You place $4,000.00 in a bank account with an interest rate of 5.25% APR and another $2,000.00 in an account with an interest ra
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Answer:
3[|AB|² + |BC|² + |AC|²] = 4[|AD|² + |BE|² + |CF|²]
Step-by-step explanation:
I've attached an image showing a triangle divided into it's medians.
Now, from the attached image, we see that AB, BC & CD are the lengths of sides of triangle while AD, BE & CF are lengths of the 3 medians of the triangle.
Now, to prove our question, we will use appolonius theorem which states that "the sum of the squares of any of the two sides of a triangle is equal to twice the square on half the third side including twice the square on the median that bisects the third side.
Applying this theorem to the image attached, we have the following;
|AB|² + |AC|² = 2[|AD|² + |BC/2|²]
|AB|² + |BC|² = 2[|BE|² + |AC/2|²]
|AC|² + |BC|² = 2[|CF|² + |AB/2|²]
Adding the 3 equations above gives us;
2|AB|² + 2|BC|² + 2|AC|² = 2|AD|² + |BC|²/2 + 2|BE|² + |AC|²/2 + 2|CF|² + |AB|²/2
Collecting like terms;
(2|AB|² - |AB|²/2) + (2|BC|² - |BC|²/2) + (2|AC|² - |AC|²/2) = 2|AD|² + 2|BE|² + 2|CF|²
Thus gives;
(3/2)[|AB|² + |BC|² + |AC|²] = 2[|AD|² + |BE|² + |CF|²]
Multiply both sides by 2 to give;
3[|AB|² + |BC|² + |AC|²] = 4[|AD|² + |BE|² + |CF|²]
Answer:
We conclude that there has been a significant decrease in the average price homes.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = $220,000
Sample mean, = $210,000
Sample size, n = 81
Significance level, α = 0.051
Population standard deviation, σ = $36,000
First, we design the null and the alternate hypothesis
We use One-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
Calculating the p-value from the z-table, we have:
P-value = 0 .00621
Since,
P-value < Significance level
We reject the null hypothesis and accept the alternate hypothesis. Thus, there has been a significant decrease in the average price homes.