A designer draws two circles, each of area 3.14 square feet. The centers of the circles are 4 feet apart. Do the circles overlap
1 answer:
Answer:
No, the circles do not overlap
Explanation:
r = Radius of circle
A = Area = 3.14 square feet
Area of one circle
The radius of the each of the circles is 1 ft.
If the circles centers are 4 ft apart then the distance between the curves of the circle will be 2 ft apart.
So, the circles do not overlap each other. This is shown in the diagram.
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Answer:
The maximum time guaranteed = 19.04 minutes.
Explanation:
From the given problem data, we have:
Let Y be the random variable which follows the normal distribution.
So,
Y ~ N(u = 15, SD = 2.4
Where, u = mean and SD = Standard Deviation
Let the maximum time guaranteed is = M
So,
P (Y > M) = 0.05 equation 1
Convert this equation 1 into standard normal variable, that is,
P(Y> M) = 0.05
1 - P(Y M) = 0.05
P(Y M) = 1 - 0.05
P(Y M) = 0.95
P = 0.95
P ( Z ) = 0.95 Equation 2
From the equation 2, we have,
= 1.644853627
1.644853627 value is from using the function of Excel
( =NORSINV(0.95)) = 1.644853627
So,
M = 1.644853627 + 2.4 + 15
M = 19.04
Hence, the maximum time guaranteed = 19.04 minutes.