turn 0.43,0.50 into a median
20 points

The cross-section of the rectangular pyramid, obtained by slicing it parallel to the longer sides of the base and through the top vertex, forms a 9-12-15 right triangle. The area of the cross-section is 54 square inches (Option C).

The rectangular pyramid has a base with sides of 5 inches and 12 inches, and diagonals measuring 13 inches. The height of the pyramid is 9 inches.

The cross-section obtained by slicing the pyramid parallel to the longer sides of the base and passing through the top vertex will form a right triangle with legs of 9 inches and 12 inches, and a hypotenuse of 13 inches (as given by the diagonals).

This right triangle is a 3-4-5 right triangle scaled up by a factor of 3, making it a 9-12-15 right triangle. The area of a right triangle is given by [tex]\(\frac{1}{2} \times \text{base} \times \text{height}\).[/tex]

So, the area of the cross-section is [tex]\(\frac{1}{2} \times 12 \times 9 = 54\)[/tex] square inches.

Therefore, the correct answer is (C) 54 square inches.

Learn more about area of the cross-section here:

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97? not an option. Maby 98

a. the answer is the first one

Answer: 67.5 minutes

Step-by-step explanation:

Since the front and backyard are the same size, then Alan will take the same time mowing them. So, if he takes 45 minutes mowing both of them, that means that he took half the time mowing the front and the other half mowing the backyard.

[tex]\frac{45}{2} =22.5[/tex]

The neighbor's front yard is the same size as well, so it will take him the same time.

[tex]45+22.5=67.5[/tex]

Then, the total time that Alan takes mowing the three yards is 67.5 minutes.

Drew could have purchased 3 books at prices of $4, $8, and $12, or at prices of $8 each.

The question states that Drew purchased 3 books, each with a different price, for a total of $24. The cost of each book is a multiple of 4. To find the possible prices of the 3 books, we need to find 3 multiples of 4 that add up to $24.

Let's start by listing the multiples of 4: 4, 8, 12, 16, 20, 24,...

We can see that the possible prices of the 3 books could be $4, $8, and $12. Another possibility is $8, $8, and $8. There may be other combinations as well, but these are the two most likely options.

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Answer:

[tex]8\frac{1}{6}[/tex] hours or 8 hours and 10 minutes.

Step-by-step explanation:

We have been given that a 155 pound person burns about 500 calories per hour playing racquetball. One pound is equal to 3500 calories.

Since the person burns 500 calories per hour, so time taken to burn 3500 calories would be:

[tex]\frac{3500\text{ cal}}{\frac{\text{500 cal}}{\text{Hour}}}[/tex]

[tex]\frac{3500\text{ cal}}{500}\times\frac{\text{Hour}}{\text{Cal}}=7\text{ Hour}[/tex]

Now, we will convert 7 hours to minutes.

1 hour equals 60 minutes.

7 hours = 7*60 minutes =420 minutes.

Since the person take a rest of 5 minutes for every 30 minutes of playing, so we will divide 420 by 30 to find the number of times the person rested to burn 3500 calories.

[tex]\frac{420}{30}=14[/tex]

Now, we will multiply 14 by 5 minutes to find minutes the person rested.

[tex]14\times 5\text{ minutes}=70\text{ minutes}[/tex]

Total number of minutes to burn 3500 calories: [tex]420\text{ minutes}+70\text{ minutes}=490\text{ minutes}[/tex]

[tex]\frac{490}{60}=\frac{49}{6}=8\frac{1}{6}[/tex]

Therefore, it will take 8 hours and 10 minutes to burn 1 pound.

After conversion, a 5-8 inch nut would require a spanner size between 127mm to 203.2mm. Unfortunately, the available spanner sizes (12mm, 14mm, 16mm) are all too small.

To find out which spanner Asta needs, we first need to convert the inch measurements to millimeters (mm), as the spanners are sold in mm. Asta's nut size is 5-8 inches. She knows one inch equals 2.54cm. To convert these to mm, we multiply the values by 10 as 1cm is equal to 10mm. So, 5 inches equals 127mm and 8 inches equals 203.2mm. Given the available sizes of spanners (12mm, 14mm, and 16mm), none of these would fit her nut, as they are all far too small.

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To find the sum of the absolute deviations, calculate the average of the data set and then subtract it from each value, taking the absolute value. Finally, sum up all the absolute deviations.

To find the sum of the absolute deviations, we first need to find the average of the data set. The average is calculated by adding up all the numbers and then dividing by the total number of values. So, the average of the data set 8, 5, 15, 12, 10 is (8 + 5 + 15 + 12 + 10) / 5 = 50 / 5 = 10.

Next, we calculate the absolute deviation for each number by subtracting the average from each value and taking the absolute value. The absolute deviations for the given data set are: |8 - 10| = 2, |5 - 10| = 5, |15 - 10| = 5, |12 - 10| = 2, |10 - 10| = 0.

Finally, we sum up all the absolute deviations: 2 + 5 + 5 + 2 + 0 = 14. Therefore, the sum of the absolute deviations is 14. So the correct choice is 14.

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The sum of the absolute deviations of the dataset 8, 5, 15, 12, 10 is calculated by finding the mean of the dataset, calculating the absolute difference of each data point from the mean, and summing up these absolute values. The result is 14.

The sum of the absolute deviations of a dataset is determined by first finding the mean of the dataset, and then finding the absolute difference of each data point from the mean. The sum of these absolute values is the sum of absolute deviations.

Here is how to do this with your dataset: 8, 5, 15, 12, 10.

So, the sum of the absolute deviations of your dataset is 14.

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Answer:

Spaghetti and Pizza are preferred almost equally.

Step-by-step explanation:

Daniel surveyed a random sample of 100 students from his middle school to learn more about what type of school lunches are preferred based on his observation the table of the following is given as:

                        Hamburgers             Spaghetti         Pizza

Sample 1:                 13                              43                     44

                      -----------------------------------------------------------------------

Sample 2:                20                              41                     39

                      -------------------------------------------------------------------------

Total:                       33                               84                   83

By looking at the table we see that the total number of spaghetti and Pizza chosen are almost equal as:

Total number of Spaghetti preferred=84.

and Total number of Pizza preferred=83.

Answer:

d

Step-by-step explanation:

The length of each side of the equilateral triangle is approximately 52 cm.

An equilateral triangle has all sides equal in length. To find the length of each side, we can use the property that an equilateral triangle's height is equal to half the length of one of its sides.

Since the height is given as 26 cm, we can set up the equation:

26 cm = (side length)/2

Multiplying both sides by 2, we get:

52 cm = side length

Therefore, the length of each side of the equilateral triangle is approximately 52 cm.

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Answer:

the person bove me is right

Step-by-step explanation:

To find Brian's commission, multiply his weekly sales of $4,580 by his commission rate of 8%. His commission for the week would be $366.40.

To calculate Brian's commission, we need to apply the commission rate to his total weekly sales. Since his commission rate is 8%, we can calculate the commission by multiplying his total sales (
$4,580) by 0.08.

The calculation would be as follows:

Commission = Total Sales x Commission Rate
Commission = $4,580 x 0.08
Commission = $366.40

Therefore, Brian will earn a commission of $366.40 on his weekly sales.