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3 years ago

If the diameter of a circle changes from 18 cm to 6 cm, how will the circumference change?

Mathematics

2 answers:

GrogVix [38]3 years ago

7 0

The answer would be multiplies by 1/3

Ket [755]3 years ago

6 0

Answer:

The circumference of a circle is changes by $\frac{1}{3}$ .

Step-by-step explanation:

Formula

$Circumference\ of\ a\ circle = 2\pi r$

Where r is the radius of the circle .

As given

If the diameter of a circle changes from 18 cm to 6 cm .

Initial diameter = 18 cm

$Initial\ radius = \frac{Initial\ diameter}{2}$

$Initial\ radius = \frac{18}{2}$

= 9 cm

$\pi = 3.14$

$Circumference\ of\ initial\ circle = 2\times 3.14\times 9$

= 56.52 cm

Final diameter = 6 cm

$Final\ radius = \frac{Initial\ diameter}{2}$

$Final\ radius = \frac{6}{2}$

= 3 cm

$\pi = 3.14$

$Circumference\ of\ final\ circle = 2\times 3.14\times 3$

= 18.84 cm

Thus

$\frac{Circumference\ of\ final\ circle}{Circumference\ of\ initial\ circle} = \frac{18.84}{56.52}$

$\frac{Circumference\ of\ final\ circle}{Circumference\ of\ initial\ circle} = \frac{1}{3}$

Therefore the circumference of a circle is changes by $\frac{1}{3}$ .

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Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.

Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.

Step-by-step explanation:

We are given the following hypothesis below;

Let p = <u><em>proportion of people who write with their left hand</em></u>

So, Null Hypothesis, $H_0$ : p = 0.22 {means that the proportion of people who write with their left hand is equal to 0.22}

Alternate Hypothesis, $H_A$ : p $\neq$ 0.22 {means that the proportion of people who write with their left hand is different from 0.22}

Now, Type I error states that we conclude that the null hypothesis is rejected when in fact the null hypothesis was actually true. Or in other words, it is the probability of rejecting a true hypothesis.

So, in our question; Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.

Type II error states that we conclude that the null hypothesis is accepted when in fact the null hypothesis was actually false. Or in other words, it is the probability of accepting a false hypothesis.

So, in our question; Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.

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