Harry fills up his Jeep with gasoline and notes that the odometer reading is miles. The next time he fills up his Jeep, he pays
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Answer:
Slope of the base segment line is zero, hence base segment is horizontal
Slope of the segment that joins the vertex angle to the midpoint of its base is undefined hence the line is vertical
Therefore, angle between base segment line and the segment line from the vertex angle to the midpoint is perpendicular
Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base
Step-by-step explanation:
Here we prove the required relation as follows;
Let the isosceles be ABC
The coordinates of the points are
C = (0, 0) (Vertex)
A = (-a, b)
C = (a, b)
P = (0, b) (Midpoint of base)
Therefore, the gradient or slope of the base AC is presented as follows;
Hence, segment AC is vertical
Hence, segment CP is vertical
Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base.
Answer:
Critical value is t = 1.9901
Step-by-step explanation:
We are given the results of the sampling :
In-House Credit Card National Credit Card <u>Sample Size</u> : 32 50
<u>Mean Monthly Purchases </u>: $45.67 $39.87
<u>Standard Deviation </u>: $10.90 $12.47
Also, the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards, using a significance level α of 0.05.
<em>Firstly, we will specify our null and alternate hypothesis;</em>
Let = Mean Monthly Purchases of In-House Credit Card
= Mean Monthly purchases of National Credit Card
So, Null Hypothesis, :
= 0 {means that there is no difference in the mean monthly purchases by customers using the two types of credit cards}
Alternate Hypothesis, :
0 {means that there is statistical difference in the mean monthly purchases by customers using the two types of credit cards}
The test statistics that will be used here is <u>Two-sample t-test statistics</u>;
T.S. = ~
where, = Sample mean Purchases of In-House Credit Card = $45.67
= Sample mean Purchases of National Credit Card = $39.87
= pooled variance
= In-house credit card sample = 32
= National credit card sample = 50
So, degree of freedom of t-value here is (32 + 50 - 2) = 80
Now, at 0.05 significance level, t table gives critical value of t = 1.9901 at 80 degree of freedom.
<em>Therefore, the critical value assuming the population standard deviations are not known but that the populations are normally distributed with equal variances is t = 1.9901.</em>