Marks books has an area of 48 in.². The perimeter of the book is 52 inches. what are the dimensions of the book
1 answer:
Answer:
dimensions of the book are 2 in. by 24 in.
Step-by-step explanation:
I assume the book is a rectangle
Let w = the width
l = the length
A = lw = 48 P = 2w + 2l = 52
w + l = 26
l = 26 - w
w(26-w) =48
26w - = 48
(w-2)(w -24) = 0
w = 2 or w = 24
if w = 2, then l = 26 - 2 = 24
if w = 24, then l = 26 - 24 = 2
So, the dimensions of the book are 2 in. by 24 in.
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Answer and Explanation:
Given : The random variable x has the following probability distribution.
To find :
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x.
c. Calculate the variance of x.
d. Calculate the standard deviation of x.
Solution :
First we create the table as per requirements,
x P(x) xP(x) x² x²P(x)
0 0.25 0 0 0
1 0.20 0.20 1 0.20
2 0.15 0.3 4 0.6
3 0.30 0.9 9 2.7
4 0.10 0.4 16 1.6
∑P(x)=1 ∑xP(x)=1.8 ∑x²P(x)=5.1
a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.
Yes it is a probability distribution.
b) The expected value of x is defined as
c) The variance of x is defined as
d) The standard deviation of x is defined as