Asmall class has 10 students. seven of the students are male and three are female. you write the name of each student on a small card. the cards are shuffled thoroughly and you choose one at random, observe the name of the student, and replace it in the set. the cards are thoroughly reshuffled and you again choose a card at random, observe the name, and replace it in the set. this is done a total of five times. let x be the number of cards observed in these four trials with a name corresponding to a male student. the random variable x has which probability distribution?

Given that the shuffling is done 5 times

So n=5

Also given that there are 7 male students and 3 female students

So total number of students = 10

Hence the probability of getting male student is selecting 7 male student from total 10 students.

Probability of selecting male student = 7 / 10 = 0.7

Therefore, its binomial distribution with parameters n=5 and p=0.7

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: