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

Question

Responses

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

(number of nominations, number of awards)
(number of nominations, number of awards)

(age, weight)
(age, weight)

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

Answer 1

To determine which of the options could use both intercepts to produce viable solutions, we need to consider the relationship between the variables in each pair. Here’s a breakdown of each option:

1. (years of experience, starting salary): This relationship typically implies that higher years of experience would correlate with higher starting salaries, where the intercept could represent starting salary with zero years of experience. This is a viable option.

2. (number of nominations, number of awards): This option suggests a relationship where more nominations could lead to more awards, but it might not always be linear or proportional. The intercepts may not provide useful insights in this case, as having zero nominations may not necessarily yield zero awards in all contexts.

3. (age, weight): This relationship may not inherently have a linear connection or meaningful intercepts. The variables can vary widely and do not have a clear connection where intercepts would yield viable solutions.

4. (temperature, number of car rentals): Although there could be a relationship suggesting that higher temperatures could lead to more car rentals (especially in tourism), the use of both intercepts is less straightforward and context-dependent. For example, a temperature might not logically correlate directly with the number of car rentals in a linear manner.

Based on this analysis, the most viable option that could use both intercepts to produce meaningful solutions is:

(years of experience, starting salary).

Answer 2

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

(−5,9)
left parenthesis negative 5 comma 9 right parenthesis

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

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

(3,2.6)

Answer 3

To determine which of the given options is a viable solution for the number of robotics kits and chemistry sets Cindy can purchase, we can start by setting up the total cost equation based on her spending:

Let:

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

The costs are:

• Robotics kit costs $10.00
• Chemistry set costs $8.00

Cindy's total winnings are $50.00, so we can write the following equation:

\[ 10y + 8x = 50 \]

Now, let's evaluate each response option to see if it satisfies this equation:

1. (−5, 9): \[ 10(9) + 8(-5) = 90 - 40 = 50 \] This does satisfy the equation, but negative units of chemistry sets are not realistic in this context.

2. (5, 1): \[ 10(1) + 8(5) = 10 + 40 = 50 \] This satisfies the equation and it is a realistic solution.

3. (0, 5): \[ 10(5) + 8(0) = 50 + 0 = 50 \] This also satisfies the equation and is a realistic solution.

4. (3, 2.6): \[ 10(2.6) + 8(3) = 26 + 24 = 50 \] This mathematically fits the equation; however, buying 2.6 robotics kits is not realistic.

The viable solutions, considering the context of purchasing whole numbers of items, are (5, 1) and (0, 5).

To answer the question directly, the best suitable options among the responses that work in the context of real purchase are (5, 1) and (0, 5). If you need to select just one: (5, 1) would be a strong choice, as it shows a mix of both types of kits.