(d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score?

*Answers are bolded down below with the explanations.  Anything bolded is an answer*

Step-by-step explanation:

To start off, let's just recap on what a unit rate is.  A unit rate is a ratio of a quantity of multiple to a quanitity of 1.

1. $11.49/3 packages=$3.83 per 1 package

2. 2,550 gallons/30 days=85 gallons in 1 day

4. 15.6°F/13 minutes=1.2°F in 1 minute

5. 175 Calories/12 ounces=14.58 Calories per 1 ounce

6. 258.5 miles/5.5 hrs=47 miles in 1 hr

7. 549 vehicles/9 acre=61 vehicles per 1 acre

8. $920/40 hrs=$23 per 1 hr

9. 13 apples/2 pies=6.5 apples per 1 pie

12. estimate: $299/4 tires≈$75 per 1 tire

reasoning: Let's round $299 to $300 first.  Now, 100/4=25, and 100*3=300, so multiply 25*3 to get 75 as your best estimate.

13. estimate: $13.47/3 yards of fabric≈$4.50 per 1 yard of fabric

reasoning: 13.47 is in between 12 and 15, which are both divisible by 3.  12/3=4 and 15/3=5.  Since, 13.47 is sort of in between those numbers, take the decimal number in the middle between 4 and 5 which is 4.50 as the best estimate.