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vagabundo [1.1K]
3 years ago
7

A storage box without a top is 18 inches long , 15 inches wide ,and 10 inches high , The outside of the box is painted yellow .

What is the total area that is painted yellow ?
Mathematics
1 answer:
Levart [38]3 years ago
3 0

Answer:

The total area that is painted yellow is 930\ in^{2}

Step-by-step explanation:

we know that

The area of the outside of the box is equal to the surface area of the box minus the area of the top

The area of the outside is

A=B+PH

where

B is the area of the base

P is the perimeter of the base

H is the height of the box

<em>Find the area of the base B</em>

B=(18)(15)=270\ in^{2}

<em>Find the perimeter of the base P</em>

P=2(18+15)=66\ in

we have

H=10\ in

substitute the values

A=270+(66)10=930\ in^{2}

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Graph the circle x2 + y2 + 10x + 6y + 18 = 0.
Minchanka [31]

Answer:

  see below for a graph

Step-by-step explanation:

Completing the square for x and y terms can help you put this in the standard form.

  (x^2 +10x) +(y^2 +6y) = -18

  (x^2 +10x +25) +(y^2 +6x +9) = -18 +25 +9 . . . . add square of half linear coefficient

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3 years ago
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There were 8 judges at a gymnastics competition. Kathleen received these scores for her performance on the uneven parallel bars.
Korolek [52]

Answer:

below

Step-by-step explanation:

mean : 8.8

The mean is the average, so you find it by adding all the numbers together and dividing by n, or how many numbers there are. For this, I added to get 70.4 and divided that by 8 (8 total scores).

70.4/8 = 8.8.

median : 8.85

The median is the middle of the data set, so you put the numbers in increasing order (lowest number to highest number) and then finding the middle of that set. For this set, since there is an even number of numbers (8), you have to find the middle by adding the two middle numbers and dividing by 2.

8.2, 8.7, 8.8, 8.8, 8.9, 8.9, 8.9, 9.2

The middle numbers are 8.8 and 8.9, so you add those together and divide by 2 to get 8.85.  

mode : 8.9

The mode is just what number appears most often. Because 8.9 appears three times in this data set, more than any other number, the mode is 8.9.

b. The mean reflects a typical score because it is the average, and is used most often when someone is expressing a typical or "average" score. It is the score most people are likely to get, and as there are no outliers in this data set, it reflects a typical score for this data set. It is also the same as the mode, or most often score, in this data set.

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Solve for x. X-8 = -20 12 -28 28 2-12​
Semmy [17]

Answer: x = − 10

Step-by-step explanation:

X − 8 = − 20 =

12 − 28 = − 16

28 = − 16

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x = − 10

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2 years ago
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The area is about twenty six thousand six hundred six and sixty three hundredths. Write in a standerd form
jek_recluse [69]
The standard form is 26,663 hope this answers your question
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3 years ago
A cone has radius 9 and a height 12. A frustum of this cone has height 4.
Anettt [7]

Answer:

Part A)

The lower base has a radius of 9 units, and the upper base has a radius of 6 units.

Part B)

5 units.

Part C)

75π or about 235.62 square units.

Step-by-step explanation:

Please refer to the figure below.

The cone has a radius of 9 units and a total height of 12 units.

A frustum of the cone has a height of 4 units.

Part A)

The lower radius of the frustum will simply be 9 units.

For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:

\displaystyle \frac{12}{8}=\frac{9}{x}

Solve for <em>x.</em> Simplify:

\displaystyle \frac{3}{2}=\frac{9}{x}

Cross-multiply:

18=3x\Rightarrow x=6

The upper base has a radius of 6 units.

Part B)

We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:

SH^2=12^2+9^2

Simplify:

SH^2=225\Rightarrow SH=15\text{ units}

Now, find the slant height of the upper cone:

(SH_\text{cone})^2=8^2+6^2=100

So:

SH_\text{cone}=10

Then the slant height of the frustum will be the cone subtracted from the total. Thus:

SH_{\text{frustum}}=15-10=5\text{ units}

Part C)

We can first find the lateral area of the entire cone. The lateral area is given by:

LA=\pi r\ell

The lateral area of the entire cone will be:

LA=\pi (9)(15)=135\pi

The lateral area of the upper cone will be:

LA_\text{cone}=\pi(6)(10)=60\pi

Then the lateral area of the frustum is:

LA_\text{frustum}=135\pi-60\pi =75\pi\text{ units}^2\approx235.62\text{ units}^2

5 0
2 years ago
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