Afitness center runs a contest for customers who enroll in its annual membership plan. the customers are allowed to draw a coupon from a jar that contains 20 coupons for 1 month of extended membership, 10 coupons for 1.5 months of extended membership, and 5 coupons for 2 months of extended membership. assuming a month has 30 days, if the expected value of extended membership (in days) on the first draw is given by the expression a + b + c, identify the correct numerical expressions for a, b, and c.

1. 20/35(30)=17.142

2. 5/35(60)=17.142

3. 10/35(60)=17.142

A = 24 , B = 12.85, C = 8.57

Step-by-step explanation:

Since we have given that

Number of coupons for 1 month = 20

Number of coupons extended for 1.5 months = 10

Number of coupons extended for 2 months = 5

Total number of coupons is given by

1 month = 30 days

So, Expected value of extended membership = A+B+C

Here, A is given by

B is given by

C is given by

So, The expected value of extended membership is given by

Hence, A = 24 , B = 12.85, C = 8.57

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

it would be:

c.parallelogram.