Answer:
1: 4
2: 2
3: 8
Step-by-step explanation:
Answer:
Step-by-step explanation:
GH : √(8-4)^2 + (2-5)^2 = √16+9 = √25 = 5
HI : √(-6-2)^2 + (2-8)^2 = √64+36 = √100 = 10
IJ : √(-2-2)^2 + (-3+6)^2 = √16 + 9 = √25 = 5
JH : √(-2-4)^2 + (-3-5)^2 = √36 + 64 = √100 = 10
Slope of the line that contains GH
(2-5)/(8-4) = -3/4
Slope of the line that contains HI
(-6-2) / (2-8) = 8/6 = 4/3
I calculated the distance between points. Thanks to that I noticed that the opposite sides are congruent, so the quadrilateral can be a rectangle or a parallelogram. So I found the slope of the lines that contain two consecutive sides and I discovered that are perpendicular. So the quadrilateral is a rectangle because its angles are all of 90 degrees
Part A: (n^2-6n)+16
[(n^2-6n+9)-9]+16
(n-3)^2+7
Part B: From the above result,
Vertex (3,7) this is the minimum point of the graph since the coefficient of a is positive
Part C: The axis of symmetry is basically the x coordinate of the vertex, so the axis of symmetry is x=3
Hope this helps!
Answer:
y = -
x²
Step-by-step explanation:
Since the vertex is at the origin and the focus at (0, - 4) then the parabola opens vertically down with equation
x² = 4py ( p is the distance from the vertex to the focus )
Here p = - 4 ( focus is below the vertex ), thus
x² = 4(- 4)y = - 16y ( divide both sides by - 16 )
y = -
x²
Answer: Required mean would be 15.
Step-by-step explanation:
Since we have given that
Number of girls G= 75
Number of boys B= 100
Probability that girls smoke = P₂ = 0.20
Probability that girls don't smoke = P'₂=1-0.20=0.80
Probability that boys smoke = P₁ = 0.30
Probability that boys don't smoke = P'₁=1-0.30=0.70
We need to find the mean of the sampling distribution of the difference in the sample proportion of girl smokers and boys smokers.
So, it becomes,
![E[P_1-P_2]=E[P_1]-E[P_2]\\\\=B\times P_1-G\times P_2\\\\=100\times 0.30-75\times 0.20\\\\=30-15\\\\=15](https://tex.z-dn.net/?f=E%5BP_1-P_2%5D%3DE%5BP_1%5D-E%5BP_2%5D%5C%5C%5C%5C%3DB%5Ctimes%20P_1-G%5Ctimes%20P_2%5C%5C%5C%5C%3D100%5Ctimes%200.30-75%5Ctimes%200.20%5C%5C%5C%5C%3D30-15%5C%5C%5C%5C%3D15)
Hence, required mean would be 15.