Henry is an agent for movie stars. He earns 10% of his clients' salaries. If he made $72,000 last year, how much did his clients
2 answers:
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Answer:
1-2a is the largest for -1 > a > -2.41
a^2 is the largest for -2.41 > a.
Step-by-step explanation:
We want to find the expression with the largest value.
Remember that the sign is important here, because:
1 is larger than -10
So we will look at the expressions that, when evaluated in a negative number, give a positive number.
The only two options in the case:
a < -1
are:
1-2a
and
a^2
So we have a linear equation and a quadratic equation.
We know that quadratic equations grow a lot faster than linear equations for all values larger than 1 (or minus one, because the sign does not matter).
if -1 < a < 1, a quadratic function grows really slow, but this is not the case.
So from now, we can guess that a^2 is larger.
But let's solve it graphically.
Let's define two functions:
f(a) = 1 - 2*a
g(a) = a^2
Now we can graph these two, and look at the region a < -1, and see which one is larger.
in the image, you can see that there is a small region from:
-1 > a > -2.41
Where the linear equation is larger, and for:
a < -2.41
The quadratic equation is larger.
Answer:
a) The lowest test score that a student could get and still meet the colleges requirement is 27.0225.
b) 156 would be expected to have a test score that would meet the colleges requirement
c) The lowest score that would meet the colleges requirement would be decreased to 26.388.
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. Find the lowest test score that a student could get and still meet the colleges requirement.
This is the value of X when Z has a pvalue of 1 - 0.12 = 0.88. So it is X when Z = 1.175.
The lowest test score that a student could get and still meet the colleges requirement is 27.0225.
b. If 1300 students are randomly selected, how many would be expected to have a test score that would meet the colleges requirement?
Top 12%, so 12% of them.
0.12*1300 = 156
156 would be expected to have a test score that would meet the colleges requirement
c. How does the answer to part (a) change if the college decided to accept the top 15% of all test scores?
It would decrease to the value of X when Z has a pvalue of 1-0.15 = 0.85. So X when Z = 1.04.
The lowest score that would meet the colleges requirement would be decreased to 26.388.
Answer:
Step-by-step explanation:
Add the amounts together:
Convert the whole number 1 into a fraction with denominator 4:
As all the denominators are the same, we can simply add the numerators:
Finally, convert the improper fraction into a mixed number: