Question
Between 1985 and 2003, data were collected every three years on the amount of plastic produced annually in the United States, in billions of pounds. The graph below shows the data and a line of best fit. The equation of the line of best fit is , where x is the number of years since 1985 and y is the amount of plastic produced annually, in billions of pounds.
Which of the following is closest to the percent increase in the billions of pounds of plastic produced in the United States from 2000 to 2003 ?
Hint:
We observe the data points, specially the highlighted ones and try to solve the problem intuitively.
The percent increase formula is as follows:
The correct answer is:
Step 1 of 2:
We need to find the percent increase of plastic produced in the USA from 2000 to 2003.
Note the highlighted points in the figure.
The left one is the data point for the year 2000, since it is on the 15th x-axis line and (1985+15)=2000. This point is exactly equal to 100 of the y-axis line.
And the right one is of the year 2003, and it is somewhere in middle of 100 and 120 of the y-axis lines. For the sake of simplicity, we consider the value as 110.
Step 2 of 2:
Now, as per the formula of percent increase, we have new value = 110 and original value = 100.
So, the % increase is given by, %-increase
Final Answer:
The closest to the percent increase from the given options is— A) 10%
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Between 1985 and 2003, data were collected every three years on the amount of plastic produced annually in the United States, in billions of pounds. The graph below shows the data and a line of best fit. The equation of the line of best fit is , where x is the number of years since 1985 and y is the amount of plastic produced annually, in billions of pounds.
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Which of the following is the best interpretation of the number 3.39 in the context of the problem?
Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches. According to the riser-tread formula, which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?
When designing a stairway, an architect can use the riser-tread formula , where h is the riser height, in inches, and d is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.
The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.
In mathematics, inequalities explain the relationship between two non-equal values. When two values are not equal, we frequently use the "not equal symbol ()" to indicate this. However, many inequalities are used to compare the values and determine whether they are less than or greater.
¶A relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols ">"; "<"; "≥"; "≤. "
¶Since the tread depth, 'd' is at least 9 inches, and the riser height, 'h' is at least 5 inches, it follows that h ≥ 5, and d ≥ 9
respectively. Solving for d in the riser tread formula 2h + d = 25 gives d = 25 - 2h. Thus the first inequality, d ≥ 9, is equivalent to
25-2h ≥ 9.
Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches. According to the riser-tread formula, which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?
When designing a stairway, an architect can use the riser-tread formula , where h is the riser height, in inches, and d is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.
The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.
In mathematics, inequalities explain the relationship between two non-equal values. When two values are not equal, we frequently use the "not equal symbol ()" to indicate this. However, many inequalities are used to compare the values and determine whether they are less than or greater.
¶A relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols ">"; "<"; "≥"; "≤. "
¶Since the tread depth, 'd' is at least 9 inches, and the riser height, 'h' is at least 5 inches, it follows that h ≥ 5, and d ≥ 9
respectively. Solving for d in the riser tread formula 2h + d = 25 gives d = 25 - 2h. Thus the first inequality, d ≥ 9, is equivalent to
25-2h ≥ 9.