When you think of the situation as a whole, you may notice that the lines in the problem actually form a triangle. First, the man driving 10 miles east forms a bottom leg of the triangle 10 units long. When he drives the 2 miles north, he adds another leg of 2 units length. When the place of work is connected to the starting position through a line, a third and final line is drawn which creates the triangle.
So, how can we find the direct distance from his place of work to his home? We can use the Pythagorean Theorem (
, where 
and 
are the lengths of the legs of the triangle and 
is the length of the hypotenuse). We know that the lengths of the legs are 10 and 2, which we can use in the formula, as shown below:
Now, we can solve this equation for :
The distance would be √104 miles, or approximately 10.2 miles.
Answer:
He score lower on the 41 out of 55
Step-by-step explanation:
32/40 = .80 or 80%
41/55 = 0.75 or 75%
Answer: The ball hits the ground at 5 s
Step-by-step explanation:
The question seems incomplete and there is not enough data. However, we can work with the following function to understand this problem:
(1)
Where 
models the height of the ball in meters and 
the time.
Now, let's find the time when the ball Sara kicked hits the ground (this is when 
):
(2)
Rearranging the equation:
(3)
Dividing both sides of the equation by 
:
(4)
This quadratic equation can be written in the form 
, and can be solved with the following formula:
(5)
Where:
Substituting the known values:
(6)
Solving we have the following result:
This means the ball hit the ground 5 seconds after it was kicked by Sara.
Answer:
Option d)
Step-by-step explanation:
We are given the following in the question:
Three of four people believed that the state of the economy was the country's most significant concern.
They would like to test the new data against this prior belief.
The null hypothesis will state that the three of four people believed that the state of the economy was the country's most significant concern.
The alternate hypothesis will state that this is not true. It states that people believed that the state of the economy was the country's most significant concern is not the same.
We design the null and the alternate hypothesis
One centimenter is 0.01 meters. So, you can write the measures as
Once this rewriting is done, getting the total length 
is quite trivial, since all measurements are in the same unit, and we can simply sum everything:
