Clark is building a large gazebo for his backyard. It is in the shape of a regular hexagon. Each side of the
gazebo is 12 feet long. The apothem is 10.4 feet. He needs to purchase stones for the floor. It costs $9.50
per square foot for a special type of interlocking stone. Find the cost of the gazebo's floor.
Round to the nearest ten dollars.

Answers

Answer 1

Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.

Given that,

In Clark's backyard, a sizable gazebo is being constructed. It has a typical hexagonal form. The gazebo has 12 feet on each side. 10.4 feet tall is the apothem. He must get stones for the flooring. The price of a particular kind of interlocking stone is $9.50 per square foot.

We have to identify the gazebo's floor's cost.

We know that,

The distance from the center of the regular polygon to the mid point of the side. Here, AB is the chord and AM =BM. O is the center of the circumcircle.

Segments joining the center of a circle to the midpoint of the chord is perpendicular to the chord.

So, OM ⊥AB

In ΔOAB,

AB is the base and OM is the height.

AB = 12 feet

OM = 10.4 feet.

The area of the triangle OAB =1/2×base×height

= 1/2×12×10.4

=62.4 square feet.

A regular hexagon is divided into 6 equilateral triangle having each side  12 feet.

Area of the regular hexagon = 6× area of the one triangle

=6×62.4=374.4 square feet

Cost of inter locking stones = $9.50 per square feet.

Total cost of gazebo's floor = 374.4× 9.50 =$3556.8

Therefore, Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.

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Clark Is Building A Large Gazebo For His Backyard. It Is In The Shape Of A Regular Hexagon. Each Side

Related Questions

Each statement describes a transformation of the graph of f(x)=3/x. which statement correctly describes the graph of y= f(x- 7) + 3?
A It is the graph of f translated 3 units up and 7 units to the left.
B. It is the graph of f translated 7 units down and 3 units to the right.
C It is the graph of f translated 7 units up and 3 units to the
right!
D. It is the graph of f translated 3 units up and 7 units to the right.

Answers

Answer is d hope this helped

Answer:

Pretty Sure its D!

Step-by-step explanation:

A paint store makes lime green paint by mixing 3 parts yellow paint to 1 part blue paint. A clerk mixès 5 parts yellow paint to 2 parts blue paint. did the clerk use the correct ratio of yellow paint to blue paint? Explain.

Answers

Answer:

No

Step-by-step explanation:

The ratio used should have been 6 parts yellow paint to 2 parts blue paint

hope this helps

bruce purchased an 8 ounce can of dr. pepper, there are approximately 30 milliliters in an ounce, which measurement is closest to the amount of dr. pepper bruce purchased in milliliters?

Answers

8 x 30 = 240ml
,,,,,,,,,,,,,,,,,,,,,,,,,,,,


Which of the following are reasons why a bank may establish a multinational operation?

Answers

Answer:

multinational banking operations help a bank prevent the erosion of its traveler's check, tourist, and foreign business markets from foreign bank competition.

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Solve the following equation for aa. Be sure to take into account whether a letter is capitalized or not.
2n= a(d+g)

Answers

The solution to the equation is given as [tex]a = \frac{2n}{(d + g)}[/tex]

How to solve for a in the equation

The equation is given as 2n= a(d+g), we are to make a the subject of the equation

in order to have a stand on its own we would have to divide the two sides of the equation by d + g

hence we would have:

[tex]\frac{2n}{(d + g)} =\frac{a(d+g)}{(d+g)}[/tex]

this would cancel out on the right hand side such that we would have:

[tex]\frac{2n}{(d + g)} =a[/tex]

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Get it right I need this bro

Answers

c because that with the that is that

Every day, Eve runs 12 mile more than the day before. Which equation can be used to discover how many miles Eve runs on x days?

y=x+12y is equal to x plus 1 half

y=12xy is equal to 1 half x

y=5xy is equal to 5 x

y=5+xy is equal to 5 plus x

Answers

Answer:

B) y=1/2x

Step-by-step explanation:

y=1/2x

Please help me with this

Answers

9514 1404 393

Answer:

  3025

Step-by-step explanation:

We observe that increasing x by 1 from 0.5 to 1.5 causes the function value to be multiplied by 55 (from 1 to 55).

So, increasing the x-value by 1 again, from 1.5 to 2.5, will again multiply the function value by 55.

  f(2.5) = 55·f(1.5) = 55^2

  f(2.5) = 3025

how many full cases and additional items are needed to fulfill the order 50 items ordered 12 items per case

Answers

Answer: Your answer is 60 divided by 13 = 4.165.

Step-by-step explanation: You would have to divide 12 out of 50, and that would be a decimal of 4.166666666666667 So you need an aditional 10 items but then another additional suitcase there is an answer to this but it would come out as a decimal or fraction, so you would have to specify what type of object is going into these suitcases, most people would just deal with it and carry it in the hands lol.  

Simplify the following expression: -16 -8/2 + 25 ÷ 5 + 1

A. -18
B. 6
C. 10
D. -6

Answers

D. -6


Calculate -16-8/2+25/5+1

-24/2+5+1

Determine the sign

-12+5+1=-6

Chen tosses a number cube 19 fewer times than Jayden. Chen tosses a number cube 38 times. How many times does Jayden toss a number cube?

Answers

Jayden tosses it 57 times!

Consider the composite function g(f(x)) =x√6.
If f(x) = 3x², what is g(x)?
O g(x)=√2x
Og(x)=√x+3
Og(x)=√6x
O g(x)=√9-x

Answers

So on solving the provided question, we can say that the function g(x) is equal to g(x) = [tex]\sqrt{2x}[/tex]

A composite function is what?

The mathematical procedure known as "function composition" takes two functions, f and g, and creates a function, h = g f, such that h(x) = g. This process involves applying the function g to the outcome of applying the function f to x. When the result of one function is utilized as the input for another, this is known as a composite function. The function f g (x) fg(x) fg(x) fg(x), also known as "f of g of x" or "f g fg fg of x," is the composition of the two functions if we have a function f and another function g.

f(f(x)) = [tex]\frac{x}{\sqrt{6} }[/tex]

f(x) = 3x^2

g(f(x)) = [tex]\frac{3x^2}{\sqrt{6} }[/tex]

g(x) = [tex]\sqrt{2x}[/tex]

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At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean 11.4 minutes and standard deviation 2.6 minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than 12.0 minutes for a random sample of 84 customers. Assuming the wait times among customers are independent, what describes the sampling distribution of the sample mean wait time for random samples of size 84?

Answers

Using the Central Limit Theorem, the sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, the population has:

Mean of 11.4 minutes, thus [tex]\mu = 11.4[/tex].Standard deviation of 2.6 minutes, thus [tex]\sigma = 2.6[/tex]

Samples of 84 are taken, thus, by the Central Limit Theorem:

[tex]n = 84, s = \frac{2.6}{\sqrt{84}} = 0.28[/tex]

The sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.

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I think its either B or D but im not sure

Answers

Answer:

Calculate the number of whole years it takes for the population to decrease from 2180 to less than 1000Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Please help will mark Brainly

Answers

Answer: 12

Step-by-step explanation: There are about 12 grams of carbohydrates in a 8 fluid ounce (240 mL) glass of whole milk. The amount of carbohydrates in milk can vary slightly depending on the type of milk you are drinking. For example, skim milk has slightly fewer carbohydrates (about 11 grams per 8 fluid ounces) than whole milk because the fat has been removed. On the other hand, milk that is high in fat, such as heavy cream, has even more carbohydrates (about 4 grams per fluid ounce).

Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?

Answers

Answer:

The slope of the line through these two points is 0.5, which means that for each hour moving a lawn, 0.5 more lands of area are mowed.

Step-by-step explanation:

Slope of a line:

Suppose we have two points in a line. The slope is the change in y divided by the change in x. It states how much y changes when x changes by 1.

In this question:

x: Time in hours to move a lawn.

y: Area of land.

Two of his points are (3, 1.5) and (5, 2.5).

Change in y: 2.5 - 1.5 = 1

Change in x: 5 - 3 = 2

Slope: 1/2 = 0.5

The slope of the line through these two points is 0.5, which means that for each hour moving a lawn, 0.5 more lands of area are mowed.

You are given 2 parallel lines on the coordinate plane. You are told to translate x + 3,y-2, rotate 180° clockwise about the origin, then reflect over the y-axis. After the transformations you will have what type of lines?

A Intersecting lines
B. The Same Line
C. Parallel Lines

Answers

Since matching angles are formed and the equal corners are congruent when a line joins two parallel lines, one of the choices isc=d.

Parallel lines are what?

Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.

Here,

Given :  vertical angles, A = d also represents a solution.

B+d=180 as a result of b+c=180 therefore

B+d=180 as a result of b+c=180 therefore Since a=d, c=d, and b+d=180, the answer is B,C,E.

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y=x-4 and y=4x+2 graph solution of the systems

Answers

Answer:

(-2,-6)

Step-by-step explanation:

we can solve this system of equations with the substitution method because y is already by itself.

since they are both equal to y, we can set both equations equal to each other.

4x+2=x-4

subtract 2 from both sides

4x=x-6

subtract x from both sides

3x=-6

divide both sides by 3

x = -2

now that we know x, we can plug this value into one of the original equations and solve for y.

y=-2-4

y=-6

so on a graph, these two equations will intersect at the point (-2,-6)

Find perimeter
Simplify answer completely

Answers

Answer:

[tex]perimeter = 14 \frac{3}{4} + 4 \frac{1}{2} + 8 \frac{1}{2} + 10 \frac{2}{5} + 10 \frac{2}{5} + 12 \frac{4}{5} \\ = \frac{59}{4} + \frac{9}{2} + \frac{17}{2} + \frac{52}{5} + \frac{52}{5} + \frac{64}{5} \\ = 61 \frac{7}{20} \: units[/tex]

Write 1 6/7 as an improper fraction.

Answers

Answer:

13/7

Step-by-step explanation:

multiply the 7 x 1 then add 6. 13 would be the numerator.

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Help pls pls help pls pls help

Answers

It's 8, it gave Y so pretty easy from there on

y = 4

y = 1/4 x + 2

______________

4 = 1/4 x + 2

4 - 2 = 1/4 x + 2 - 2

2 = 1/4 x

2 × 4 = 4 × ( 1/4 ) × x

x = 8

Thus the correctly answer is option D.

To determine the inverse of function f,
change f(x) to y, switch
and y,
and solve for
The resulting function can be written as
f(x) = (x - 3.

Answers

Answer:

To determine the inverse of function f, change f(x) to y, switch x and y, and solve for y.

[tex]\frac{1}{8} (x-4)^3[/tex]

Step-by-step explanation:

f(x) = [tex]\sqrt[3]{8x} +4[/tex]

Change f(x) to y: y = [tex]\sqrt[3]{8x} +4[/tex]

Switch x and y: x = [tex]\sqrt[3]{8y} +4[/tex]

Solving for y: x - 4 = [tex]\sqrt[3]{8y}[/tex]

(x-4)^3 = 8y

y = [tex]\frac{1}{8}[/tex][tex](x-4)^3[/tex]

Therefore: inverse of function f = [tex]\frac{1}{8} (x-4)^3[/tex]

The inverse function of f(x) will be f⁻¹(x) = 1/8(x - 4)³.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) is given below.

f(x) = ∛(8x) + 4

Then the inverse function of f(x) will be

Put x = f⁻¹(x) and f(x) = x. Then we have

            x = ∛{8f⁻¹(x)} + 4

∛{8f⁻¹(x)} = x - 4

Cube on both sides, then we have

8f⁻¹(x) = (x - 4)³

 f⁻¹(x) = 1/8(x - 4)³

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Find the GCF of the list of terms.
3x^2,6x^6 and -12x^3

Answers

Answer:

3x²

Step-by-step explanation:

3x²

They would all reduce to 1, 2x^4, and -4x

150, 60, 24,...
Find the 9th term.

Answers

Arithmetic Sequences
Divided by 2.5
150, 60, 24, 9.6, 3.84, 1.536, 0.6144, .24576, 0.098304
The 9th term is 0.098304

Answer this! I WILL GIVE BRAINLIEST TO PERSON WHO GIVES CORRECT ANSWER!!!!!!!!!

Answers

Answer:

An 18-month loan with a 4.75% annual simple interest rate

Step-by-step explanation:

have a good day/night

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A real estate developer wishes to study the relationship between the size of home a client will purchase (in square feet) and other variables. Possible independent variables include the family income, family size, whether there is a senior adult parent living with the family (1 for yes, 0 for no), and the total years of education beyond high school for the husband and wife. The sample information is reported below.
Family Square Feet Income (000s) Family Size Senior Parent Education
1 2,240 60.8 2 0 4
2 2,380 68.4 2 1 6
3 3,640 104.5 3 0 7
4 3,360 89.3 4 1 0
5 3,080 72.2 4 0 2
6 2,940 114 3 1 10
7 4,480 125.4 6 0 6
8 2,520 83.6 3 0 8
9 4,200 133 5 0 2
10 2,800 95 3 0 6
Develop an appropriate multiple regression equation. Which independent variables would you include in the final regression equation? Use the stepwise method.

Answers

Answer:=Answer1 has the regression analysis with all 4 independent variables. Using the stepwise method, we toss the one with the largest non-significant p-value which is Senior Present. Then do another regression analysis with only 3 independent variables. Answer2 has this. From this analysis we can toss education (has the largest non-significant p-value) and do another analysis which is in Answer3. In this analysis we see that Income is not quite significant (p=.0586) at the 0.05 level so we can toss it and do an analysis with Family Size as the only independent variable. This result is given in Answer4. The final regression equation has Family Size as the only independent variable and it can stay in the regression equation because it is statistically significant (p=.0003). The prediction equation is given at the bottom of Answer4. This should answer your question. If not let me know.

Step-by-step explanation:

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I need help with this, I need to simplify but I don't know how

Answers

Answer: solve the same variables

Step-by-step explanation:

1. 3y + 4.1

2. 4x +

3. 5x + 22½

4. 4y²

5. + 25

6. 0

25 Points, will give brainliest


If a basketball has a diameter of 9.4 inches, which is closest to the volume of the ball in cubic inches?


A. 521.62 in

B. 434.89 in

Answers

Answer:

B. 434.89

Step-by-step explanation:

A basketball is a sphere and the volume formula is:

V = 4/3πr³

Given:

d = 9.4

r = 9.4/2

r = 4.7

Work:

V = 4/3πr³

V = 4/3π(4.7)³

V = 4/3π(103.823)

V = 434.89

Based on past experience, the daily revenue, X, for a coffee shop in a city is a normally distributed random variable with a mean daily revenue of $900. The first co-owner of the shop feels that the shop is known throughout the city and as such they could reduce the amount of money spent on advertising without causing a decrease in the population mean daily revenue. The second co-owner is concerned that a reduction in advertising would in fact result in a decrease in the population mean daily revenue. To settle the issue, the first co-owner decides to decrease the advertising dollars for a period of time, during which she will select 64 days at random and compute the sample mean daily revenue. She will then perform a hypothesis test to determine if the sample mean daily revenue provides significant evidence to conclude that the population mean daily revenue is less than $900 when the advertising dollars are reduced. The first co-owner observes a sample mean daily revenue of $892.50 with a sample standard deviation of $24 when the advertising dollars have been reduced. What is the p-value for her test

Answers

Answer:

The p-value for her test is 0.0075.

Step-by-step explanation:

She will then perform a hypothesis test to determine if the sample mean daily revenue provides significant evidence to conclude that the population mean daily revenue is less than $900 when the advertising dollars are reduced.

At the null hypothesis, we test that the mean is less than 900, that is:

[tex]H_0: \mu = 900[/tex]

At the alternate hypothesis, we test that the mean is less than 900, that is:

[tex]H_a: \mu < 900[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

900 is tested at the null hypothesis:

This means that [tex]\mu = 900[/tex]

Sample of 64 days. The first co-owner observes a sample mean daily revenue of $892.50 with a sample standard deviation of $24 when the advertising dollars have been reduced.

This means that [tex]n = 64, X= 892.50, s = 24[/tex]

Value of the test:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{892.50 - 900}{\frac{24}{\sqrt{64}}}[/tex]

[tex]t = -2.5[/tex]

What is the p-value for her test?

The pvalue of the test is the probability of a sample mean below 892.5, which is a left-tailed test for t = -2.5 with 64 - 1 = 63 degrees of freedom.

Using a calculator, the p-value for her test is 0.0075.

which of the following is the solution to the equation 3^X+9=81^X
a) x=-6
b)x=6
c)x=-3
d)x=3

Answers

9514 1404 393

Answer:

  d)  x = 3

Step-by-step explanation:

The given equation resolves to a quartic equation in (3^x). It has a solution near ...

  x = 0.541770946714

__

Perhaps you want the solution to ...

  3^(x+9) = 81^(x)

Rewriting in powers of 3, this is ...

  3^(x+9) = (3^4)^x = 3^(4x)

Taking logarithms base 3 gives ...

  x +9 = 4x

  9 = 3x . . . . . . subtract x

  3 = x . . . . . . . divide by 3 . . . . matches choice D

_____

Additional comment

The Order of Operations requires that exponential terms be evaluated before addition and subtraction. That means (3^x) must be evaluated before the sum (3^x) + 9. If you want the sum of x and 9 to be evaluated first, it must be in parentheses: 3^(x+9).

In typeset equations, the superscript font serves to group parts of the exponent. In plain text, a grouping symbol (parentheses) must be used.

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