The number of calls that come into a small mail-order company follows a poisson distribution. currently, a single operator services these calls. the manager knows from past experience that an additional operator will be needed if the rate of calls exceeds 20 per hour. the manager observes that 9 calls came into the mail-order company during a randomly selected 15-min a. if the rate of calls is actually 20 per hour, what is the probability that 9 or more calls will come in during a given 15- minute b. if the rate of calls is really 30 per hour, what is the probability that 9 or more calls will come in during a given 15- c. based on the calculations in parts a and b, do you think that the rate of incoming calls is more likely to be 20 or 30 per hour? d. would you advise the manager to hire a second operator? explain.

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.

.25

step-by-step explanation:

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x