In a survey of 300 college graduates, 63% reported that they entered a profession closely related to their college major. if 9 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 4 or fewer of them entered a profession closely related to their college major?
a)0.793

b)0.0512

c)0.149

d)0.207

D) 0.207

Step-by-step explanation:

Binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

Here, n = 9, p = 0.63, and q = 0.37.

If r = 4:

P = ₉C₄ (0.63⁴) (0.37⁹⁻⁴)

P = 0.1376

If r = 3:

P = ₉C₃ (0.63³) (0.37⁹⁻³)

P = 0.0539

If r = 2:

P = ₉C₂ (0.63²) (0.37⁹⁻²)

P = 0.0136

If r = 1:

P = ₉C₁ (0.63¹) (0.37⁹⁻¹)

P = 0.0020

If r = 0:

P = ₉C₀ (0.63⁰) (0.37⁹⁻⁰)

P = 0.0001

The total probability is:

P = 0.1376 + 0.0539 + 0.0136 + 0.0020 + 0.0001

P = 0.2072

a

b

d

step-by-step explanation:

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.