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Marianna
2 months ago
14

You are given a rectangular sheet of cardboard that measures 11 in. by 8.5 in. (see the diagram below). A small square of the sa

me size is cut from each corner, and each side folded up along the cuts to from a box with no lid.
1. Anya thinks the cut should be 1.5 inches to create the greatest volume, while Terrence thinks it should be 3 inches.

Explain how both students can determine the formula for the volume of the box.

Determine which student's suggestion would create the larger volume.

Explain how there can be two different volumes when each student starts with the same size cardboard.

2. Why is the value of x limited to 0 in. < x < 4.25 in.?

Mathematics
1 answer:
AnnZ [12.3K]2 months ago
7 0

Answer:

Terrence's

Step-by-step explanation:

The cut length of the square corresponds to the box height.

1. a

In Anya's approach: 8.5 - 1.5 = 7, 11 - 1.5 = 9.5; with the height being 1.5, the volume calculates as height x length x width = 1.5 x 9.5 x 7 = 99.75 square inches.

Terrence's method: 8.5 - 3 = 5.5, 11 - 3 = 8. Volume = 5.5 x 8 x 3 = 132 square inches. Clearly, 99.75 < 132 square inches, indicating Terrence's approach would yield a larger volume.

1. b

The dimensions of the box rely on the length, width, and height of the cardboard cutout, thus varying cutting measurements for the same cardboard size can produce different box dimensions.

2. Squares are cut from each corner, thus the combined size of the two squares on the cardboard must be less than the shorter cardboard side. The shorter side is 8.5 inches, which divided by 2 results in 4.25 inches, therefore squares cannot exceed this size. If squares are taken out measuring 4.25 inches, it will leave a strip 2.5 inches wide that cannot form a box.

To cut out squares of 5 inches, how you position them can cause overlap or extend beyond the cardboard. While 5 + 5 equals ten, making the longer side of 11 inches adequate, the 8.5 inches side allows zero room for the 10 inches.

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According to the U.S. Census Bureau (2016), a substantial pay gap still exists. The average American man, with an advanced colle
Leona [12618]

Answer:

The earnings gap, over a career spanning 30 years, between men and women totals $1,200,150

Step-by-step explanation:

Calculated annually.

The typical male earns $90,761 each year.

The typical female earns $50,756 per annum.

Therefore, the annual difference is:

90,761 - 50,756 = 40,005

Across 30 years:

30*40,005 = 1,200,150

The earnings gap over a 30-year career, when comparing men and women, is $1,200,150

0 0
3 months ago
If 6 components are drawn at random from the container, the probability that at least 4 are not defective is . If 8 components a
Svet_ta [12734]
The question is missing some information. It should be phrased as follows:

<span><span>A container has 50 electronic components, with 10 identified as defective. If 6 components are randomly selected from the container, what is the probability that at least 4 of them are not defective? Additionally, if 8 components are drawn at random from the container, what is the probability that exactly 3 are defective?

</span>Answers
<span>Part 1.  0.02
Part 2. </span></span>0.0375<span><span>

</span>Explanation
Probability denotes the likelihood of an event occurring. It is computed as:
probability = (Number of favorable outcomes)/(Number of total outcomes)

Part 1
When 6 components are chosen, if 4 are confirmed functioning, then 2 must be defective.
P(at least 4 functional) = 4/40</span>× 2/10
                                            = 1/10 × 1/5
                                            = 1/50
                                            = 0.02

Part 2
Choosing 8 components, if 3 are defective, then 5 are functioning.
P(3 defective) = 3/40 × 5/10
                             = 15/400
                             = 3/80
                            = 0.0375
4 0
2 months ago
Robert was able to travel 292.0 miles in 4.000 hours and used 38 liters of gasoline. What was robert's speed in feet per second?
zzz [12365]

Robert covered a distance of 292 miles.

He took 4 hours to complete this journey.

Next, let's convert miles to feet.

1 mile equals 5280 feet.

Thus, 292 miles in feet equals 292 * 5280 = 1541760 feet.

Now, converting 4 hours into seconds.

1 hour translates to 3600 seconds.

Therefore, 4 hours equals 3600 * 4 = 14400 seconds.

The question asks for speed in feet per second.

speed = \frac{distance}{time}

Thus,

\frac{1541760}{14400}

is 107.067 feet per second.

8 0
2 months ago
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 2780 seats. The students
zzz [12365]

Respuesta:

Un total de 1242 estudiantes de sexto grado participaron en la excursión.

Explicación paso a paso:

A partir de los datos proporcionados, se sabe que el teatro tiene 2760 asientos y que los estudiantes ocuparon el 45% de ellos, por lo que para encontrar cuántos estudiantes de sexto grado asistieron a la excursión, hay que calcular el 45% de 2760:

2760*45%=1242

Así que, de acuerdo a esto, la respuesta es que 1242 estudiantes de sexto grado estuvieron en la excursión.

5 0
2 months ago
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