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fredd [130]
3 years ago
10

A circle with a radius of 4 in. is dilated by a scale factor of 1/2

Mathematics
2 answers:
Lunna [17]3 years ago
7 0
Radius after dilation = 4 * 1/2 = 2 in

Now, C = 2πr
C = 2π(2)
C = 4π
Or C = 4 * 3.14 = 12.56

In short, Your Answer would be 4π or 12.56 in

Hope this helps!
olga2289 [7]3 years ago
4 0

Answer:

The circumference after dilation is 12.56 in.

Step-by-step explanation:

Given : A circle with a radius of 4 in. is dilated by a scale factor of 1/2.

To find : What will be the circumference of the circle after dilation?

Solution :

Radius is 4 in.

Radius is dilated by scale factor \frac{1}{2}

Radius after dilation = 4 \times\frac{1}{2}= 2

Circumference of circle is C=2\pi r

Put radius = 2 in. and \pi =3.14

C=2\pi r

C=2\times 3.14\times2

C= 12.56

Therefore, The circumference after dilation is 12.56 in.

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marissa [1.9K]

Answer:

0.375, Terminating

Step-by-step explanation:

Mackenzie has 32 books and 12 of which are by her favorite author.

One of the easier ways to convert something to a decimal is to first start as a fraction. We need to have it be the number of books by her favorite author (12) out of the total number of books that she owns (32)

This in the form of a fraction would be \frac{12}{32}

Now, let us reduce this fraction.

Both terms can be divided by 4

\frac{12}{32}/\frac{4}{4} \\\\\frac{3}{8}

Recall that \frac{1}{8} =0.125

This means that

\frac{3}{8} =3*0.125=0.375

As you can see. this decimal stops after 3 places, which means that it is terminating.

7 0
3 years ago
Employees from A and company B receive annual bonuses. What information would you need to test the claim that the difference in
lyudmila [28]

Answer:

1. The required information are

The average annual bonuses, \bar {x}_1 received by employees from company A

The average annual bonuses, \bar {x}_2 received by employees from company B

The standard deviation, σ₁, of the average annual bonuses for employees from company A

The standard deviation, σ₂, of the average annual bonuses for employees from company A

The number of employees in company A, n₁

The number of employees in company B, n₂

2. The null hypothesis is H₀: \bar {x}_1 - \bar {x}_2 ≤ 100

The alternative hypothesis is Hₐ: \bar {x}_1 - \bar {x}_2 > 100

Step-by-step explanation:

1. The required information are

The average annual bonuses, \bar {x}_1 received by employees from company A

The average annual bonuses, \bar {x}_2 received by employees from company B

The standard deviation, σ₁, of the average annual bonuses for employees from company A

The standard deviation, σ₂, of the average annual bonuses for employees from company A

The number of employees in company A, n₁

The number of employees in company B, n₂

2. The null hypothesis is H₀: \bar {x}_1 - \bar {x}_2 ≤ 100

The alternative hypothesis is Hₐ: \bar {x}_1 - \bar {x}_2 > 100

The z value for the hypothesis testing of the difference between two means is given as follows;

z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}-\frac{\sigma _{2}^{2}}{n_{2}}}}

At 0.5 level of significance, the critical z_\alpha = ± 0

The rejection region is z > z_\alpha and z < -z_\alpha

Therefore, the value of z obtained from the relation above more than or less than 0, we reject the null hypothesis, and we fail to reject the alternative hypothesis.

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3 years ago
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8 (32) -14

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