A softball pitcher has a 0.675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If the softball pitcher throws 29 pitches, we want to know the probability that exactly 19 of them are strikes.

The probability that exactly 19 of them are strikes is 0.1504

Step-by-step explanation:

The binomial probability parameters given are;

The probability that the pitcher throwing a strike, p = 0.675

The probability that the pitcher throwing a ball. q = 0.325

The binomial probability is given as follows;

Where:

x = Required probability

Therefore, the probability that the pitcher throws 19 strikes out of 29 pitches is found as follows;

The probability that exactly 19 of them are strikes is given as follows;

Hence the probability that exactly 19 of them are strikes = 0.1504

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet