On the first play of the game, the Wildcats gained 8 yd. What integer represents a gain of 8 yd?

Answer:

The composite function;

f(g(x) = 2x^2 + 15

Step-by-step explanation:

Given f(x) = 2x + 1 and g(x) = x^2 + 7;

we are tasked with calculating f(g(x))

This represents a composite function where we substitute g(x) into f(x)

Consequently, we find

f(g(x)) = 2(x^2 + 7) + 1

f(g(x)) = 2x^2 + 14 + 1

f(g(x)) = 2x^2 + 15

Answer:

There is a probability of 24.51% that the weight of a bag exceeds the maximum permitted weight of 50 pounds.

Step-by-step explanation:

Problems dealing with normally distributed samples can be addressed using the z-score formula.

For a set with the mean and a standard deviation , the z-score for a measure X is calculated by

Once the Z-score is determined, we consult the z-score table to find the related p-value for this score. The p-value signifies the likelihood that the measured value is less than X. Since all probabilities total 1, calculating 1 minus the p-value gives us the probability that the measure exceeds X.

For this case

Imagine the weights of passenger bags are normally distributed with a mean of 47.88 pounds and a standard deviation of 3.09 pounds, thus

What probability exists that a bag’s weight will surpass the maximum allowable of 50 pounds?

That translates to

Thus

has a p-value of 0.7549.

Additionally, we have that

There is a probability of 24.51% that the weight of a bag will exceed the maximum allowable weight of 50 pounds.

Answer:

150 short-sleeve shirts were ordered

100 long-sleeve shirts were ordered

Conclusion:

Please refer to the explanation provided.

Detailed explanation:

Starting with these facts:

Total revenue = $250

Fee charged = $70 per car

Tips received = $50

Equation 1 representing the above:

(Fee per car × number of cars) + tips = total revenue

Let the number of cars be c.

Thus, we have:

$70c + $50 = $250

Part B:

Total revenue = $250

Fee charged = $75 per car

Tips received = $35

Supplies cost per car washed = $5

Equation 2:

(Fee per car × number of cars) + tips - (supplies cost × number of cars) = total revenue

$75c + $35 - $5c = $250

$70c + $35 = $250

Part C:

Equation 1 does not factor in costs associated with washing the car, while equation 2 does incorporate costs, which are deducted from the amount charged per car. Additionally, tips in equation 1 total $50 compared to a $35 fee in equation 2.