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3 years ago

Find the area of the shaded region. Round to the nearest tenth if necessary.

Mathematics

1 answer:

Ket [755]3 years ago

7 0

Find the area of the large circle, and subtract the areas of the three smaller circles.

Large circle: diameter = 22 cm; radius = 11 cm

A = pi r^2 = pi * (11 cm)^2 = 121pi cm^2

Circle with 7 cm radius:

A = pi r^2 = pi * (7 cm)^2 = 49pi cm^2

Two small circles:
The largest circle has diameter = 22 cm.
The next larger circle has radius = 7 cm, so diameter = 14 cm
22 cm - 14 cm = 8 cm
The two smallest circles have a sum of diameters = 8 cm
Each smallest diameter = 4 cm, so each smallest radius = 2 cm
A = pi r^2 = pi * (2 cm)^2 = 4pi cm^2 (for each of the smallest circles)

Shaded area = 121pi cm^2 - 49pi cm^2 - 4pi cm^2 - 4 pi cm^2

Shaded area = 64pi cm^2 = 64 * 3.14159... cm^2 = 201.0619... cm^2

Answer: The shaded area is 201.1 cm^2

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Answer:

Step-by-step explanation:

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3 years ago

A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with σ=0.0

oksian1 [2.3K]

<h2>Answer with explanation:</h2>

The confidence interval for population mean is given by :-

$\overline{x}\pm z^* SE$ (1)

, where $\overline{x}$ = sample mean

z* = critical value.

SE = standard error

and $SE=\dfrac{\sigma}{\sqrt{n}}$ , $\sigma$ = population standard deviation.

n= sample size.

As per given , we have

$\overline{x}=74.021$

$\sigma=0.001$

n= 15

It is known that ring diameter is normally distributed.

$SE=\dfrac{0.001}{\sqrt{15}}=0.000258198889747\approx0.000258199$

By z-table ,

The critical value for 95% confidence = z*= 1.96

A 99% two-sided confidence interval on the true mean piston diameter :

$74.021\pm (2.576) (0.000258199)$ (using (1))

$74.021\pm 0.000665120624$

$74.021\pm 0.000665120624\\\\=(74.021- 0.000665120624,\ 74.021+ 0.000665120624)\\\\=(74.0203348794,\ 74.0216651206)\approx(74.020,\ 74.022)$ [Rounded to three decimal places]

∴ A 99% two-sided confidence interval on the true mean piston diameter = (74.020, 74.022)

By z-table ,

The critical value for 95% confidence = z*= 1.96

A 95% lower confidence bound on the true mean piston diameter:

$74.021- (1.96) (0.000258199)$ (using (1))

$74.021- 0.00050607004=74.02049393\approx74.020$ [Rounded to three decimal places]

∴ A 95% lower confidence bound on the true mean piston diameter= 74.020

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2 years ago

In a class of 30 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose

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There are 4 students who have piercings both on their ear and their noses.

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2 years ago

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mars1129 [50]

What???????? Lol I don’t get it

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2 years ago

Read 2 more answers

Write a function for the situation discribed and find the value after 5 yrs. A $12,500 car depreciates 9% each year. Please help

sweet [91]

$\bf \qquad \textit{Amount for Exponential Decay}\\\\
A=P(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &12500\\
r=rate\to 9\%\to \frac{9}{100}\to &0.09\\
t=\textit{elapsed time}\\
\end{cases}
\\\\\\
A=12500(1-0.09)^t\implies A=12500(0.91)^t
\\\\\\
\textit{after 5 years t = 5}\qquad A=12500(0.91)^5$

and surely you know how much that is.

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3 years ago