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Irina-Kira [14]

3 years ago

10

A sugar mixture has 3 parts water and 2 parts sugar. Suppose the chef adds one more part to each. What is the new ratio of sugar

to water?

2 answers:

Margaret [11]3 years ago

5 0

Answer:

Wet farts on johny!

Step-by-step explanation:

ira [324]3 years ago

4 0

3 parts sugar and 4 parts water
3:4

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Find three consecutive odd integers such that

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Answer:

17, 19, 21

Step-by-step explanation:

x = first number

x+2 = second number

x+4 = third number

4x + 3(x+2) + 2(x+4) = 167

simplify:

4x + 3x + 6 + 2x + 8 = 167

combine like terms:

9x + 14 = 167

subtract 14 from each side of the equation:

9x = 153

divide both sides by 9:

x = 17

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How do you solve 3^5

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Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increas

polet [3.4K]

Answer:

a) The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

Step-by-step explanation:

a) Develop a 90% confidence interval estimate of the population mean monthly rent.

Our sample size is 120.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 120-1 = 119$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.90}{2} = \frac{0.10}{2} = 0.05$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 119 and 0.05 in the t-distribution table, we have $T = 1.6578$ .

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{650}{\sqrt{120}} = 59.34$

Now, we multiply T and s

$M = T*s = 59.34*1.6578 = 98.37$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 98.37 = $3387.63.

The upper end of the interval is the mean added to M. So it is 3486 + 98.37 = $3584.37.

The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) Develop a 95% confidence interval estimate of the population mean monthly rent.

Now we have that $\alpha = 0.95$

So

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

With 119 and 0.025 in the t-distribution table, we have $T = 1.9801$ .

$M = T*s = 59.34*1.9801 = 117.50$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 117.50 = $3368.5.

The upper end of the interval is the mean added to M. So it is 3486 + 117.50 = $3603.5.

The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) Develop a 99% confidence interval estimate of the population mean monthly rent.

Now we have that $\alpha = 0.99$

So

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.005$

With 119 and 0.025 in the t-distribution table, we have $T = 2.6178$ .

$M = T*s = 59.34*2.6178 = 155.34$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 155.34 = $3330.66.

The upper end of the interval is the mean added to M. So it is 3486 + 155.34 = $3641.34.

The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain.

The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

4 0

3 years ago

The circumference of a circle is 7π m. <br> what is the area

Helen [10]

Answer: <u>38.4845100065m²</u>

<em>when rounded to the nearest tenth: </em><u>38.5m²</u>

<em>when rounded to the nearest hundredth: </em><u>38.48m²</u>

<em>when rounded to the nearest thousandth: </em><u>38.485m²</u>

Step-by-step explanation:

the formula for finding the area of a circle is $A = \pi r^{2}$ , where A = area and r = the radius of the circle.

since you're only given the circumference, we need to calculate the radius of the circle before we can find the area.

to find the radius of a circle, you can either <u>divide the measure of the diameter by 2</u> <em>OR</em> <u>use the formula</u> $r=\frac{C}{2\pi}$ where r = radius and C = circumference.
because there is no given diameter measurement in your question, <u>the best way to find the radius is to use the formula</u> $r=\frac{C}{2\pi}$ .

first, plug the given values into the equation.

since $7\pi$ is the given circumference, plug in $7\pi$ for $C$ .

$r=\frac{C}{2\pi}$ ⇒ $r=\frac{7\pi}{2\pi}$

the equation becomes $r=\frac{7\pi}{2\pi}$ , aka <em>radius equals seven times pi divided by two times pi</em>.

now divide $\frac{7\pi}{2\pi}$ .

$\frac{7\pi}{2\pi} = 3.5$

now we know that the radius of the circle is 3.5 :) since we have this information, we can now solve for the area of the circle using the formula $A = \pi r^{2}$ .

first, plug in $3.5$ for $r$ .

$A = \pi r^{2}$ ⇒ $A = \pi 3.5^{2}$

now multiply $\pi 3.5^2$ , aka <em>pi times three and five tenths squared</em>.

$\pi 3.5^2 = 38.4845100065$ <em>(if needed, you can round this result to the nearest tenth, hundredth, etc.)</em>

<em />

the area of the circle is 38.4845100065m². i hope this helps! have an amazing day <3

<em />

6 0

3 years ago