-3}{2}*4=-6\\\\\\t_3=\dfrac{-3}{2}*(-2)^3=\dfrac{-3}{2}*(-8)=12[/tex]

Based on the given inequality; x < 9 or x ≥ 14, the possible values of x are $8 and $14

x < 9 or x ≥ 14

From the options

All values less than 9 are

$8

All values greater than or equal to 14 are

$14

Therefore, based on the options given, the possible values of x are $8 and $14

Complete question:

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15

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[tex]f(x) = 3(x + 2)(x - 5)[/tex]

[tex]solving \: f(x) = 0 \\ 3(x + 2)(x - 5) = 0 \\ (x + 2)(x - 5) = \frac{0}{3} \\ (x + 2)(x - 5) = 0 \\ x + 2 = 0 \: \: \: \: \: \: \: \: \: \: x - 5 = 0 \\ x = - 2 \: \: \: \: \: \: \: \: \: \: x = + 5[/tex]

The coordinates of the fourth vertex are (6, -2)

The coordinates of three vertices of a rectangle are given as: (3,7), (-3,5), and (0,-4).

Calculate the slope of the first two coordinates using

m = (y2 - y1)/(x2 - x1)^2

Substitute the known values in the above equation

d = (7 - 5)/(3 + 3)

Let the fourth coordinate be (x, y)

Calculate the slope of the other two coordinates using

m = (y2 - y1)/(x2 - x1)^2

Substitute the known values in the above equation

m = (y + 4)/x

Equate both slope equations

(y + 4)/x = (7 - 5)/(3 + 3)

Simplify the fraction

(y + 4)/x = 1/3

Cross multiply

x = 3y + 12

Let y = -2

So, we have:

x = 3 *-2 + 12

Evaluate

x = 6

Substitute x = 6 and y = -2 in (x, y)

This gives (6, -2)

Hence, the coordinates of the fourth vertex are (6, -2)

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Answer:

18

Step-by-step explanation:

first we divide both parties by 5 making it so that 1/6 =3 and then we multiply  by 6 to make it 6/6 = 18

Percent of the original volume that is removed is; 18%

Formula for volume of a box is;

V = lbh

where;

l is length

b is breadth

h is height

Thus;

V_original = 15 * 10 * 8

V_original = 1200 cm³

Volume for each cube removed = 3 * 3 * 3 = 27 cm³

Since there are 8 corners on the box, then 8 cubes are removed.

So the total volume removed is; 8 * 27 = 216

Thus;

Percent of the original volume that is removed is;

216/1200 * 100% = 18%

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One sample Z Test is used by cate.

According to the statement

The average tuition in Illinois is $28,950 with a standard deviation of $3,470.

Assuming we have a large enough sample, since we are testing one group's mean relative to a hypothesized value, this would be a one-sample z-test.

So, One sample Z Test is used by cate.

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The value of the expression 6/5 * 240 is 288

The expression is given as:

6/5 * 240

Divide 240 by 5

6 * 48

Multiply 6 and 48

288

Hence, the value of the expression 6/5 * 240 is 288

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Using it's concept, the probability of D is 4/7.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, A, B and C all have a probability of 1/7. The sum of all probabilities is of 1 = 100%, hence:

[tex]3 \times \frac{1}{7} + P(D) = 1[/tex]

[tex]P(D) = 1 - \frac{3}{7}[/tex]

[tex]P(D) = \frac{4}{7}[/tex]

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Answer: [tex]y=-2x+6[/tex]

Step-by-step explanation:

The slope of line l is

[tex]\frac{5-1}{0-2}=-2[/tex]

Since parallel lines have the same slope, the slope of the line we need to find is -2.

Substituting into point-slope form,

[tex]y=-2(x-3)\\\\y=-2x+6[/tex]

The value of the expression if x = -1/2 is 15

Given the expression below shown;

f(x) = -6(x - 2)

If the value of x is -1/2, hence;

f(-1/2) = -6(-1/2 - 2)

Simplify

f(-1/2) = -6(-5/2)

f(-1/2) = 6 * 5/2

f(-1/2) = 3 * 5 = 15

Hence the value of the expression if x = -1/2 is 15

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Answer: [tex]\frac{2}{25} +\frac{11}{25}i[/tex]

Step-by-step explanation:

To get the following you have multiply the conjugate. [tex]\frac{(2-i)(3-4i)}{(3+4i)(3-4i)}[/tex]