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3 years ago

Match the correct letter

Mathematics

1 answer:

svet-max [94.6K]3 years ago

5 0

Answer:

1) f

4 * ¼ = 1 (Multiplicative inverse property)

2) c

6 * 1 = 6 (Identity property of multiplication)

3) h

5 + 7 = 7 + 5 (Commutative property of addition)

4) j

If 5 + 1 = 6 and 4 + 2 = 6, then 5 + 1 = 4 + 2 (Transitive property)

5) a

4(x - 3) = 4x - 12 (Distributive property)

6) i

3(5) = 5(3) (Commutative property of multiplication)

7) k

Rules that allow us to take short cuts when solving algebraic problems.(Properties)

8) d

5 * (3 * 2) = (5 * 3) * 2 (Associative property of multiplication)

9) g

4 + (-4) = 0 (Additive inverse property)

10) e

2 + 0 = 2 (Identity property of addition)

11) b

A + (B + C) = (A + B) + C (Associative property of addition)

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For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

zhannawk [14.2K]

Answer:

a) 0.6032

Lower limit: 0.48

Upper limit: 0.72

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Question a:

In a random sample of 63 professional actors, it was found that 38 were extroverts.

We use this to find the sample proportion, which is the point estimate for p. So

$\pi = \frac{38}{63} = 0.6032$

Question b:

Sample of 63 means that $n = 63$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6032 - 1.96\sqrt{\frac{0.6032*0.3968}{63}} = 0.4824$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6032 + 1.96\sqrt{\frac{0.6032*0.3968}{63}} = 0.724$

Rounding to two decimal places:

Lower limit: 0.48

Upper limit: 0.72

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VARVARA [1.3K]

Its a convex hexagon

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Start with

$S = \pi r^2 + \pi r l$

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Divide both sides by $\pi r$

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And thus we solved the expression for l:

$l=\dfrac{S-\pi r^2}{\pi r}$

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