Answer:
Option B
Step-by-step explanation:
From the figure attached,
Circle D is drawn with the radius = DG or DE
A tangent FG has been drawn at a point G on the circle from an external point F.
By theorem,
Radius of a circle is always perpendicular to the tangent, drawn to the circle from an external point.
Therefore, DG ⊥ FG.
Option B will be the correct option.
Answer: Expected value of the daily cost of operating the machine is 235.264.
Step-by-step explanation:
Since we have given that
E[x]= 0.96 repairs per day
And Var[x] = 0.96 repairs per day.
![E[c]=160+40E[x^2]\\\\E[c]=160+40(Var[x]+(E[x])^2)\\\\E[c]=160+40(0.96+0.96^2)\\\\E[c]=235.264](https://tex.z-dn.net/?f=E%5Bc%5D%3D160%2B40E%5Bx%5E2%5D%5C%5C%5C%5CE%5Bc%5D%3D160%2B40%28Var%5Bx%5D%2B%28E%5Bx%5D%29%5E2%29%5C%5C%5C%5CE%5Bc%5D%3D160%2B40%280.96%2B0.96%5E2%29%5C%5C%5C%5CE%5Bc%5D%3D235.264)
Hence, Expected value of the daily cost of operating the machine is 235.264.
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant
This problem is an Arithmetic Sequence
where
the first term is 
and
the common difference is 
In general we can write an Arithmetic Sequence as a rule
where
a1 is the first term
d is the common difference
so
<u>Find the term a7</u>
![an=a1+d*(n-1)\\ \\ a7=23+(-2)*[7-1]\\ \\\\ a7=23-12\\ \\\\ a7=11](https://tex.z-dn.net/?f=%20an%3Da1%2Bd%2A%28n-1%29%5C%5C%20%5C%5C%20%20a7%3D23%2B%28-2%29%2A%5B7-1%5D%5C%5C%20%5C%5C%5C%5C%20a7%3D23-12%5C%5C%20%5C%5C%5C%5C%20%20%20%20a7%3D11%20%20%20%20%20)
therefore
<u>the answer is</u>
Answer: 15.7 minutes
Step-by-step explanation:
Let x be the time in the beginning (in minutes).
Given: The track team is trying to reduce their time for a relay race.
First they reduce their time by 2.1 minutes.
Then they are able to reduce that time by 10
If their final time is 3.96 minutes, then
x-t1-t2= 3.6
x= 3.6+ t1+ t2
x= 3.6+ 2.1+ 10
x= 15.7
Hence, their beginning time was 15.7 minutes.
Answer:
The answer to the question is
The probability that at least one of the next three customers purchases premium gas is the complement of the probability that none of the next three customers purchase premium gas = 1 - (1-P(A))³ = 0.834
Step-by-step explanation:
The probability that a customer would purchase premium grade = 45 %
That is P(A) = 0.45 and
The probability that the customer would purchase another grade = P(B) = 0.55
Therefore the probability of at least one of the next three customers purchase premium gas is
P(k=0) = (1 - P)ⁿ and the probability of at least one customer purchases premium gas is the compliment of the probability that the next three customers purchase another gas brand
that is (1 - P(A))×(1 - P(A))×(1 - P(A)) = P(B)×P(B)×P(B) = 0.55³ and the complement is 1 - 0.55³ = 0.834
