Questions: Assignment 2 150quez, F20 Part 1 of 3 The graphs, on the right, show the percentage of jobs in a country's labor force held by men and women from 1970 through 2010. The formula p=2.8 sqrt(t)+31.6 models the percentage of jobs in the labor force, p, held by women t years after 1970. Answer parts a through c. Percentage of Jobs Held by Men and Women a. Use the appropriate graph to estimate the percentage of jobs in the labor force held by women in 2000. Give your estimation to the nearest percent. p= % (Round to the nearest whole number as needed.)

Assignment 2 150quez, F20 Part 1 of 3 The graphs, on the right, show the percentage of jobs in a country's labor force held by men and women from 1970 through 2010. The formula p=2.8 sqrt(t)+31.6 models the percentage of jobs in the labor force, p, held by women t years after 1970. Answer parts a through c. Percentage of Jobs Held by Men and Women a. Use the appropriate graph to estimate the percentage of jobs in the labor force held by women in 2000. Give your estimation to the nearest percent. p= % (Round to the nearest whole number as needed.)
Transcript text: Assignment 2 \{150quez, F20\} Part 1 of 3 The graphs, on the right, show the percentage of jobs in a country's labor force held by men and women from 1970 through 2010. The formula $p=2.8 \sqrt{t}+31.6$ models the percentage of jobs in the labor force, $p$, held by women $t$ years after 1970. Answer parts a through c. Percentage of Jobs Held by Men and Women a. Use the appropriate graph to estimate the percentage of jobs in the labor force held by women in 2000. Give your estimation to the nearest percent. $p=$ $\square$ $\%$ (Round to the nearest whole number as needed.)
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Solution

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Solution Steps

Step 1: Identify the Year Difference

To find the percentage of jobs held by women in 2000, we need to determine the value of \( t \), which is the number of years after 1970.

\[ t = 2000 - 1970 = 30 \]

Step 2: Apply the Given Formula

The formula provided is \( p = 2.8 \sqrt{t} + 31.6 \). Substitute \( t = 30 \) into the formula.

\[ p = 2.8 \sqrt{30} + 31.6 \]

Step 3: Calculate the Square Root

Calculate the square root of 30.

\[ \sqrt{30} \approx 5.48 \]

Step 4: Perform the Multiplication

Multiply 2.8 by the square root of 30.

\[ 2.8 \times 5.48 \approx 15.34 \]

Step 5: Add the Constant

Add 31.6 to the result from the previous step.

\[ p = 15.34 + 31.6 = 46.94 \]

Step 6: Round to the Nearest Whole Number

Round 46.94 to the nearest whole number.

\[ p \approx 47 \]

Final Answer

The estimated percentage of jobs in the labor force held by women in 2000 is \( 47\% \).

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