What is an estimate of 23 times 67

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.

MrRa [10]

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.

8 0

3 years ago

Write the interval (5 , 100) as an inequality and using set notation.

Alex_Xolod [135]

Answer:

5

Step-by-step explanation:

5 100

500

100

600

10000

3 0

3 years ago

In the scale used on a blueprint, 34

nydimaria [60]

Answer:

67

Step-by-step explanation:

123£

5 0

3 years ago

If the pond has a radius of 6.5 ft how much fencing will he need

andre [41]

6.5 times 2 then that time pi or 3.14

5 0

3 years ago

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

motikmotik

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$