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Keith_Richards [23]
3 years ago
12

Combine the like terms to create an equivalent expression:-5r+8r+5​

Mathematics
1 answer:
Olegator [25]3 years ago
3 0
Answer : 3r+5 hope this helps!
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A common way for two people to settle a frivolous dispute is to play a game of rock-paper-scissors. In this game, each person si
Leokris [45]

Answer:

(a) P(A) = 0.34

(b) P(B) = 0.33

(c) P(C) = 0.33

(d) The Complement of event A = 1 - P(A) = 0.66

Step-by-step explanation:

We are given that in the long run, roommate A chooses rock 36% of the time, and roommate B chooses rock 22% of the time; roommate A selects paper 32% of the time, and roommate B selects paper 25% of the time; roommate A chooses scissors 32% of the time, and roommate B chooses scissors 53% of the time.

Let the probability that roommate A chooses rock = P(R_A) = 0.36

The probability that roommate A chooses paper = P(P_A) = 0.32

The probability that roommate A chooses scissors = P(S_A) = 0.32

The probability that roommate B chooses rock = P(R_B) = 0.22

The probability that roommate B chooses paper = P(P_B) = 0.25

The probability that roommate B chooses scissors = P(S_B) = 0.53

(a) Let A = event that roommate A wins the game and thus does not have to wash the dishes.

This will happen only when roommate A chooses rock and roommate B chooses scissors or roommate A chooses paper and roommate B chooses rock or roommate A chooses scissors and roommate B chooses paper.

So, P(A) =  P(R_A) \times P(S_B) + P(P_A) \times P(R_B) + P(S_A) \times P(P_B)  

             =  (0.36 \times 0.53) + (0.32 \times 0.22) + (0.32 \times 0.25)  

             =  0.1908 + 0.0704 + 0.08

    P(A)  =  0.34

(b) Let B = event that roommate B wins the game and thus does not have to wash the dishes.

This will happen only when roommate B chooses rock and roommate A chooses scissors or roommate B chooses paper and roommate A chooses rock or roommate B chooses scissors and roommate A chooses paper.

So, P(B) =  P(R_B) \times P(S_A) + P(P_B) \times P(R_A) + P(S_B) \times P(P_A)  

             =  (0.22 \times 0.32) + (0.25 \times 0.36) + (0.53 \times 0.32)  

             =  0.0704 + 0.09 + 0.1696

    P(B)  =  0.33

(c) Let C = event that the game ends in a tie.

This will happen only when roommate A chooses rock and roommate B also chooses rock or roommate A chooses paper and roommate B also chooses paper or roommate A chooses scissors and roommate B also chooses scissors.

So, P(C) =  P(R_A) \times P(R_B) + P(P_A) \times P(P_B) + P(S_A) \times P(S_B)  

             =  (0.36 \times 0.22) + (0.32 \times 0.25) + (0.32 \times 0.53)  

             =  0.0792 + 0.08 + 0.1696

    P(C)  =  0.3288 ≈ 0.33

(d) The complement of event A = P(A') = 1 - P(A)

                                                       = 1 - 0.34 = 0.66.

4 0
3 years ago
‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️PLEASE HELP!!! PLEASE EXPLAIN AND ONLY ANSWER IF YOU KNOW YOU HAVE THE CORRECT ANSWE
Lena [83]

We are given the expression x³ - 2y² - 3x³ + z⁴. We have to evaluate it at a given set of x, y, and z values. Before then, let's combine like terms.

x³ - 2y² - 3x³ + z⁴

= -2x³ - 2y² + z⁴ <-- by combining like terms

Now we evaluate for x=3 y=5 z = -3

= -2(3³) - 2(5²) + (-3⁴) <-- by putting in for x, y, z

= -2(27) - 2(25) + 81 <--- parentheses and exponents first in order of operations

= -54 - 50 + 81 <---- multiplication is next

= -4 + 81

= 77


Thus, we evaluate and it's 77.

7 0
3 years ago
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