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Ainat [17]
2 years ago
5

The length of a rectangle is four times its width.

Mathematics
1 answer:
Irina-Kira [14]2 years ago
6 0

Answer:

Length = 24 yd

Width = 6 yd

Step-by-step explanation:

To start out, we can begin by saying that "l" is the length of the rectangle, and "w" is the width.

Since we know that the length (l) is 4 times its width we can say that 4 times the width is equal to its length. We would write this out this way :

4w = l

Next, we know that the perimeter is 60yd (as it is given in the question). We also know that the perimeter of a rectangle is all of its sides, added. Meaning the length plus the length, plus the width and the width. So, we can use the equation :

2l + 2w = p

"p" being the perimeter. And, since the perimeter is 60, we can place in 60 for "p"

2l + 2w = 60

Now we can use this information to combine the terms, and find the width and length. We first do this by noticing that in the first equation, it shows that "l" (the length) is equal to 4w. This means that we can put 4w in place of the "l" in the second equation. We can do this, becuase we know that "l" is equal to 4w. (from the first eqaution)

2 (4w) + 2w = 60

Now, we solve

2 * 4w = 8w

8w + 2w = 10w

So now we have :

10w = 60

To get the width, all we have to do is simply get "w" alone. We can do this by dividing both sides by 10.

10w = 60

/10     /10

w = 6

Therefore, the width is 6.

Now, going back to the first equaiton, we already know that the length is 4 times the width, meaning all we have to do is multiply 6 by 4 to get the length.

6 * 4 = 24.

Therefore, the length is 24.

Lastly, to check and make sure we are correct, we can go back to the second equation. 2l + 2w = 60

2 (24) + 2 (6) = 60

2 * 24 = 48

2 * 6 = 12

48 + 12 = 60

60 = 60

Now, we officially know that the length of the rectangle is 24 and the width is 6.

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Answer:

x = -8

Step-by-step explanation:

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4x - 18 = 6x - 2

Isolate x.

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I hope this helps! :)

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Mandy was making 6 pillows to give as gifts to her family. She needed 5/8 of a yard of material for each pillow. How many yards
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  3 3/4

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  6(5/8) = 30/8 = 3 6/8/ = 3 3/4 . . . yards

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Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65
erma4kov [3.2K]

Answer:

Probability that the sample average is at most 3.00 = 0.98030

Probability that the sample average is between 2.65 and 3.00 = 0.4803

Step-by-step explanation:

We are given that the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65 and standard deviation 0.85.

Also, a random sample of 25 specimens is selected.

Let X bar = Sample average sediment density

The z score probability distribution for sample average is given by;

               Z = \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = population mean = 2.65

           \sigma  = standard deviation = 0.85

            n = sample size = 25

(a) Probability that the sample average sediment density is at most 3.00 is given by = P( X bar <= 3.00)

    P(X bar <= 3) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } <= \frac{3-2.65}{\frac{0.85}{\sqrt{25} } } ) = P(Z <= 2.06) = 0.98030

(b) Probability that sample average sediment density is between 2.65 and 3.00 is given by = P(2.65 < X bar < 3.00) = P(X bar < 3) - P(X bar <= 2.65)

P(X bar < 3) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{3-2.65}{\frac{0.85}{\sqrt{25} } } ) = P(Z < 2.06) = 0.98030

 P(X bar <= 2.65) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } <= \frac{2.65-2.65}{\frac{0.85}{\sqrt{25} } } ) = P(Z <= 0) = 0.5

Therefore, P(2.65 < X bar < 3)  = 0.98030 - 0.5 = 0.4803 .

                                                                             

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