Write the ratio that compares 24 apples to 14 oranges using fractional notation. Simplify the improper fraction in lowest terms
The ratio of 24 apples to 14 oranges can be written as 24/14.
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2.
Therefore, the simplified fraction is 12/7.
Which of the following, Option 1 or Option 2, is a proportion?
A.
4/5 = 20/25
B.
4/5 = 16/30
To determine which of the given options is a proportion, we need to check if the ratios are equivalent.
Option A:
4/5 = 20/25
To simplify, we can reduce both sides by dividing by a common factor, which is 5.
This gives us 4/5 = 4/5, which shows that the ratios are equivalent. Therefore, Option A is a proportion.
Option B:
4/5 = 16/30
To simplify, we can see that both the numerator and denominator can be divided by a common factor, which is 2.
This gives us 4/5 = 8/15, which shows that the ratios are not equivalent. Therefore, Option B is not a proportion.
In conclusion, Option 1 (A) is a proportion.
The cost of a piece of candy is described by the equation y = $0.35x. What is the cost of one piece of candy?
In the given equation, y represents the cost of the candy and x represents the number of pieces.
Given the equation y = $0.35x, this equation tells us that the cost of one piece of candy is $0.35.
Therefore, the cost of one piece of candy is $0.35.
The number of points that Yuki scored in a basketball game is represented by the equation 5y = 110x. In this equation, y represents the total number of points and x represents number of games. How many points did Yuki average per game?
In the equation 5y = 110x, we are looking to find the average number of points Yuki scored per game. This would be the total number of points scored (represented by y) divided by the number of games played (represented by x).
To find the points per game, we can isolate y in the equation:
5y = 110x
y = 110x / 5
y = 22x
This equation tells us that for every game played (x), Yuki scored an average of 22 points. Therefore, Yuki averaged 22 points per game.
The amount of money earned for hours spent babysitting is displayed on the graph. Derive the equation of the line through the origin.
image shows a graph with the first dot at (5.50,1) then (11.00, 2) then (16.50, 3) then (20.00,4)
To find the equation of the line through the origin that represents the amount of money earned for hours spent babysitting based on the given points (5.50, 1), (11.00, 2), (16.50, 3), and (20.00, 4), we need to calculate the slope of the line.
The slope (m) of a line passing through two points (x1, y1), and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Taking the points (5.50, 1) and (11.00, 2):
m = (2 - 1) / (11.00 - 5.50)
m = 1 / 5.50
This simplifies to: m = 2/11
Now that we have the slope of the line, and since the line passes through the origin, the equation of the line is of the form y = mx, where m is the slope.
Therefore, the equation that represents the amount of money earned for hours spent babysitting is:
y = (2/11)x