Answer:
(-3, 5), (-1, -1), (5, -3)
Step-by-step explanation:
Each pair of vertices can be one of the diagonals. Then the missing point will be found at the coordinates that are the sum of those, less the coordinates of the third point.
Given points are ...
A(-2, 2), B(1, 1), C(2, -2)
For AB a diagonal, D1 is ...
A+B-C = (-2+1-2, 2+1-(-2)) = (-3, 5)
For AC a diagonal, D2 is ...
A+C-B = (-2+2-1, 2-2-1) = (-1, -1)
For BC a diagonal, D3 is ...
B+C-A = (1+2-(-2), 1-2-2) = (5, -3)
_____
For a lot of parallelogram problems I find it easiest to work with the fact that the diagonals bisect each other. This means they both have the same midpoint, so for quadrilateral ABCD, we have (A+C)/2 = (B+D)/2. Multiplying this by 2 gives the equation we used above, A+C = B+D, so D=A+C-B. Remember, in ABCD, AC and BD are the diagonals.
Answer:
We conclude that the population mean is 24.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 24
Sample mean, = 22.8
Sample size, n = 100
Alpha, α = 0.05
Sample standard deviation, s = 8.3
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
We calculate the p-value with the help of standard z table.
P-value = 0.1498
Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.
Now,
Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.