Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-

Answer:

The equation 0 = 3x² + 17x - 160 might be useful in determining the length.

Step-by-step explanation:

The area of the vegetable garden is specified as 170 ft².

Now, regarding the provided equations;

1) For 0 = 3x² + 2x + 180, applying the quadratic formula results in:

x = [-2 ± √(3² - 4(3 × 180)]/(2 × 3)

x = [-2 ± √(-2151)]/6

The square root value is negative, indicating no real solution for x.

Thus, this equation does not help find the length.

2) For the equation 0 = 3x² + 10x + 180, employing the quadratic formula, the square root value is also negative, hence there's no natural root for x. This means this equation can't be used to determine the length.

3) For 0 = 3x² + 17x - 160, the roots when using the quadratic formula yield -10.67 or 5. The value 5 is viable since it is a whole number. Considering the area is also a whole number, this equation can be applied to ascertain the length.

4) For 0 = 3x² - 160, simplifying gives;

3x² = 160

x² = 160/3

x = ±√(160/3)

x = ±7.303

Since the area is a whole number but this length isn't, this equation may not accurately determine the length.

Answer:

With the addition of a child, both the family's income and expenses increase. Although the initial expenses might be higher, the financial benefits will manifest over time.

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.

Response:

Tan x = 125/500 = 0.25

therefore, x = arctan (0.25)

= 14 degrees