Find one value of xxx that is a solution to the equation: (2x+3)^2-4(2x+3)-12=0(2x+3) 2 −4(2x+3)−12=0
1 answer:
Answer:
x = -5/2 or 3/2
Step-by-step explanation:
If we let z = 2x+3, the equation can be written ...
... z² -4z -12 = 0
and can be factored as
... (z -6)(z +2) = 0
Then the solutions are z = -2, z = 6.
This means the values of x that are solutions are ...
... 2x +3 = {-2, 6} . . . . work with both possibilities at once
... 2x = {-5, 3} . . . . . . . subtract 3
... x = {-5/2, 3/2} . . . . .divide by 2
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Answer:
Exactly 16%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean of a certain set of measurements is 27 with a standard deviation of 14.
This means that
The proportion of measurements that is less than 13 is
This is the p-value of Z when X = 13, so:
has a p-value of 0.16, and thus, the probability is: Exactly 16%.