Let's tackle each part of your question step by step.
Part A: Show that the amount of salad is a rational number.
A rational number is defined as any number that can be expressed as the quotient or fraction of two integers (a/b), where "a" and "b" are integers and "b" is not zero.
The amount of salad Rafael is buying is \( 1 \frac{3}{8} \) pounds. This is a mixed number that can be expressed as an improper fraction:
\[ 1 \frac{3}{8} = \frac{8}{8} + \frac{3}{8} = \frac{11}{8} \]
Since \( \frac{11}{8} \) can be expressed as the quotient of two integers (11 over 8), it is indeed a rational number.
Part B: Write the amount of salad as a decimal.
To convert the fraction \( \frac{11}{8} \) into a decimal, you can perform the division:
\[ 11 \div 8 = 1.375 \]
Thus, the amount of salad in decimal form is \( 1.375 \) pounds.
Part C: What will Rafael pay for the salad?
To determine how much Rafael will pay for the salad, we would need to know the price per pound of salad at the salad bar. If that information is given, you could calculate the total cost by multiplying the price per pound by the total weight in pounds.
For example, if the price per pound is \( p \) dollars, then the total cost \( C \) would be calculated as:
\[ C = p \times 1.375 \]
Without the specific price per pound, we cannot determine the exact amount Rafael will pay.
Temperature Drop Question:
The temperature dropped steadily by 40°F over a 20-hour period. We need to find the quotient of -40 divided by 20 and explain what it means in this context.
To compute the quotient:
\[ -40 \div 20 = -2 \]
This result means that the temperature dropped at a rate of 2°F per hour. In other words, every hour, the temperature decreased by 2 degrees Fahrenheit until it reached a total drop of 40°F over the span of 20 hours.