A swimming pool is shaped like the figure below. Each end is a semicircle, and the length and
width of the rectangle are 40 feet and 20 feet, respectively. If there were a -foot-wide cement
border around the pool, what would be the area of the border?

The Volume of the composite figure = Volume of the rectangular prism + Volume of the square pyramid = 4,050 ft³.

The composite figure shown is composed of a square pyramid and a rectangular prism. To find the volume of the composite figure, find the volume of the square pyramid and the volume of the rectangular prims respectively.

Volume of the square pyramid = 1/3(B)(h), where:

Base area (B) = (l)(w) = (15)(15)

Base area (B) = (l)(w) = 225 ft³.

h = 9 ft

Volume of the square pyramid = 1/3(225)(9)

Volume of the square pyramid = 675 ft³.

Volume of the rectangular prism = (length)(width)(height)

Volume of the rectangular prism = (15)(15)(15)

Volume of the rectangular prism = 3,375 ft³.

The Volume of the composite figure = Volume of the rectangular prism + Volume of the square pyramid

The Volume of the composite figure = 3,375 + 675

The Volume of the composite figure = 4,050 ft³.

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Answer:

Step-by-step explanation:

difference=1-(-12)=13°F

Answer:

(-1,1) (-4,1) (-4,3)

Step-by-step explanation:

literally mirror shape A to the y-axis

the original cordinates:

(1,1) (4,1) (4,3)

would now be

(-1,1) (-4,1) (-4,3) because it's reflected

Answer:

C.) 85

Explanation:

Given following:

While solving these function questions, go from right to left.

Steps:

The amount of money she started with is $5750

The given parameters are:

Interest = $115

Rate = 3%

Time = 8 months

The amount she start with (P) is calculated using:

P = I/(RT/12)

This gives

P = 115/(3% * 8/12)

Evaluate the product

P = 115/(0.02)

Divide

P = 5750

Hence, the amount of money she started with is $5750

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Answer:

fraction form: 7/25

Decimal form: 0.28

Step-by-step explanation:

Answer:

Exact form - 13/15

Decimal Form - 0.86

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine

The underlined place is tenths.

Rounding off o the tenth place = 75.7.

The tenths of a number is the first digit after a decimal point. To round off a number to the nearest tenth, if the number next to the tenth digit is not up to 5, let it be assumed as 0.

The underlined place is the tenths. Rounding 75.733 to the nearest tenth would give us: 75.7. This is because the next digit close to 7 is 3. It is not up to 5.

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Using proportions, it is found that:

a) He has 24 videogames left.

b - I) He kept 15 videogames for himself.

b - II) The selling price of a videogame was of $800.

c) He received $15,200 from the sale of the videogames.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Item a:

He has 3/5 of 40 videogames left, hence:

3/5 x 40 = 3 x 8 = 24.

He has 24 videogames left.

Item b:

He kept 5/8 of the 24 videogames, hence:

5/8 x 24 = 5 x 3 = 15.

He kept 15 videogames for himself.

He also sold 9 videogames for $7,200, hence the selling price of one of them is:

7200/9 = $800.

Item c:

Earned $7,200 plus 500 for 16, hence:

T = 7200 + 500 x 16 = $15,200.

He received $15,200 from the sale of the videogames.

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Answer:

62 meters

Step-by-step explanation:

So the area of a rectangle can be defined as: [tex]A = wl[/tex] where A=area, w=width, l=length. So if we plug in the known values we can solve for the unknown, which in this case is the width. So let's plug in the known values:

[tex]2356 m^2 = 38 m * w[/tex]

Divide both sides by 38 m

[tex]62 m = w[/tex]

A bisector is the required line that divides a given line or an angle into two equal parts. The required construction of the bisectors is shown in the attachment to this answer.

Bisection is the process in which a given line or angle is divided into two equal parts by constructing the required bisector. Thus the steps to bisect the given arcs are stated below:

For figure 1:

For figure 2:

For figure 3:

For figure 4:

NB: The point of intersection of the bisectors in relation to arc AC is the radius of the given arc.

The required constructions are attached to this answer.

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Answer:

Step-by-step explanation:

Answer

When you translate either left or right, the x coordinate is the one that you change. To go right when you are dealing with a point, you must add the amount you are asked to go right.  So when you go right 3 units, add 3 to the 5.

(5 + 3,1) = (8,1)

when going across the y axis, you are still only changing the x coordinate.

All you need do is put a minus sign in front of the  x coordinate. So your final answer is (-8,1)

Answer:

h = 2.4

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

271.4 = pi ( 6)^2 *h

271.4 = 36* pi* h

Letting 3.14 = pi

271.4 = 113.04 h

Divide each side by 113.04

271.4 /113.04 = 113.04h/113.04

2.424805379 = h

Rounding to the nearest tenth

2.4 = h

OR if we use the pi button

271.4 = 36 * pi *h

Divide each side by 36 pi

271.4/36pi = h

h=2.3997

Rounding to the nearest tenth

h =2.4

Answer: LCD = 100

Step-by-step explanation:

16/25 = 64/100

13/20 = 65/100

Answer:

A = 120

Step-by-step explanation:

To find angle A we will need to use the law of cosines, since we know the three sides of the triangle.

a^2=b^2+c^2−2*b*c*cosA

(2 sqrt(13)) ^2 = 6^2 + 2^2  + 2 * 6 * 2 cos A

4*13 = 36 + 4 - 24 cos A

52 = 40- 24 cos A

12 = -24 cos A

-1/2 = cos A

Take the inverse cos of each side

cos^-1(-1/2) = cos^-1(cos A)

120 = Cos A  or 240 = Cos A

A cannot be greater than 180 so A = 120

Answer:

A = 120°

Step-by-step explanation:

We can use the cosine rule to solve for angle A, since lengths of all sides are known:

[tex]a^2 = b^2+ c^2 - 2(b)(c) \space\ cos A[/tex]

where a, b, and c are the sides opposites angles A, B, and C respectively.

∴ a = 2√3 , b = 6, c = 2

• Rearranging the formula to make A the subject:

[tex]2(b)(c) \space\ cos A = b^2 + c^2 -a^2[/tex]

⇒  [tex]cos A = \frac{b^2 + c^2 -a^2}{2(b)(c)}[/tex]

⇒  [tex]A = cos^{-1}(\frac{b^2 + c^2 -a^2}{2(b)(c)} )[/tex]

• Now we can substitute the values into the equation to calculate the value of angle A:

[tex]A = cos^{-1}(\frac{6^2 + 2^2 -(2\sqrt{13})^2}{2(6)(2)} )[/tex]

⇒  [tex]A = cos^{-1} (-\frac{1}{2} )[/tex]

⇒  A = 120°

Answer:

x=-12,y=3

Step-by-step explanation:

1/2x+6y=12

y=x+15

since y=x+15

substitute y in first equation, we have

1/2x+6(x+15)=12

open the bracket

1/2x+6x+90=12

1/2x+6x=12-90

x/2+6x= -78

13x/2=-78

13x=2×-78

x=-12

Now x=-12, put x=-12 in the second equation, we have

y=x+15

y=-12+15

y=3

hope it helps

Answer:

x=-8, y=2

Step-by-step explanation:

if 1/2x+6y=12 then 1/2x+y=2 and x+y=1 and y=1-x..if y=1-x then 1-x=x=15 and 2x=16 so x=8 if x=8 then 1/2(8) +6y=12 or 4=6y=12.. then 2y=4 and y=2

The equation of the line of best fit is y = -4.75X + 88.6 and the absolute value of the correlation coefficient is 0.906

The data values of the question are as follows:

(1, 88), (2, 75), (3, 71), (4, 69), (5,66), (6, 68), (7, 50)

To determine the equation of the line of best fit, we make use of a graphing calculator.

From the graphing calculator, we have the following summary:

The line of best fit equation is

y = bx + a

Where

b = SP/SSX = -133/28 = -4.75

a = MY - bMX = 69.57 - (-4.75*4) = 88.57143

So, we have:

y = -4.75X + 88.57143

Approximate

y = -4.75X + 88.6

Hence, the equation of the line of best fit is y = -4.75X + 88.6

In (a), we have:

The value of R is: -0.906.

This represents the correlation coefficient.

The absolute value is

|R| = 0.906.

Hence, the absolute value of the correlation coefficient is 0.906

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Answer:

Should be W

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.

Hope this helps!!

Answer:

32 different ways.

Step-by-step explanation:

There are 2 combinations for each question, and there are 5 questions. Therefore there are [tex]2\times2\times2\times2\times2[/tex] = 32 different ways the student could do the exam.

Have a nice day!

Answer:

3÷8

=37.5%

$704x37.5%

=$264

ANSWER D

it's is a if you didn't know

An approximate linear equation that would model these data is:

(a) B = 0.338t+20.6

The general form of a linear equation in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

We are told that In 1983, 10.8 million adults were in enrolled in a Bachelor Degree program while in 2012, 20.6 million adults were enrolled.

Thus:

Rate of increase = (20.6 - 10.8)/(2012 - 1983)

Rate of increase = 9.8/29 = 0.338

Thus, the equation is:

B = 0.338t+20.6

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The simplification form of the provided expression is 560v¹¹u⁴ after using the property of the exponent.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The complete question is:

How do you simplify:

[tex]\rm 7v^3\cdot \:10u^3v^5\cdot \:8uv^3[/tex]

By using the property of the integer exponent:

[tex]\rm =560v^3u^3v^5uv^3[/tex]

[tex]\rm =560v^{11}u^4[/tex]

or

= 560v¹¹u⁴

Thus, the simplification form of the provided expression is 560v¹¹u⁴ after using the property of the exponent.

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Benefits 1 and 2 in the 'Pros and Cons of Patents' significantly throws light on the opportunity of owning a market, and securing funds respectively.

What is the primary importance of benefits 1 and 2?

Benefit 1 of 'Pros and Cons of Patents' is about the possibility of owning a market.

Since the US government will protect your creation for 20 years, you will essentially control the market for that product during that time. For instance, Eli Lilly invented Prozac in 1987 and had the monopoly for 14 years until 2001.

Benefit 2 of 'Pros and Cons of Patents' concerns around attracting and accumulating the sources of funding and investors.

If an invention is not protected, no one will put their money at risk The only way an invention can ensure a return is through patent protection since investors don't care about good intentions; they only care about money.

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Answer:

According to the article, patents allow inventors to “own the market” for their ideas, meaning the US government has deemed the idea original and protected the idea from being reproduced by others for 20 years. This makes the idea more marketable, which allows the inventor to attract investors. These benefits support the idea that patents promote invention.

Step-by-step explanation: edmentum sample answer

The rewritten form of the expression as a single logarithm is; log {(x+3)²(x-2)^5}/(x-7)³(x²).

The expression given in the task content can be rewritten as a single logarithm by virtue of the laws of logarithms as follows;

2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)

= log(x+3)² - log(x-7)³ +log(x-2)^5-log(x^2)

= log {(x+3)²(x-2)^5}/(x-7)³(x²)

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Using a linear function, it is found that he drove the truck for 240 miles.

A linear function is modeled by:

y = mx + b

In which:

Researching the problem on the internet, there was a base fee of $18.99, which is the y-intercept, and there was an additional charge of 75 cents for each mile driven, which is the slope, hence the cost function for m miles driven is given by:

C(m) = 18.99 + 0.75m.

He paid $199, hence the number of miles he drove is found as follows:

C(m) = 18.99 + 0.75m.

199 = 18.99 + 0.75m

m = (199 - 18.99)/0.75

m = 240 miles.

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Step-by-step explanation:

rules of the logarithm :

e.g.

log(a×b) = log(a) + log(b)

log10(9) = log10(3×3) = log10(3) + log10(3) =

= 0.4771 + 0.4771 = 0.9542

log10(49) = log10(7×7) = log10(7) + log10(7) =

= 0.8451 + 0.8451 = 1.6902

The value of z from the cyclic quadrilateral as described is; 173/22.

Since the quadrilateral TUVW is a cyclic quadrilateral, it follows that the opposite angles of the quadrilateral are supplementary and hence, amount to 180.

On this note, 14z -7 +8z = 360

22z -7 = 180

22z = 180 -7

z = 173/22

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Answer:

350$ for dryer

Step-by-step explanation:

x = cost of dryer
x + 50 = cost of washer

750 = x + (x + 50)
750 = 2x + 50
700 = 2x
350 = x

Answer:

C

Step-by-step explanation:

The formula for the equation of a circle is [tex](x-a)^2+(y-b)^2=r^2[/tex].

Since the center of this circle is (0,0) and the radius is 4, the equation will be [tex]x^2+y^2=4^2[/tex]

Have a nice day!

For Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

A future value refers to a value on a future date based on an assumed growth rate of interest over some period.

The future value can be determined using the FV formula or table.

We can also compute the future value using an online finance calculator as follows:

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $430,000

Results:

PMT = $34,186.97

Sum of all periodic payments = $341,869.70

Total Interest= $88,130.30

Thus, for Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

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