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

Question

Determine the value of n that will make the ratios equivalent.(1 point)
5/4=30/n

n = 
..

GPT-4o mini · Answer

To determine the value of $ n $ that will make the ratios $ \frac{5}{4} = \frac{30}{n} $ equivalent, we can cross-multiply. Cross-multiplying gives us: $$ 5n = 4 \cdot 30 $$ Calculating $ 4 \cdot 30 $: $$ 4 \cdot 30 = 120 $$ So, we have: $$ 5n = 120 $$ Now, divide both sides by 5 to solve for $ n $: $$ n = \frac{120}{5} = 24 $$ Therefore, the value of $ n $ is $$ \boxed{24} $$

Answer

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?

(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)
open paren 1 comma 4 close paren
Skip to navigation
page 13 of 13

GPT-4o mini · Answer

To find the ratio that represents the constant of proportionality in Julian's case, we can start by determining his walking speed based on the information provided:

Julian walks 2 miles in $ \frac{1}{2} $ hour.

First, we can calculate his speed:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ miles}}{\frac{1}{2} \text{ hour}} = 2 \text{ miles} \times 2 = 4 \text{ miles per hour} \]

Now that we know Julian's speed is $ 4 $ miles per hour, we can see how this relates to the options provided, interpreting them as a representation of distance (y) and time (x) in some form of proportional relationship.

If we examine the options in terms of distance per time (which is essentially speed):

(1/4, 1): This could imply $ \frac{1}{4} \text{ miles/hour} $, which is not the speed we calculated.
(1/2, 2): This could imply $ 2 \text{ miles} $ in $ \frac{1}{2} \text{ hour} $. This relates to his walking since he indeed walks $ 2 $ miles in $ \frac{1}{2} $ hour, which gives a constant of $ 4 $ when considered as the speed.
(3/4, 3): This implies $ 3 \text{ miles} $ in $ \frac{3}{4} \text{ hour} $, which again does not equate to $ 4 \text{ miles/hour} $.
(1, 4): This implies $ 4 \text{ miles} $ in $ 1 \text{ hour} $, which indeed equals $ 4 \text{ miles/hour} $ too.

Given the options, the ratio $ \left(\frac{1}{2}, 2\right) $ corresponds directly to the data (2 miles in $ \frac{1}{2} $ hour), hence making it a constant of proportionality based directly on his known speed.

However, if we are looking strictly for representation akin to his exact speed, then $ (1, 4) $ would also infer a proportional relationship confirming the speed.

Thus, the ratio $ \left(\frac{1}{2}, 2\right) $ is likely the most directly related to Julian's speed situation, but $ (1, 4) $ also stands for his calculated speed.

So, without knowing more about what you meant by "the constant of proportionality," both $ (1/2, 2) $ and $ (1, 4) $ are valid answers depending on interpretation. If I must choose one based on his initial walking situation, I would choose $ \boxed{(1/2, 2)} $ as it derives directly from his known walking information.