Which is the area of a circle with circumference of 15.7 units?( Use 3.14 for )

2 answers:

7 0

Circumference of a circle= 2πr = 15.7
from this radius r= 15.7/ 2π
r= 15.7/(2x 3.14)
r= 15.7/ 6.28 = 2.5
therefore area = π r^2= π x r x r
= 3.14 x 2.5 X 2.5 = 19.625 sq units

damaskus [11]3 years ago

4 0

A = π(r²) --- r is radius

C = πd --- d is diameter

First, the circumference must be found. If the circumference is 15.7, plug it in.

15.7 = πd

We know what pi is.

15.7 = 3.14 (d)

Now, simply divide 3.14 by 15.7 to find the diameter (d). You get 5. Since the radius is half of the diameter, the radius is 2.5. Plug this into the area formula, and plug pi in, too.

A = 3.14(2.5²)

2.5 to the second power is 6.25.

A = 3.14(6.25)

Tada! Multiply, and you're left with 19.625!

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3 years ago

Boxes of raisins are labeled as containing 22 ounces. Following are the weights, in the ounces, of a sample of 12 boxes. It is r

ZanzabumX [31]

Answer:

A 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Step-by-step explanation:

We are given the weights, in the ounces, of a sample of 12 boxes below;

Weights (X): 21.88, 21.76, 22.14, 21.63, 21.81, 22.12, 21.97, 21.57, 21.75, 21.96, 22.20, 21.80.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean weight = $\frac{\sum X}{n}$ = 21.88 ounces

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 0.201 ounces

n = sample of boxes = 12

$\mu$ = population mean weight

Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.796 < $t_1_1$ < 1.796) = 0.90 {As the critical value of t at 11 degrees of