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IceJOKER [234]
4 years ago
12

Martina chose a random sample of 10 bags of candy from two different Brands, A and B. All bags in the sample are the same size.

Martina counts the number of candy pieces in each bag and plots the results on two dot plots.
A dot plot is shown. The title of the plot is Brand A. The line is numbered with tick marks at 40, 45, 50, 55, 60, 65, and 70 and is labeled Number of Candy Pieces. There are 2 dots at 52, 1 dot at 53, 2 dots at 55, 1 dot at 56, 2 dots at 57, and 2 dots at 62. A dot plot is shown. The title of the plot is Brand B. The line is numbered with tick marks at 40, 45, 50, 55, 60, 65, and 70 and is labeled Number of Candy Pieces. There is 1 dot at 44, 1 dot at 46, 2 dots at 52, 1 dot at 55, 1 dot at 62, 1 dot at 65, 2 dots at 67 and 1 dot at 69

Based on the plots, which statement is a valid comparison of the number of candies in the bags of the two Brands?
Mathematics
2 answers:
natali 33 [55]4 years ago
7 0

Answer:

The Answer is B

Step-by-step explanation:

weqwewe [10]4 years ago
4 0

B. The number of candies in the bags from Brand B is greater and less consistent than the number of candies in the bags from Brand A.

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Answer:

Lateral Area = 624 square units

Surface area = 1,200 square units

Volume = 960 cubic units

Step-by-step Explanation:

==>Given:

Dimensions of the square pyramid as shown in the figure are:

length of 1 side of the square base (s) = 24

Slant height (l) = 13

Perpendicular height (h) = ?

==>Required:

a. Lateral area (L.A) = 4 × ½sl

b. Surface Area (S.A) = Base area (s²) × Lateral area (4 × ½sl)

c.Volume of the pyramid = ⅓ × Base area (s²) × perpendicular height (h)

==>SOLUTION:

a. Lateral area (L.A) = the area of the 4 lateral faces of the pyramid, which are triangular faces.

L.A = 4 × ½sl

From the figure given, s = 24; l = 13,

Therefore, L.A = 4 × ½ × 24 × 13

= 4 × 1 × 12 × 13

Lateral Area = 624 square units

b. Surface Area (S.A) = Base area (s²) × Lateral area (4 × ½sl)

Base area (s²) = 24² = 576 square units

Lateral area (4 × ½sl) = 624 square units

Therefore, total surface area = 576 + 624

= 1,200 square units

c. c.Volume of the pyramid using the formula ⅓ × Base area (s²) × perpendicular height (h)

Base area (s²) = 576 square units

Perpendicular height (h) is not given in the figure = h

Since already know the slant height (s), let's use Pythagorean theorem to find the perpendicular height (h) bearing in mind that a right triangle is formed in the middle of the pyramid as illustrated in the figure attached below.

The base of the right triangle = ½ of side length of the base (s) = ½ × 24 = 12

The hypotenuse (l) = 13

Therefore using the Pythagorean Theorem formula a² + b² = c², let's find the perpendicular height (h).

Where,

a² = h²

b² = (½s)² = 12²

c² = l² = 13²

Thus, h² + 12² = 13²

h² = 13² - 12²

h² = 169 - 144

h² = 25

h = √25

h = 5

==>Volume of pyramid (V) = ⅓ × Base area (s²) × perpendicular height (h)

V = ⅓ × 576 × 5

V = ⅓ × 2,880

V = 960 cubic units

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