Nancy recorded the height (in centimetres) of her friends which gave the data 89, 77, 78, 95, and 89. She later added the heights of four more friends at 77, 78, 77, and 100. Which of the following statements is true? A
By adding the extra friends to the data set, the mode decreased, the median increased, and the mean decreased.
B
By adding the extra friends to the data set, the mode increased, the median decreased, and the mean increased.
C
By adding the extra friends to the data set, the mode increased, the median increased, and the mean increased.
D
By adding the extra friends to the data set, the mode decreased, the median decreased, and the mean decreased.

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

alaska, florida, nevada, south dakota, texas, washington and wyoming, tenessee and new hampshire.

step-by-step explanation:

3+3+3+2*2*2+29*12 = 365

step-by-step explanation: