The value of b is 12.5 and the value of YZ is 100
<h3>How to determine the variable and yz?</h3>
The given parameters are:
XY = 6b
YZ = 8b
XZ = 175
This means that
XZ = XY + YZ
So, we have:
6b + 8b = 175
Evaluate the sum
14b = 175
Divide by 14
b = 12.5
Substitute b = 12.5 in YZ = 8b
YZ = 8 * 12.5
Evaluate
YZ = 100
Hence, the value of b is 12.5 and the value of YZ is 100
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Answer:
φ ≈ 1.19029 radians (≈ 68.2°)
Step-by-step explanation:
There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.
We want to compare ...
y(t) = Asin(ωt +φ)
to
y(t) = Psin(ωt) +Qcos(ωt)
Using trig identities to expand the first equation, we have ...
y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Matching coefficients with the second equation, we have ...
P = Acos(φ)
Q = Asin(φ)
The ratio of these eliminates A and gives a relation for φ:
Q/P = sin(φ)/cos(φ)
Q/P = tan(φ)
φ = arctan(Q/P) . . . . taking quadrant into account
__
We can also use our equations for P and Q to find A:
P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²
A = √(P² +Q²)
_____
Here, we want φ.
φ = arctan(Q/P) = arctan(5/2)
φ ≈ 1.19029 . . . radians
Answer:
Option B) 16
Step-by-step explanation:
We are given the following in the question:
where x is the student's original test score and y is the student's adjusted test score.
We have to find the standard deviation of the adjusted test scores of the students in the class, if the standard deviation of the original test scores of the students in the class was 20.
We know that:
- Adding a constant to each value in a data set does not change the value of the standard deviation.
- Multiplying each value in a data set by a constant also multiplies the standard deviation by that constant.
Thus, if we add 20 to each data set then, the standard deviation does not change.
But multiplying each score by 0.8, changes the standard deviation 0.8 times.
Thus, we can write:
Thus, standard deviation of adjusted score is 16.
Answer:
7.93%
Step-by-step explanation:
504/100 = 5.04
40/5.04 = 7.93%
