Question
three dozen muffins cost $9.00 determine the cost per muffin determine the cost per muffin.
which process will you use to solve this problem?
a. 9÷12
b. 9÷3
c. 9÷(3x12)
d. 12÷3x9
e. 9÷3x12
which process will you use to solve this problem?
a. 9÷12
b. 9÷3
c. 9÷(3x12)
d. 12÷3x9
e. 9÷3x12
Answers
GPT-4o mini
To find the cost per muffin when three dozen muffins cost $9.00, you first need to determine the total number of muffins in three dozen.
Since one dozen equals 12 muffins, three dozen equals:
\[
3 \times 12 = 36 \text{ muffins}
\]
Next, to find the cost per muffin, you need to divide the total cost by the total number of muffins:
\[
\text{Cost per muffin} = \frac{\text{Total Cost}}{\text{Total Muffins}} = \frac{9.00}{36}
\]
Now, let's simplify this:
\[
9.00 \div 36 = 0.25
\]
So, the cost per muffin is $0.25.
Now, looking at the options you provided:
- a. \( 9 \div 12 \) – doesn't give total muffins
- b. \( 9 \div 3 \) – doesn't give total muffins
- c. \( 9 \div (3 \times 12) \) – this is \( 9 \div 36 \), which is the correct process to find the cost per muffin
- d. \( 12 \div 3 \times 9 \) – doesn't correctly calculate the cost per muffin
- e. \( 9 \div 3 \times 12 \) – doesn’t calculate the cost per muffin
The correct answer is **c. \( 9 \div (3 \times 12) \)**.
Since one dozen equals 12 muffins, three dozen equals:
\[
3 \times 12 = 36 \text{ muffins}
\]
Next, to find the cost per muffin, you need to divide the total cost by the total number of muffins:
\[
\text{Cost per muffin} = \frac{\text{Total Cost}}{\text{Total Muffins}} = \frac{9.00}{36}
\]
Now, let's simplify this:
\[
9.00 \div 36 = 0.25
\]
So, the cost per muffin is $0.25.
Now, looking at the options you provided:
- a. \( 9 \div 12 \) – doesn't give total muffins
- b. \( 9 \div 3 \) – doesn't give total muffins
- c. \( 9 \div (3 \times 12) \) – this is \( 9 \div 36 \), which is the correct process to find the cost per muffin
- d. \( 12 \div 3 \times 9 \) – doesn't correctly calculate the cost per muffin
- e. \( 9 \div 3 \times 12 \) – doesn’t calculate the cost per muffin
The correct answer is **c. \( 9 \div (3 \times 12) \)**.
which three equations represent non-proportional relationships?
a. y=-15x
b. y=x2
c. y=2/3x
d. y=10x+10
e. y=5/x-9
(the 2 in (b.) is an exponent)
a. y=-15x
b. y=x2
c. y=2/3x
d. y=10x+10
e. y=5/x-9
(the 2 in (b.) is an exponent)
GPT-4o mini
To determine which equations represent non-proportional relationships, we need to identify those that do not fit the form of \( y = kx \), where \( k \) is a constant. Proportional relationships pass through the origin (0,0), while non-proportional relationships do not.
Let's analyze each equation:
a. **\( y = -15x \)**
This is a linear equation in the form \( y = kx \) (with \( k = -15 \)). **Proportional relationship**.
b. **\( y = x^2 \)**
This is a quadratic equation. It does not have a constant ratio between \( y \) and \( x \), especially since \( y(0) = 0^2 = 0 \) but the relationship is not linear. **Non-proportional relationship**.
c. **\( y = \frac{2}{3}x \)**
This is also in the form \( y = kx \) (with \( k = \frac{2}{3} \)). **Proportional relationship**.
d. **\( y = 10x + 10 \)**
This is a linear equation but includes a constant term \( +10 \), which means it does not pass through the origin. **Non-proportional relationship**.
e. **\( y = \frac{5}{x} - 9 \)**
This is a rational equation, and it has a variable in the denominator. It does not represent a constant ratio between \( y \) and \( x \). **Non-proportional relationship**.
**In summary**, the three equations that represent non-proportional relationships are:
- **b. \( y = x^2 \)**
- **d. \( y = 10x + 10 \)**
- **e. \( y = \frac{5}{x} - 9 \)**
Let's analyze each equation:
a. **\( y = -15x \)**
This is a linear equation in the form \( y = kx \) (with \( k = -15 \)). **Proportional relationship**.
b. **\( y = x^2 \)**
This is a quadratic equation. It does not have a constant ratio between \( y \) and \( x \), especially since \( y(0) = 0^2 = 0 \) but the relationship is not linear. **Non-proportional relationship**.
c. **\( y = \frac{2}{3}x \)**
This is also in the form \( y = kx \) (with \( k = \frac{2}{3} \)). **Proportional relationship**.
d. **\( y = 10x + 10 \)**
This is a linear equation but includes a constant term \( +10 \), which means it does not pass through the origin. **Non-proportional relationship**.
e. **\( y = \frac{5}{x} - 9 \)**
This is a rational equation, and it has a variable in the denominator. It does not represent a constant ratio between \( y \) and \( x \). **Non-proportional relationship**.
**In summary**, the three equations that represent non-proportional relationships are:
- **b. \( y = x^2 \)**
- **d. \( y = 10x + 10 \)**
- **e. \( y = \frac{5}{x} - 9 \)**
i forgot to write down
f y=4.08x
f y=4.08x
GPT-4o mini
Let's reassess all the equations including the new equation **f**:
1. **a. \( y = -15x \)**
This is in the form \( y = kx \) (with \( k = -15 \)). **Proportional relationship**.
2. **b. \( y = x^2 \)**
This is a quadratic equation and does not represent a constant ratio between \( y \) and \( x \). **Non-proportional relationship**.
3. **c. \( y = \frac{2}{3}x \)**
This is in the form \( y = kx \) (with \( k = \frac{2}{3} \)). **Proportional relationship**.
4. **d. \( y = 10x + 10 \)**
This includes a constant term \( +10 \), meaning it does not pass through the origin. **Non-proportional relationship**.
5. **e. \( y = \frac{5}{x} - 9 \)**
This equation has a variable in the denominator and does not maintain a constant ratio between \( y \) and \( x \). **Non-proportional relationship**.
6. **f. \( y = 4.08x \)**
This is in the form \( y = kx \) (with \( k = 4.08 \)). **Proportional relationship**.
**In summary**, the three equations that represent non-proportional relationships are:
- **b. \( y = x^2 \)**
- **d. \( y = 10x + 10 \)**
- **e. \( y = \frac{5}{x} - 9 \)**
The proportional relationships are:
- **a. \( y = -15x \)**
- **c. \( y = \frac{2}{3}x \)**
- **f. \( y = 4.08x \)**
If you need anything else, feel free to ask!
1. **a. \( y = -15x \)**
This is in the form \( y = kx \) (with \( k = -15 \)). **Proportional relationship**.
2. **b. \( y = x^2 \)**
This is a quadratic equation and does not represent a constant ratio between \( y \) and \( x \). **Non-proportional relationship**.
3. **c. \( y = \frac{2}{3}x \)**
This is in the form \( y = kx \) (with \( k = \frac{2}{3} \)). **Proportional relationship**.
4. **d. \( y = 10x + 10 \)**
This includes a constant term \( +10 \), meaning it does not pass through the origin. **Non-proportional relationship**.
5. **e. \( y = \frac{5}{x} - 9 \)**
This equation has a variable in the denominator and does not maintain a constant ratio between \( y \) and \( x \). **Non-proportional relationship**.
6. **f. \( y = 4.08x \)**
This is in the form \( y = kx \) (with \( k = 4.08 \)). **Proportional relationship**.
**In summary**, the three equations that represent non-proportional relationships are:
- **b. \( y = x^2 \)**
- **d. \( y = 10x + 10 \)**
- **e. \( y = \frac{5}{x} - 9 \)**
The proportional relationships are:
- **a. \( y = -15x \)**
- **c. \( y = \frac{2}{3}x \)**
- **f. \( y = 4.08x \)**
If you need anything else, feel free to ask!
consider the graph
( the graph shows (1,5), (3,15), and (6,30). )
what is the constant of proportionality (unit rate) ?
a. 1
b. 0
c.1/5
d. 5
( the graph shows (1,5), (3,15), and (6,30). )
what is the constant of proportionality (unit rate) ?
a. 1
b. 0
c.1/5
d. 5
GPT-4o mini
To determine the constant of proportionality (or the unit rate) from the given points in the graph—(1, 5), (3, 15), and (6, 30)—we look for a consistent ratio of \( y \) to \( x \).
The constant of proportionality \( k \) can be calculated by dividing \( y \) by \( x \).
Let's calculate this for the given points:
1. For the point \( (1, 5) \):
\[
k = \frac{y}{x} = \frac{5}{1} = 5
\]
2. For the point \( (3, 15) \):
\[
k = \frac{y}{x} = \frac{15}{3} = 5
\]
3. For the point \( (6, 30) \):
\[
k = \frac{y}{x} = \frac{30}{6} = 5
\]
Since the ratio \( k \) is consistently 5 for all points, the constant of proportionality is **5**.
So the answer is: **d. 5**.
The constant of proportionality \( k \) can be calculated by dividing \( y \) by \( x \).
Let's calculate this for the given points:
1. For the point \( (1, 5) \):
\[
k = \frac{y}{x} = \frac{5}{1} = 5
\]
2. For the point \( (3, 15) \):
\[
k = \frac{y}{x} = \frac{15}{3} = 5
\]
3. For the point \( (6, 30) \):
\[
k = \frac{y}{x} = \frac{30}{6} = 5
\]
Since the ratio \( k \) is consistently 5 for all points, the constant of proportionality is **5**.
So the answer is: **d. 5**.
The amount of money that Sarah earns varies directly with the number of hours worked. If Sarah earns $320 for working 40 hours, determine the constant of proportionality. $__ per hour (remember to include the hundredths place, two digits after the decimal)
GPT-4o mini
To determine the constant of proportionality (the unit rate) for Sarah's earnings, we can use the formula for the unit rate:
\[
k = \frac{\text{Total Earnings}}{\text{Total Hours Worked}}
\]
From the information given:
- Total Earnings = $320
- Total Hours Worked = 40 hours
Now, we can calculate the constant of proportionality \( k \):
\[
k = \frac{320}{40} = 8
\]
This means that Sarah earns $8 per hour.
In terms of the question, we need to express this amount to two decimal places:
\[
k = 8.00
\]
So, the constant of proportionality is **$8.00 per hour**.
\[
k = \frac{\text{Total Earnings}}{\text{Total Hours Worked}}
\]
From the information given:
- Total Earnings = $320
- Total Hours Worked = 40 hours
Now, we can calculate the constant of proportionality \( k \):
\[
k = \frac{320}{40} = 8
\]
This means that Sarah earns $8 per hour.
In terms of the question, we need to express this amount to two decimal places:
\[
k = 8.00
\]
So, the constant of proportionality is **$8.00 per hour**.
the table represents the time it took bill to complete sets of math problems which equation represents this relationship?
time(in minuets) number of problems in set
___________________________________
| 30 | 36 |
| 40 | 48 |
| 50 | 60 |
| 60 | 72 |
___________________________________
a. y=x+1.2
b. y=1.2x
c. y=x+12
d. y=12x
time(in minuets) number of problems in set
___________________________________
| 30 | 36 |
| 40 | 48 |
| 50 | 60 |
| 60 | 72 |
___________________________________
a. y=x+1.2
b. y=1.2x
c. y=x+12
d. y=12x
GPT-4o mini
To find the equation that represents the relationship between the time (in minutes) and the number of problems in the set, let’s analyze the given data.
We have:
- When time is 30 minutes, problems = 36
- When time is 40 minutes, problems = 48
- When time is 50 minutes, problems = 60
- When time is 60 minutes, problems = 72
Let's observe the relationship between the time (x) and the number of problems (y).
1. **Find the rate of problems per minute:**
You can calculate the ratio of the number of problems to the time for each entry:
- For 30 minutes: \( \frac{36}{30} = 1.2 \)
- For 40 minutes: \( \frac{48}{40} = 1.2 \)
- For 50 minutes: \( \frac{60}{50} = 1.2 \)
- For 60 minutes: \( \frac{72}{60} = 1.2 \)
The ratio is consistently \( 1.2 \) problems per minute.
2. **Write the equation:**
The relationship can be represented as:
\[
y = 1.2x
\]
Where:
- \( y \) is the number of problems,
- \( x \) is the time in minutes, and
- \( 1.2 \) is the number of problems completed per minute.
So, the equation that represents this relationship is:
**b. \( y = 1.2x \)**.
We have:
- When time is 30 minutes, problems = 36
- When time is 40 minutes, problems = 48
- When time is 50 minutes, problems = 60
- When time is 60 minutes, problems = 72
Let's observe the relationship between the time (x) and the number of problems (y).
1. **Find the rate of problems per minute:**
You can calculate the ratio of the number of problems to the time for each entry:
- For 30 minutes: \( \frac{36}{30} = 1.2 \)
- For 40 minutes: \( \frac{48}{40} = 1.2 \)
- For 50 minutes: \( \frac{60}{50} = 1.2 \)
- For 60 minutes: \( \frac{72}{60} = 1.2 \)
The ratio is consistently \( 1.2 \) problems per minute.
2. **Write the equation:**
The relationship can be represented as:
\[
y = 1.2x
\]
Where:
- \( y \) is the number of problems,
- \( x \) is the time in minutes, and
- \( 1.2 \) is the number of problems completed per minute.
So, the equation that represents this relationship is:
**b. \( y = 1.2x \)**.