Shelly buys 10 candy bars and gives 4 to her friends. How many candy bars does she have left
1 answer:
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Answer: The correct option is (B) 24 : 25.
Step-by-step explanation: Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.
We are to find the ratio of the area of R to the area of S.
Let 2x, 3x be the sides of rectangle R and y be the side of square S.
Then, according to the given information, we have
Therefore, the ratio of the area of R to the area of S is
Thus, the required ratio of the area of R to the area of S is 24 : 25.
Option (B) is CORRECT.
Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:
f(x) = λ.
and the cumulative distribution function, which describes the probability distribution of a random variable X, is:
F(x) = 1 -
(a) <u>Probability</u> of distance at most <u>100m</u>, with λ = 0.0143:
F(100) = 1 -
F(100) = 0.76
<u>Probability</u> of distance at most <u>200</u>:
F(200) = 1 -
F(200) = 0.94
<u>Probability</u> of distance between <u>100 and 200</u>:
F(100≤X≤200) = F(200) - F(100)
F(100≤X≤200) = 0.94 - 0.76
F(100≤X≤200) = 0.18
(b) The mean, E(X), of a probability distribution is calculated by:
E(X) =
E(X) =
E(X) = 69.93
The standard deviation is the square root of variance,V(X), which is calculated by:
σ =
σ =
σ = 69.93
<u>Distance exceeds the mean distance by more than 2σ</u>:
P(X > 69.93+2.69.93) = P(X > 209.79)
P(X > 209.79) = 1 - P(X≤209.79)
P(X > 209.79) = 1 - F(209.79)
P(X > 209.79) = 1 - (1 - )
P(X > 209.79) = 0.0503
(c) Median is a point that divides the value in half. For a probability distribution:
P(X≤m) = 0.5
= 0.5
= 0.5
=
= 0.5
= - 0.5
ln() = ln(0.5)
-0.0143.m = - 0.0693
m = 48.46