Answer:
He would have worked 8 hours
<span>The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + â‹Ż is a divergent series. The nth partial sum of the series is the triangular number
{\displaystyle \sum _{k=1}^{n}k={\frac {n(n+1)}{2}},} \sum_{k=1}^n k = \frac{n(n+1)}{2},
which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting</span>
Answer:
-72
Step-by-step explanation:
-32 + (2-6)(10)
PEMDAS
Parenthases first
(-4)(10)
multiply together
(-40)
Then just add the -32 and since a negative plus a negative is always negative the answer is going to be negative
-32 + (-40)
= -72
Answer:
Step-by-step explanation:
We can use the Law of Sines to find segment AD, which happens to be a leg of 
and the hypotenuse of 
.
The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:
Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is 
. The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:
Now use this value in the Law of Sines to find AD:
Recall that 
and 
:
Now that we have the length of AD, we can find the length of AB. The right triangle is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio 
, where 
is the side opposite to the 30 degree angle and 
is the length of the hypotenuse.
Since AD is the hypotenuse, it must represent in this ratio and since AB is the side opposite to the 30 degree angle, it must represent in this ratio (Derive from basic trig for a right triangle and 
).
Therefore, AB must be exactly half of AD:
