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)?????????

Question

Responses

$50.00
$50.00

$375.00
$375.00

$425.00
$425.00

$1,265.00
$1,265.00
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Answer 1

To calculate the total cost for a school to take a class of 25 students to see The Nutcracker, we can create an equation with two variables to represent the total cost \( C \).

Let:

• \( s \) be the number of students (in this case, 25)
• \( p \) be the price per ticket ($15.00)
• \( f \) be the flat fee ($50.00)

The equation for the total cost \( C \) can be represented as:

\[ C = f + (p \times s) \]

Substituting the values into the equation:

1. The flat fee \( f = 50.00 \)
2. The price per ticket \( p = 15.00 \)
3. The number of students \( s = 25 \)

Now substituting these values into the equation:

\[ C = 50.00 + (15.00 \times 25) \] \[ C = 50.00 + 375.00 \] \[ C = 425.00 \]

Thus, the total cost for a class of 25 students to see The Nutcracker would be $425.00.

So the correct answer is $425.00.

Answer 2

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

400 bags
400 bags

40 bags
40 bags

$400.00
$400.00

Answer 3

To determine how many bags of chips the school soccer team needs to sell to raise $1,000.00 when each bag is sold for $2.50, you can set up the equation:

Let:

• \( x \) be the number of bags of chips sold.
• The total amount raised needs to equal $1,000.00.

The equation can be represented as:

\[ 2.50x = 1000 \]

To solve for \( x \), divide both sides by 2.50:

\[ x = \frac{1000}{2.50} \] \[ x = 400 \]

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

The correct answer is 400 bags.

Answer 4

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

average score on a test
average score on a test

distance between points
distance between points

number of tests passed
number of tests passed

Answer 5

A discrete data constraint refers to data that can only take on specific, distinct values, often counted in whole numbers. Among the options provided, we need to identify which example fits this criterion.

1. Average weight of all the newborns in a hospital ward: This involves continuous data since weight can take on any value and is not restricted to whole numbers.

2. Average score on a test: This also involves continuous data. Though test scores can be whole numbers, calculating an average can produce decimal values.

3. Distance between points: This typically involves continuous data as distances can be measured in fractions or decimals (e.g., 2.5 miles).

4. Number of tests passed: This is a discrete data constraint because it refers to whole numbers (0, 1, 2, 3, etc.). You cannot pass a fraction of a test.

Thus, the example that represents a discrete data constraint with viable solutions is:

Number of tests passed.

Answer 6

Which of the following options could use both intercepts to produce viable solutions? (1 point)
Responses

(age, weight)
(age, weight)

(years of experience, starting salary)
(years of experience, starting salary)

(temperature, number of car rentals)
(temperature, number of car rentals)

(number of nominations, number of awards)

Answer 7

To determine which of the given options could use both intercepts to produce viable solutions, we need to consider pairs of variables and whether both can logically be represented in a way that interprets intercepts in a meaningful context.

1. (age, weight): Age can take on continuous values, while weight can also be continuous. However, it is not typical to represent them in a way that involves intercepts—they don’t have a clear linear relationship where both axes (age and weight) make sense when the other is zero.

2. (years of experience, starting salary): This is a common relationship in economics and business. As an employee's years of experience increase, their starting salary typically increases, showing a positive relationship. The intercepts will provide context: the salary at zero experience and the experience at a $0 salary.

3. (temperature, number of car rentals): While temperature can affect car rentals, this relationship might not yield meaningful intercepts since temperature could be zero (especially in scales like Celsius or Fahrenheit), but the number of car rentals does not make sense at a temperature of zero.

4. (number of nominations, number of awards): This pair could also work under certain conditions. If a person doesn't receive any nominations, they would not receive awards (zero nominations could lead to zero awards), but this does not strongly utilize both intercepts meaningfully.

Among these options, (years of experience, starting salary) typically has a clearer interpretation with both intercepts providing viable solutions in a professional context.

Therefore, the best choice is (years of experience, starting salary).

Answer 8

Cindy won $50.00 for getting first place in the Science Fair. She spent her winnings on robotics kits and chemistry sets. Each robotics kit (y) costs $10.00, while each chemistry set costs $8.00 (x). Which of the following is a viable solution to the number of robotics kits and chemistry sets Cindy can purchase, assuming she spends her entire winnings?(1 point)
Responses

(3,2.6)
left parenthesis 3 comma 2.6 right parenthesis

(5,1)
left parenthesis 5 comma 1 right parenthesis

(0,5)
left parenthesis 0 comma 5 right parenthesis

(−5,9)

Answer 9

To identify the viable solution for the number of robotics kits and chemistry sets Cindy can purchase with her winnings of $50.00, we need to set up the equation based on their costs:

Let:

• \( x \) = number of chemistry sets
• \( y \) = number of robotics kits

The cost for the chemistry sets is \( 8x \), and the cost for the robotics kits is \( 10y \). Thus, the equation representing the total spending becomes:

\[ 8x + 10y = 50 \]

Now let's evaluate each of the answer choices to see if they satisfy this equation:

1. (3, 2.6): \[ 8(2.6) + 10(3) = 20.8 + 30 = 50.8 \quad (\text{not valid since it exceeds } 50) \]

2. (5, 1): \[ 8(1) + 10(5) = 8 + 50 = 58 \quad (\text{not valid since it exceeds } 50) \]

3. (0, 5): \[ 8(5) + 10(0) = 40 + 0 = 40 \quad (\text{valid, but doesn't spend entire amount}) \]

4. (−5, 9): \[ 8(9) + 10(-5) = 72 - 50 = 22 \quad (\text{not valid, negative quantity}) \]

None of the options provided use the entire $50.00, except (0, 5) which spends only $40.00. The option (3, 2.6) and (5, 1) exceed the total and (−5, 9) provides negative purchases.

Given the choices, the only viable option (though it's under budget) is:

(0, 5).

This indicates that Cindy can purchase 0 robotics kits and 5 chemistry sets.