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3 years ago

The diameter of a semicircle is 8 miles. What is the semicircle's perimeter? Use 3.14 for .

Mathematics

2 answers:

deff fn [24]3 years ago

8 0

Answer:

Circumference of the semicircle $=12.56 miles$

Step-by-step explanation:

Diameter of the semicircle= $8 miles$

Radius of the semicircle= $8/2=4 miles$

Perimeter of a circle or semicircle is called its Circumference:

Circumference of a circle= $2*\pi *r$

Circumference of a semicircle= $\frac{2*\pi *r}{2}=\pi *r$

As, $\pi =\frac{22}{7}=3.14$

Putting the values in the formula of the circumference of the semicircle:

Circumference of the semicircle= $3.14*4$

$=12.56 miles$

The Circumference of the semicircle with the radius of 4 miles $=12.56 miles$

wlad13 [49]3 years ago

7 0

Answer:

41.13 cm

Step-by-step explanation:

ITSSSS RIGHTTTTTTTTT

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Step-by-step explanation:

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3 years ago

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Mars2501 [29]

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3 years ago

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the f

Verizon [17]

Answer:

CI(95%): [205,5;400.8]dolars

Step-by-step explanation:

Hello!

So you need to construct a confidence interval for the average family dental expenses (μ) using the sample given in the problem. To estimate it you need to first choose a statistic. For this small sample, considering that the variable has a normal distribution (I made a quick Shapiro Wilks test, with p-value 0.3234, you can assume normality) the best statistic to use is the Student's t-test.

t= [x(bar)-μ]/S/√n ≈ t₍ₙ₋₁₎

The formula for the confidence interval to estimate the mean is

x(bar)± $t_{n-1; 1-\alpha/2}$ * (S/√n)

The critical value is from a t-distribution with 11 degrees of freedom

± $t_{n-1; 1-\alpha/2} = t_{11; 0.975} = 2.201$

>remember since it's two-tailed, to get the right critical value you have to divide α by 2. So in the text, you received a confidence level of 1-α=0.95 so α=0.05 then α/2=0.025 and 1-α/2=0.975

To construct the interval, you need to first calculate the sample mean and the standard derivation.

Sample

115; 370; 250; 593; 540; 225; 117; 425; 318; 182; 275; 228

n= 12

∑xi = 3638 ∑xi² = 1362670

Sample mean

x(bar): (∑xi)/n = 3638/12 = 303.17 dolars

Standard derivation

S²= 1/n-1*[∑xi²- (∑xi)²/n] = 1/11 * [1362670-((3638)²/12)] = 23614.47 dolars²

S= 153.67 dolars

Confidence interval (95%)

303.17± 2.201* (153.67/√12)

[205,5;400.8]dolars

I hope you have a SUPER day!

3 0

4 years ago

Find a matrix representation of the transformation L(x, y) = (3x + 4y, x − 2y).

mario62 [17]

Answer:

$\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}3&1\\4&-2\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]$

Step-by-step explanation:

The general matrix representation for this transformation would be:

$\left[\begin{array}{cc}x&y\end{array}\right] * A = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]$

As the matrix A should have the same amount of rows as columns in the firs matrix and the same amount of columns as the result matrix it should be a 2x2 matrix.

$\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]$

Solving the matrix product you have that the members of the result matrix are:

3x+4y = a*x + c*y

x - 2y = b*x + d*y

So the matrix A should be:

$\left[\begin{array}{cc}3&1\\4&-2\end{array}\right]$

8 0

3 years ago

The diameter of a semicircle is 8 miles. What is the semicircle's perimeter? Use 3.14 for ​.

The diameter of a semicircle is 8 miles. What is the semicircle's perimeter? Use 3.14 for .