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jek_recluse [69]
3 years ago
14

The heights in inches of orangutans Are normally distributed with a population standard deviation of 3" and an unknown populatio

n mean if a random sample of 17 orangutans is taken and results in a sample mean of 57" find the error bound of the confidence interval with a 95% confidence level
Mathematics
1 answer:
CaHeK987 [17]3 years ago
7 0

Answer: The 95% confidence interval is approximately (55.57, 58.43)

======================================================

Explanation:

At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.

The sample size is n = 17

The sample mean is xbar = 57

The population standard deviation is sigma = 3

The lower bound of the confidence interval is

L = xbar - z*sigma/sqrt(n)

L = 57 - 1.960*3/sqrt(17)

L = 55.5738905247863

L = 55.57

The upper bound is

U = xbar + z*sigma/sqrt(n)

U = 57 + 1.960*3/sqrt(17)

U = 58.4261094752137

U = 58.43

Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.

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If a triangular road sign has a center height of
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Answer:

Formula

A = 1/2 b * h

Substitute

Area = 60 in^2

b = x

h = 2x - 1

60= 1/2 * x * (2x - 1)

Solve

60 = 1/2 * x (2x - 1) Multiply by 2

60 * 2 = x(2x - 1)

120 = x (2x - 1) Remove the brackets.

120 = 2x^2 - x  Subtract 120 from both sides.

2x^2 -  x - 120 = 0 This factors.

(2x + 15)(x - 8) = 0

Solve for x

2x + 15 = 0

2x = - 15

x = -15/2

x = - 7.5 a negative measurement is useless. Discard this answer.

x - 8 = 0

x = 8

Area (Check)

base = 8

height = 16 - 1 = 15

Area = 1/2 * 8 * 15 = 60 as it should

Answer

Use Area = 1/2 * b * h to find the base and the height.Step-by-step explanation:

3 0
2 years ago
Nina’s sister has 386 stickers that she wants to put in a book. Each page can hold 42 stickers. How many pages will she need? Ex
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Answer:

10 pages

Step-by-step explanation:

386/42=9.1 pages

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3 years ago
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You fell sharply behind your expected schedule with regard to saving

Look your test

Step-by-step explanation:

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Tell whether each statement is a proportion:
erma4kov [3.2K]

Answer:

1. Yes

2. No

3. No

4. No

5. Yes

Step-by-step explanation:

Do you mean equal proportion?

1. 3 : 9 = 6 : 18 TRUE because 3 : 9 = 1 : 3 and 6 : 18 = 1 : 3

2. 28 : 7 = 64 : 16 FALSE because they are just not related.

3. 95 : 100 = 17 : 20 FALSE because the closest they get are 19 : 20 ≠ 17 : 20

4. 60 : 80 = 14 : 16 FALSE because the closest they get are 60 : 80 = 6 : 8 and 14 : 16 = 7 : 8

5. 200 : 300 = 24 : 36 TRUE because 200 : 300 = 2 : 3 and 24 : 36 = 2 : 3

6 0
3 years ago
Derivative, by first principle<br><img src="https://tex.z-dn.net/?f=%20%5Ctan%28%20%5Csqrt%7Bx%20%7D%20%29%20" id="TexFormula1"
vampirchik [111]
\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}h

Employ a standard trick used in proving the chain rule:

\dfrac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\cdot\dfrac{\sqrt{x+h}-\sqrt x}h

The limit of a product is the product of limits, i.e. we can write

\displaystyle\left(\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\right)\cdot\left(\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt x}h\right)

The rightmost limit is an exercise in differentiating \sqrt x using the definition, which you probably already know is \dfrac1{2\sqrt x}.

For the leftmost limit, we make a substitution y=\sqrt x. Now, if we make a slight change to x by adding a small number h, this propagates a similar small change in y that we'll call h', so that we can set y+h'=\sqrt{x+h}. Then as h\to0, we see that it's also the case that h'\to0 (since we fix y=\sqrt x). So we can write the remaining limit as

\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan\sqrt x}{\sqrt{x+h}-\sqrt x}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{y+h'-y}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{h'}

which in turn is the derivative of \tan y, another limit you probably already know how to compute. We'd end up with \sec^2y, or \sec^2\sqrt x.

So we find that

\dfrac{\mathrm d\tan\sqrt x}{\mathrm dx}=\dfrac{\sec^2\sqrt x}{2\sqrt x}
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