Adding up all 6 probabilities gives a total of 1, which means that this is a valid distribution function. Observing that P(0) = P(5), P(1) = P(4), and P(2) = P(3), this is a symmetric distribution.
Its mean will be in the middle, which is at x = 2.5.
The standard deviation is calculated by multiplying each P(x) by the square of deviation (x - average)^2: (0.032)(0 - 2.5)^2 + (0.152)(1 - 2.5)^2 + (0.316)(2 - 2.5)^2 + (0.316)(3 - 2.5)^2 + (0.152)(4 - 2.5)^2 + (0.032)(5 - 2.5)^2 = 1.242, then taking the square root: sqrt(1.242) = 1.1145.
N=number of nickles
d=number of dimes
q=number of quarters
use cents for everything
total value=585
5n+10d+25q=585
divide everybody by 5 to simplify
n+2d+5q=117
we have
nicles are 5 more than quarters
n=5+q
4 times as many dimes as quarters
d=4 times q
d=4q
sub those in
5+q+2(4q)+5q=117
5+6q+8q=117
5+14q=117
minus 5
14q=112
q=8
sub back
n=5+q
n=5+8
n=13
d=4q
d=4(8)
d=32
13 nickles
32 dimes
8 quarters
divide both sides by 22
91
Explanation: Since the ones digit ends in a 3, that means the the ones digits of the two consecutive integers must be 1 and 2 or 6 and 7. However, you see 18 in the number 183. 9 + 9 = 18. When you add 6 and 7, you have to carry over one. However, when you add 1 and 2, you do not. Therefore, the two consecutive numbers are 91 and 92. 91 is the smaller integer, so that is the answer.
Answer: 6
Step-by-step explanation:
