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3 years ago

Work out the area of this circle.

Mathematics

2 answers:

Over [174]3 years ago

6 0

<h2><u>Given</u> :</h2>

Radius of circle - 6mm

Area of circle

<h2><u>Formula Using</u> : </h2>

Area of circle = πr²

<h2><u>Solution</u> :</h2>

Area of circle = π(6mm)²

Area of circle = 36π mm²

Hence, the area of circle is 36π mm²

exis [7]3 years ago

3 0

We know that

Area of circle = πr²

=> π × (6)²

=> π × 36

=> 36π mm²

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What set/sets of real numbers does -54/19 belong to?

ahrayia [7]

That is a rational number since you can write it as a ratio (=fraction).

7 0

4 years ago

Read 2 more answers

ASK YOUR TEACHER An article reported that for a sample of 42 kitchens with gas cooking appliances monitored during a one-week pe

xxMikexx [17]

Answer:

$654.16-2.02\frac{165.23}{\sqrt{42}}=602.66$

$654.16+2.02\frac{165.23}{\sqrt{42}}=705.66$

So on this case the 95% confidence interval would be given by (602.66;705.66)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=654.16$ represent the sample mean

$\mu$ population mean (variable of interest)

s=165.23 represent the sample standard deviation

n=42 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=42-1=41$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that $t_{\alpha/2}=2.02$

Now we have everything in order to replace into formula (1):

$654.16-2.02\frac{165.23}{\sqrt{42}}=602.66$

$654.16+2.02\frac{165.23}{\sqrt{42}}=705.66$

So on this case the 95% confidence interval would be given by (602.66;705.66)

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4 years ago

You and your friend go shopping with $846,375,593. (that's literally the question) You spend 250,678 dollars on shoes, 10,008 do

Eddi Din [679]

Answer:

Initial money -->$846,375,593

You spend 250,678 dollars on shoes, 10,008 dollars on clothes, and 40,034 dollars on accesories.

$846,375,593-$250,678-$10,008-440,034 = $845,674,873

Later, your friend and you get robbed and the robber takes half of the remaining money. How much do you have left?

$845,674,873/2 = $422,837,436.5

You have $422,837,436.5 left.

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3 years ago

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Solving radical equation

Darya [45]

$\bf \sqrt{k-9}-\sqrt{k}=-1\implies \sqrt{k-9}=\sqrt{k}-1\impliedby \textit{squaring both sides}
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(\sqrt{k-9})^2=(\sqrt{k}-1)^2\implies k-9=(\sqrt{k}-1)(\sqrt{k}-1)\impliedby \textit{FOIL}
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6 0

4 years ago

Find the indicated value. Use either half angle formulas or sum and difference formulas.

MrMuchimi

By the angle difference formula for sines, we have:

$\sin 15^\circ = \sin 45^\circ \cos 30^\circ - \sin 30^\circ \cos 45^\circ = \frac{sqrt{6}}{4} - \frac{sqrt{2}}{4} = \frac{\sqrt{6} - \sqrt{2}}{4}.$

By the angle sum formula for tangents, we have:

$\tan 75^\circ = \frac{\tan 45^\circ + \tan 30^\circ}{1 - \tan 45^\circ \tan 30^\circ} = \frac{1+\frac{\sqrt{3}}{3}}{1 - \frac{\sqrt{3}}{3}} = \frac{3 + \sqrt{3}}{3 - \sqrt{3}}$ .

Rationalizing the denominator gives $\frac{12+6\sqrt{3}}{6} = 2+\sqrt{3}$ as the final answer.

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4 years ago