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yulyashka [42]
3 years ago
9

Write and equation for each situation. Solve the equation.

Mathematics
1 answer:
aleksley [76]3 years ago
5 0

Answer: The length of the rectangle is 13.5 units and the width is 4.5 units

Step-by-step explanation: The perimeter of the rectangle has been given as 36 units. The formula applied to calculate the perimeter is

Perimeter = 2(L + W)

However the details in the question states that the rectangle is three times as long as it is wide. That is, the length is three times it’s width. So if the width is W then the length is 3W.

Therefore, to calculate the perimeter we shall apply the following;

Perimeter = 2(3W + W)

If the perimeter is given as 36 units, then we have;

36 = 2(4W)

We cross multiply and we have

36/2 = 4W

18 = 4W

Divide both sides of the equation by 4

4.5 = W

So the width is calculated as 4.5, hence the length would be 3W which equals 3 x 4.5 and that equals 13.5

Therefore, Length = 13.5 units and Width = 4.5 units

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Based on the sample of 500 people, 42% owned cats. Calculate the test statistic. Round to two decimal places.
Tanzania [10]

Answer:

z= 3.63

z for  significance level = 0.05 is ± 1.645

Step-by-step explanation:

Here p = 42% = 0.42

n= 500

We formulate our null and alternative hypotheses as

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From this we can find q which is equal to 1-p= 1-0.42 = 0.58

Taking p`= 0.5

Now using the z  test

z= p`- p/ √p(1-p)/n

Putting the values

z= 0.5- 0.42/ √0.42*0.58/500

z= 0.5- 0.42/ 0.0220

z= 3.63

For one tailed test the value of z for  significance level = 0.05 is ± 1.645

Since the calculated value does not fall in the critical region we reject our null hypothesis  and accept the alternative hypothesis that more than 42%  people owned cats.

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3 years ago
The center of a circle is at (2, −5) and its radius is 12.
stiv31 [10]

Answer:

The equation of the circle is (x - 2)² + (y + 5)² = 144 ⇒ A

Step-by-step explanation:

The form of the equation of the circle is (x - h)² + (y - k)² = r², where

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∴ (x - 2)² + (y + 5)² = 144

∴ The equation of the circle is (x - 2)² + (y + 5)² = 144

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