( 2 + 3 ) + ( 4 + x )
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Answer: a. CI for the mean: 17.327 < μ < 26.473
b. CI for variance: 29.7532 ≤ ≤ 170.9093
Step-by-step explanation:
a. To construct a 95% confidence interval for the mean:
The given data are:
mean = 21.9
s = 7.7
n = 12
df = 12 - 1 = 11
1 - α = 0.05
= 0.025
t-score = = 2.2001
Note: since the sample population is less than 30, it is used a t-score.
The formula for interval:
mean ±
Substituing values:
21.9 ± 2.200.
21.9 ± 4.573
The interval is: 17.327 < μ < 26.473
b. A 95% confidence interval for the variance:
The given values are:
=
= 59.29
α = 0.05
= 0.025
= 0.975
= 21.92
= 3.816
Note: To find the values for and
, look for them at the chi-square table
The formula to calculate interval:
()
are the lower and upper limits, respectively.
Substituing values:
()
(29.7532, 170.9093)
The interval for variance is: 29.7532 ≤ ≤ 170.9093
ANSWER
The orthocenter is
<u>EXPLANATION</u>
The orthocenter is the point of intersection of all the altitudes of a triangle.
If it is a right angle triangle then the orthocenter is the point at which the <em>right angle is made.</em>
If it is not a right angle triangle, then you have to find the equations of any two of the altitudes and solve simultaneously.
So you must first check to see if it is a right angle triangle that way you do not have to do bunch work.
The given triangle has vertices ,
, and
.
Since the denominator is zero, the slope is undefined.
If the slope of a straight line is undefined, then that line is <em>parallel to the y-axis</em>. In other words, it is a <em>vertical line</em>.
if a straight line has a slope of zero, that line is parallel to the <em>x-axis</em> or it is <em>horizontal.</em>
From the slopes we can see that side KL of the triangle is horizontal and side JK is vertical. This two sides will meet at right angles at K.
See graph.
Therefore the coordinates of K, is the orthocenter of the given triangle.
