Suppose a population is known to be approximately normal and you are finding a 98% confidence interval with a sample size of 32. Identify the critical value you will use if you are using a

An appropriate and interesting word for 15,000 is "fifteen thousand," while for 3,000, it is "three thousand."

To solve this question, we need to write the numbers 15,000 and 3,000 as words. To do this, first, we look at the place values of each digit. In 15,000, the "15" is in the thousands place, so we write it as "fifteen thousand." Similarly, in 3,000, the "3" is in the thousands place, so we write it as "three thousand."

By doing this, we have expressed the numbers using their word forms, which helps in understanding and communicating numerical values more effectively, especially in written or spoken contexts. Remember, when writing large numbers as words, we use the place values to guide us in expressing them accurately and understandably.

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The line passes through the same point on figure A and D.

From the figure, we have the original shape to be figure E

The center point of figure E is the origin

This means that a line drawn from the origin that passes through point A must pass through the same point on the shape

From the figure, the line passes through the same point on figure A and D.

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The amount of milk left is given by A = 1.150 Liters of milk = 1150 mL

Given data ,

Let the total amount of milk be = 2 Liters = 2000 mL

Now , Tom gave Kevin 350 ml and Sold 500mL to Bob

So , the remaining amount of milk is given by A

where A = total amount of milk - 350mL - 500mL

On simplifying the equation , we get

A = 2000 - 350 - 500

A = 1150 mL

Hence , the amount of milk left is 1150 mL

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You can look the image.

It is very clear.

Answer:

[tex]\sin (Z)=\sf\dfrac{9}{15}[/tex]        [tex]\cos (Z)=\sf\dfrac{12}{15}[/tex]        [tex]\tan(Z)=\sf \dfrac{9}{12}[/tex]

Step-by-step explanation:

To create trigonometric ratios for angle Z in the given right triangle XYZ, we can use the trigonometric ratios.

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the right triangle XYZ:

Substitute these values into the three ratios to create the trigonometric ratios for angle Z:

[tex]\sin (Z)=\sf \dfrac{O}{H}=\dfrac{9}{15}[/tex]

[tex]\cos (Z)=\sf \dfrac{A}{H}=\dfrac{12}{15}[/tex]

[tex]\tan(Z)=\sf \dfrac{O}{A}=\dfrac{9}{12}[/tex]

The car depreciated at an annual rate of approximately 45.81%.

In 2016, Dave bought a new car for $15,500, and its current value is $8,400. To find the annual depreciation rate, we'll use the formula A(t) = P(1 ± r)t, where A(t) is the future value, P is the initial value, r is the annual rate, and t is the time in years.

Here, A(t) = $8,400, P = $15,500, and t = 1 (one year). We are solving for r, the annual depreciation rate.

$8,400 = $15,500(1 - r)¹

To isolate r, we'll first divide both sides by $15,500:

$8,400/$15,500 = (1 - r)

0.541935 = 1 - r

Now, subtract 1 from both sides:

-0.458065 = -r

Finally, multiply both sides by -1 to find r:

0.458065 = r

To express r as a percentage, multiply by 100:

0.458065 x 100 = 45.81%

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The car depreciated at an annual rate of 12.2%.

The car depreciated in value over time, so we want to find the rate of decrease. We can use the formula:

A(t) = P(1 - r)t

where A(t) is the current value of the car, P is the original price of the car, r is the annual rate of depreciation, and t is the time elapsed in years.

We can plug in the given values and solve for r:

$8,400 = $15,500(1 - r)⁵

Dividing both sides by $15,500, we get:

0.54 = (1 - r)⁵

Taking the fifth root of both sides, we get:

(1 - r) = 0.878

Subtracting 1 from both sides, we get:

-r = -0.122

Dividing both sides by -1, we get:

r = 0.122

Multiplying by 100 to express as a percentage, we get:

r = 12.2%

Therefore, the car depreciated at an annual rate of 12.2%.

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The number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.

From the given histogram,

A. Between the age 20-29 there are 10 members.

B. Under the age of 40 = 10+18

= 28

40 and older = 12+7+2+1

= 22

C) Total staff members = 28+22=50

D) Number of staff members are 50 years or older

= 7+2+1

= 10

Therefore, the number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.

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The solutions to each trigonometric equation are:

Case 6: x = 50.768° (0.282π) or x = 129.232° (0.718π) or x = 230.768° (1.282π) or x = 309.232° (1.718π)

Case 9: x = 41.810° (0.232π) or x = 138.190° (0.768π) or x = 199.471° (1.108π) or x = 340.529° (1.892π)

Case 11: x = 208.164° (1.156π) or x = 331.836° (1.844π)

In this problem we find four cases of quadratic-like trigonometric equations, whose solutions must be found by means of algebra properties and trigonometric formulas. Now we proceed to solve for each case:

Case 6

cos² x + 3 / 5 = 1

cos² x = 2 / 5

cos x = ± √(2 / 5)

x = 50.768° (0.282π) or x = 129.232° (0.718π) or x = 230.768° (1.282π) or x = 309.232° (1.718π)

Case 9

9 · sin² x - 3 · sin x - 2 = 0

sin x = 2 / 3 or sin x = - 1 / 3

x = 41.810° (0.232π) or x = 138.190° (0.768π) or x = 199.471° (1.108π) or x = 340.529° (1.892π)

Case 11

sin² x - 8 · sin x - 4 = 0

sin x = - 0.472

x = 208.164° (1.156π) or x = 331.836° (1.844π)

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A fraction that is greater than 1/2 and less than 4/5, we need to consider fractions between these two values. A fraction that is greater than 1/2 and less than 4/5 is 6/10.

Compare the two given fractions by finding a common denominator.
The lowest common denominator for 1/2 and 4/5 is 10.
Convert both fractions to equivalent fractions with a denominator of 10.
1/2 = 5/10
4/5 = 8/10
Identify a fraction between 5/10 and 8/10.
One possible fraction between these two is 6/10.
A fraction that is greater than 1/2 and less than 4/5 is 6/10.

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(a) Given: f(x) = x^2 + 4x + 3.

The partial fraction decomposition of f(x) is:

f(x) = (x+1)(x+3)

Now, we need to find the integral of this function from 1 to infinity:

∫[1,∞] (x+1)(x+3) dx

Since the integral converges, we can conclude that the series also converges.

(b) This series is not geometric, so we don't know what it converges to. However, we can decompose the given series as the difference of two sums:

Σ(n^2 + 4n + 3) = Σ(n^2) - Σ(4n)

(c) We can use index shifts to make these sums look similar enough to rewrite the expression without Σ:

Σ(n^2) - Σ(4n) = Σ(n^2 - 4n)

(d) To find the limit as B approaches 0, we can evaluate the limit of the expression n^2 + 4n + 3:

lim(B→0) (n^2 + 4n + 3) = n^2 + 4n + 3

So, the limit of the series is n^2 + 4n + 3.

Answer:

There are 16 unit squares on the geoboard. Each unit square represents 5 meters, so the total area is 16*5 = 80 square meters.

Here is a diagram of the geoboard with the unit squares labeled:

[Image of a geoboard with 16 unit squares labeled]

I hope this helps! Let me know if you have any other questions.

A) The equation relates the number of cups of flour to the number of pound cakes that the bakery makes is f = 2.75p

B) Cups of flour are needed for 14 cakes is 38.5

A) The number of cups of flour, f, that a bakery needs for the number of pound cakes that they make, p is directly proportional to each other which can be written in form ,

f/p = 8.25/3

f = (8.25/3)×p

f = 2.75 p

The equation forms is f = 2.75p

B) Cups of flour are needed for 14 cakes

Here p = 14

by putting the value in the equation we get ,

f = 2.75(14)

f = 38.5

hence , cups of flour are needed for 14 cakes is 38.5

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The average rate of change of g(x) from x = 1 to x = 6 is 7

The average rate of change of a function over an interval is given by the difference in the values of the function at the endpoints of the interval, divided by the length of the interval.

In this case, we want to find the average rate of change of g(x) = 2x² - 7x from x = 1 to x = 6.

The value of g(x) at x = 1 is:

g(1) = 2(1)² - 7(1) = -5

The value of g(x) at x = 6 is:

g(6) = 2(6)² - 7(6) = 30

So the difference in the values of g(x) is:

g(6) - g(1) = 30 - (-5) = 35

The length of the interval is:

6 - 1 = 5

Therefore, the average rate of change of g(x) from x = 1 to x = 6 is:

Rate = 35/5

Evaluate

Rate = 7

So, the rate is 7

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The average rate of change is 7.

We know that,

The average rate of change = (final value - initial value)/change in the value of x.

Now,

The given function is,

g(x)=2x²-7x

The initial value of x is 1 (given)

∴ The initial value of the function g(x), at x=1,

g(1)=2(1)²-7(1)=2-7

or, g(1)= -5

Now, the final value of x is 6,

∴ Finding the final value of the function g(x) at x=6,

i.e, g(6)=2(6)²-7(6)

or,  g(6)=72-42 = 30

∴ The change in the value of function g(x), from x= to x=6,

= g(6)-g(1)

= 30-(-5)

= 35

Now, change in the value of x = 6-1=5

∴ The average rate of change = 35/5 = 7

Hence the average rate of change is 7.

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Your answer is D. 1/18  is the probability that she will choose a chocolate bar and then a piece of gum

First, let's determine the total number of snacks in the bag:
4 bags of chips + 5 fruit snacks + 6 chocolate bars + 3 pieces of bubble gum = 18 snacks

Next, let's find the probability of choosing a chocolate bar:
There are 6 chocolate bars and 18 snacks total, so the probability is 6/18, which simplifies to 1/3.

Since she puts the chocolate bar back, the total number of snacks remains the same. Now, let's find the probability of choosing a piece of gum:
There are 3 pieces of gum and 18 snacks total, so the probability is 3/18, which simplifies to 1/6.

Finally, to find the probability of both events happening, multiply the probabilities together:
(1/3) * (1/6) = 1/18

So, the probability that Debra will choose a chocolate bar and then a piece of gum is 1/18. Your answer is D. 1/18.

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The profit per pig is $4 and the profit per goose is $8.

Let's start by defining the variables:

a = number of pigs Farmer Jones raises

y = number of geese Farmer Jones raises

The problem tells us that he wants to raise at most 16 animals, so we can write:

a + y ≤ 16

It also tells us that he wants no more than 12 geese, so we can write:

y ≤ 12

We know that it costs $5 to raise a pig and $2 to raise a goose, and he has $550 available to spend. So the cost of raising the animals can be expressed as:

5a + 2y ≤ 550

Finally, we want to maximize his profits. The profit per pig is $4 and the profit per goose is $8. So the objective function for Farmer Jones' profits is:

Profit = 4a + 8y

To summarize, the linear programming model for this problem is:

Maximize: Profit = 4a + 8y

Subject to:

a + y ≤ 16

y ≤ 12

5a + 2y ≤ 550

where a and y are non-negative integers.

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To evaluate the indefinite integral ∫x tan^2 x dx, we can use integration by parts.

Let u = x and dv = tan^2 x dx. Then, du/dx = 1 and v = ∫tan^2 x dx = tan x - x.

Using the formula for integration by parts, we have:

∫x tan^2 x dx = uv - ∫v du/dx dx
= x(tan x - x) - ∫(tan x - x) dx
= x(tan x - x) + ln|cos x| + C

Therefore, the indefinite integral of x tan^2 x dx is x(tan x - x) + ln|cos x| + C, where C is the constant of integration.
To evaluate the indefinite integral ∫x tan^2(x) dx, we can use integration by parts, which is defined as ∫udv = uv - ∫vdu.

First, let's choose our u and dv:
u = x, so du = dx
dv = tan^2(x) dx

To find v, we need to integrate dv. Since tan^2(x) = sec^2(x) - 1, we get:
v = ∫(sec^2(x) - 1) dx = tan(x) - x

Now, using integration by parts:
∫x tan^2(x) dx = x(tan(x) - x) - ∫(tan(x) - x) dx

Let's evaluate the remaining integral:
∫(tan(x) - x) dx = ∫tan(x) dx - ∫x dx
= ln|sec(x)| - (1/2)x^2 + C

So, the final answer is:
∫x tan^2(x) dx = x(tan(x) - x) - [ln|sec(x)| - (1/2)x^2] + C

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A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles. The volume of a rectangular prism can be found by multiplying the length, width, and height of the prism.

In this case, Sam's box has a height of 1/6 inches, a width of 1/3 inches, and a length of 1/2 inches. To find the volume, we need to multiply these three dimensions:

(1/6) x (1/3) x (1/2) = 1/36 cubic inches.

Therefore, the volume of Sam's box is 1/36 cubic inches, which is an improper fraction because the numerator is greater than the denominator.

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So the polynomial 2x² + x³ - 7x + 1 in standard form is x³ + 2x² - 7x + 1.

To rewrite the polynomial 2x² + x³ - 7x + 1 in standard form, we need to write the terms in descending order of degree.

So we start with the highest degree term:

x³

Then we add the next highest degree term: 2x²

Followed by the next highest degree term: -7x

Finally, we add the constant term: +1

Putting all the terms together, we get:

x³ + 2x² - 7x + 1

So the polynomial 2x² + x³ - 7x + 1 in standard form is x³ + 2x² - 7x + 1.

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We can solve this problem by using some properties of centroids of the triangle and the fact that the centroid divides each median in a 2:1 ratio.

The centroid of a triangle is the point intersection of the three medians of the triangle.

First find the value of MR. The centroid divides each median in a 2:1 ratio, so we have:

MR = 2/3 * R + 1/3 * M

R is the centroid, so R = (P + V + M)/3.

Substituting, we get: MR = 2/3 * [(P + V + M)/3] + 1/3 * M

= 2/9 * P + 2/9 * V + 5/9 * M

Now, substitute the given values of PV and M to find MR:

MR = 2/9 * (3w+7) + 2/9 * (12y-9) + 5/9 * (5x-9) = (2w/3 + 8y/9 + 25x/9) - 1

Simplifying the expression: MR = (2w + 24y + 25x - 27)/9

Next, let's find the value of RP using the centroid. Since R is the midpoint of PV:

RP = 2/3 * R + 1/3 * P

Substituting the values of R and P:

RP = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (3w+7)

= (2w/9 + 8y/9 + 5x/3 + 7/3) + (w+7)/3

= (5w/3 + 8y/9 + 5x/3 + 10)/3

Simplifying this:

RP = (5w + 8y + 5x + 30)/9

Next, find the value of RV using the centroid. R is the midpoint of PV:

So, RV = 2/3 * R + 1/3 * V

Substituting R and V values:

RV = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (12y-9) = (2w/9 + 8y/9 + 5x/3 + 7/3) + 4y/3 - 3

Simplifying: RV = (5w + 20y + 5x - 18)/9

Find the value of RW using the centroid. R is the midpoint of VW, so: RW = 2/3 * R + 1/3 * W

Substituting the values of R and W:

RW = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * 1.75x = (2w/9 + 8y

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For the given data set of miles driven to see a space shuttle launch, the mean is 28.14, the median is 28, and the mode is 28.

To analyze this data, let's find the mean (average), median, and mode.

1. Mean (average): Add all the miles together and divide by the total number of data points.
(19 + 27 + 14 + 28 + 30 + 51 + 28) / 7 = 197 / 7 = 28.14

The mean miles driven to see a space shuttle launch is 28.14.

2. Median: Arrange the data points in ascending order and find the middle value.
14, 19, 27, 28, 28, 30, 51
Since there are 7 data points, the median is the 4th value, which is 28.

The median miles driven to see a space shuttle launch is 28.

3. Mode: Identify the most frequently occurring value in the data set.
14, 19, 27, 28, 28, 30, 51
The number 28 appears twice, which is more than any other value.

The mode for miles driven to see a space shuttle launch is 28.

In summary, for the given data set of miles driven to see a space shuttle launch, the mean is 28.14, the median is 28, and the mode is 28.

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In the next 20 students surveyed, you would expect 5 to own a dog and a cat

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

Dog = 42

Cat = 34

Dog and cat = 15

Neither = 9

This means that

P(Dog and cat) = 15/100

When evaluated, we have

P(Dog and cat) = 5/20

So, when the next 20 students surveyed, we have

Dog and cat = 5/20 * 20

Evaluate

Dog and cat = 5

Hence, the number of dogs and cats is 5

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Cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth

To determine how many more cubic inches of popcorn the jumbo size holds compared to the regular size, you would need to:

1. Find the volume (in cubic inches) of both the jumbo and regular size popcorn containers.
2. Subtract the volume of the regular size container from the volume of the jumbo size container.

Unfortunately, without specific dimensions for the jumbo and regular size popcorn containers, I cannot provide a numerical answer. Please provide the dimensions, and I would be happy to help you with the calculations.

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The surface area of pyramid B to the nearest hundredth is 58.67 cm²

Similar figures are two figures having the same shape. The ratio of the corresponding sides of similar shapes are equal.

The scale ratio of the height of the pyramid A to B is

9/6 = 3/2

Area factor = (3/2)² = 9/4

9/4 = 132/x

9x = 132×4

9x = 528

divide both sides by 9

x = 528/9

x = 58.67cm²

Therefore the surface area of pyramid B is 58.67cm².

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Answer:

Annual % Rate: 26.43%

Amount of time it takes to double: 2.62yr

Step-by-step explanation:

Solving for r(Annual%Rate)

A=P⋅e^(r⋅t)

1405=100⋅^(r⋅10)

1405=100⋅e(^10r)

1405/100=100/100⋅e^(10r)

14.05 = e^(10r)

log(14.05) = log(e^10r)

1.1476 = 10r⋅log(e)

1.1476/log(e) = 10r

1.1476/10⋅log(e) = r

r = 0.26426

=26.43%

Now we have r=26.43%. We can use this information to solve for t, the time period to double the initial investment:

2P = Pe^(rt)

2 = e^(0.2643t)

ln(2) = 0.2643t

t = ln(2)/0.2643

t = 2.62yr

Gabby does not have any fabric left, as she used more fabric than she had to start with.

How much fabric does Gabby have left after using 3215 yards, and what is the estimate?

Based on the information given, Gabby started with 578 yards of fabric and used 3215 yards of fabric. To estimate the amount of fabric Gabby has left, we need to subtract the amount of fabric used from the starting amount of fabric:

578 yards - 3215 yards = -2637 yards

Since the result is a negative number, it doesn't make sense in this context. It's possible that there was a mistake in the numbers given, or Gabby used more fabric than she had to start with.

Without further information or clarification, we cannot estimate the amount of fabric Gabby has left.

To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount of fabric she had initially.

So, to find the estimate for the amount of fabric Gabby has left, we can perform the following calculation:

Estimate for the amount of fabric Gabby has left = 578 yards (initial amount) - 3215 yards (amount used)

Estimate for the amount of fabric Gabby has left = -2637 yards

However, the result is negative, which means that Gabby doesn't have any fabric left, and she needs to purchase an additional 2637 yards to make up for the shortfall.

Therefore, the estimate for the amount of fabric Gabby has left is 0 yards (she needs to purchase more fabric to continue her work).

Answer:

x^9√x

Step-by-step explanation:

The next time they will coincide is on November 21. when Lorena uses a social network every 8 days, Luis logs in every 6 days, and his sister and Alexa log in every 10 days.

To find the time when all three coincided, we need to find the least common multiple (LCM) of 6, 8, and 10. The LCM of 6, 8, and 10 is given as,

6 8 10 | 2

3  4  5 | 3

1   4  5 | 4

1   1  5 | 5

1   1   1

LCM = 2 × 3 × 4 × 5 = 120

if they coincided on July 24, To find the time when all three coincided we need to add 120 days to July 24 to find the next time they will coincide.  if we add 120 days to July 24 we will get the result as November 21.

Therefore, The next time they will coincide is on November 21.

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The question is,

Lorena is a student who uses a social network every 8 days. His friend Luis logs in every 6 days and his sister Alexa logs in every 10 days. If they coincided with their visit to this social network on July 24 when will they coincide next time?

The tomatoes start to get mushy after more than 6 days.

Note: The calculation assumes that the number of tomatoes harvested is large enough for the continuous division process to approach zero.

Let's assume that Marcos initially harvested X cherry tomatoes.

According to the given information, each day Marcos keeps one-third of the tomatoes and brings the remaining amount into the office. This means that after the first day, Marcos would have 2/3 (or 2/3X) of the original harvest left.

On the second day, he would keep one-third of the remaining tomatoes and bring 2/3 × 1/3 (or 2/9) of the original harvest into the office. This would leave him with 2/3 × 2/3 (or 4/9) of the original harvest.

In general, after N days, the amount of tomatoes left can be calculated using the following formula:

Amount of tomatoes left = (2/3)^N × X

The question states that Marcos has less than one eighty-first of the original harvest left when the tomatoes start to get mushy. In other words, when the amount of tomatoes left is less than 1/81 of the original harvest, we can write the following inequality:

[tex](2/3)^N × X < 1/81[/tex]

To find the number of days (N) when the tomatoes start to get mushy, we need to solve for N in the inequality above.

Taking the logarithm (base 2/3) of both sides of the inequality:

[tex]N > log2/3(1/81) / log2/3(2/3)[/tex]

N > 4 / (2/3)

N > 4 × 3/2

N > 12/2

N > 6

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The vocabulary for the segment a is the apothem

The area of the polygon is about 41.6 yd²

The area of a regular figure is the extent of the planer space the figure occupies.

The length of each side of the regular polygon, s = 4 yd

The length of the segment a = 2·√3

The vocabulary term for the segment a drawn from from the center of the polygon and perpendicular to one of its sides is the apothem

Therefore, the vocabulary term for segment a is the apothem

The polygon is a hexagon.

The area of a hexagon is; A = ((3·√3)/2) × s²

Therefore, the area of the polygon is; A = ((3·√3)/2) × (4)² = 24·√3 ≈ 41.6

The area of the polygon is about 41.6 yd²

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Answer:

(Credit to guy/girl above) 63 miles 10 1/2 x 6 is 63.

Step-by-step explanation:

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