9514 1404 393
Answer:
23°
Step-by-step explanation:
The angle a vector makes relative to the +x axis is found as ...
α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°
The angle is about 23°.
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<em>Additional comment</em>
This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)
There are two ways to find or determine for the value of
c. In the first method, we can use addition and subtraction to isolate the
variable c from the other variables. In the second method, we can use the
transposition of variables to isolate the variable c from the other variables.
So solving for the value of c:
<span>Using 1st method: Addition and Subtraction</span>
We are given:
240 = 6 z + c
Simply subtract 6 z on both sides:
240 – 6 z = 6 z + c – 6 z
Cancelling 6 z – 6 z on the right side:
240 – 6 z = c
or
c = 240 – 6 z
<span>Using the 2nd method: Transposition</span>
240 = 6 z + c
What we are going to do here is to simply transpose the
variable 6 z from the right side to the left side of the equation so that we
are left with c alone on the right side. Always remember that when we
transpose, the symbol becomes opposite. That is:
240 + (- 6 z) = c
240 – 6 z = c
or
<span>c = 240 – 6 z</span>
Answer:
0.5015 = 50.15% probability that it came from manufacturer A.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: From manufacturer A.
Probability a unit is defective:
2% of 43%(from manufacturer A)
1.5% of 57%(from manufacturer B). So
Probability a unit is defective and from manufacturer A:
2% of 43%. So
What is the probability that it came from manufacturer A?
0.5015 = 50.15% probability that it came from manufacturer A.
Answer:
Step-by-step explanation:
x+6/11=10/11
This is a linear equation, because x has no power, so it will be solved by making x the subject of the equation.
Make x the subject
x+6/11=10/11
x=-6/11+10/11
x=10/11-6/11
Since both fractions have the same denominator, the LCM remains 11
x=(10-6)/11
x=4/11
To check if the answer is correct, we substitute x for 4/11 in the equation. And both sides of the equation must be equal
x+6/11=10/11
4/11+6/11=10/11
(4+6)/11=10/11
10/11=10/11
