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3 years ago

Take a factor out of the square root:

Mathematics

1 answer:

klasskru [66]3 years ago

8 0

Answer:

1. |y| sqrt(10)

2. |x| sqrt(x)

3. a^2 sqrt(a)

4. 4 |y|^3 sqrt(3)

5. 1/4 *|x| sqrt(3x)

Step-by-step explanation:

1. sqrt(10y^2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(y^2) sqrt(10)

|y| sqrt(10)

We take the absolute value of y because -y*-y = y^2 and the principle square root is y

2. sqrt(x^3)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(x^2) sqrt(x)

|x| sqrt(x)

3. sqrt(a^5)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(a^4) sqrt(a)

a^2 sqrt(a)

4. sqrt(16 y^7)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(16) sqrt(y^6)sqrt(y)

4 |y|^3 sqrt(3)

5. sqrt(3/16x^3)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(1/16) sqrt(x^2)sqrt(3x)

1/4 *|x| sqrt(3x)

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Answer:

The sample size required is 910.

Step-by-step explanation:

The confidence interval for population proportion is:

$CI=\hat p\pm z_{ \alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }$

The margin of error is:

$MOE=z_{ \alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }$

Given:

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The critical value of <em>z</em> for 90% confidence level is:

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Compute the sample size required as follows:

$MOE=z_{ \alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }\\0.02=1.645\times \sqrt{\frac{0.16(1-0.16)}{n} }\\n=\frac{(1.645)^{2}\times 0.16\times (1-0.16)}{(0.02)^{2}} \\=909.2244\\\approx910$

Thus, the sample size required is 910.

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Answer:

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2nd and 3rd week = 62 hours and each hour = $22.79

Total amount earned in 2nd and 3rd week = 62 * 22.79 = $1412.98

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4th week = (48 / 100) * 439.50 = $210.96

Total amount she earned = 1st week + 2nd & 3rd week + 4th week

Total amount = $439.50 + $1412.98 + $210.96

Total amount = $2063.44

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