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?
We need to find the greatest value of x that satisfies the inequality x + 3.5 < 20, from the set {12.5, 14.5, 16.5, 18.5}.
We can check each value in the set by substituting it for x in the inequality and checking if the inequality is true:
- For x = 18.5: 18.5 + 3.5 < 20, which is true.
- For x = 16.5: 16.5 + 3.5 < 20, which is true.
- For x = 14.5: 14.5 + 3.5 < 20, which is true.
- For x = 12.5: 12.5 + 3.5 < 20, which is false.
Therefore, the greatest value of x from the set {12.5, 14.5, 16.5, 18.5} that makes the inequality true is x = 16.5.
Which inequality is true for x = 2?
There can be multiple inequalities that are true for a given value of x. In this case, we would need more information to determine which inequality(s) is/are true for x = 2.
If the inequality is already given, we can substitute x = 2 into the inequality to check if it is true. If the inequality is not given, we would need more context or information to determine which inequality is relevant and true for x = 2.
Which inequality is true for x = 2? Responses
A 14x + 10 < 37
B 7x − 10 < 11
C 6x + 20 < 29
D 15x − 18 < 12
Let us substitute x = 2 into each inequality to see which one is true:
A) 14x + 10 < 37 becomes 14(2) + 10 < 37, which simplifies to 38 < 37. This is not true.
B) 7x - 10 < 11 becomes 7(2) - 10 < 11, which simplifies to 4 < 11. This is true.
C) 6x + 20 < 29 becomes 6(2) + 20 < 29, which simplifies to 32 < 29. This is not true.
D) 15x - 18 < 12 becomes 15(2) - 18 < 12, which simplifies to 12 < 12. This is not true.
Therefore, the only inequality that is true for x = 2 is B) 7x - 10 < 11.
You and your family attend your brother’s championship baseball game. Between innings you decide to go to the snack stand. You go to the snack stand with $15 and find that sodas are $2.50 and that popcorn is $3.75. Write an inequality that models the number of sodas you can buy if you get a bag of popcorn too. What is the maximum number of sodas you can buy in this situation?
Responses
A 2.5x + 3.75 ≤ 15; 5 sodas2.5x + 3.75 ≤ 15; 5 sodas
B 2.5x + 3.75 < 15; 4 sodas2.5x + 3.75 < 15; 4 sodas
C 2.5x + 3.75 ≤ 15; 4 sodas2.5x + 3.75 ≤ 15; 4 sodas
D 2.5x + 3.75 < 15; 5 sodas2.5x + 3.75 < 15; 5 sodas
The amount of sodas you can buy is represented by the variable x, and the total cost of purchasing sodas and popcorn cannot exceed the amount of money you have, which is $15.
The total cost of x sodas is 2.5x, and the cost of popcorn is $3.75. Therefore, the inequality that models the number of sodas you can buy if you get a bag of popcorn too is:
2.5x + 3.75 ≤ 15
To find the maximum number of sodas you can buy, we need to solve for x:
2.5x + 3.75 ≤ 15
2.5x ≤ 11.25
x ≤ 4.5
Therefore, the maximum number of sodas you can buy in this situation is 4, as you cannot buy a fraction of a soda.
The correct option is C) 2.5x + 3.75 ≤ 15; 4 sodas.
This graph shows the relationship between the age of a planet in millions of years and the number of moons the planet has.
Which of these statements is true about the graph?
Responses
A Since the number of moons is staying the same, there is no independent variable.Since the number of moons is staying the same, there is no independent variable.
B The independent variable is the number of moons.The independent variable is the number of moons.
C The slope is undefined.The slope is undefined.
D Since the number of moons is staying the same, there is no dependent variable.Since the number of moons is staying the same, there is no dependent variable.
E The dependent variable is the number of moons.
E The dependent variable is the number of moons.
On the graph, the number of moons is represented on the vertical (y) axis, while the age of the planet is represented on the horizontal (x) axis. The number of moons is changing with respect to the age of the planet, so it is the dependent variable. Therefore, the correct option is E) The dependent variable is the number of moons.
Rectangle PQRS will be drawn on the coordinate grid. Where should point S be located?
Responses
A (3, -3)(3, -3)
B (-3, 3)(-3, 3)
C (-3, -3)(-3, -3)
D (3, 3)
We cannot determine where point S should be located based solely on the given information.
We know that rectangle PQRS will be drawn on the coordinate grid, but we do not know the coordinates of any of the other points (P, Q, or R), nor do we know any other specifications about the rectangle (e.g. its side lengths or whether it is a square).
Without more information, any point in the coordinate plane is a valid location for point S.
Jesse is not allowed to work more than 20 hours each week at his part time job . He has already worked 4 hours this week. The inequality shown can be used to find h, the number of hours Jesse can still work this week.
h + 4 ≤ 20
Which inequality represents the solution set for this situation?
Responses
A h ≤ 24h ≤ 24
B h ≤ 16h ≤ 16
C h ≥ 16h ≥ 16
D h ≥ 24
We start with the inequality h + 4 ≤ 20, which represents the constraint that Jesse can work no more than 20 hours per week, and he has already worked 4 hours. To find the solution for h, we need to isolate h on one side of the inequality:
h ≤ 20 - 4
h ≤ 16
Therefore, the solution for h is h ≤ 16.
The correct inequality that represents the solution set for this situation is option B) h ≤ 16.
Write an equation that gives the proportional relationship of the graph.
Responses
A y = 7xy = 7x
B y = 35xy = 35x
C y = 5xy = 5x
D y = 17x
Looking at the graph would help in identifying the proportional relationship. Please provide the graph associated with the question.
Identify the corresponding word problem given the inequality: 1,200x < 50,000
Responses
A An export company needs to purchase containers to ship cargo overseas, and the expense must be $50,000 or less. If a standard container costs $1,200, how many containers can be purchased?An export company needs to purchase containers to ship cargo overseas, and the expense must be $50,000 or less. If a standard container costs $1,200, how many containers can be purchased?
B An export company needs to purchase containers to ship cargo overseas, and the expense must be $50,000 or less. If 41 containers are purchased, what is the cost of each container?An export company needs to purchase containers to ship cargo overseas, and the expense must be $50,000 or less. If 41 containers are purchased, what is the cost of each container?
C An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?
D An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If 41 containers are purchased, what is the cost of each container?
A An export company needs to purchase containers to ship cargo overseas, and the expense must be $50,000 or less. If a standard container costs $1,200, how many containers can be purchased?
An export company needs to purchase containers to ship cargo overseas, and the expense must be $50,000 or less. If a standard container costs $1,200, how many containers can be purchased?
The inequality 1,200x < 50,000 can be used to represent the relationship between the number of containers (x) and the total cost of purchasing those containers. The export company cannot spend more than $50,000, so we can solve for x to find the maximum number of containers that can be purchased while staying under budget:
1,200x < 50,000
x < 50,000/1,200
x < 41.67
Since the number of containers must be a whole number (we cannot purchase a fraction of a container), the maximum number of containers the export company can purchase is 41.
Therefore, the export company can purchase a maximum of 41 containers if each container costs $1,200 or less and the total cost must be $50,000 or less.
Kate is allowed to work no more than 20 hours a week. She has already worked 13 hours this week. At most, how many more hours CAN she work? Write an inequality and solve.
Responses
A x + 13 ≥ 20; x ≥ 7x + 13 ≥ 20; x ≥ 7
B x + 13 > 20; x > 7x + 13 > 20; x > 7
C x + 13 < 20; x < 7x + 13 < 20; x < 7
D x + 13 ≤ 20; x ≤ 7x + 13 ≤ 20; x ≤ 7
To find how many more hours Kate can work at most, we need to subtract the number of hours she has already worked from the maximum number of hours she is allowed to work:
Maximum number of hours - Number of hours already worked ≤ Remaining hours she can work
This can be written as:
20 - 13 ≤ x
7 ≤ x
Therefore, the inequality that represents the situation is x ≥ 7.
The maximum number of hours Kate can work is 7 hours, since she has already worked 13 hours and is not allowed to work more than 20 hours in total.
The correct option is A) x + 13 ≥ 20; x ≥ 7.
Which ordered pair COULD represent point P on the graph?
Responses
A (-2, -5)(-2, -5)
B (-3, 6)(-3, 6)
C (6, -3)(6, -3)
D (2, 6)(2, 6)
E (3, -5)(3, -5)
Without the graph for reference, we cannot accurately determine which ordered pair could represent point P.
Represent the proportional relationship described with an equation where p equals pillows and b equals beds:
four pillows for each bed
Responses
A b = 4pb = 4 p
B 4p = b4p = b
C p = 4bp = 4b
D p = 4bp = 4 b
The proportional relationship "four pillows for each bed" implies that the number of pillows (p) is proportional to the number of beds (b), with a constant of proportionality of 4 (since there are 4 pillows for each bed).
We can write this relationship as:
p = 4b
Therefore, the correct equation that represents the proportional relationship described is option D) p = 4b.
A dump truck driver must haul 112 cubic yards of dirt to a construction site. The maximum load for the dump truck is 14 cubic yards. Which inequality represents the solution set that shows the number of loads, n, that the dump truck driver will haul?
Responses
A n ≤ 12n ≤ 12
B n ≥ 8n ≥ 8
C n ≥ 12n ≥ 12
D n ≤ 8