What is the exponential regression equation that fits these data? X y 1 3 2 8 3 27 4 85 5 240 6 570 A. Y = 2.93(1.03x) B. Y = 38.73x2 – 168.58x + 158.1 C. Y = 102.54x – 203.4 D. Y = 1.03(2.93x)

D)

Step-by-step explanation:

To Find the exponential regression equation that fits these data, we substitute the value of x into the equation and see if it produces the value of y.

x: 1 2 3 4 5 6

y: 3 8 27 85 240 570

A. Y = 2.93()

Substituting x = 1 to get

Y = 2.93(1.03) ≅ 3

Substituting x = 2 to get

Y = 2.93() ≅ 3.1

Option A is wrong

B. Y = 38.73x² – 168.58x + 158.1

Substituting x = 1 to get:

Y = 38.73(1)² – 168.58(1) + 158.1 = 28.25

Therefore option B is wrong

C. Y =

Substituting x = 1 to get:

Y = 102.54 – 203.4 = -100.86

D)

Substituting x = 1 to get:

Substituting x = 2 to get:

Substituting x = 3 to get:

Option D is the closest, it is the correct option

70.30

step-by-step explanation:

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