Question

A local arcade charges $15.00 for unlimited play time for the first hour, then $5.00 per additional hour. On a piece of paper, write an equation that represents the cost to play, C , based on the number of hours played, h. Then use the equation to calculate how much it would cost to play for three hours. Enter your answer for C , including cents.(1 point) $

Answer 1

To create an equation that represents the cost to play, C, based on the number of hours played, h, we can divide the pricing structure into two parts:

1. For the first hour (when \(0 < h \leq 1\)), the cost is $15.00.
2. For any additional hours (when \(h > 1\)), the cost is $5.00 for each additional hour after the first hour.

Thus, the equation can be represented as:

\[ C = \begin{cases} 15 & \text{if } 0 < h \leq 1 \ 15 + 5(h - 1) & \text{if } h > 1 \end{cases} \]

Now, to calculate the cost for three hours played (\(h = 3\)):

Using the equation for \(h > 1\):

\[ C = 15 + 5(3 - 1) \]

Calculating further:

\[ C = 15 + 5(2) = 15 + 10 = 25 \]

Thus, the cost to play for three hours is:

\[ C = 25.00 \]

So, the final answer for \(C\) is:

$25.00

Answer 2

The bowling alley charges a flat rate for a lane, plus a fee per shoe rental. Use the equation C=15+3x to solve for the cost of getting a lane and four shoe rentals. Enter your answer, including cents.(1 point) $

Answer 3

In the equation \( C = 15 + 3x \):

• \( C \) represents the total cost.
• The flat rate for a lane is $15.
• The variable \( x \) represents the number of shoe rentals.
• The fee per shoe rental is $3.

For four shoe rentals (i.e., \( x = 4 \)), we can substitute \( x \) into the equation:

\[ C = 15 + 3(4) \]

Calculating this step-by-step:

1. Calculate \( 3(4) \): \[ 3 \times 4 = 12 \]

2. Now, substitute back into the equation: \[ C = 15 + 12 \]

3. Add the values: \[ C = 27 \]

Thus, the total cost for getting a lane and four shoe rentals is:

\[ C = 27.00 \]

So, the final answer is:

$27.00

Answer 4

For a large group of students, the Boston Ballet charges a flat rate of $50.00, plus $15.00 per ticket. How much would a school need to take a class of 25 students to see The Nutcracker? Use an equation with two variables to solve this problem.(1 point) Responses $1,265.00 $1,265.00 $50.00 $50.00 $425.00 $425.00 $375.00

Answer 5

To find the total cost for a school to take a class of 25 students to see The Nutcracker, we can use the equation:

\[ C = 50 + 15n \]

Where:

• \(C\) is the total cost.
• \(50\) is the flat rate charged by the Boston Ballet.
• \(15\) is the cost per ticket.
• \(n\) is the number of tickets (students).

For a class of 25 students, we can substitute \(n = 25\) into the equation:

\[ C = 50 + 15(25) \]

Calculating this step-by-step:

1. Calculate \(15(25)\): \[ 15 \times 25 = 375 \]

2. Now, substitute back into the equation: \[ C = 50 + 375 \]

3. Add the values: \[ C = 425 \]

Thus, the total cost for the class of 25 students is:

\[ C = 425.00 \]

The correct response for the school's total cost is:

$425.00

Answer 6

The school soccer team is selling chips to fundraise for new jerseys. If they charge $2.50 per bag of chips, how many bags would they need to sell in order to raise $1,000.00?(1 point) Responses 500 bags 500 bags 40 bags 40 bags $400.00 $400.00 400 bags 400 bags

Answer 7

To determine how many bags of chips the school soccer team needs to sell to raise $1,000.00, we can set up the following equation:

Let \( x \) be the number of bags sold. The revenue generated from selling \( x \) bags at $2.50 per bag can be expressed as:

\[ 2.50x = 1000 \]

To solve for \( x \), we divide both sides of the equation by 2.50:

\[ x = \frac{1000}{2.50} \]

Calculating that:

\[ x = 1000 \div 2.50 = 400 \]

So, the school soccer team needs to sell 400 bags of chips in order to raise $1,000.00.

The correct response is:

400 bags

Answer 8

Which of the following examples represents a discrete data constraint with viable solutions?(1 point) Responses average weight of all the newborns in a hospital ward average weight of all the newborns in a hospital ward number of tests passed number of tests passed distance between points distance between points average score on a test

Answer 9

Discrete data consists of countable values that can only take certain specific values, usually whole numbers, and often represent items or events that cannot be subdivided.

Among the provided options, the example that represents a discrete data constraint with viable solutions is:

number of tests passed

This is because the number of tests passed can only take whole number values (e.g., 0, 1, 2, etc.), making it a discrete variable.

The other options, such as average weight, distance, and average score, involve measurements that can take on any value within a range and are typically considered continuous data.

Thus, the answer is:

number of tests passed

Answer 10

Which of the following options could use both intercepts to produce viable solutions? (1 point) Responses (temperature, number of car rentals) (temperature, number of car rentals) (age, weight) (age, weight) (number of nominations, number of awards) (number of nominations, number of awards) (years of experience, starting salary) (years of experience, starting salary)

Answer 11

To determine which pairs of variables could use both intercepts to produce viable solutions, we generally want to look for pairs of quantities that can have meaningful interpretations involving both axes in a Cartesian coordinate system.

Here’s a breakdown of the options:

1. (temperature, number of car rentals): While temperature might influence the number of car rentals, it does not naturally lead to meaningful "intercepts" in a typical sense.

2. (age, weight): Age and weight are both continuous and directly related, but using both intercepts in a meaningful way is not generally applicable.

3. (number of nominations, number of awards): This could potentially use both intercepts. For example, one could have zero nominations leading to zero awards, and conversely, if the relationship is linear, one could have specific patterns of nominations leading to specific awards.

4. (years of experience, starting salary): This is a good combination as well, often leading to meaningful intercepts. In many cases, years of experience could lead to a certain starting salary that logically starts at zero for entry-level positions.

Given these considerations, the options that can use both intercepts meaningfully would likely be:

• (number of nominations, number of awards)
• (years of experience, starting salary)

Both of these combinations make sense in terms of linking two variables that can have meaningful starting points (intercepts) and corresponding values on the other variable.

Ultimately, you could argue for either of those pairs, but if the question asks for only one response that is the most representative of using both intercepts effectively, I'd say:

(years of experience, starting salary)

This option typically has a clearer relationship and intercept interpretation in a business or employment context.