# Tutor profile: Katherine R.

## Questions

### Subject: Trigonometry

A person stands 15 feet from a mushroom that is flat on the ground, and takes a picture of it. If you know the person's height, can you determine the angle at which they took the picture of the mushroom?

Yes. If, for example, the person was six feet tall, the angle at which the person holds the camera would be the inverse tangent of 15/6 (opposite side over adjacent). That yields 0.2507 radians. Converting this to degrees (0.2507 * (180/pi)), we get 14.36 degrees.

### Subject: Statistics

A university conducted a study to determine if a certain type of gum can discourage smoking in a person. 20 smokers from the university recorded how many cigarettes they smoked during a week without the gum and then how many cigarettes they smoked during a week in which they also chewed the gum once a day. What is your null and alternative hypothesis, what type of test would you use to determine the gum's effectiveness in discouraging smoking, and why?

The null hypothesis is that the participants smoke the same average amount of cigarettes during the week they chew the gum as during the week they do not chew the gum. The alternative hypothesis is that the participants smoke fewer cigarettes the week they chew the gum than during the week they do not chew the gum. You would use a paired t-test to compare the means since the samples are dependent.

### Subject: Algebra

A single ticket to the fair is $9. A 5-day pass to the fair is $33. How many times do you need to go to the fair for the 5-day pass to be a good deal?

The 5-day pass is a "good deal" if you visit enough times that it is less expensive than paying $9 per visit. I.e, 9x < 33, where x = number of visits. Divide by 9 on each side to get x = 3.667. Round up to four visits.

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