At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two

1) 4.55

2) Short hit

Step-by-step explanation:

1)

The score and corresponding probabilities are shown in the following table:

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Let us define

X = Miguel's score on the Water Hole

The expected value of the variable X can be represented as:

where

represents the different possible outcomes of X

denotes the associated probabilities

Accordingly, the expected value of Miguel's score is calculated as follows:

2)

Here, we will again consider:

X = Miguel's score on the Water Hole

In this case:

- For a successful long hit, the expected value of X is

- Conversely, if the long hit isn't successful, the expected value of X becomes

We also know that the likelihood of succeeding with a long hit is

Consequently, the chance of failure in a long hit is

Thus, the expected value of X when opting for the long hit strategy is:

In the first part of this question, we calculated the expected value using the short hit strategy, yielding:

Given that the expected value for X is smaller (which is better) when utilizing the short hit option, we can conclude that this approach is superior.

At Super Saver, 4 packs are priced at $10, which gives us 12 × 4 = 48 cans for ratio calculation. The ratio translates to 48 cans for $10, or 4.8 cans per dollar. For Shop Smart, similarly, 24 × 2 results in 48 cans priced at $9, creating a ratio of 48 cans for $9, or 5 1/3 cans per dollar. At Price Busters, 12 × 3 results in 36 cans for $9, translating to a cost of 3 cans per dollar. Overall, Shop Smart offers the best value per can, followed by Super Saver, and lastly Price Busters.