Answer:
the answer is 4 of it will help you
Answer:
3) (98.08, 124.16)
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 111.12
Standard deviation = 13.04
Calculate an interval that is symmetric around the mean such that it contains approximately 68% of fines.
68% of the fines are within 1 standard deviation of the mean speed. So
From 111.12 - 13.04 = 98.08 to 111.12 + 13.04 = 124.16
The interval notation in the smallest value before the highest value.
So the correct answer is:
3) (98.08, 124.16)
Please find the attached diagram for a better understanding of the question.
As we can see from the diagram,
RQ = 21 feet = height of the hill
PQ = 57 feet = Distance between you and the base of the hill
SR= h=height of the statue
=Angle subtended by the statue to where you are standing.
= which is unknown.
Let us begin solving now. The first step is to find the angle 
which can be found by using the following trigonometric ratio in 
:
Which gives to be:
Now, we know that and can be added to give us the complete angle 
in the right triangle 
.
We can again use the tan trigonometric ratio in to solve for the height of the statue, h.
This can be done as:
Thus, the height of the statue is approximately, 8.45 feet.
Answer:
You could just replace all the given possible values of k in the inequality and see which ones are solutions, but let's solve this in a more interesting way:
First, remember how the absolute value works:
IxI = x if x ≥ 0
IxI = -x if x ≤ 0
Then if we have something like:
IxI < B
We can rewrite this as
-B < x < B
Now let's answer the question, here we have the inequality:
I-k -2I < 18
Then we can rewrite this as:
-18 < (-k - 2) < 18
Now let's isolate k:
first, we can add 2 in the 3 parts of the inequality:
-18 + 2 < -k - 2 + 2 < 18 + 2
-16 < -k < 20
Now we can multiply all sides by -1, remember that this also changes the direction of the signs, then:
-1*-16 > -1*-k > -1*20
16 > k > -20
Then k can be any value between these two limits.
So the correct options (from the given ones) are:
k = -16
k = -8
k = 0
