Find the slope of the line that passes through the pair of points.

(5,-4) AND (9,-4)

USE THE SLOPE FORMULA

Answer:

D. Apothem

Step-by-step explanation:

An Apothem is a line from the center of a regular polygon at right angles to any of its sides.

The correct describes the line the arrow is pointing to in the regular pentagon below is,

⇒ Apothem

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

A regular pentagon is shown in figure.

Now, The line is vertical line.

Hence, From the center of the pentagon to the edge is called ''Apothem.''

Therefore, The correct describes the line the arrow is pointing to in the regular pentagon below is,

⇒ Apothem

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Answer:

$1,968.6

Step-by-step explanation:

Compound Interest = [P * (1 + i)ⁿ] - P

P = principal = $7,500

i = annual interest rate = 6%

n = number of periods = 4 years

Compound Interest = [$7,500 * (1 + 0.06)⁴] - $7,500

Compound Interest = [$7,500 * (1.06)⁴] - $7,500

Compound Interest = [$7,500 * (1.06)⁴] - $7,500

Compound Interest = [$7,500 * 1.26247696] - $7,500

Compound Interest = $9,468.5772 - $7,500

Compound Interest = $1,968.5772

Answer:

y=1.7

Step-by-step explanation:

4y+18=14.7y

18=14.7y-4y

18=10.7y

18/10.7=10.7y/10.7

1.7=y

Answer:

x = [tex]x = \frac{2+r}{p-8}[/tex]

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer:

(2+r)/(p-8) = x

Step-by-step explanation:

-px+r=-8x-2

Add px to each side

-px+r+px=-8x+px-2

r = -8x+px -2

Add 2 to each side

2+r = px-8x

Factor out an x

(2+r) = x(p-8)

Divide each side by (p-8)

(2+r)/(p-8) = x(p-8)/(p-8)

(2+r)/(p-8) = x

Answer:

7 fishes

Step-by-step explanation:

Given the growth of the population of fish which is modeled by the exponential function:

[tex]P(t)=7 \cdot b^t[/tex]

Where:

t=time in weeks after release

b=growth rate of the fish

At t=0

[tex]P(0)=7 \cdot b^0\\P_0=7 \cdot 1 \\P_0=7[/tex]

The initial number, [tex]P_0[/tex] of fish which was released into the lake is 7.

Answer:

56

Step-by-step explanation:

The product of 2 numbers is what you get multiplying them together:

12x4 = 48

Now we need 8 more of that product so:

48 + 8 = 56

Answer:

6(x+3)

Step-by-step explanation:

6x+18

6*x + 3*6

Factor out a 6

6(x+3)

Answer:

a) 0.65

b) 0.1581

Step-by-step explanation:

We are given the following in the question:

Distribution of X:

Mean = 0.125

Standard deviation = 0.05

Distribution of Y:

Mean = 0.350

Standard deviation = 0.10

Solution:

[tex]M = X + 1.5Y[/tex]

a) mean of M

[tex]\mu_M = \mu_X + 1.5(\mu_Y) = 0.125 + 1.5(0.350) = 0.65[/tex]

b) standard deviation of M

If X and Y are independent then,

[tex]Var(X+Y) = Var(X) + Var(Y)\\Var)aX) = a^2Var(X)[/tex]

[tex]Var(M) = Var(X+1.5Y)\\Var(M) =Var(X) + (1.5)^2Var(Y)\\Var(M) = (0.05)^2 + (1.5)^2(0.10)^2 = 0.025[/tex]

Standard deviation of M =

[tex]=\sqrt{Var(M)} = \sqrt{0.025} = 0.1581[/tex]

The mean of M is 0.650. The standard deviation of M is approximately 0.1581.

To find the mean of M, we need to substitute the mean values of X and Y into the equation M = X + 1.5Y. Given that X has a mean of 0.125 and Y has a mean of 0.350, we can calculate the mean of M as follows:

Therefore, the mean of M is 0.650.

To find the standard deviation of M, we can use the fact that X and Y are independent. The formula for the standard deviation of the sum of independent random variables is given by:

σM = √(σX2 + (1.5σY)2)

Given that X has a standard deviation of 0.05 and Y has a standard deviation of 0.10, we can substitute these values into the formula to calculate the standard deviation of M:

Therefore, the standard deviation of M is approximately 0.1581.

Answer:

^C

Step-by-step explanation:

The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,

y = 1/8x²

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

Given that;

The vertex of parabola = (0, 0)

And, The focus of parabola = (0, 2)

Hence, We get;

a = 2

So, The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,

x² = 4ay

x² = 4 × 2y

x² = 8y

y = 1/8x²

Thus, The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,

y = 1/8x²

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Answer:

In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR

Step-by-step explanation:

Probability of a teacher being certified in Cardio-Pulmonary Resuscitation (CPR).

36 of 80

So

[tex]p = \frac{36}{80} = 0.45[/tex]

In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

45% of the days

0.45*180 = 81

In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR

To calculate the number of days a teacher certified in CPR will be on bus duty, use the ratio of certified teachers (9/20) multiplied by the total number of school days (180), resulting in an expectation of 81 days.

The student is asking to calculate the number of days one can expect a teacher certified in CPR to be on bus duty at a local intermediate school. Given that 36 out of 80 teachers are certified in CPR, the ratio of certified to non-certified teachers is 36/80, which can be simplified to 9/20. To find out how many days a teacher on bus duty will likely be certified in CPR, we apply this ratio to the total number of school days, which is 180.

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Answer:

The sixth term;

= 16 + (6-1)4 = 16 +20 = 36

Sixth term = 36

Pattern; a = 16, d = 4

16,20,24,28,32,36...

Completed question;

Chairs for an orchestra are positioned in a curved form with the conductor at the center. The front row has 16 chairs, the second has 20 and the third has 24, and so on. describe the pattern of the sequence. How many chairs are in the 6th row?

Step-by-step explanation:

This scenario can be represented by an arithmetic progression sequence.

nth term of an AP = a + (n-1)d

Where;

a = first term

d = common difference

n = term number

Given;

First term a = 16

Second term = a + d = 20

since a = 16

a+d = 16+d = 20

d = 20-16 = 4

The sixth term;

= 16 + (6-1)4 = 16 +20 = 36

Sixth term = 36

Pattern; a = 16, d = 4

16,20,24,28,32,36...

Answer:

x = 3/4 x 21

Step-by-step explanation:

Answer:

I believe it is #2:

x = 3/4 × 21.

Answer:

[tex]P(\bar X <38)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 38 we got:

[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]

So then we want to find this probability:

[tex] P(z<-1.265)[/tex]

And we can use the normal standard distribution or excel and we got:

[tex] P(z<-1.265)=0.103[/tex]

Step-by-step explanation:

For this case we define the random variable X as the annual income for people at certain city. And we know the following properties:

[tex] E(X) = 42, Sd(X) =42[/tex]

They select a sample size of n = 90>30. So then we can assume that the central limit can be applied.

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

We want to calculate this probability:

[tex]P(\bar X <38)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 38 we got:

[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]

So then we want to find this probability:

[tex] P(z<-1.265)[/tex]

And we can use the normal standard distribution or excel and we got:

[tex] P(z<-1.265)=0.103[/tex]

Answer:

The solution is (0.4;-4.2). I'm not sure since my solution is none of your alternatives, but I don't think I have made any mistakes.

Step-by-step explanation:

Replace the y at the second eq.

-8x-4(2x-5)=-20

-16x+20=-20

-16x=-40

x=0.4

Therefore y equals:

2×0.4-5=-4.2

Answer:

one solution: (2.5,0)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Edge Trust

The value of the h(2), in the given graphed function, is determined as: C. 0.

The value of a function is the corresponding x-value of the function at that particular point or given y-value.

On the given function graph, when h(2), which is y = 2, the corresponding value of x is 0.

Therefore, the value of h(2) is: C. 0.

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Answer:

2 feet

Step-by-step explanation:

We are given that

[tex]b_1=21 feet[/tex]

[tex]b_2=5feet[/tex]

Area of trapezoid=26 square ft

We have to find the height of the cross section.

We know that

Area  of trapezoid=[tex]\frac{1}{2}(b_1+b_2)h[/tex]

Using the formula

[tex]26=\frac{1}{2}(21+5)[/tex]

[tex]26=\frac{1}{2}(26)h[/tex]

[tex]h=\frac{26\times 2}{26}=2 feet[/tex]

Hence, the height of cross section =2 feet

The answer is: No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.

Answer:

The answer is C.

Step-by-step explanation:

Answer:

y=2x+4

y=-1/2x+4

linear quations

both have the same y intercept (=4).

y=2x+4  is positive straight line, slope = 2

y=-1/2x+4 is negative straight line, slope=-1/2

Step-by-step explanation:

Answer:

  8

Step-by-step explanation:

You want to know the number of sunflower plants (S) that can be watered along with 10 lily plants (L) if the water supply is described by ...

  0.7S +0.5L ≤ 11

Substituting 10 for L, we have ...

  0.7S +0.5(10) ≤ 11

  0.7S +5 ≤ 11

  0.7S ≤ 6

  S ≤ 6/0.7 ≈ 8.57

We want to count only plants that can be watered completely, so we need to round this number to the next lower integer.

Ezra can water 8 sunflower plants with the remaining water.

Answer:

  5.1

Step-by-step explanation:

Since there is no diagram provided here, we assume that c is the length of the hypotenuse, so we have ...

  c² = a² +b² . . . . . . Pythagorean theorem

  c² = 2.7² +4.3² = 25.78

  c = √25.78 ≈ 5.0774

  c ≈ 5.1

Answer:

"90% confidence" means there is a probabilty of 90% that the population mean (average compensation for the population of party clowns) lies within the confidence interval.

Step-by-step explanation:

The confidence interval is a range of values in which, according to the level of confidence that is calculated, is likely to include a parameter of the population. In this case, this parameter is the population mean compensation of party clowns.

The level of confidence is 90%, so there is 90% of confidence (or probability) that the population mean compensation for party clowns lie within $9394 and $9926.

None of the options below is correct.

Answer:

The right question that describes what we need to examine is that:

If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%?

Step-by-step explanation:

For hypthesis testing, it is the p-value that needs to be obtained, to know the significance of the result. It is in the definition of what the p-value stands for that one would be able to pick which question best describes what we need to determine?

The p-value is actually defined as the probability of obtaining results as extreme as the observed results in the statistical analysis provided that the null hypothesis is true.

It is the probability of obtaining the claim to be tested that is usually contained in the alternative hypothesis, provided the null hypothesis is true.

So, since the null hypothesis states that the proportion of Millennial students at their campus, that live at home with their parents = 36%

The p-value is how likely it is or the probability that more than 36% of Millennial students at their campus live at home with their parents.

Hope this Helps!!!

Answer:

B?

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D is not a function because for every X value, there may be more than 1 corresponding Y value past 0. For instance, if you input x=1 into this function, you get both 2 and -2, which does not make this a proper function.

Answer:

We reject the null hypothesis

Step-by-step explanation:

In statistical hypothesis testing, the p-value or probability value is the probability of obtaining test results at least as extreme as the results actually observed during the test, assuming that the null hypothesis is correct

Since the p value is less than a, you would reject the null hypothesis and conclude that women take more personal time than men.

Answer:

818.87

Step-by-step explanation:

£650 = $710.76

$1.00 = £0.91

To calculate the surface area of a rectangular pyramid, you need to find the base area and the areas of the triangular faces, then sum them up. In this case, the surface area of the given rectangular pyramid is 65 square millimeters.

The surface area of a rectangular pyramid is calculated by adding the base area to the sum of the areas of the four triangular faces.

Answer:

168 cm³

Step-by-step explanation:

The base area of the oblique hexagonal prism = 42 cm²

the height of the prism = 4 cm

Volume of the prism = Base area × height = 42 cm² × 4 cm = 168 cm³

The volume of the oblique hexagonal prism is 260.00 cubic centimeters. This is calculated by multiplying the base area (65.00 square cm) by the height (4 cm) using the formula Volume = Base Area × Height.

To find the volume of an oblique hexagonal prism, you can use the formula:

Volume = Base Area × Height

You're given that the base area is 42 square cm and the height is 4 cm. Now, let's determine the base shape of the hexagonal prism.

A hexagon has six sides, and each side is an equilateral triangle with an edge length of 5 cm. To find the area of one of these equilateral triangles, you can use the formula:

Area of Equilateral Triangle = (side length^2 * √3) / 4

Area of Equilateral Triangle = (5 cm^2 * √3) / 4 ≈ 10.83 square cm

Since there are six identical triangles in the hexagonal base, the total base area is:

Base Area = 6 * Area of Equilateral Triangle ≈ 6 * 10.83 square cm ≈ 65.00 square cm

Now, you can calculate the volume:

Volume = Base Area × Height

Volume = 65.00 square cm × 4 cm = 260.00 cubic cm

So, the volume of the oblique hexagonal prism is 260.00 cubic centimeters.

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Answer:

P(t) = 100e^[(ln2.4/lne)t]

or

P(t) = 100e^0.87546t

Step-by-step explanation:

see attached picture

Answer:

False, there are infinite solutions

Step-by-step explanation:

Try solving this

3y - 6x = 24

8 + 2x = y

3(8 + 2x) - 6x = 24

24 + 6x - 6x = 24

24 = 24  true