Find the values of a and b such that x² - 4x+9 = (x+a)² + b
1 answer:
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Answers:
When we evaluate a logarithm, we are finding the exponent, or <u> power </u> x, that the <u> base </u> b, needs to be raised so that it equals the <u> argument </u> m. The power is also known as the exponent.
The value of b must be <u> positive </u> and not equal to <u> 1 </u>
The value of m must be <u> positive </u>
If 0 < m < 1, then x < 0
A <u> logarithmic </u> <u> equation </u> is an equation with a variable that includes one or more logarithms.
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Explanation:
Logarithms, or log for short, basically undo what exponents do.
When going from to
, we have isolated the exponent.
More generally, we have turn into
When using the change of base formula, notice how
If b = 1, then log(b) = log(1) = 0, meaning we have a division by zero error. So this is why
We need b > 0 as well because the domain of y = log(x) is the set of positive real numbers. So this is why m > 0 also.
Answer:
A person must get an IQ score of at least 138.885 to qualify.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
(a). [7pts] What IQ score must a person get to qualify
Top 8%, so at least the 100-8 = 92th percentile.
Scores of X and higher, in which X is found when Z has a pvalue of 0.92. So X when Z = 1.405.
A person must get an IQ score of at least 138.885 to qualify.