The probability that a student uses Smarthinking Online Tutoring on a regular basis is 0.31 . In a group of 21 students, what is the probability that exactly 5 of them use Smarthinking Online Tutoring on a regular basis?

0.0241

Step-by-step explanation:

This is solved using the probability distribution formula for random variables where the combination formula for selection is used to determine the probability of these random variables occurring. This formula is denoted by:

P(X=r) = nCr × p^r × q^n-r

Where:

n = number of sampled variable which in this case = 21

r = variable outcome being determined which in this case = 5

p = probability of success of the variable which in this case = 0.31

q= 1- p = 1 - 0.31 = 0.69

P(X=5) = 21C5 × 0.31^5 × 0.69^16

P(X=5) = 0.0241

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

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