In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. what is the probability (rounded to the nearest whole percent) that a randomly selected student will have dark hair, given that the student has blue eyes?

hint:
p(a|b)=p(a∩b) / p(b)

46%

43%

21%

67%

The correct answer option is 43%.

Step-by-step explanation:

We are given that 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair.

We are to find the probability of a student getting selected will have dark hair with blue eyes.

P(D|B) = P(D∩B) / P(B)

Substituting the given values in it to get:

P(D|B) = 0.3 / 0.7 = 0.428

Rounding it to the nearest whole percent we get:

0.428 × 100 = 42.8% ≈ 43%

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

-4, -2, 1, 4

step-by-step explanation:

domain = x values

range = y values