One third of the candidates for a job were 25 years old or younger. two sevenths of the candidates were at least 50 years old. if 84 people applied for the job, how many were between 25 and 50?

1/3 * 84 = 28 were under 25

2/7 * 84 = 24 were at least 50

28 + 24 = 52

84-52 = 32 were between 25 and 50

32 candidates are between 25 and 50.

Step-by-step explanation:

84 people applied for the job. of the candidates for a job were 25 years old or younger.

of 84 candidates = × 84 = 28 candidates

of the candidates were at least 50 years old.

of 84 candidates = × 84 = 24 candidates

age 25 and below + age 50 above = 28 + 24 = 52 candidates

Candidates between 25 and 50  =  84 - 52 = 32 candidates

32 candidates are between 25 and 50.

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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