What is f(–3) for the function f(a) = –2a2 – 5a + 4?
2 answers:
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Answer:
The minimum score required for an A grade is 88.
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:
Find the minimum score required for an A grade.
Top 12%, which is at least the 100-12 = 88th percentile, which is the value of X when Z has a pvalue of 0.88. So it is X when Z = 1.175.
Rounding to the nearest whole number
The minimum score required for an A grade is 88.
Answer:
200 pounds of Vigoro
300 pounds of Parker
Step-by-step explanation:
We are going to solve this problem by a system of equations.
I am going to say that is the number of 100 pound bags of Vigoro and
is the number of 100 pound bags of Parker.
With the problem's statements, we can build the system:
We need to find a mixture containing 112 pounds of nitrogen. A 100 pound bag of Vigoro contains 29 pounds of nitrogen, and a 100 pound bag of Parker has 18 pounds of Nitrogen. So:
We need to find a mixture containing 81 pounds of phosporic acid. A 100 pound bag of Vigoro contains 3 pounds of phosporic acid, and a 100 pound bag of Parker has 25 pounds of phosporic acid. So:
We need to find a mixture containing 26 pounds of potash. A 100 pound bag of Vigoro contains 4 pounds of potash, and a 100 pound bag of Parker has 6 pounds of potash. So:
Solving the system
We have the following system
I am going to solve this system by substitution. I am going to write as a function of
in equation 3) and replace it in equation 1).
So
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We are going to need 2 100 pound bags of Vigoro = 200 pounds of Vigoro
We are going to need 3 100 pound bags of Parker = 300 pounds of Parker
We now replace the values in the equation 2) to verify that the system is consistent.
The system is consistent, so the answer that we found is correct.