You may notice that all of the terms have a common factor: . So, let's take the
out of all the terms. This gives us:
Using the Zero Product Property, we can say that both and
.
Let's solve both. is obvious, but we still need to solve our other term:
Our answer is x = -6, 0, 4.
Answer:
a) 51.60% probability that in a given year there will be less than 21 earthquakes.
b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.
Step-by-step explanation:
Problems of normally distributed samples can be 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 probability that in a given year there will be less than 21 earthquakes.
This is the pvalue of Z when X = 21. So
has a pvalue of 0.5160.
So there is a 51.60% probability that in a given year there will be less than 21 earthquakes.
b) Find the probability that in a given year there will be between 18 and 23 earthquakes.
This is the pvalue of Z when X = 23 subtracted by the pvalue of Z when X = 18. So:
X = 23
has a pvalue of 0.7611
X = 18
has a pvalue of 0.2676
So there is a 0.7611 - 0.2676 = 0.4935 = 49.35% probability that in a given year there will be between 18 and 23 earthquakes.
Answer:
Hey there!
First, we want to find the side length of the large triangle.
1/2bh=y cm^2
bh=2y cm^2
Since b and h are the same here, we have b^2= 2y, .
And we have FC=.
Area of shaded triangle: .
This is equal to: , or y/4.
Let me know if this helps :)