The glee club has $90 to spend on pens and pencils. Each pen costs $0.75 and each pencil costs $0.15. Let x represent the number

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Answer:

1458/3456 reduces to 27/64 (after simplification)

The cube root of 27/64 equals 3/4

The square of 3/4 calculates to 9/16

Multiplying 9/16 by 1024 results in 576.

THIS IS THE ACTUAL WORK AND RESULT

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The last part of the question is asking;

What was the total amount spent by all (99.7%) students on textbooks in a semester?

Response:

almost all (99.7%) of the students spent between $165 and $315 on textbooks in a semester.

Stepwise clarification:

The standard deviation rule informs that for normally distributed data, approximately 99.7% of observations fall within three standard deviations from the mean.

In this case, we have the given mean as 240, and standard deviation as 25

Thus, calculating three standard deviations below the mean: Mean - 3(standard deviation)

equals 240 - (3 × 25)

yielding 240 - 75 = 165

Now, for three standard deviations above the mean: Mean + 3 (standard deviation) = 240 + (3 × 25)

equals 240 + 75 = 315

Therefore, nearly all (99.7%) of the students spent between $165 and $315 on textbooks in a semester.

The total number of individuals surveyed is 280. From the survey results, 65% were satisfied with the park's condition. Given that this satisfied group represents 182 people, we can calculate the overall survey population using this information.

Part A:

Considering the best possible outcome

The ideal case occurs if the two missing socks are from the same pair.
Consequently, there are 4 complete pairs remaining.

To choose 2 from the total of 10 socks (5 pairs), the number of combinations is given by 10C2 = 45.

Choosing 2 that are from the same pair means selecting one from 5 pairs, so the count is 5C1 = 5.

Thus, the probability for this best case is 5 / 45 = 1 / 9.

Part B:

Considering the worst-case outcome

This scenario occurs when the two missing socks are from different pairs.
As a result, we have 3 complete pairs left.

The total ways to select 2 socks from 10, again, is 10C2 = 45.

To select 2 that do not belong to the same pair, we calculate as follows: 10C2 - 5C1 = 45 - 5 = 40.

Therefore, the probability for the worst-case scenario is 40 / 45 = 8 / 9.