A regular pentagon has an apothem of 3.2 and an area of 37.2 m. What

1 answer:

soldier1979 [14.2K]3 years ago

8 0

The area of any regular polygon can be expressed as:

(ns^2)/(4tan(180/n)) where n is number of sides and s is a side length (no apothem needed :D)

37.2=5s^2/(4tan36)

s^2=(148.8tan36)/5

s≈4.65m

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.In the Star Wars franchise, Yoda stands at only 66 centimeters tall. Suppose you want to see whether or not hobbits from the Lo

r-ruslan [8.4K]

Answer:

We conclude that the average height of hobbit is taller than Yoda.

Step-by-step explanation:

We are given that in the Star Wars franchise, Yoda stands at only 66 centimetres tall.

From a sample of 7 hobbits, you ﬁnd their mean height $\bar X$ = 80 cm with standard deviation s = 10.8 cm.

Let $\mu$ = average height of hobbit.

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 66 cm {means that the average height of hobbit is shorter than or equal to Yoda}

Alternate Hypothesis, $H_A$ : $\mu$ > 66 cm {means that the average height of hobbit is taller than Yoda}

The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}$ ~ $t_n_-_1$

where, $\bar X$ = sample mean height = 80 cm

s = sample standard deviation = 10.8 cm

n = sample of hobbits = 7

So, test statistics = $\frac{80-66}{\frac{10.8}{\sqrt{7}}}$ ~ $t_6$

= 3.429

The value of t test statistics is 3.429.

Now, at 0.01 significance level the t table gives critical value of 3.143 for right-tailed test. Since our test statistics is more than the critical value of t as 3.429 > 3.143, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average height of hobbit is taller than Yoda.

3 0

3 years ago

21. Carrie withdraws $10 from her account each day for 7 days.

Fiesta28 [93]

Answer:

a.70. b.50

Step-by-step explanation:

If Cartie takes $10 from her account for 7 days she would have taken $70 out.

$7 \times 10 = 70$

Next we look at the net problem it is asking us how much is left we already know from the equation above that we need to subtract 70 from 120
$70 - 120 = 50$
We now have both answers A. being that she would have taken $70 in total out of her account and B. being that she would have $50 left in her account.