The magnitude of the resulting vector, u - v, is approximately 5.83
and its angle of direction is approximately 59.04°.
<h3>How to find the magnitude of the resulting vector?</h3>
We want to subtract vector v from vector u.
We are given;
v = <2, -3> = 2i - 3j
u = <5, 2> = 5i + 2j
u - v = 5i + 2j - (2i - 3j)
= 5i + 2j - 2i + 3j
= 3i + 5j
Resultant vector = √(3² + 5²)
Resultant vector = √34 ≈ 5.83
Angle of direction of resultant vector is;
tan θ = (5/3)
θ = tan⁻¹(5/3)
θ = 59.04°
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Answer:
10.63
Step-by-step explanation:
Data provided in the question
Data = 30 subjects
The Variance of scores = 113.00
The calculation of standard deviation is shown below:-
As we know that
Variance = Standard deviation^2
Therefore,
Standard deviation = 
= 
= 10.63
Therefore for computing the standard deviation we simply applied the above formula.
Answer:
I don't understand the question being asked
Answer: 1,376
Step-by-step explanation: All we need to do is take our explicit formula and plug in the information we need to know for the problem.
Explicit formula - 
We are trying to find the 77th term of this sequence so we first have
.
We know
is 8 because that's the first term in our arithmetic sequence.
The variable <em>n</em> represents the number of terms we're trying to solve for which is 77. So that will be 77 - 1 and then we are going to multiply that by our common difference which is 18.
So plugging into the formula, we have 
So now we can go ahead and simplify this
information and see what we get.
So simplifying inside parentheses first, we get 76 and we multiply that by 18 to get 1,368.
So therefore we have
which is 1,376.