Brent claims that more students at his school prefer hot dogs over hamburgers. His friend Shaun doesn’t agree. To settle their argument they conduct a random survey of 542 males and 635 females. When the survey results come in, hamburgers are chosen by 34.2% of the females and hot dogs are preferred by 184 males.

Brent, satisfied with the results, proclaims “Yes, hot dogs it is!” Shaun is dismayed by the results and believes that the results are influenced by surveying too many females. How can Shaun use probabilities to convince Brent that the outcome is influenced by gender?

Explanation:

To prove that the results are influenced by gender you can calculate both the probability of preferring hot dogs and the conditional probability of preferring a hot dog given that is a female.

If the two results are different the probability of preferring hot dog is dependent on whether the person is a female or a male.

The probability of preferring hot dogs given that is a female is stated by the problem: 34.2%.

The probability of preferring hot dogs by the whole sample is:

         100% - 34.2% = 65.8%

         65.8% of 635 = 0.658 × 635 = 417.83 ≈ 418

              number of students that preffer hot dogs / number of students =

              (184 + 418) / 1177 = 602 / 1177 = 0.5115 ≈ 51.2%

Thus, the probability of preferring hot dogs given that the student is a female (34.2%) is different from the probability of preferring hot dog for the whole sample, making the results dependent of the gender.

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

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8