Two race cars,car x an y,are at the starting point of a two km track at the same time.car x and car y make one lap every 60 s an

a) q(p) = -15p + 300; b) R(p) = -15p² + 300p; c) C(p) = -30p + 1600; d) 1) P(p) = -15p² + 330p - 1600; d) 2) p = $11. To develop the demand equation, we plot the values of the cover charge against the number of guests per night for the given coordinates (9,165) and (10,150). The slope provides the relationship needed to formulate the linear equation relating guests and cover charge. The revenue function follows from multiplying price by guests, while the cost function encompasses overhead and beverage expenses associated with operational costs. The profitability equation emerges from subtracting costs from revenues, allowing us to determine the optimal entrance fee for maximum profit.

Response:

If there are "p" pounds of peanuts and "m" pounds of a mixture containing '20% peanuts and 80% almonds', then we can formulate the following equations:

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

The solution yields 5 lb peanuts and 5 lb mixture.

Detailed explanation:

In the mixture that Delaney desires to create, there will be

lb

= 6 lb of peanuts

Thus, there will be (10 - 6) lb

= 4 lb of almonds

If Delaney has "p" pounds of peanuts and "m" pounds of the '20% peanuts and 80% almonds' mixture, then based on the problem statement,

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

From equation (2), we derive

m = 5 --------------(3)

From (1) and (3), we find that

p = (10 - 5) = 5

Answer:

M=2,179.29

The average exceeds the estimate

Her expenses would need to be $1,625.00

Step-by-step explanation:

1.) What is the mean of her friends' personal expenses?

The mean is defined as the average expense value, calculated as follows:

2.) Is the average higher or lower than the estimate?

Given the estimate of $2,110, the average is indeed higher than this estimate.

3.)What amount of personal expenses would Ashley need to maintain a combined average of $2,110 with her friends' amounts for that school year?

Her needed amount of expenses would be $1,625.00.

<span>The flag's dimensions are 40 inches by 55 inches.

Reasoning<span>:
The perimeter equals the sum of all sides. Being rectangular, opposite sides have equal lengths. Thus, the equation is
y + 11/8 y + y + 11/8 y = 190.

Simplifying, we get
2y + 22/8 y = 190.

Expressing 22/8 as a mixed fraction results in
2y + 2 3/4 y = 190.

Combining terms: 4 3/4 y = 190.

Divide both sides by 4 3/4:
y = 190 ÷ 4 3/4.

Converting 4 3/4 to an improper fraction: y = 190 ÷ 19/4.

Dividing by a fraction means multiplying by its reciprocal:
y = 190 × 4/19 = 760/19 = 40.

Since y = 40, calculate 11/8 y = 11/8 × 40 = 440/8 = 55.</span></span>

Answer:

Yes, the cost in dollars and the quantity of yogurt are indeed proportional.

The relationship can be expressed as:

Step-by-step explanation:

1. If varies directly with , it can be represented as:

Here, represents the constant of proportionality.

2. We'll calculate the proportionality constant. Given that and , we have:

3. Thus, the equation becomes:

4. Now, we need to verify proportionality. Substituting , which is the quantity of yogurt purchased by Jonah, we should arrive at $0.48:

5. They are indeed directly proportional.