After Mia gave 1/4 of her milk to Dante, Dante had twice the amount of milk as Mia. What was the ratio of the amount of milk Mia

To start, calculate the return for each price per unit

Return = quantity sold x price per unit

Return1 = 5000 units x Php 900

Return1 = Php 4,500,000

Next, figure out the return for the other price per unit

Return2 = quantity sold x price per unit

Return2 = (5000 + 1500 units) x ( Php 900 – 100)

Return2 = Php 5,200,000

Thus, a price of Php 800 per unit will result in a higher return.

a(t) = 210 - 5t

(1) What does t represent?

Since t is given in minutes, it stands for time.

Interpreting t as the balloon’s altitude is incorrect since a(t) represents altitude.

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Time elapsed since the balloon starts descending

This is the correct interpretation.

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Time for the balloon to reach ground level is incorrect because that would be a fixed moment, not a variable t.

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(2) What does a(t) represent?

The balloon’s altitude

This is the correct answer.

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Time since descent began is incorrect because that is represented by t.

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Time to reach the ground is inaccurate since a(t) is altitude, not time.

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(3) What does a(5.5) signify?

It does not represent the time to reach 5.5 feet altitude.

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The altitude of the balloon after 5.5 minutes

This is the correct interpretation since a(5.5) is altitude when t = 5.5 minutes.

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It is not the time needed to reach the ground.

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5.5 minutes alone is not correct because a(t) denotes altitude, not time.

a(5.5) refers to altitude at t = 5.5 minutes.

Here’s a counterexample: consider

Select the subsets in the following manner:

It's accurate that and and that , but

Let's apply the Pythagorean theorem to determine whether a triangle could be formed.

Assuming we have two wooden dowels each measuring 8 inches, we can break one dowel in half, resulting in two pieces of 4 inches each.

Now we have three wooden dowels with lengths of 4 inches, 4 inches, and 8 inches.

According to the Pythagorean theorem:

a² + b² = c²
4² + 4² = 8²
16 + 16 = 64
34 ≠ 64

To form a triangle, the length of the cut wooden dowel needs to exceed that of the uncut dowel.

I also visually attempted this exercise on paper, cutting according to the assumed dimensions. No triangle can be constructed with these pieces. 

Answer: c. We can state with 95 percent confidence that the percentage of individuals surveyed who regard climate change as a significant issue is between 0.146 and 0.214.

Step-by-step explanation:

Interpretation of the 95% confidence interval :

This means one can be 95% certain that the actual proportion in the broader population falls within this range.

From the provided details, we identify the population parameter as p (the proportion of individuals that believe in climate change )

As a result, the 95 percent confidence interval is represented as (0.146, 0.214)

Interpretation: We can assert with 95% confidence that the actual population proportion of individuals who perceive climate change as a problem ranges from 0.146 to 0.214.

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c. We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214.

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