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2 years ago

The standard IQ test has a mean of 97 and a standard deviation of 17. We want to be

1 answer:

6 0

Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,

μ = 97

Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is

σ = 17/√n

We want to be 95% certain

97 - 5 ≤ x ≤ 97 + 5

By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that

μ - 2σ ≤ x ≤ μ + 2σ

Comparing to what we want, that's means we have to solve

2σ = 5

2 (17/√n) = 5

√n = 2 (17/5)

n = (34/5)² = 46.24

We better round up.

Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean

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The number sentence 4x7=(4×3)+(4×4) is an example of what property

Zinaida [17]

4x7

=4x(3+4)

=(4×3)+(4×4).....this is the distributive property

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2 years ago

What is m < 8 if m < 4 = 50° ? <br> A) 50°<br> B) 180° <br> C) 70°<br> D) 40°

icang [17]

Answer:

Step-by-step explanation:

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2 years ago

Describe the continuity of the graphed function

marusya05 [52]

we know that

Any function f(x) is continuous at x=a only if

$\lim_{x \to a-} f(x) = \lim_{x \to a+} f(x)=f(a)$

We can see that this curve is smooth everywhere except at x=3

so, we will check continuity at x=3

Left limit is:

$\lim_{x \to 3-} f(x) = -\infty$

Right limit is:

$\lim_{x \to 3+} f(x) = +\infty$

Functional value:

$f(3)= DNE$

we can see that left limit is not equal to right limit

so, limit does not not exist

so, this function is discontinuous at x=3

Since, limit does not exist

so, there will be non-removal discontinuity at x=3

so, option-C........Answer

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2 years ago

Directions : Factor each of the following Differences of two squares and write your answer together with solution

N76 [4]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Factor each of the following differences of two squares and write your answer together with solution.

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

$\sf \: x ^ { 2 } - 36$

Rewrite $\sf\:x^{2}-36 as x^{2}-6^{2}$ . The difference of squares can be factored using the rule: $\sf\: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\boxed{ \boxed{ \bf\left(x-6\right)\left(x+6\right) }}$

__________________

$\sf \: 49 - x ^ { 2 }$

Rewrite 49-x² as 7²-x². The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\sf \: \left(7-x\right)\left(7+x\right)$

Reorder the terms.

$\boxed{ \boxed{ \bf\left(-x+7\right)\left(x+7\right) }}$

__________________

$\sf \: 81 - c ^ { 2 }$

Rewrite 81-c²as 9²-c². The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\sf\left(9-c\right)\left(9+c\right)$

Reorder the terms.

$\boxed{ \boxed{ \bf\left(-c+9\right)\left(c+9\right) }}$

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$\sf \: m ^ { 2 } n ^ { 2 } - 1$

Rewrite m²n² - 1 as $\sf\left(mn\right)^{2}-1^{2}$ . The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\boxed{ \boxed{ \bf\left(mn-1\right)\left(mn+1\right) }}$

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2 years ago

Read 2 more answers

Given the following mAB = mBC= mCD in circle F what is the measure of angle AFB

Svetach [21]

50° <span>is the measure of angle AFB</span>

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2 years ago