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3 years ago

In ΔPQR, what is the m∠Q? Enter your answer in the box.

Mathematics

1 answer:

Orlov [11]3 years ago

8 0

Answer:

105°

Step-by-step explanation:

11x-5 + 6x+5 + x = 180

18x = 180

x = 10

m∠Q = 11(10)-5 = 110-5 = 105°

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3 years ago

Select the correct answer from each drop-down menu.

podryga [215]

Answer with explanation:

$\text{Average}=\frac{\text{Sum of all the observation}}{\text{Total number of Observation}}$

Average Height of tallest Building in San Francisco

$=\frac{260+237+212+197+184+183+183+175+174+173}{10}\\\\=\frac{1978}{10}\\\\=197.8$

Average Height of tallest Building in Los Angeles

$=\frac{310+262+229+228+224+221+220+219+213+213}{10}\\\\=\frac{2339}{10}\\\\=233.9$

→→Difference between Height of tallest Building in Los Angeles and Height of tallest Building in San Francisco

=233.9-197.8

=36.1

⇒The average height of the 10 tallest buildings in Los Angeles is 36.1 more than the average height of the tallest buildings in San Francisco.

⇒Part B

Mean absolute deviation for the 10 tallest buildings in San Francisco

|260-197.8|=62.2

|237-197.8|=39.2

|212-197.8|=14.2

|197 -197.8|= 0.8

|184 -197.8|=13.8

|183-197.8|=14.8

|183-197.8|= 14.8

|175-197.8|=22.8

|174-197.8|=23.8

|173 -197.8|=24.8

Average of these numbers

$=\frac{62.2+39.2+14.2+0.8+13.8+14.8+14.8+22.8+23.8+24.8}{10}\\\\=\frac{231.2}{10}\\\\=23.12$

Mean absolute deviation=23.12

5 0

3 years ago

An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne

lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

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3 years ago