In a certain college, 33% of the physics majors belong to ethnic minorities. if 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

To answer this question, we must first note that the probability of x successes in n trials is: 

P = nCx**  where p and q are the probabilities of success and failure respectively.

In this case:

p = 33% = .33

q = .67

n = 10

x = 6

Calculating *:

*=0.00026

Now the number of combinations of x in n trials is:

 nCx = 

Using the calculator to calculate for nCx from x= 1 to 6:

10C1  = 1

10C2  = 45

10C3  = 120

10C4  = 210

10C5  = 252

10C6  = 210

total nCx = 838

Substituting known values to the P equation:

P(6 or below are physics majors) = 838 * 0.00026

P(6 or below are physics majors) = 0.218

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240