Concept explainers
(a)
To find: The complete table.
(a)
Answer to Problem 18PPS
The complete table is shown in table 1.
Explanation of Solution
Given;
The radius of the spinner is 2.5 inches.
Calculation:
The formula for the area is given as,
Complete the table.
Color | Probability | Sector Area | Total Area | Ratio |
Red | (1/6) | 3.27 in2 | 19.63 in2 | 0.166 |
Orange | (1/6) | 3.27 in2 | 19.63 in2 | 0.166 |
Yellow | (1/6) | 3.27 in2 | 19.63 in2 | 0.166 |
Green | (1/4) | 4.91 in2 | 19.63 in2 | 0.25 |
Blue | (1/4) | 4.91 in2 | 19.63 in2 | 0.25 |
Table 1
Thus, the complete table is shown in table 1.
(b)
To find: The relationship between the ratio of the area of the sector and the total area and the probability of the spinner landing on each color.
(b)
Answer to Problem 18PPS
The probability is equal.
Explanation of Solution
Consider the table (1) I part (a),
The probability is equal to the ratio of sector area to the total area.
Thus, the probability is equal.
(c)
To find: The prediction of the probability of a dart landing in each area of the board.
(c)
Answer to Problem 18PPS
The probability of a dart landing in each area of the board is calculated.
Explanation of Solution
Calculate the probability for the green area.
Calculate the probability for the blue area.
Calculate the probability for the yellow area.
Thus, the probability of a dart landing in each area of the board is calculated.
(d)
To find: The relative frequency table for throwing 100 darts.
(d)
Answer to Problem 18PPS
The relative frequency table for throwing 100 darts is shown in table 2.
Explanation of Solution
The table is drawn as,
Color | Frequency | Relative Frequency |
Green | 9 | 0.09 |
Yellow | 36 | 0.36 |
Blue | 55 | 0.55 |
Table 2
Thus, the relative frequency table for throwing 100 darts is shown in table 2.
(e)
To find: The graph for probability distribution.
(e)
Answer to Problem 18PPS
The graph for probability distribution is shown in figure 1.
Explanation of Solution
From Table 2, the graph is drawn as,
Thus, the graph for probability distribution is shown in figure 1.
Chapter 11 Solutions
Glencoe Algebra 2 Student Edition C2014
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