Football teams toss a coin to see who will get their choice of kicking or receiving to begin a game. Unfortunately, the coin is not fair, and has a probability of .7 of showing up heads. If a team always guesses tails, what is the probability that they will lose the coin toss 3 games in a row?a. .027b. .125c. .343d. .657

Correct option is (c). 0.343

Step-by-step explanation:

The coin used to decide which team will receive the choice of kicking or receiving is biased.

The probability of Heads for this biased coin is, P (H) = 0.70.

Then the probability of Tails is, P (T) = 1 - 0.70 = 0.30.

A team always guesses Tails.

Compute the probability that they will lose the coin toss 3 games in a row, i.e. the toss result was Heads for 3 tosses, as follows:

P (A team losses the toss 3 times in a row) = [P (H)]³

Thus, the probability that the team will lose the coin toss 3 games in a row is 0.343.

The correct option is (c).

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500