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professor190 [17]
2 years ago
8

Pete's Pottery observes the heights of the vases in inventory. The results are represented by the box plot shown below.

Mathematics
1 answer:
KIM [24]2 years ago
4 0

Answer:

  • <u>The box plot gives data on the heights of vases in inventory.</u>
  • <u>The heights are measured in inches.</u>

Step-by-step explanation:

Given the question and the image, the following are the solution steps to answer the question.

STEP 1: Define box plot.

In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread, and skewness groups of numerical data through their quartiles.

STEP 2: Choose the correct statement

The box plot shows the minimum height, maximum height, first and third quartiles, and the median.

Therefore,

The box plot does not show the number of vases recorded

The box plot does not show the heights of mugs, just vases.

The height is measured in inches, not centimeters.

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The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the pris
Georgia [21]

Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume =  80 tan 36° × 16 = 1280  tan 36° = 1280  × 0.726542528

volume = 929.974435847  cm³

volume ≈ 930 cm³ (nearest cubic cm)

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3 years ago
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