Can someone help please.
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You roll a 6-sided die. The probability of getting prime is 50%.
<u>Solution:</u>
Given, that we have rolled a 6 – sided die.
We have to find the P(prime) as percentage.
Now, It means that we have to find the probability of getting a prime number on the face.
On rolling a six sided die, the total possible outcomes are 1, 2, 3, 4, 5, 6
Number of possible outcomes = 6
We have to get a prime number on rolling a die
The prime numbers in possible outcomes are 2, 3, 5
So number of favorable outcomes = 3
Hence, probability of getting prime is 50%.
Answer:
-4
Step-by-step explanation:
x³ + cx + 4 divided by x + 2 has a remainder of 4, so:
(x³ + cx + 4) / (x + 2) = ax² + bx + d + 4 / (x + 2)
Multiply both sides by x + 2:
x³ + cx + 4 = (ax² + bx + d) (x + 2) + 4
Distribute:
x³ + cx + 4 = ax²(x + 2) + bx(x + 2) + d(x + 2) + 4
x³ + cx + 4 = ax³ + 2ax² + bx² + 2bx + dx + 2d + 4
x³ + cx + 4 = ax³ + (2a + b)x² + (2b + d)x + 2d + 4
Match the coefficients.
a = 1
2a + b = 0
2b + d = c
2d + 4 = 4
Solving, a = 1, b = -2, and d = 0. So c = -4.
We can also solve this using long division (see picture).
