Answer:
a) 3/64 = 0.046 (4.6%)
b) 63/64 = 0.9843 (98.43%)
c) 1/64 = 0.015 (1.5%)
d) 1/4 = 0.25 (25%)
Step-by-step explanation:
in order to verify that the f(x) is a probability mass function , then it should comply the requirement that the sum of probabilities over the entire space of x is equal to 1. Then
∑f(x)*Δx = 1
if f(x)=(3/4)(1/4)^x , x = 0, 1, 2, ...
then Δx=1 and
∑f(x) = (3/4)∑(1/4)^x = (3/4)* [ 1/(1-1/4)] = (3/4)*(4/3) = 1
then f represents a probability mass function
a) P(X = 2)= f(x=2) = (3/4)(1/4)^2 = 3/64 = 0.046 (4.6%)
b) P(X ≤ 2) = ∑f(x) = f(x=0)+ f(x=1) + f(x=2) = (3/4) + (3/4)(1/4) + 3/64 = 63/64 = 0.9843 (98.43%)
c) P(X > 2)= 1- P(X ≤ 2) = 1 - 63/64 = 1/64 = 0.015 (1.5%)
d) P(X ≥ 1) = 1 - P(X < 1) = 1 - f(x=0) = 1- 3/4 = 1/4 = 0.25 (25%)
28/7 =4
7•4 is 28 or
7+7+7+7 is also 28
First you’d start off by finding the volume of the rectangular prism on the bottom. The formula for this is lwh or (length*width*height) so you’d plug in the numbers and get 4*4*5 which multiplies out to be 80inches cubed. Next you’d have to find the volume of the pyramid by using the formula lwh/3 or ((length*width*height)/3) so it would be ((4*4*6)/3) and that equals 32inches cubed. Finally, you add the 2 volumes together so 80inches cubed+32inches cubed and get 112inches cubed. Hope this helps
X^2-9=0 add 9 to both sides
x^2=9 take the square root of both sides
x=±3
