If a dozen pencils cost $1.35, what is the unit cost?(1 point)
Responses
$0.11
$0.11
$1.23
$1.23
$0.13
$0.13
$4.29
To find the unit cost, divide the total cost by the number of units. In this case, the total cost is $1.35 and the number of units is a dozen, which is equal to 12 pencils.
Therefore, the unit cost is $1.35/12 = $0.11.
So the correct answer is $0.11.
Find the Equation of the Line:
y=mx+b
by solving for y using the Point Slope Equation.
y−y1=m(x−x1)
y−1=3(x−0)
y−1=3x−(3×0)
y−1=3x−0
y=3x−0+1
y=3x+1
m=3
The equation of the line is y = 3x + 1.
The distance traveled in a car varies directly as the amount of gasoline used. If a car travels 640 miles and uses 32 gallons of gas, find the constant of variation or miles per gallon (mpg).(1 point)
Responses
18 mpg
18 mpg
22 mpg
22 mpg
20 mpg
20 mpg
24 mpg
24 mpg
To find the constant of variation or miles per gallon (mpg), divide the distance traveled by the amount of gasoline used. In this case, the distance traveled is 640 miles and the amount of gasoline used is 32 gallons.
Therefore, the mpg is 640 miles / 32 gallons = 20 mpg.
So the correct answer is 20 mpg.
In her science classroom, Mrs. Hall noticed that the lengths (in inches) and weights (in ounces) of the class's pet ferret
were directly related by the equation y = kx, where x is the length and y is the weight. Use the information in the table
to find k, the constant of proportionality.
6
9
12
15
Length (x) Weight (y)
15
22.5
30
37.5
(1 point)
k = 2.0
k= 2.5
k= 1.5
k= 3.0
To find the constant of proportionality, we can choose any pair of length and weight from the table and divide the weight by the length.
Let's take the first pair, (6, 15).
k = weight / length = 15 / 6 = 2.5.
So the constant of proportionality is k = 2.5.
Therefore, the correct answer is k = 2.5.
The table shows the grade, g, on a test when the number of problems, n, are correct. Write an equation to model the
situation.
Problems on a Test
n
g
40
72
84
10
18
21
(1 point)
n= 4g
g = 4n
g =n + 30
n=g - 30
To model the situation, we need to find a relationship between the number of problems, n, and the grade, g. From the given table, it appears that the grade is directly related to the number of problems.
Let's look at the first pair, (40, 72). We can write the equation as:
g = k * n
Substituting the values from the first pair:
72 = k * 40
To solve for k, divide both sides by 40:
k = 72 / 40
Simplifying:
k = 1.8
Therefore, the equation to model the situation is:
g = 1.8 * n
So the correct answer is g = 1.8n.
n / g
10/40
18/72
21/84
Given that the ratio n/g is given for three pairs of values, we can write an equation to model the situation.
Let's take the first pair, where n is 10 and g is 40. The ratio n/g can be written as:
10/40
To find the equation, we can set up a proportion using the ratios:
10/40 = n/g
To solve for g, we can cross multiply:
10 * g = 40 * n
Simplifying:
g = 4n
Therefore, the equation to model the situation is:
g = 4n
So the correct answer is g = 4n.
Which table shows y as directly proportional to x?
1)
x
-9
x
y
-4
-18
-2
-6
-6
-12
-3
2)
y
24
6
49
72
18
7
8
9
3)
x
x
y
-6
-4
12
-8
2
-3
-1
-24
4)
7
-13
y
49
-91
-6
-42
29
203
To determine which table shows y as directly proportional to x, we need to check if the ratio of y to x is constant for each pair of values in the table.
1) We have the pairs (-9, -4), (-2, -6), and (-3, -12). If we calculate the ratios y/x, we get -4/-9, -6/-2, and -12/-3, which simplify to 4/9, 3, and 4, respectively. These ratios are not constant, so this table does not show y as directly proportional to x.
2) We have the pairs (6, 24), (49, 72), and (18, 7). If we calculate the ratios y/x, we get 24/6, 72/49, and 7/18, which simplify to 4, 72/49, and 7/18, respectively. These ratios are not constant, so this table does not show y as directly proportional to x.
3) We have the pairs (-6, -8), (-4, 2), and (-1, -24). If we calculate the ratios y/x, we get -8/-6, 2/-4, and -24/-1, which simplify to 4/3, -1/2, and 24, respectively. These ratios are not constant, so this table does not show y as directly proportional to x.
4) We have the pairs (-13, -91), (-6, -42), and (7, 29). If we calculate the ratios y/x, we get -91/-13, -42/-6, and 29/7, which simplify to 7, 7, and 29/7, respectively. These ratios are constant, so this table shows y as directly proportional to x.
Therefore, the correct answer is table 4) with the pairs (7, -13), (-6, -42), and (7, 29).
The equation y=6x+6 describes the relationship between quantities x and y. Are the quantities in a proportional relationship?(1 point)
Responses
Yes, because the graph of the equation is a straight line.
Yes, because the graph of the equation is a straight line.
Yes, because the graph of the equation passes through the origin.
Yes, because the graph of the equation passes through the origin.
No, because the graph of the equation is not a straight line.
No, because the graph of the equation is not a straight line.
No, because the graph of the equation does not pass through the origin.
No, the quantities described by the equation y = 6x + 6 are not in a proportional relationship.
In a proportional relationship, the equation would be y = kx, where k is the constant of proportionality. However, in this equation, the y-intercept is 6, indicating that even when x is zero, y is not zero. Therefore, the graph of the equation does not pass through the origin.
So the correct answer is No, because the graph of the equation does not pass through the origin.
Which two ratios form a proportion?(1 point)
Responses
12 and 841 half and 8 fourths
21 and 1682 over 1 and 16 eighths
12 and 421 half and 4 halves
21 and 48
To determine which two ratios form a proportion, we need to check if the two ratios are equivalent, meaning that their values are equal.
Let's analyze each option:
1) 12 and 8 - These are not equivalent ratios, so they do not form a proportion.
2) 21 and 16 - These are not equivalent ratios, so they do not form a proportion.
3) 12 and 4 - These are equivalent ratios because 12/4 = 3, simplifying to the same value. Therefore, these two ratios form a proportion.
4) 21 and 48 - These are not equivalent ratios, so they do not form a proportion.
Therefore, the correct answer is:
12 and 4 (half and 4 halves) form a proportion.
Which linear equation represents a non-proportional relationship?(1 point)
Responses
y=x+3y is equal to x plus 3
y=45xy is equal to 4 fifths x
y=−3xy is equal to negative 3 x
y=1.5x
The equation y = 1.5x represents a non-proportional relationship.
In a proportional relationship, the equation would be y = kx, where k is the constant of proportionality. However, in this equation, the coefficient of x is 1.5, indicating that the relationship between y and x is not constant but varies based on the value of x. Therefore, the relationship is non-proportional.
So the correct answer is y = 1.5x.
In a second grade classroom, a student earns 25 stars for 5 compliments for good behavior. The teacher tracks the number of stars (y, vertical axis) and compliments (x, horizontal axis) on a graph. Which statements are correct? Choose more than 1 answer.(1 point)
Responses
Point (20, 100) represents earning 20 compliments.
Point (20, 100) represents earning 20 compliments.
Point (100, 20) represents earning 20 compliments.
Point (100, 20) represents earning 20 compliments.
Point (5, 1) represents the unit rate.
Point (5, 1) represents the unit rate.
Point (1, 5) represents the unit rate.
Point (1, 5) represents the unit rate.
Point (0, 50) represents the unit rate.
The statement "Point (20, 100) represents earning 20 compliments" is incorrect.
The correct statements are:
- Point (5, 1) represents the unit rate. This is because for every 5 compliments, the student earns 1 star. The ratio of stars to compliments is 1 star for every 5 compliments, which is the unit rate.
- Point (1, 5) represents the unit rate. This is because for every 1 compliment, the student earns 5 stars. The ratio of stars to compliments is 5 stars for every 1 compliment, which is the unit rate.
So the correct answers are Point (5, 1) represents the unit rate and Point (1, 5) represents the unit rate.
Question
Two points on a graph are (-4, 1) and (0, 2). Identify the slope between these two points.(1 point)
Responses
-4
-4
4
4
−14negative 1 fourth
141 fourth
To find the slope between two points on a graph, we use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates are (-4, 1) and (0, 2). Substituting the values into the formula:
slope = (2 - 1) / (0 - (-4))
slope = 1 / 4
Therefore, the slope between these two points is 1/4.
So the correct answer is 1/4.