So this is not too hard, as with any math problem we write what we know.
Starting speed: 80km/h
Time from P to Q: 2.5h
Increase in speed: 20km/h (25% is dividing by 4)
Distance from Q to R: 150 kilometers
So let's find the speed and distance for both legs of the trip.
Speed for P to Q: 80km/h
Distance from PtoQ: 200km (2.5h * 80km/h)
Speed from Q to R: 100km/h (80 +20)
Distance from QtoR: 150km.
Now we multiply the speeds by their respective distances add them and then divide by the total distance.
((80 *200) + (100 * 150))/350 = ~88.57143
To get the variance, start with finding the mean of your data points:
(23 + 19 + 22 + 30 + 28) / 5 = 24.4
Now take each data point and subtract the mean from it, then square that value:
23 - 24.4 = -1.4 * -1.4 = 1.96
19 - 24.4 = -5.4 * -5.4 = 29.16
22 - 24.4 = -2.4 * -2.4 = 5.76
30 - 24.4 = 5.6 * 5.6 = 31.36
28 - 24.4 = 3.6 * 3.6 = 12.96
Now get the average of those new numbers. That is your variance:
(1.96 + 29.16 + 5.76 + 31.36 + 12.96) / 5 = 16.24
The standard deviation will be the square root of the variance:
√(16.24) = 4.0299 (rounded to 4DP)
Answer:
the answer is 0! combine the n.subtract numbers, rearrange subtract 5 from both sides and simplify so the answer is 0
Answer:
C. b^27
Step-by-step explanation:
By the definition of exponents
![(b^9)^3=b^9*b^9*b^9](https://tex.z-dn.net/?f=%28b%5E9%29%5E3%3Db%5E9%2Ab%5E9%2Ab%5E9)
And since for any real numbers
and ![y](https://tex.z-dn.net/?f=y)
![r^x*r^y=r^{(x+y)}](https://tex.z-dn.net/?f=r%5Ex%2Ar%5Ey%3Dr%5E%7B%28x%2By%29%7D)
This makes
![(b^9)^3=b^9*b^9*b^9=b^{{9+9+9}}=\boxed{b^{27}}](https://tex.z-dn.net/?f=%28b%5E9%29%5E3%3Db%5E9%2Ab%5E9%2Ab%5E9%3Db%5E%7B%7B9%2B9%2B9%7D%7D%3D%5Cboxed%7Bb%5E%7B27%7D%7D)
Which is choice C.
Alternatively, we could use the identity
![(r^x)^y=r^{xy}](https://tex.z-dn.net/?f=%28r%5Ex%29%5Ey%3Dr%5E%7Bxy%7D)
in which case
![(b^9)^3=b^{(9*3)}= \boxed{b^{27}}](https://tex.z-dn.net/?f=%28b%5E9%29%5E3%3Db%5E%7B%289%2A3%29%7D%3D%20%5Cboxed%7Bb%5E%7B27%7D%7D)
which is the same answer.
Answer:
P(80-90)=66.666666...% Or 0.666666...
Step-by-step explanation:
Total tests = 21
Tests with 80-90 = 14
14 ÷ 21 = 2/3 which is 66.66666% or 0.66666