Ah! I love these questions!
To find the area of the shaded region, you must find the area of the circle. Then, you must find the area of the triangle inscribed in the circle. Lastly, you must subtract the area of the triangle from the area of the circle.
Area of Circle:

x

=

x 10^2
=

x 100
Usually these problems will not require you to convert pi into a decimal, but if it does, then the area of the circle would be 314.
Area of Equilateral Triangle:

To find the side, draw a perpendicular line from the center to a side of a triangle. This line will create two more triangles inside the big triangle. You will notice how in these smaller triangles, the angles are 30, 60, 90. From that we can deduce that half the length of a side is 5

because of the 30, 60, 90 ratio. Multiply that by 2 to get 10

as the length of the side of the large triangle. Now substitute this value into the formula above.

Final Answer: 100

- 75
Answer:
450 students
Step-by-step explanation:
Let s = number of students
1/2 are Americans 1/2s are Americans
s -1/2s = number of students left
1/2 s = number of students left
1/3 of the students left are Europeans
1/3 (1/2s) = 1/6s are Europeans
The rest are Australians = 150
Students = Americans + Europeans + Australians
s = 1/2s + 1/6s + 150
Combine like terms
s = 1/2*3/3 *s + 1/6s +150
s = 3/6s + 1/6s +150
s = 4/6s + 150
Subtract 4/6s from each side
s -4/6s = 150
6/6s - 4/6s = 150
2/6s = 150
1/3s = 150
Multiply each side by 3
3* 1/3s = 150*3
s = 450
There are 450 students
Answer: f) None of the above
= ( 5.283, 5.917)
Therefore at 90% confidence interval (a,b) = ( 5.283, 5.917)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 5.6ft
Standard deviation r = 1.0ft
Number of samples n = 27
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
5.6+/-1.645(1.0/√27)
5.6+/-1.645(0.192)
5.6+/-0.317 ft
= ( 5.283, 5.917)
Therefore at 90% confidence interval (a,b) = ( 5.283, 5.917)
Answer:
0.8178
Step-by-step explanation:
To make a 13% decrease in a value, we need to make the difference between the value (X) and 13% of the value:
X - 13% of X = X - 0.13*X = 0.87*X
To make a 6% decrease, following the same method, we just need to multiply the value by (1-0.06) = 0.94
So, to represent in a single decimal value a decrease of 13% and then a decrease of 6%, we just need to multiply the value by 0.87 and then by 0.94:
X*0.87*0.94 = X*0.8178
So the single decimal multiplier is 0.8178
Answer:
and 
Step-by-step explanation:
The number of people is
and the number of hours they are present in the space is
.
Per person entry cost is $8.
Per hour cost of rent is $40.
They plan to earn a minimum of $600.
Donations by all the people entering the space is 
Total cost of renting the space is
which will be subtracted from the total amount of donations.
The inequality that represents the situation is
and
.