Write the ratio 12:9

Question

Write the ratio 12:9
12
:
9
 as an equivalent ratio of 4:x
4
:
𝑥
. Write your answer as a complete ratio. (1 point)

GPT-4o mini · Answer

To find an equivalent ratio of $ 4:x $ that is equivalent to the ratio $ 12:9 $, we can first simplify $ 12:9 $. The greatest common divisor (GCD) of 12 and 9 is 3. Dividing both terms by 3, we get: $$ 12 \div 3 = 4 \quad \text{and} \quad 9 \div 3 = 3 $$ So, the simplified ratio $ 12:9 $ is $ 4:3 $. Now we can set $ 4:x $ equal to the simplified ratio $ 4:3 $: $$ \frac{4}{x} = \frac{4}{3} $$ To find $ x $, we can cross-multiply: $$ 4 \cdot 3 = 4 \cdot x $$ This simplifies to: $$ 12 = 4x $$ Now, divide both sides by 4: $$ x = \frac{12}{4} = 3 $$ The equivalent ratio of $ 4:x $ is therefore: $$ 4:3 $$ So, the answer is $ \mathbf{4:3} $.

Answer

Use the table to answer the question. Cost of Ground Beef Pounds Cost ($) 10 37.50 8 30.00 6 22.50 4 15.00 What is the cost for 1 pound of ground beef? (1 point)

GPT-4o mini · Answer

To find the cost for 1 pound of ground beef, we can calculate the cost per pound for the given amounts.

We can see from the table:

For 10 pounds, the cost is $37.50.
For 8 pounds, the cost is $30.00.
For 6 pounds, the cost is $22.50.
For 4 pounds, the cost is $15.00.

Now, let's calculate the cost per pound for each entry:

For 10 pounds: \[ \text{Cost per pound} = \frac{37.50}{10} = 3.75 \]
For 8 pounds: \[ \text{Cost per pound} = \frac{30.00}{8} = 3.75 \]
For 6 pounds: \[ \text{Cost per pound} = \frac{22.50}{6} = 3.75 \]
For 4 pounds: \[ \text{Cost per pound} = \frac{15.00}{4} = 3.75 \]

In all cases, the cost per pound of ground beef is consistently $3.75.

Thus, the cost for 1 pound of ground beef is $\mathbf{3.75}$.

Answer

There are 48 inches in 4 feet, which is represented by the equation 4y=48x 4 𝑦 = 48 𝑥 . Determine the number of inches per foot.(1 point) inches

GPT-4o mini · Answer

To determine the number of inches per foot using the equation $ 4y = 48x $, we can interpret the variables as follows:

Let $ y $ be the number of inches.
Let $ x $ be the number of feet.

We know from the problem statement that there are 48 inches in 4 feet.

To find the number of inches per foot, we can solve for the value of $ y $ when $ x = 1 $:

We can start by simplifying the equation: \[ 4y = 48x \]

Now, divide both sides of the equation by 4: \[ y = 12x \]

This simplified equation $ y = 12x $ indicates that for every foot ($ x = 1 $), the number of inches ($ y $) is: \[ y = 12 \times 1 = 12 \]

Therefore, there are 12 inches in a foot.

Thus, the answer is $\mathbf{12}$ inches per foot.

Answer

The graph shows the proportional relationship. Derive the equation of the line y=mx 𝑦 = 𝑚 𝑥 through the origin. (1 point)

GPT-4o mini · Answer

To derive the equation of a line in the form $ y = mx $, where the line passes through the origin (0,0), you need to determine the slope $ m $.

The slope $ m $ is calculated from the rise over run between two points on the line. If the graph provides specific points, you can use their coordinates to find $ m $.

Here is how you can derive the equation step-by-step:

Identify Points: Determine two distinct points on the line from the graph. Let's say these points are (x1, y1) and (x2, y2).
Calculate the Slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Construct the Equation: Once you have the slope $ m $, substitute it into the equation $ y = mx $.

Example:

Let's say you find two points on the graph: (2, 6) and (4, 12).

Calculate the slope $ m $:
- Point 1: $(2, 6)$ → $x_1 = 2, y_1 = 6$
- Point 2: $(4, 12)$ → $x_2 = 4, y_2 = 12$
\[ m = \frac{12 - 6}{4 - 2} = \frac{6}{2} = 3 \]
Construct the Equation: \[ y = 3x \]

Thus, the equation of the line, which passes through the origin, would be $ y = 3x $.

To provide a specific equation, please refer to the actual points on your graph. However, the process will remain the same regardless of the points used.

Answer

he proportional relationship between calories and ounces of soda is shown in the graph. How many calories are in 1 ounce? (1 point) There are calories in 1 ounce of soda

GPT-4o mini · Answer

To determine the number of calories in 1 ounce of soda from the graph showing the proportional relationship between calories and ounces, you would need to find the coordinates of the points on this graph. Specifically, you should look for the point where the ounces equal 1.

Assuming there is a point on the graph at coordinates $ (1, y) $, where $ y $ represents the calories corresponding to 1 ounce, you can read the value of $ y $ directly from the graph.

If you don't have access to the graph right now, you can use similar triangles or the concept of proportionality to calculate the calories per ounce based on two known points on the graph.

Example Process:

Identify Known Points: Suppose you identify that:
- 2 ounces correspond to 100 calories (point (2, 100)),
- and you need to find how much that corresponds to 1 ounce.
Calculate Calories per Ounce: \[ \text{Calories per ounce} = \frac{\text{Calories at 2 ounces}}{\text{Ounces}} \] \[ \text{Calories per ounce} = \frac{100 \text{ calories}}{2 \text{ ounces}} = 50 \text{ calories/ounce} \]

Therefore, depending on the specific values from the graph, you can calculate:

There are $ \text{calories in 1 ounce of soda} $.

If you provide the specific point or data from the graph, I can give you the exact number of calories per ounce.

Answer

how many

GPT-4o mini · Answer

To determine the number of calories in 1 ounce of soda, I need specific information from the graph you mentioned (like the coordinates of a point on the graph). Since I don’t have access to the graph itself, I can’t give you an exact number.

However, if you have data points from the graph, such as:

If the graph shows that 2 ounces corresponds to 100 calories, you would divide 100 by 2 to find that there are 50 calories in 1 ounce.
If 4 ounces corresponds to 240 calories, then you would divide 240 by 4, giving you 60 calories in 1 ounce.

If you can provide any specific data points or values from the graph, I would be able to help you calculate the number of calories in 1 ounce of soda. Please share any relevant numbers!