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3 years ago

How do I work this out?

Mathematics

2 answers:

marin [14]3 years ago

4 0

Area of a full circle is: PI x r^2

so full circle is 4^2 x PI = 16PI

the shaded part is 3/4 of the circle

16 x 3/4 = 12
so 12 PI ft^2 is shaded

Vikentia [17]3 years ago

3 0

First, find the area of the circle as a whole. Then find the percentage or fraction of that area.

STEP ONE

As you probably know, you use this formula to find the area of any circle.

$A=\pir^2$

We know what the radius is, so substitute the 4 for the r in the formula.

$A=4^2\pi$

Simplify.

$A=4^2\pi$
$A=16\pi$

STEP TWO

Now that we know what the area of the circle is as a whole, let's find the fraction of that area. We want to the know the area of the shaded part.

Multiply the area by 3/4.

$(16\pi)(3/4)$
$(48\pi)/4$
$12\pi$

So, the answer is the first option.

You might be interested in

Find x. problem is in picture

Masja [62]

Answer:

x=21

Step-by-step explanation:

We know that C is a right angle, which means that x + 3x+6 = 90

$4x+6=90\\4x=84\\x=21$

Have a nice day. hope I helped please rate brainliest!

3 0

3 years ago

g If a hypothesis test with a significance level of α rejects H0: μ1=μ2 in favor of Ha: μ1≠μ2, then thecorresponding (1- α)% con

Effectus [21]

Answer:

The statement, (1- α)% confidence interval for (μ₁ - μ₂) does not contain zero is TRUE.

Step-by-step explanation:

The hypothesis for a test is defined as follows:

H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂

It is provided that the test was rejected st the significance level α%.

If a decision is to made using the confidence interval the conditions are:

If the null hypothesis value is not included in the (1 - α)% confidence interval then the null hypothesis will be rejected and vice versa.

In this case the null hypothesis value is:

H₀: μ₁ - μ₂ = 0.

If the value 0 is not included in the (1 - α)% confidence interval for the difference between two means, then the null hypothesis will be rejected.

Thus the statement, (1- α)% confidence interval for (μ1- μ2) does not contain zero is TRUE.

5 0

3 years ago

Simplify the expression: –3(3 + 2n)

noname [10]

Answer:

-9 - 6n is the answer

8 0

3 years ago

Read 2 more answers

I need help on this plz i don’t understand the question

AnnZ [28]

We know that the area of a circle in terms of π will be πr². However the area with respect to the diameter will be a different story. The first step here is to find a function relating the area and diameter of any circle --- ( 1 )

For any circle the diameter is 2 times the radius,

d = 2r

Therefore r = d / 2, which gives us the following formula through substitution.

A = π(d / 2)² = πd² / 4

Hence the area of a circle as the function of it's diameter is A = πd² / 4. You can also say f(d) = πd² / 4.

Now we can substitute " d " as 4, solving for the area ( A ) or f(4) --- ( 2 )

f(4) = π(4)² / 4 = 16π / 4 = 4π - This makes the area of circle present with a diameter of 4 inches, 4π.

3 0

3 years ago

A fast food restaurant executive wishes to know how many fast food meals adults eat each week. They want to construct a 98% conf

adelina 88 [10]

Answer:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.07 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.01;0;1)", and we got $z_{\alpha/2}=2.326$ , replacing into formula (b) we got:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

3 0

3 years ago