Identify the first quartile in the following dataset:
5, 7, 9, 4, 3, 2, 1, 0, 11, 12, 6, 3, 4, 3, 2, 6
To find the first quartile, we need to first arrange the data in order from smallest to largest:
0, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 11, 12
The first quartile is the median of the lower half of the dataset. Since there are 16 values in the dataset, the median of the lower half would be the average of the values in positions 1/4 and 1/2 when the data is sorted.
1/4 of 16 is 4, and 1/2 of 16 is 8, so the first quartile would be the average of the 4th and 8th values in the dataset:
Q1 = (2 + 4)/2 = 3
Therefore, the first quartile in this dataset is 3.
Which graph shows the solution to the inequality?
x - 4 ≥ -1
To graph the solution of the inequality x - 4 ≥ -1, we first isolate x by adding 4 to both sides:
x - 4 + 4 ≥ -1 + 4
x ≥ 3
This inequality means that all values of x that are greater than or equal to 3 satisfy the original inequality. We can represent this solution graphically with a shaded region on the number line, as shown below:
```
<---|------|------|------|------|------|------|------|--->
0 1 2 3 4 5 6 7
shaded region ---^
```
The graph that shows the solution to the inequality is a number line with a shaded region to the right of (and including) the point x = 3.
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03:11
Identify the corresponding word problem given the equation: x + 12.50 = 55.75
A For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $55.75, how much money did he have before?For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $55.75, how much money did he have before?
B For mowing the neighbor's yard, Jessy was paid $43.25. If he now has $55.75, how much money did he have before?
C For mowing the neighbor's yard, Jessy was paid $55.75. If he now has $12.50, how much money did he have before?
D For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $68.25, how much money did he have before?
A For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $55.75, how much money did he have before?
A basketball player has been playing 10 minutes a game and scoring 2 points per game. The coach notices that he is a slow starter and begins giving the player additional minutes. This table shows the player's increased production. What can you say about the effect of the extra time on the player's scoring?
A For every 2 extra minutes, he scores 1 more point
B For every 3 extra minutes, he scores 1 more point
C For every extra minute, he scores 1 more point
D For every 4 extra minutes, he scores 1 more point.
A For every 2 extra minutes, he scores 1 more point.
From the table, we can see that the player scores 2 points in the first 10 minutes, 3 points in the next 2 minutes, 4 points in the next 2 minutes, and so on. This means that for every 2 additional minutes he plays, he scores an additional point. Thus, the correct option is A: "For every 2 extra minutes, he scores 1 more point."
Consider that point A is located at (x, y) in Quadrant I of the coordinate plane. In which quadrant is point B with coordinates (-x, -y) located?
A Quadrant I
B Quadrant IV
C Quadrant III
D Quadrant II
B Quadrant IV.
Since point A is located in Quadrant I, both x and y are positive. When we negate x and y to get point B, we get (-x, -y). Since negating a positive number gives us a negative number, both the x- and y-coordinates of B are negative. Therefore, point B is located in Quadrant IV.
x + 3.5 < 20
What is the greatest value of x from the set {12.5, 14.5, 16.5, 18.5} that makes the inequality true?