Answer:
The standard deviation has changed for the worse
Step-by-step explanation:
We need to compare the sample standard deviation of 52.3 to the known population standard deviation of 43.7. The test we will use will use Chi-Square distribution...
The hypothesis for this test are...
H0: σ = 43.7
Ha: σ ≠ 43.7
This is a 2 tailed test.
We have n = 81
s = 52.3
s² = 52.3² = 2735.29
σ = 43.7
σ² = 1909.69
The degrees of freedom are: n - 1, in this case, 80
Our significance level is 95%, so our critical values are
Χ² < 57.153 and Χ² > 106.629
The test static is found with the formula:
Χ² = [(n - 1)s²]/σ²
Plug in what we have and find the test stastic....
Χ² = [80(2735.29)]/1909.69
Χ² = 114.586
114.586 > 106.629, we reject the null hypothesis. There is evidence that shows that the standard deviation has changed. The evidence suggests that it has increased, which would make the new method worse than the old method.
Answer:
Step-by-step explanation:
Given
5 tuples implies that:
implies that:
Required
How many 5-tuples of integers are there such that
From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.
Also considering that repetition is allowed: This implies that, a number can be repeated in more than 1 location
So, there are n + 4 items to make selection from
The selection becomes:
Expand the numerator
<u><em>Solved</em></u>
Answer:
The square root of 49 is rational
Step-by-step explanation:
If we take the square root of 49, we get 7, which is a rational number.
Answer:
10
Step-by-step explanation:
ANSWER
the area of the trim around the glass in the window is option ( D)
i.e (x²+7x+3)
REASON
As given in the question
A window frame has a length of (5x+3) inches an a width of (x+6) inches.
As the shape of the window in the form of rectangle.
Formula
Area of the rectangle = length × breadth
put the value in the above equation
we get
Area of window = (5x+3)× ( x + 6)
= 5x² + 33x + 18 inches²
As given in the question
The area of the glass in the window is (4x²+26x+15) square inches.
Area trim around the glass in the window = area of the window - area of the glass.
put the value
we get
= ( 5x² + 33x + 18 ) - ( 4x²+26x+15)
= 1x²+ 7x + 3 inches²
therefore the correct option is (D)
Hence proved