<span>Use inductive reasoning</span>
Answer:
probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)
=194/285 or 0.6807.
Step-by-step explanation:
The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.
The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.
Hence
|E'| = C(14,3)
= 14×13×12/3!.
Therefore probability P(E')
= |E'|/|S|
= (14×13×12)/(20×19×18)
= (14×13×2)/(20×19×3)
=(7×13)/(5×19×3)
= 91/285.
Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.
Answer:
161 pounds
Step-by-step explanation:
There are two ways to do this
ratio is 2:5
Amanda : Wim
from the ratio we know that the whole is 2+5 = 7 parts
so Amanda gets 2/7 parts and Wim gets 5/7 parts
Wim gets 115 which means that his part is equal to that amount of money
5/7 = 115
so we can find for all of the parts in two different ways.
1. Either we find Amanda's part and add it to Wim's part to find the total like this:
If 5/7 = 115 then
1/7 = 115/5
= 23
Amanda's part = 2/7
2/7 = 23×2
= 46 pounds
total = 115 pounds + 46 pounds
= 161 pounds altogether
OR
2. Just find the whole:
If 5/7 = 115
then 1/7 = 115/5
=23
and 7/7 (which is the whole) = 23×7
= 161 pounds altogether
Hope that helps
Answer:
m=4
m: 8
Step-by-step explanation: