Our middle school is having a fall carnival. Admission into the carnival is $3 and each game inside the carnival costs $.25. Write an inequality that represents the possible number of games that can be played having $10. What is the maximum number of games that can be played?(1 point)
Responses
0.25x+3≤10
; 28 games
0 point 2 5 x plus 3 is less than or equal to 10; 28 games
0.25x−3≤10
; 52 games
0 point 2 5 x minus 3 is less than or equal to 10; 52 games
0.25x−3<10
; 52 games
0.25x−3<10
; 52 games
0.25x+3<10
; 28 games
and can you explain how you got the answer?
The correct inequality is 0.25x + 3 ≤ 10.
To determine the maximum number of games that can be played with $10, we need to solve this inequality.
First, subtract 3 from both sides of the inequality:
0.25x ≤ 7
Next, divide both sides of the inequality by 0.25:
x ≤ 28
This means that the maximum number of games that can be played with $10 is 28.
Ashley and Liam both have playlists on their music apps.
The number of playlists on Ashley’s app can be represented by X.
The number of playlists on Liam’s app is 4 times the number of playlists on Ashley’s app.
The total number of playlists on both their apps is at least 45.
What is the solution set for x, representing the number of playlists on Ashley’s app?
(1 point)
Responses
x≤−9
x is less than or equal to negative 9
x≥−9
x is greater than or equal to negative 9
x≥9
x is greater than or equal to 9
x≤9
and explain
The correct solution set is x ≥ 9.
According to the problem, the number of playlists on Liam's app is 4 times the number of playlists on Ashley's app. Therefore, the number of playlists on Liam's app can be represented by 4x.
The total number of playlists on both their apps is at least 45, which means the sum of the number of playlists on Ashley's app (x) and Liam's app (4x) is greater than or equal to 45:
x + 4x ≥ 45
Combining like terms:
5x ≥ 45
Dividing both sides of the inequality by 5:
x ≥ 9
This means the number of playlists on Ashley's app (x) must be greater than or equal to 9 in order to satisfy the given conditions.
Preston solved the inequality and graphed it on the number line. Which of the following is the inequality that he solved?
number line from -10 to positive 10 the closed dot is at 1.5 going to positive 10
(1 point)
Responses
2.1x+5.6≥8.75
2 point 1 x plus 5 point 6 is greater than or equal to 8 point 7 5
0.9x+2.8≤5.95
0 point 9 x plus 2 point 8 is less than or equal to 5 point 9 5
5.6x−18.9≤0.7
5 point 6 x minus 18 point 9 is less than or equal to 0 point 7
3.4x−1.2≥4.75
The correct inequality that Preston solved is 3.4x - 1.2 ≥ 4.75.
From the description of the number line, we can see that there is a closed dot at 1.5 and it goes towards the positive side up to 10. This means the inequality is greater than or equal to, and the inequality that matches this description is 3.4x - 1.2 ≥ 4.75.
Which one of these is NOT a characteristic of a proportional graph?(1 point)
Responses
The line passes through the origin (0,0).
The line passes through the origin (0,0).
The y values are always larger than the x values.
The y values are always larger than the x values.
The graph is a straight line.
The graph is a straight line.
The value of y/x is the same for all points on the line.
The characteristic that is NOT a characteristic of a proportional graph is: "The y values are always larger than the x values."
In a proportional graph, the value of y/x remains constant for all points on the line, regardless of the numerical values of x and y.
The weather report predicts rain for the next 3 days. Assuming the prediction is true and there is no rain on the other days of the week, what is the ratio of rainy days to the total number of days in the week?(1 point)
Responses
7:3
7:3
3:10
3:10
3:4
3:4
3:7
The correct ratio of rainy days to the total number of days in the week is 3:7.
Since the weather report predicts rain for the next 3 days and assumes no rain on the remaining days, we consider only those 3 days as rainy days. The total number of days in a week is 7.
Therefore, the ratio of rainy days to the total number of days in the week is 3:7.