Jessica records the number of winners at the dunk a teacher booth at the town fair as shown in the table. if there are 750 contestants on monday how many times would jessica expect to dunk a teacher.
day contestants winners
fri 215 27
sat 417 54
sun 368 39

The expected number of winners that will dunk a teacher on Monday = 90

Step-by-step explanation:

For the three days leading to Monday, the total number of contestants, the number of winners that dunked a teacher and the proportion of contestants that are winners is given in the table

day | contestants | winners | proportion

fri | 215 | 27 | 0.1256

sat | 417 | 54 | 0.1295

sun | 368 | 39 | 0.1060

Making the informed prediction that the proportion of contestants that will be winners on Monday is an average of the proportions from Fri, Sat and Sun

(0.1256 + 0.1295 + 0.1060)/3 = 0.1204

So, the expected number of winners on Monday = np = 750 × 0.1204 = 90.3 = 90 winners.

OR

We could also estimate the expected proportion of contestants that will be winners on Monday by summing up all the winners from Fri, Sat and Sun, and dividing it by the total number of winners from those three days.

Expected proportion of winners on Monday

= (27 + 54 + 39) ÷ (215 + 417 + 368)

= 0.12

Expected number of winners on Monday = np = 0.12 × 750 = 90

Hope this Helps!!!

the 3rd option is right

step-by-step explanation:

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