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Gemiola [76]
3 years ago
7

The length of a rectangle is three times the width. the parameter is 240 inches. find the length and width​

Mathematics
1 answer:
Bezzdna [24]3 years ago
7 0

Answer:

L = 90 inches

W = 30 inches

Step-by-step explanation:

Give the length of a rectangle L is three times the width

That’s

L = 3w

And perimeter = 240 inches

Recall that the perimeter of a rectangle is given by

P = 2(L + W)

L = 3w

We now have two equations

Now substitute 3w for L in The above formula and 240 for P.

We have

240 = 2(3w + w)

Distribute 2 into (3w + w)

240 = 2 x 3w + 2 x w

240 = 6w + 2w

240 = 8w

Divide both sides by 8

240/8 = 8w/8

30 = w

W = 30inches

Now substitute 30 for w into either of the above equations to get L .

Using

L = 3w

L = 3 x 30

L = 90 inches

L = 90 inches and

W = 30 inches

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Modification has not reduced the number of accidents.

Step-by-step explanation:

H_0: \mu\geq0\\H_a:\mu

                                 A  B  C   D   E   F  G   H

Before modification 5  7  6   4    8   9   8   10

After modification    3  7  7   0    4   6   8    2

Difference                -2 0  1   -4   -4   -3  0   -8

Mean of differences M_d = \frac{sum}{8}=\frac{2+0-1+4+4+3-0+8}{8}=2.5

Standard deviation of differences = \sqrt{\frac{\sum(x-\bar{x})^2}{n}}=2.9277

Formula of paired t test :

t=\frac{M_d}{\frac{s}{\sqrt{n}}}\\t=\frac{2.5}{\frac{2.9277}{\sqrt{8}}}\\t = 2.4152

Df = n-1 = 8-1 =7

t critical = t_{(df, \alpha)}=t_{7,0.01}=2.998

t critical> t calculated

So, We failed to reject null hypothesis

Hence modification has not reduced the number of accidents.

6 0
3 years ago
Last year, Shane grew 2/3 of an inch and his brother grew 1/3 of an inch. How much more did Shane grow than his brother?
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Literal equations 5y-72=7+5x
joja [24]

Step 1. Add 72 to both sides

5y = 7 + 5x + 72

Step 2. Simplify 7 + 5x + 72 to 5x + 79

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3 years ago
What is the length of AC?
sladkih [1.3K]
When the question says that triangle ABC ~ triangle DEF, that means the triangles are similar. This means that their proportions are the same.
In triangle ABC, side length AB is the equivalent of side length DE in triangle DEF.

Since the proportions must be the same, we can take the known side from triangle ABC, find the equivalent of it on triangle DEF, and find the proportions.
We already found that side length AB ~ side length DE.
Now we can divide the lengths to find the proportions.
28 / 8 = 3.5
This means that each side on triangle ABC will be 3.5 times greater than the equivalent side on triangle DEF.

The length of AC in triangle ABC is 3.5 times the length of DF in triangle DEF.
Side length DF is 10.
Multiply 3.5 by 10 to get the length of AC.
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So the length of AC is 35 units.

Answer:
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