Which system of inequalities is represented by the graph?
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
We don't need choices to find out the correct answer. Solve this problem by completing the square. Begin by setting the quadratic equal to 0 and moving over the constant, like this:
and factor out the -1 in front of the x-squared, since the leading coefficient HAS to be a 1:
Now take half the linear term, square it, and add it to both sides. Our linear term is -2. Half of -2 is -1, and squaring that gives us 1. So we add a 1 into both sides. But that -1 out front there on the left is a multiplier, so what we actually added in was -1(1) which is -1:
On the left side we have a perfect square binomial, which is why we do this, and on the right side we have -2:
and we can move that constant back over and set the quadratic back equal to y:
which gives us a max height of 2.
(If this was modeling parabolic motion, we would know that the time it takes to get to that max height is 1 second. The vertex of this parabola is (1, 2))
Answer:
a) 26.76% probability that a student in the psychology department has a score less than 480.
b) 69.73% probability that a student in the psychology department has a score between 480 and 730.
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 haev that:
a. Find the probability that a student in the psychology department has a score less than 480.
This is the pvalue of Z when X = 480. So
has a pvalue of 0.2676.
26.76% probability that a student in the psychology department has a score less than 480.
b. Find the probability that a student in the psychology department has a score between 480 and 730.
This probability is the pvalue of Z when X = 730 subtracted by the pvalue of Z when X = 480.
X = 730
has a pvalue of 0.9649.
X = 480
has a pvalue of 0.2676.
0.9649 - 0.2676 = 0.6973
69.73% probability that a student in the psychology department has a score between 480 and 730.