What is the circumference of this circle in millimeters

A carpenter has a rectangular wooden board. The diagonal of the board is 18 inches long and one side of the board is 12 inches l

BaLLatris [955]

In this question, it is given that the diagonal of the board is 18 inches long and one side of the board is 12 inches long.

Let the other side is of length b inches .

Now we use pythagorean identity, which is

$a^2 + b ^2 = c^2$

Here, a = 12 and c=18

Substituting these values, we will get

$12^2 + b^2 = 18^2 \\ 144 + b ^2 = 324 \\ b^2 = 324-144 \\ b^2 = 180 \\ b= \sqrt{180} \\ b = 13.4164 inches$

And the formula of perimeter is

$Perimeter = 2(Sum\ of \ legs)$

Substituting the values of the two legs, we will get

$Perimeter = 2(12+13.4164) = 50.83 inches$

3 0

3 years ago

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Simplify the expression. 4(11 + 7) ÷ (7 – 5) 40 36 47 5

vodomira [7]

Answer:

36

Step-by-step explanation:

6 0

3 years ago

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What is the area of the figure

svp [43]

Formula for the area of a triangle:

( Base X Height ) Divided by 2 or (B×H) ÷ 2

Formula for the area of a circle:

PI times the radius squared or PI × r^2

Area of the triangule part of this figure:

Base: 8ft. Height: 6ft

(8ft × 6ft) ÷ 2

48ft^2 ÷ 2

24ft^2

Since the circular part of the figure is a SEMICIRCLE, we are finding the area of a circle with the same radius but dividing it by 2 since thats just a half of a circle

Area of the semicricle:

Diameter: 10ft,

Therefore the radius is 5ft

(PI x 5ft^2) ÷ 2

39.2699081699 ft^2

39.27 ft^2

Now add these two areas together:

24ft^2 + 38.27ft^2 = 62.27ft^2

Hope it helps

6 0

3 years ago

In triangle ABC, AC=13, BC=84, and AB=85. find the measure of angle C.

Lapatulllka [165]

The sides all satisfy the Pythagorean Theorem so it is a right triangle. I attached an image of how the triangle should look like and as you can see, the angle is 90 degrees or pi/2 radians.

4 0

2 years ago

Let X represent the full height of a certain species of tree. Assume that X has a normal distribution with a mean of 137.1 ft an

Rama09 [41]

Answer:

0.0668 = 6.68% probability that the height of a randomly selected tree is as tall as mine or shorter.

0.0228 = 2.28% probability that the full height of a randomly selected tree is at least as tall as hers.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 137.1, \sigma = 3.2$

A tree of this type grows in my backyard, and it stands 132.3 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.

This is the pvalue of Z when X = 132.3. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{132.3 - 137.1}{3.2}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.0668 = 6.68% probability that the height of a randomly selected tree is as tall as mine or shorter.

My neighbor also has a tree of this type growing in her backyard, but hers stands 143.5 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.

This is 1 subtracted by the pvalue of Z when X = 143.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{143.5 - 137.1}{3.2}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the full height of a randomly selected tree is at least as tall as hers.

7 0

3 years ago

What is the circumference of this circle in millimeters​

What is the circumference of this circle in millimeters