A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result?

The theoretical probability of the event a numbers is P(1),P(2),P(3),P(4),P(5),P(6) is.16,.18,.22,.1,.15,.19 respectively solved below.

Step-by-step explanation:

Given : A die is rolled 200 times with the following results.

Outcome          1            2         3           4           5           6

Frequency       32        36       44         20        30         38

Event - P(1),P(2),P(3),P(4),P(5),P(6),

To find : What is the theoretical probability of the given event?

Solution : .

Probability is defined as division of favorable outcome by total number of outcome.

Therefore, the theoretical probability of the event a numbers are as follow:

P(1)= =.16

P(2)==.18

P(3)==.22

P(4)==.10

P(5)==.15

P(6)= =.19

Therefore, the theoretical probability of the event a number for given is above.

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