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2 answers:
Draw or Cut two similar squares with sides units long.
Draw or cut four pairs of similar right triangles with side lengths as indicated in the diagram.
Now arrange the similar triangles at the corners of the squares such that the sides of one similar triangle plus the side
of a second similar triangle coincides with the length of the square.
We do another arrangement of the similar triangles. This time arrange another 4 similar triangles in the opposite corners, such that each pair forms a square.
Now comparing the two different arrangements we got two different areas that are equal.
The area of the uncovered squares in the first arrangement is
The area of the two uncovered squares in the second arrangement is
Equating the two areas gives the Pythagoras Theorem
Note that is the hypotenuse,
and
are two shorter sides of the similar right triangles.
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Answer:
a)
b) The inverse function is a reflection of the original function across the line
y = x. For example, if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x. So you would use it to find the x-value at a y just like you use the original to find the y value at an x.
Step-by-step explanation:
To do an inverse of a function you first switch the independent variable (d) and the dependent variable (c).
d = 0.45c + 5.50
Then you solve for c
d - 5.50 = 0.45 c
c = (d-5.50)/0.45
Answer:
13 is two and two thirds of four and seven eighths.
Step-by-step explanation:
To solve this, all you need to do is divide 13 by 2 and two thirds. Let's do it:
Answer:
The value of the test statistic is
Step-by-step explanation:
Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
Sample 2:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that
Distribution of the difference:
What is the value of the test statistic?
The value of the test statistic is