1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
laiz [17]
3 years ago
10

If r = 3.2, what is the area of the shaded region? Round your answer to the nearest hundredth. Use your calculator's value of π.

Mathematics
1 answer:
MrRa [10]3 years ago
8 0

Answer: The shaded area is 99.55 units squared.

Step-by-step explanation:

r = 3.2

Now, we can see that the sides of the square are equal to two times the diameter of the circles (or four times the radius of the circles), so the length of the sides of the square is:

L = 2*(2*3.2) = 12.8

The area of the square is A1 = L^2 = 12.8*12.8 = 163.84 units squared.

the shaded semicircle has a diameter of 4 times r (so the radius is 2 times r), and the area is equal to half the area of a circle:

A2 = (1/2)*pi*(2r)^2 = (1/2)*3.14*(6.4)^2 = 64.31 units squared.

And now we must subtract the area of the four smaller circles inside the square, the area of each one is:

A3 = pi*r^2 = 3.14*(3.2)^2 = 32.15 units squared.

Then the shaded area is:

A = A1 + A2 - 4*A3 = 163.84 + 64.31 - 4* 32.15 = 99.55 units squared.

You might be interested in
Colby wants to set up square tiles on the top of a wooden box. The top of the wooden box is a rectangle 7 1/2 inches long and 5
Andrei [34K]
Yes he can, because when the area of the top of the box is divided by 3/4, you get a whole number, meaning there would be no tile pieces left over, which means that he could cover the top. SEE PICTURE FOR WORK.

6 0
3 years ago
HELP!! VERY TIME TIME SENSITIVE
guapka [62]

Answer:

B is your correct answer

Step-by-step explanation:

3 0
2 years ago
The mean rent of a 3-bedroom apartment in Orlando is $1300. You randomly select 10 apartments around town. The rents are normall
lana [24]

Answer:

96.49% probability that the mean rent is more than $1100

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 1300, \sigma = 350, n = 10, s = \frac{350}{\sqrt{10}} = 110.68

What is the probability that the mean rent is more than $1100?

This is 1 subtracted by the pvalue of Z when X = 1100. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{1100 - 1300}{110.68}

Z = -1.81

Z = -1.81 has a pvalue of 0.0351

1 - 0.0351 = 0.9649

96.49% probability that the mean rent is more than $1100

7 0
3 years ago
Someone give me the answers to this
strojnjashka [21]
Range: the set of all y-values of a graph or equation.

Y-intercept: the y-value where the graph intersects the y-axis.

Domain: the set of all x-values of a graph or equation.

X-intercept: the x-values where the graph intersects the x-axis.

Hope this helps! :)
6 0
3 years ago
Read 2 more answers
If (a+7,b+3)=(0,7)find a and b​
Lerok [7]
A+7=0
A+7-7=0-7
A=-7

B+3=7
B+3-3=7-3
B=4
3 0
3 years ago
Other questions:
  • What would you do first to solve 5x−24=6
    10·1 answer
  • Consider the following incomplete deposit ticket.
    13·2 answers
  • (2.01) solve -2(2x + 5) - 3 = -3(x - 1)
    13·2 answers
  • Which of the following is a mixed number? A. 5/2 B. 2.3 C. 2 1/2 D. 2/5
    14·2 answers
  • Mario has a remaining balance of $1,300 on his credit card. His credit card has an APR of 20 percent. How much will he pay in in
    15·1 answer
  • What’s number 3 & 4 ?!?!?!
    11·1 answer
  • #middleschoolstruggles Please help me with the page. Could u please include an answer and how u got it. Thanks
    10·1 answer
  • X+2y=0<br> 4x+3y=1<br> What's the solution
    13·1 answer
  • Find the x-intercepts, y-intercepts, and the vertex of the following equation. y=x2 – 2x – 15​
    11·1 answer
  • Determine if the ordered pairs represent a function.<br> {(2,5),(4,7), (2,9), (6,10)}
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!