Answer:
The lower limit is 36
Upper limit is 96
Standard deviation is 30
Step-by-step explanation:
Considering the range of the test score which is 60. i.e the difference between the largest and the smallest number is 60. The mean is 66 which is a measure of central tendency. That is it is at the centre of the distribution. Dividing 60 by 2 gives 30.
Adding 30 to the mean will indicate our upper limit i.e 30+66=96
Also, subtracting 30 from 66 will give the lower limit i.e. 66-30=36
The Distance between the range and the mean is the standard deviation
Which in this case is +30 or -30
Answer:
1. BC = 86 Km
2. 090°
Step-by-step explanation:
1. Determination of BC
AB = 27 Km
AC = 82 Km
BC =?
Since the figure is a right angle triangle, we shall determine BC by using pythagoras theory. This is illustrated below:
BC² = AB² + AC²
BC² = 27² + 82²
BC² = 729 + 6724
BC² = 7453
Take the square root of both side
BC = √7453
BC = 86 Km
2. Determination of the bearing of C from A.
From the diagram given above, we can see that angle from A and C is 90°. Thus, the bearing of C from A is 090°
Answer:
4<x<12
Step-by-step explanation:
8.0+4.0=12.0
8.0-4.0=4.0 or 4
9514 1404 393
Explanation:
∠MRQ ≅ ∠NQR . . . . given
QR ≅ RQ . . . . reflexive property
∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR
ΔQNR ≅ Δ RMQ . . . . ASA postulate
We're given
![\displaystyle \int_4^{-10} g(x) \, dx = -3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_4%5E%7B-10%7D%20g%28x%29%20%5C%2C%20dx%20%3D%20-3)
which immediately tells us that
![\displaystyle \int_{-10}^4 g(x) \, dx = 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-10%7D%5E4%20g%28x%29%20%5C%2C%20dx%20%3D%203)
In other words, swapping the limits of the integral negates its value.
Also,
![\displaystyle \int_4^6 g(x) \, dx = 5](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_4%5E6%20g%28x%29%20%5C%2C%20dx%20%3D%205)
The integral we want to compute is
![\displaystyle \int_{-10}^6 g(x) \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-10%7D%5E6%20g%28x%29%20%5C%2C%20dx)
which we can do by splitting up the integral at x = 4 and using the known values above. Then the integral we want is
![\displaystyle \int_{-10}^6 g(x) \, dx = \int_{-10}^4 g(x) \, dx + \int_4^6 g(x) \, dx = 3 + 5 = \boxed{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-10%7D%5E6%20g%28x%29%20%5C%2C%20dx%20%3D%20%5Cint_%7B-10%7D%5E4%20g%28x%29%20%5C%2C%20dx%20%2B%20%5Cint_4%5E6%20g%28x%29%20%5C%2C%20dx%20%3D%203%20%2B%205%20%3D%20%5Cboxed%7B8%7D)