The average rate of the first part of Yi’s walk on a park loop was 4 miles per hour. She then met up with a friend and the two w

Answer:

together they rake leaves in one minute.

Step-by-step explanation:

If Maya takes x minutes to rake, then in one minute, she rakes leaves.

For Carla, if her raking takes y minutes, in one minute she rakes leaves.

Thus, to find the amount they work together in one minute, we add both of their contributions for that minute, resulting in:

Finally, simplifying this expression gives:

As a result, they collectively rake leaves in a minute.

Response:

Detailed explanation:

Probability for an event is calculated as the ratio of the size of the event space compared to that of the sample space.

The sample space encompasses all possible outcomes.

Event space represents the number of favorable outcomes for the event in question.

Thus

Let

x ------> size of event space

y ----- → size of sample space

so

Calculate the probability of the first student being left-handed

we have

substituting values

Simplify

Calculate the probability of the second student being left-handed

we have

substituting values

Calculate the probability that both selected students will be left-handed

Multiply the probabilities together.

Convert to percentage

Multiply by 100

Response:

2:3 is

✔ lesser than

5:6

10:12 is

✔ greater than

6:9

The ratios shown in Table 1 are

✔ smaller than

those in Table 2

Step-by-step explanation:

Response:

The connection between battery capacity and time is:

The associated graph is provided.

Step-by-step explanation:

We will plot the battery's charged capacity against time.

The charging rate remains steady; hence, the relationship is linear.

Initially, at time t=0, the battery's capacity measures 0.2 (or 20%).

With each passing minute, an additional 5% of its capacity is accumulated. Thus, at t=1, the capacity becomes 0.2 + 0.05 = 0.25 (or 25%).

We can derive the slope for the linear function as:

Consequently, the correlation between battery capacity and time is:

Answer:

A. Combining one pound of pistachios with one pound of almonds costs $20.

C. Decreasing the almond quantity by one pound leads to a total price of $40.

E. The price p (in dollars) per pound of pistachios is represented by the equation 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let:

x = cost per pound of pistachios

y = cost per pound of almonds

We know that

x = y + 4 (Equation A)

2x + 3y = 48 (Equation B)

Substitute x from Equation A into Equation B:

2(y + 4) + 3y = 48

2y + 8 + 3y = 48

5y = 48 – 8

y = 8

Find x:

x = 8 + 4 = 12

Therefore, pistachios cost $12 per pound and almonds cost $8 per pound.

Verify the statements:

Case A) One pound of each equals $20.

True, since 12 + 8 = 20.

Case B) Pistachios cost twice as much as almonds.

False, because 2 × 8 = $16 ≠ $12.

Case C) Reducing almond pounds by 1 yields $40 total.

True, as 2(12) + 2(8) = 24 +16 = 40.

Case D) The almond cost modeled by 2(a – 4) + 3a = 48.

False; it should be 2(a + 4) + 3a = 48.

Case E) The pistachio cost modeled by 2p + 3(p – 4) = 48.

True, since p = a + 4 implies a = p – 4.