Solve the following equation for x: 2x − 3y = 6.
2 answers:
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Answer:
x =
Step-by-step explanation:
The absolute value always returns a positive value but the expression inside can be positive or negative, that is
x + 4 = 3x - 5 ( subtract 3x from both sides )
- 2x + 4 = - 5 (subtract 4 from both sides )
- 2x = - 9 ( divide both sides by - 2 )
x =
OR
-(x + 4) = 3x - 5
- x - 4 = 3x - 5 ( subtract 3x from both sides )
- 4x - 4 = - 5 ( add 4 to both sides )
- 4x = - 1 ( divide both sides by - 4 )
x =
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions
| + 4 | = |
| =
right side = - 5 =
left side = right side , thus x = is a solution
check second solution
| + 4 | = |
| =
right side = - 5 = -
right side ≠ left sides, hence not a solution
Answer:
The probability is 0.0014
Step-by-step explanation:
When we have two possible outcomes p, q and we repeat the experiment multiple times, we apply the Binomial distribution, in this distribution the probability of getting exactly k successes in n trials is given by
where p represents the probability of success. nCk refers to the combinations of k elements out of n elements.
In this case, p= .29 (the probability that the person says "yes" being confident that passenger trips to the moon will occur in their lifetime.
q = .71 (The probability that the person says "no")
We sample 200 americans, therefore, we have n = 200 and we need the probability that less than 40% of the people sampled answer "yes".
The 40% of 200 is 80. So, in other words, we need less than 80 people to answer yes to the question.
P(x<80) = P(x=0) + P(x=1) + P(x=2) + .... + P(x=79) = 0.00143466294 (we can use a Binomial Distribution calculator to compute this result)
Therefore, P(x < 80) = 0.0014