Determine the value of n that will make the ratios equivalent.(1 point)

Question

5/4=30/n

n =
/....

Answer 1

To find the value of \( n \) that makes the ratios \( \frac{5}{4} = \frac{30}{n} \) equivalent, you can cross-multiply:

\[ 5n = 4 \cdot 30 \]

Calculating the right side:

\[ 4 \cdot 30 = 120 \]

Now, we have:

\[ 5n = 120 \]

Next, divide both sides by 5 to solve for \( n \):

\[ n = \frac{120}{5} = 24 \]

Thus, the value of \( n \) is

\[ \boxed{24} \]

Answer 2

It takes Julian 1/2
hour to walk 2 miles. He decides to start working in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear?

hours Miles walked
1/4 1
1/2 2
3/4 3
1 4

(1 point)
Responses

(1/4,1)
open paren 1 fourth comma 1 close paren

(1/2, 2)
(1/2, 2)

(3/4, 3)
(3/4, 3)

(1,4)

Answer 3

To determine the ratio that reflects the constant of proportionality in Julian's data, we can look at the given pairs (hours, miles walked) and find the consistent ratio between hours and miles.

Let's calculate the ratio for each pair:

1. For \( (1/4, 1) \):

   • Ratio = \( \frac{1}{1/4} = 4 \)

2. For \( (1/2, 2) \):

   • Ratio = \( \frac{2}{1/2} = 4 \)

3. For \( (3/4, 3) \):

   • Ratio = \( \frac{3}{3/4} = 4 \)

4. For \( (1, 4) \):

   • Ratio = \( \frac{4}{1} = 4 \)

In each case, the ratio of miles walked to hours taken is consistent and equal to 4, which means that this is the constant of proportionality.

Since we are looking for the pair that appears as the ratio in relation to the constant of proportionality, we can choose any pair. However, all pairs give us the same constant ratio.

The ratio appears at:

• \( (1/4, 1) \)
• \( (1/2, 2) \)
• \( (3/4, 3) \)
• \( (1, 4) \)

All of these ratios support the same constant of proportionality, which is 4.

If you must choose a specific pair as the answer, you can pick any of them. One appropriate response could be

\[ \boxed{(1/2, 2)} \]

since it represents an exact doubling of the distance and aligns well with the initial example given (1/2 hour for 2 miles). But all would technically be valid as they reflect the same constant of proportionality.

Answer 4

Determine if each table represents a proportional relationship.(6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
PROPORTIONAL NOT PROPORTIONAL

x 2 5 8 12
y 8 20 32 48

time (min) distance (ft)
2 6
4 12
6 18
numbers of socks (x)1 2 3 4
cost (y) $2 $4 $6 $6

numbers of adults 1 2 3 5 10 100
cost of tickets 75 150 225 375 750 7500

pounds of bananas cost
2 2.50
3 3.75
5 6.25
7 8.75

Answer 5

To determine if each table represents a proportional relationship, you need to check if the ratio of \( y \) to \( x \) (where applicable) is constant across all pairs in the table. A proportional relationship has a constant ratio, which means:

\[ \frac{y_1}{x_1} = \frac{y_2}{x_2} = \frac{y_3}{x_3} = \ldots \]

Let's analyze each table:

1.

Table:

• \( x: 2, 5, 8, 12 \)
• \( y: 8, 20, 32, 48 \)

Ratios: \[ \frac{8}{2} = 4, \quad \frac{20}{5} = 4, \quad \frac{32}{8} = 4, \quad \frac{48}{12} = 4 \] All ratios are equal to 4.

Conclusion: PROPORTIONAL

2.

Table:

• Time (min): 2, 4, 6
• Distance (ft): 6, 12, 18

Ratios: \[ \frac{6}{2} = 3, \quad \frac{12}{4} = 3, \quad \frac{18}{6} = 3 \] All ratios are equal to 3.

Conclusion: PROPORTIONAL

3.

Table:

• Number of socks (x): 1, 2, 3, 4
• Cost (y): $2, $4, $6, $6

Ratios: \[ \frac{2}{1} = 2, \quad \frac{4}{2} = 2, \quad \frac{6}{3} = 2, \quad \frac{6}{4} = 1.5 \] The last ratio (1.5) is not equal to the others.

Conclusion: NOT PROPORTIONAL

4.

Table:

• Number of adults: 1, 2, 3, 5, 10, 100
• Cost of tickets: 75, 150, 225, 375, 750, 7500

Ratios: \[ \frac{75}{1} = 75, \quad \frac{150}{2} = 75, \quad \frac{225}{3} = 75, \quad \frac{375}{5} = 75, \quad \frac{750}{10} = 75, \quad \frac{7500}{100} = 75 \] All ratios are equal to 75.

Conclusion: PROPORTIONAL

5.

Table:

• Pounds of bananas: 2, 3, 5, 7
• Cost: 2.50, 3.75, 6.25, 8.75

Ratios: \[ \frac{2.50}{2} = 1.25, \quad \frac{3.75}{3} = 1.25, \quad \frac{6.25}{5} = 1.25, \quad \frac{8.75}{7} \approx 1.25 \] All ratios are equal to approximately 1.25.

Conclusion: PROPORTIONAL

Summary of Each Table:

1. PROPORTIONAL
2. PROPORTIONAL
3. NOT PROPORTIONAL
4. PROPORTIONAL
5. PROPORTIONAL

Please feel free to ask if you need more information!

Answer 6

Last Saturday, Mr. Stone drove 320 miles in 5 hours. What is the unit rate of miles per hour?(1 point)
miles per hour​​​​​​

Answer 7

To find the unit rate of miles per hour, you can use the formula:

\[ \text{Unit Rate} = \frac{\text{Total Miles}}{\text{Total Hours}} \]

In this case, Mr. Stone drove 320 miles in 5 hours.

\[ \text{Unit Rate} = \frac{320 \text{ miles}}{5 \text{ hours}} = 64 \text{ miles per hour} \]

Thus, the unit rate is

\[ \boxed{64} \text{ miles per hour} \]

Answer 8

A caterpillar can crawl 1/2
of an inch in 1/4
of a minute. How far can he crawl in 1 minute?(1 point)
The caterpillar can crawl
inch(es) in one minute.

Answer 9

To determine how far the caterpillar can crawl in one minute, we start with the information that it can crawl \( \frac{1}{2} \) inch in \( \frac{1}{4} \) minute.

To find out how far it can go in 1 minute, we can set up a proportion or use straightforward multiplication. If the caterpillar crawls \( \frac{1}{2} \) inch in \( \frac{1}{4} \) minute, then in 1 minute (which is four times \( \frac{1}{4} \) minute), it will crawl:

\[ \text{Distance in 1 minute} = \left( \frac{1}{2} \text{ inch} \times 4 \right) = 2 \text{ inches} \]

Therefore, the caterpillar can crawl

\[ \boxed{2} \text{ inch(es) in one minute.} \]

Answer 10

Denise is making snacks for a party. She thinks more people will eat sandwiches than chicken wings. She decides to make 40 sandwiches and 25 chicken wings. Determine the ratio of chicken wings to sandwiches in simplest terms.(1 point)
The ratio of chicken wings to sandwiches in simplest terms is
:

Answer 11

To determine the ratio of chicken wings to sandwiches, we start with the numbers given:

• Chicken wings: 25
• Sandwiches: 40

The ratio can be expressed as:

\[ \text{Ratio} = \frac{\text{Chicken Wings}}{\text{Sandwiches}} = \frac{25}{40} \]

Next, we simplify the fraction \( \frac{25}{40} \).

To simplify, we can find the greatest common divisor (GCD) of 25 and 40. The GCD is 5. Now, we divide both the numerator and the denominator by their GCD:

\[ \frac{25 \div 5}{40 \div 5} = \frac{5}{8} \]

Thus, the ratio of chicken wings to sandwiches in simplest terms is:

\[ \boxed{5:8} \]