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3 years ago

The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.

Mathematics

1 answer:

ryzh [129]3 years ago

4 0

Answer:

Option (2). 14 m

Step-by-step explanation:

Formula to get the area of a circle 'A' = $\pi r^{2}$

where r = radius of the circle

Given in the question,

Area of the circle = 153.86 square meters

By putting the values in the formula,

153.86 = πr²

r = $\sqrt{\frac{153.86}{\pi } }$

r = $\sqrt{49}$

r = 7 meters

Diameter of circle = 2 × (radius of the circle)

= 2 × 7

= 14 meters

Therefore, diameter of the circle is 14 meters.

Option (2) is the answer.

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A news report states that the 99% confidence interval for the mean number of daily calories consumed by participants in a medica

expeople1 [14]

Answer:

The sample mean is of 1925 calories.

The margin of error is of 75 calories.

The sample standard deviation is of 109.7992 calories.

Step-by-step explanation:

Sample mean:

The sample mean is the mean value of the two bounds of the confidence interval. So

$M = \frac{1850 + 2000}{2} = 1925$

The sample mean is of 1925 calories.

The margin of error

Difference between the bounds and the sample mean. So

2000 - 1925 = 1925 - 1850 = 75 calories.

The margin of error is of 75 calories.

Sample standard deviation:

Here, I am going to expand on the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 2.898

The margin of error is:

$M = T\frac{s}{\sqrt{n}}$

In which s is the standard deviation of the sample and n is the size of the sample.

Since $M = 75, T = 2.898, n = 18$

$M = T\frac{s}{\sqrt{n}}$

$75 = 2.898\frac{s}{\sqrt{18}}$

$s = \frac{75\sqrt{18}}{2.898}$

$s = 109.7992$

The sample standard deviation is of 109.7992 calories.

6 0

2 years ago

The following table shows the monthly defect rate for a product at a manufacturing company.

Lapatulllka [165]

Answer:

Step-by-step explanation:

3 0

3 years ago

PLEASE HELP ME ASAP I don't understand this

Pachacha [2.7K]

Answer:

18 times 15 times 9 = 2430 cubed inches

Step-by-step explanation:

7 0

2 years ago

The diameter of Mercury is approximately 4.9×103 kilometers. The diameter of Saturn is approximately 1.2×105 kilometers. About h

soldier1979 [14.2K]

As soon as you see "How many times . . .", that usually tells you that finding the answer involves division. (It certainly does in this one.)

(1.2 x 10⁵) / (4.9 x 10³) =

(1.2/4.9) x (10⁵⁻³) =

0.245 x 10² = 24.5 times

It looks like B is the closest choice.

8 0

3 years ago

Deacon had 12 1/3 ounces of juice, but he drank 3 2/3 ounces. How much juice is left?

alexandr1967 [171]

You need to know:

$a \frac{b}{c} = a + \frac{b}{c} = \frac{(a*c) + b}{c}$

Be careful though:

$a \frac{b}{c} ≠ a(\frac{b}{c})$

Using this principle, we can say:
12 1/3 = 37/3
3 2/3 = 11/3
Quantity of juice left = Initial quantity - Quantity drunk
So:
Quantity of juice left = 37/3 - 11/3 = 26/3

There will be 26/3 ounces of juice remaining after 3 2/3 are drunk from the total of 12 1/3 ounces that Deacon had initially.

8 0

3 years ago