1.
b.Between the years 1975 and 2000, do women or men have the greater life expectancy?
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c.Explain using slope: is the life expectancy of men or women increasing more rapidly?
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2.Using the given equations above for the life expectancy of men and women, write an inequality to determine the birth years where the life expectancy of men is greater than that of women.
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3.Solve the inequality from question 2. Round your answer to the nearest whole number.
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4.a.Write an inequality to determine the birth years of women whose life expectancy is at least 85.
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b.Solve the inequality in question 4.
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6.The consumption of cigarettes is declining. If t represents the number of years since 1985, then the consumption, C, is modeled by
where C represents the number of billions of cigarettes smoked per year.
a.Write an inequality to show the first year cigarette consumption is less than 200 billion cigarettes a year.
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b.Solve the inequality from part a.
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7.The sign on the elevator in a seven-story building states that the maximum weight it can carry is 1500 pounds. As part of your work-study program, you need to move a large shipment of books to the sixth floor. Each box weighs 60 pounds.
a.Let n represent the number of boxes placed in the elevator. You weigh 185 pounds. Write an expression that represents the total weight in the elevator.
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b.Using the expression in part a, write an inequality that can be used to determine the maximum number of boxes that you can place in the elevator at one time and solve.
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1. To determine whether women or men have a greater life expectancy between 1975 and 2000, you would need to find the average life expectancies for both groups during that time period. You could do this by obtaining the life expectancy for each year between 1975 and 2000 and then calculating the average for women and men separately. Once you have the average life expectancies, you can compare them to determine which group has a greater life expectancy during that time period.
c. To determine which gender's life expectancy is increasing more rapidly, you can examine the slope of the line representing their life expectancies over time. If the slope for women's life expectancy is steeper (i.e., a larger positive value), then their life expectancy is increasing more rapidly. If the slope for men's life expectancy is steeper, then their life expectancy is increasing more rapidly.
2. To write an inequality to determine the birth years where the life expectancy of men is greater than that of women, you would need to use the equations provided for the life expectancy of men and women. Let's say the equation for men's life expectancy is represented by y = mx + b and the equation for women's life expectancy is represented by y = nx + c. To find the birth years where men's life expectancy is greater than women's, you would set up the following inequality: mx + b > nx + c, where m, n, b, and c are the respective coefficients and constants from the equations.
3. To solve the inequality from question 2, you would need to rearrange the inequality to isolate the variable (birth years) on one side of the inequality sign. Once the variable is isolated, you can then solve for the birth years. Remember to round your answer to the nearest whole number.
4.a. To determine the birth years of women whose life expectancy is at least 85, you would need to use the equation provided for women's life expectancy and set up an inequality. Let's say the equation for women's life expectancy is represented by y = nx + c. To find the birth years where women's life expectancy is at least 85, you would set up the following inequality: nx + c ≥ 85, where n and c are the respective coefficients and constants from the equation.
4.b. To solve the inequality from question 4.a, you would need to rearrange the inequality to isolate the variable (birth years) on one side of the inequality sign. Once the variable is isolated, you can then solve for the birth years. Remember to round your answer to the nearest whole number.
6.a. To show the first year cigarette consumption is less than 200 billion cigarettes a year, you would need to use the given inequality: C < 200, where C represents the number of billions of cigarettes smoked per year.
6.b. To solve the inequality from question 6.a, you would need to rearrange the inequality to isolate the variable (number of years since 1985) on one side of the inequality sign. Once the variable is isolated, you can then solve for the number of years since 1985.
7.a. To write an expression that represents the total weight in the elevator, you would multiply the weight of each box (60 pounds) by the number of boxes placed in the elevator (n) and add your weight (185 pounds). The expression would be: 60n + 185.
7.b. To determine the maximum number of boxes you can place in the elevator at one time, you would need to use the given maximum weight limit of 1500 pounds. You can set up the following inequality: 60n + 185 ≤ 1500, where n represents the number of boxes. To solve the inequality, you would need to rearrange it to isolate the variable (number of boxes) on one side of the inequality sign. Once the variable is isolated, you can then solve for the maximum number of boxes.