A bag contains 11 blocks numbered from 1 to 11. Two blocks are selected from the bag at the same time. (order does not matter) Let event E = the two numbers are odd. How many outcomes are in the complement of E? A) 40 B) 30 C) 25 D) 20

(A) n(Eᶜ)=40

Step-by-step explanation:

The Sample Space for is given as:

(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11)

(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11)

(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11)

(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11)

(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)

(6,7),(6,8),(6,9),(6,10),(6,11)

(7,8),(7,9),(7,10),(7,11)

(8,9),(8,10),(8,11)

(9,10),(9,11)

(10,11)

n(S)=55

Event E is the Event that the two numbers are odd.

Therefore: Complement of E will be the event that any of the  two numbers is even.

The Sample Space of the complement of E is:

Therefore:

n(Eᶜ)=40

company a

step-by-step explanation:

using the linear regression models , it is found that company a   pays about $14 more. but using the same regression (linear) company b pays about $10 more.

so company a pays more than b

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