Answer:
Step-by-step explanation:
Change the mixed number into a regular fraction.
Subtract the numerator.
As a mixed number:
We have been given for a normal distribution the mean time it takes to walk to the bus stop is 8 minutes with a standard deviation of 2 minutes. And the mean time it takes for the bus to get to school is 20 minutes with a standard deviation of 4 minutes.
(a) Average time that it would take reach school can be obtained by adding the average times.
8+20 = 28 minutes.
(b) Standard deviation of the trip to school can be found as:
Therefore, standard deviation of the entire trip is 4.47 minutes.
(c) Let us first find z score corresponding to 30 minutes.
We need to find the probability such that
Therefore, the required probability is 0.67.
(d) If average time to walk to school is 10 minutes, then overall average time for the trip will be 10+20 = 30 minutes.
(e) Standard deviation won't change it will remain 4.47
(f) The new probability will be:
Therefore, probability will be 0.50.
Answer:
Step-by-step explanation:
The domain of this quadratic is "all real numbers." The function is defined for all x.
Answer:
In the given figure the point on segment PQ is twice as from P as from Q is. What is the point? Ans is (2,1).
Step-by-step explanation:
There is really no need to use any quadratics or roots.
( Consider the same problem on the plain number line first. )
How do you find the number between 2 and 5 which is twice as far from 2 as from 5?
You take their difference, which is 3. Now splitting this distance by ratio 2:1 means the first distance is two thirds, the second is one third, so we get
4=2+23(5−2)
It works completely the same with geometric points (using vector operations), just linear interpolation: Call the result R, then
R=P+23(Q−P)
so in your case we get
R=(0,−1)+23(3,3)=(2,1)
Why does this work for 2D-distances as well, even if there seem to be roots involved? Because vector length behaves linearly after all! (meaning |t⋅a⃗ |=t|a⃗ | for any positive scalar t)
Edit: We'll try to divide a distance s into parts a and b such that a is twice as long as b. So it's a=2b and we get
s=a+b=2b+b=3b
⇔b=13s⇒a=23s