*see attachment for diagram
Answer:
Perimeter = 38
Step-by-step explanation:
Recall: when two tangents are drawn to meet at a point outside a circle, the segments of the two tangents are congruent.
Given,
CQ = 5
PQ = 10
PR = 14
Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR
CQ = QB = 5 (tangents drawn from an external point)
BP = PQ - QB
BP = 10 - 5 = 5
BP = PA = 5 (tangents drawn from an external point)
AR = PR - PA
AR = 14 - 5 = 9
AR = RC = 9 (tangents drawn from an external point)
✔️Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR
= 9 + 5 + 5 + 5 + 5 + 9
Perimeter = 38
Answer:
(a): Marginal pmf of x


(b): Marginal pmf of y


(c): Mean and Variance of x


(d): Mean and Variance of y


(e): The covariance and the coefficient of correlation

Step-by-step explanation:
Given
<em>x = bottles</em>
<em>y = carton</em>
<em>See attachment for complete question</em>
<em />
Solving (a): Marginal pmf of x
This is calculated as:

So:






Solving (b): Marginal pmf of y
This is calculated as:

So:






Solving (c): Mean and Variance of x
Mean is calculated as:

So, we have:




Variance is calculated as:

Calculate 




So:




Solving (d): Mean and Variance of y
Mean is calculated as:

So, we have:




Variance is calculated as:

Calculate 




So:




Solving (e): The covariance and the coefficient of correlation
Covariance is calculated as:

Calculate E(xy)

This gives:




So:




The coefficient of correlation is then calculated as:





--- approximated
3 + 2k
This is because multiplying by 1/5 is like dividing each term by 5
So I'm hoping you mean 6, or else the probability is 0. So the possible ways of getting a sum of 6 is 1&5, 2&4, 3&3, 4&2, 5&1. There are 36 different ways of rolling the dice, so divide the 5 possible ways by 36. Then, we need to add the possibility of getting at least one 6 in the roll. It doesn't matter what the other die is, so for each die, the probability is 1/6, and for both, the probability is 2/6. Add this to the probability of getting a sum of 6, and you get your answer.
1/4-1/16=
=1*4/16 - 1*1/16
=4/16-1/16
=3/16
Or 1/8