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3 years ago

which is the rationalized form of the expression the square root of x divided by the square root of x +the square root of 7

Mathematics

1 answer:

Ilya [14]3 years ago

8 0

Answer:

I assume your goal is to rationalize the denominator -

So you need to multiply the denominator by its conjugate.

So we have:

$\frac{\sqrt{x} }{\sqrt{x}-\sqrt{7} } *\frac{\sqrt{x} +\sqrt{7} }{\sqrt{x} +\sqrt{7}}$

$\frac{x-\sqrt{7}\sqrt{x} }{x-7}$

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Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true

Feliz [49]

Answer:

a) The 95% CI for the true average porosity is (4.51, 5.19).

b) The 98% CI for true average porosity is (4.11, 5.01)

c) A sample size of 15 is needed.

d) A sample size of 101 is needed.

Step-by-step explanation:

a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96*\frac{0.78}{\sqrt{20}} = 0.34$

The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.34 = 4.51

The upper end of the interval is the sample mean added to M. So it is 4.35 + 0.34 = 5.19

The 95% CI for the true average porosity is (4.51, 5.19).

b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with a sample average of 4.56.

Following the same logic as a.

98% C.I., so $z = 2.327$

$M = 2.327*\frac{0.78}{\sqrt{16}} = 0.45$

4.56 - 0.45 = 4.11

4.56 + 0.45 = 5.01

The 98% CI for true average porosity is (4.11, 5.01)

c. How large a sample size is necessary if the width of the 95% interval is to be 0.40?

A sample size of n is needed.

n is found when M = 0.4.

95% C.I., so Z = 1.96.

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.4 = 1.96*\frac{0.78}{\sqrt{n}}$

$0.4\sqrt{n} = 1.96*0.78$

$\sqrt{n} = \frac{1.96*0.78}{0.4}$

$(\sqrt{n})^{2} = (\frac{1.96*0.78}{0.4})^{2}$

$n = 14.6$

Rounding up

A sample size of 15 is needed.

d. What sample size is necessary to estimate the true average porosity to within 0.2 with 99% confidence?

99% C.I., so z = 2.575

n when M = 0.2.

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.2 = 2.575*\frac{0.78}{\sqrt{n}}$

$0.2\sqrt{n} = 2.575*0.78$

$\sqrt{n} = \frac{2.575*0.78}{0.2}$

$(\sqrt{n})^{2} = (\frac{2.575*0.78}{0.2})^{2}$

$n = 100.85$

Rounding up

A sample size of 101 is needed.

8 0

4 years ago

Cerra Co. expects to receive 5 million euros tomorrow as a result of selling goods to the Netherlands. Cerra estimates the stand

Jlenok [28]

Answer:

$58,075

Step-by-step explanation:

Given:

Expected amount to be received = 5 million euros

Standard deviation of daily percentage change of euros, σ = 1%

Confidence level = 95%

Expected percentage change of the euro tomorrow = 0.5 percent

let,

the current spot rate of the euro (before considering the maximum one-day loss = $1.01

Now,

The maximum one-day percentage loss

= Expected change of euro - 1.65 × σ

(here 1.65 is constant for 95% confidence)

= 0.5% - 1.65 × 1%

= -1.15% (Here negative sign depicts the loss)

Therefore,

maximum one-day loss in dollars

= maximum one-day percentage loss × Exchange rate × Amount to be received

= -1.15% × $1.01 × 5 million euros

= -0.0115 × 1.01 × 5,000,000

= -$58,075 (Here negative sign depicts the loss)

8 0

3 years ago

How much money is borrowed if the interest rate is 9.25% simple interest and the loan is made for 3.5 years and has 904.88 inter

Mars2501 [29]

The amount borrowed is 2795

<h3>What is Principal?</h3>

Principal is the amount loaned or invested in a bank or a financial institution that gives a certain interest on a specific rate over a period of time.

Analysis:

P = principal = unknown

R = rate = 9.25%

T = time = 3.5 years

I = interest = 904.88

simple interest(I) = PRT/100

P = 100I/RT

P = 100 x 904.88/3.5 x 9.25 = 2795

In conclusion, the amount borrowed is 2795.

Learn more about simple interest: brainly.com/question/20690803

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6 0

2 years ago

Which best describes this quadrilateral?

Tomtit [17]

Answer:

fourth option... ...dmdmdjxn

4 0

3 years ago

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The diameter of a circular swimming pool is 10 feet. Find its circumference. Round to the nearest tenth.

MariettaO [177]

answer

31.4 ft squared

explanation

the circumference of a circle is c = 2r * pi = d * pi

plug in 10 for d (diameter) and 3.14 for pi

c = 10 * 3.14

c = 31.4 ft squared

3 0

4 years ago

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