Expected Mean, E(X), is obtained by multiplying each pair of
and its
and add up the answers
E(X) = (0×0.7) + (1×0.2) + (2×0.1) = 0.4
The formula to calculate the variance, Var(X), is given by E(X)² - (E(X))²
E(X²) = (0²×0.7) + (1²×0.2) + (2²×0.1) = 0+0.2+0.4 = 0.6
(E(X))² = (0.4)² = 0.16
Var(X) = 0.6 - 0.16 = 0.44
Translating these answers into the context we have
E(Y) = 0.4×500 = $200
Var(Y) = $110
Answer:
0.7673
Step-by-step explanation:
We have the following:
The null and alternative hypothesis is,
H0: m = 290
Ha: m> 290
x = 285.2
m = 290
sd = 59.3
n = 82
is m the mean, sd the standard deviation and n the population size
Now we calculate the value of z like this:
z = (x - m) / sd / (n ^ (1/2))
z = (285.2 - 290) / 59.3 / (82 ^ (1/2))
z = -0.73
now
P (z> -0.73) = 1 - P (z <-0.73)
we look at the normal distribution table
P = 1 - 0.2327 = 0.7673
Therefore the value of p is equal to 0.7673
Ming-Li had $75 to begin with. Just add all the numbers
Answer: at 11:54
Step-by-step explanation:
Let's define the 10:30 as our t = 0 min.
We know that Train A stops every 12 mins, and Train B stops every 14 mins, they will stop at the same time in the least common multiple of 12 and 14.
To find the least common multiple of two numbers, we must do:
LCM(a,b) = a*b/GCD(a,b)
Where GCD(a, b) is the greatest common divisor of a and b.
In this case the only common divisior of 12 and 14 is 2.
So we have:
LCM(12, 14) = 12*14/2 = 84.
Then the both trains will stop 84 minutes after 10:30
one hour has 60 mins, so we can write 84 minutes as:
1 hour and 24 minutes = 1:24
Then they will stop at the same time at 10:30 + 1:24 = 11:54
using the ratio, the length of the sides are:
25x + 14x + 12x = 170
51x = 170
x = 170 / 51
x = 3 1/3
The lengths of the sides are: 25 * 3 1/3 = 83 1/3 feet
14 x 3 1/3 = 46 2/3 feet
12 x 3 1/3 = 40 feet
Using Heron's formula
the semi perimeter (S) = 170/2 = 85 ft.
The area of the triangle = SQRT(S*(S-83 1/3) * (S - 46 2/3) * (S-40))
= SQRT (85 * (85-83 1/3) * (85 - 46 2/3) * (85-40)
= SQRT (85 * 1 2/3 * 38 1/3 * 45)
= SQRT(244374)
= 494.34 square feet ( round answer as needed).
