8a^3 - 26a^2b + 11ab^2 + 10b^3
Consider the polynomials p left parenthesis x right parenthesis equals 21 x minus 4 x squared and q left parenthesis x right par
enthesis equals 5 . Find the x -coordinate(s) of the point(s) of intersection of these two polynomials. What is the sum of these x -coordinates
1 answer:
Answer:
21/4 = 5.25
Step-by-step explanation:
You want the sum of the x-values that are solutions to ...
21x -4x² = 5
4x² -21x +5 = 0 . . . . . subtract the left side, rearrange to standard form
x² -(21/4)x +5/4 = 0 . . . divide by 4
In this form the sum of the x-values that solve this equation is the opposite of the x-coefficient. That sum will be 21/4 = 5.25. (The attached graph confirms this result.)
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Consider a quadratic with roots p and q. It factors as ...
(x -p)(x -q) = 0 = x² -(p+q)x +pq
That is, the x-coefficient is the opposite of the sum of the roots p and q.
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Complete Question
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.
Answer:
The sample size is
Step-by-step explanation:
From the question we are told that
The margin of error is
The confidence level is %
Given that the confidence level is 95% the level of significance is mathematically represented as
%
Next we obtain the critical value of from the normal distribution table , the values is
The reason we are obtaining critical values of
instead of
is because
represents the area under the normal curve where the confidence level interval (
) did not cover which include both the left and right tail while
is just the area of one tail which what we required to calculate the sample size
Now the sample size is mathematically represented as
substituting values