Recall that for

, i.e. a random variable

following a binomial distribution over

trials and with probability parameter

,

So you have




The expected value of

is simply

, while the standard deviation is

. In this case, they are

and

, respectively.
Answer: 2nd diagram, explanation below
Step-by-step explanation:
Since it is 8 magnet students for 3 magic students, the second diagram is correct.
The second part, you would need to set up a system of equations:
Let m = magnet students and t = magic students
t + 25 = m
(8/3)t = m. Since m = m, substitute: t + 25 = (8/3)(t). Now solve for t: t = 8t/3 - 25,
t = (8t - 75)/3, in this step I turned 25 into 75/3 and place it with 8t so it doesn't change the value of the equation.
3t = 8t - 75, in this step I multiplied every term by 3 to eliminate the demoninator. Now I solve the final steps:
-5t = -75, 5t = 75
t = 15
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set up an equation for this. x will be the score of the losing team. x+2x=96. Then solve for x. 3x=96. x=96/3 x=32. So the losing team got 32 points and the winning team got 64
<span>Slope of JK=((-1)-2)/(4-(-3)=-3/7
Slope of KL=((-5)-(-1)/(2-4=2
Slope of LM=((-2)-(-5))/(-5-2)=-3/7
Slope of MJ=(2-(-2))/((-3)-(-5))= 2
JK is parallel to LM and KL is parallel to MJ. Therefore JKLM is a parallelogram.</span>
Answer:
4089
Step-by-step explanation:
798/8 x 41=
99.75 x 41 =
4089.75
Hope it helps