The guidance department has reported that of the senior class, 7.8% are members of key club, K, 8.6% are enrolled in AP Physics, P, and 6.7% are in both. 1) Determine the probability of P given K, to the nearest tenth of a percent. 2) The principal would like a basic interpretation of these results. Write a statement relating your calculated probabilities to student enrollment in the given situation.

the probability of P given K is 0.86

Step-by-step explanation:

Conditional probability is defined as the probability that an event would happen based on the occurrence of an event that has already happened. It is calculated by multiplying the probability of the both the preceding event and the succeeding event together. It is given by the formula:

Given that:

Probability of members in the key club P(K) = 7.8% = 0.078

Probability of members enrolled in AP physics P(P)  = 8.6% = 0.086

Probability of members in both P(P n K) = 6.7% = 0.067

Therefore:

the probability of P given K is 0.86

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

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

happy to

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