The owners of a motel in Florida have noticed that in the long run, about 40% of the people who stop and inquire about a room for the night actually rent a room. (a) How many inquires must the owner answer to be 99% sure of renting at least one room? inquiries (b) If 20 separate inquiries are made about rooms, what is the expected number of inquiries that will result in room rentals? inquiries

(a) n = 9 inquiries

The owner must answer 9 inquiries to be 99% sure of renting at least one room.

(b) E(x) = 8 inquiries

Therefore, the expected number of inquiries that will result in room rentals is 8.

Step-by-step explanation:

The given problem can be solved by Binomial distribution.

Let x be the people who stop and inquire about a room for the night actually rent a room.

P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ  

Where n is the number of trials, x is the variable of interest and p is the probability of success.  

(a) How many inquires must the owner answer to be 99% sure of renting at least one room?

For the given case, we have p = 0.40 and we want to find n such that

P(x ≥ 1) = 0.99

we know that

P(x ≥ 1) = 1 - P(x < 1)

P(x ≥ 1) = 1 - P(x = 0)

So,

1 - P(x = 0) = 0.99

P(x = 0) = 1 - 0.99

P(x = 0) = 0.01

For x = 0 and p = 0.40

P(x = 0) =(ⁿC₀) (0.40)⁰ (1 - 0.40)ⁿ⁻⁰

0.01 = (1)(1)(0.60)ⁿ

0.01 = 0.60ⁿ

ln(0.01) = ln(0.60ⁿ)

ln(0.01) = n ln(0.60)

n = ln(0.01)/ln(0.60)

n = 9.01

Rounding off to nearest whole number

n = 9 inquiries

Therefore, the owner must answer 9 inquiries to be 99% sure of renting at least one room.

(b) If 20 separate inquiries are made about rooms, what is the expected number of inquiries that will result in room rentals?

The expected number of inquiries is given by

E(x) = n×p

For the given case, we have n = 20 and p = 0.40

E(x) = 20×0.40

E(x) = 8 inquiries

Therefore, the expected number of inquiries that will result in room rentals is 8.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

10

step-by-step explanation: