Answer:
C. JKM is not a right triangle because KM ≠ 15.3.
Step-by-step explanation:
We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.
In order to triangle JKM be a right triangle
.
We will find length of side KM using our right triangles JLM and JLK as
.
Using Pythagorean theorem in triangle JLM we will get,


Now let us find length of side KL.


Now let us find length of KM by adding lengths of KL and LM.

Now let us find whether JKM is right triangle or not using Pythagorean theorem.



Upon taking square root of both sides of equation we will get,
We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.
The fencing line x is the height of a rectangle triangle of base = y, hypothenuse of 9 m, so we use Pythagoras theorem to solve:
hyp^2 = height^2 + base^2
9^2 = x^2 + y^2
x^2 = 81 - y^2
we can see that x is also the height of another rectangle triangle of base = 15 - y, hypothenuse of 12 m, so we use Pythagoras theorem to solve:
hyp^2 = height^2 + base^2
12^2 = x^2 + (15 - y)^2
lets expand:
144 = x^2 + 225 - 30y + y^2
substitute x^2 from the first equation in the last:
144 = 81 - y^2 + 225 - 30y + y^2
144 = 81 + 225 - 30y
30y = -144 + 81 + 225
y = 5.4 m
substitute in the fence equation:
x^2 = 81 - y^2
x^2 = 81 - 5.4^2
x = 7.2 m that is the length of the fence
Answer:
Ox>5
x is less than 5
means nothing more than 5 but anything less than 5
Answer:
1 mile = 15 seconds
Step-by-step explanation:
3 minutes and 15 seconds = 3 min + 15 sec
1 minute = 60 seconds
15 seconds =15/60 = 0,25 min
then
3minutes and 15 seconds = 3.25 minutes
13miles in 3 minutes and 15 seconds
= 13 miles / 3.25 minutes
= 4 miles / 1 minute
every minute Jose ran 4 miles
then:
4 miles is a 1 minute
1 mile is a T minutes
T = 1*1/4
T = 1/4 minute
1 minute = 60 secomds
1/4 minute = 60*1/4 = 60/4 = 15 seconds
Answer:
B. 0.835
Step-by-step explanation:
We can use the z-scores and the standard normal distribution to calculate this probability.
We have a normal distribution for the portfolio return, with mean 13.2 and standard deviation 18.9.
We have to calculate the probability that the portfolio's return in any given year is between -43.5 and 32.1.
Then, the z-scores for X=-43.5 and 32.1 are:

Then, the probability that the portfolio's return in any given year is between -43.5 and 32.1 is:
