on a road trip, the Morgan family traveled 408 miles in 6 hours, how many miles did the family travel in 4 1/2 hours?
1 answer:
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Answer:
a) 0.984
b) 20 people
Step-by-step explanation:
a)
If The probability that a person carries the gene is 0.1, then in a sample of 20 people, 2 should carry the gene.
Now, we want to know how many samples there are with this property.
Since we have 20 elements where 18 are alike (do not carry the gene) and 2 are alike (carry the gene), we have to compute the number of permutations of 20 elements in which 18 are alike and 2 are alike. This number is
In this 190 20-tuples there are only 3 where the 2 carriers of the gene are in the first 3 places, namely
(1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
(1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
(0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
where 1=carries the gene, 0=does not carry the gene.
So there are 190-3 = 187 elements in which the first 3 elements have no 2 carriers, hence the probability that 4 or more people will have to be tested until 2 of them with the gene are detected is 187/190 = 0.984 (98.4%) rounded to three decimal places.
b)
Given that the probability that a person carries the gene is 0.1, then in a sample of 20 people, 20*0.1 = 2 should carry the gene.
Let's use the variable x to represent the length of the first and second pieces.
If the third piece has twice the length of the first and second, its length is 2x.
If the fourth piece has half the length of the first and second, its length is 0.5*x.
Adding all four pieces and equating to 54 inches, we have:
So the length of each piece is:
12 inches, 12 inches, 24 inches and 6 inches.
Answer:
PS=5.4
Step-by-step explanation:
The centroid divides each median in the ratio 2:1
If U is the centroid, then
We use ratio to obtain;
Cross multiply;
Expand;
Group similar terms;
x=1
PS=PU+US
PS=3.6+1+0.8
PS=3.6+1+0.8
PS=5.4