Hello from MrBillDoesMath!
Answer: NO points of intersection. The two lines are parallel
Discussion:
Rewrite the equations so the variables and constants line up vertically
x - 2y + 8 = 0
x - 2y -6 = 0 (I added "x" to both sides of the second equation)
Subtract the bottom equation from the the top one:
(x - 2y + 8) - ( x - 2y -6) = 0 or
x - 2y + 8 - x + 2y + 6 = 0 or
(x-x) + (-2y +2y) + (8 + 6) = 0 or
0 + 0 + 14 = 0
14 = 0 !
No solution exists. (Another approach: What is the slope of each line? Hint: 1/2. Since the slopes are the same the lines are parallel and have no points of intersection)
Thank you,
MrB
Answer:
A rectangle.
Step-by-step explanation:
Since the cross-section will be perpendicular to the base, it is parallel to the lateral faces of the prism. This means it will be the same shape as the lateral faces.
The lateral faces of a rectangular prism are rectangles; this means this cross-section will be a rectangle as well.
Answer:
2.28% of tests has scores over 90.
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:
What proportion of tests has scores over 90?
This proportion is 1 subtracted by the pvalue of Z when X = 90. So
has a pvalue of 0.9772.
So 1-0.9772 = 0.0228 = 2.28% of tests has scores over 90.
Answer:
Step-by-step explanation:
<u>Exponential Function</u>
When we need to express the exponential relation between two variables, we use the equation
where C, r are constants to be determined by using the given points from the table
For x=0, y=2, thus
We find that C=2
The equation is now
Now we use the point x=1, y=1
We find that
Thus, the equation is
Rearranging
The required equation is
We can easily verify the last two points are also obtained by using the equation
9514 1404 393
Answer:
44
Step-by-step explanation:
A ∪ B is the set of all elements that are in either the Blue or Green circles, or both. The number of its elements is ...
8 + 7 + 14 + 6 + 1 + 8 = 44
n(A∪B) = 44