David has a triangular prism that has an equilateral base. Also, the base of the prism is of the same length as its height. Pick
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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>
Answer:
C and E
Step-by-step explanation:
Let's factor this the "old fashioned" way. The standard form of a quadratic is
If you're familiar with the quadratic formula I'd say throw it into that, but if not, again, let's do it the "old fashioned" way.
We need to find the product of our a and c. Our a = 2 and our c = -3. So that gives us a -6. Now we have to find the factors of 6 (the negative right now doesn't matter so much). The factors of 6 are 1, 6 and 2, 3. Both of those possibilities will work to give us a +5, which is the linear term. Puttng in the 2, 3 first:
Now group the terms together into groups of 2:
The idea is to factor out something common in each term so that what's left over in the parenthesis in both terms is exactly the same. In the first term we can factor out a common x, and in the second term, the only thing common is a 1. So that looks like this:
What's inside those parenthesis are not actually identical, so 2 and 3 won't work. Lets try 1 and 6. For those 2 numbers to equal a +5, the 6 is positive and the 1 is negative. So let's try that:
In the first term we can factor out the common 2x and in the second term we can factor out the common -1:
2x(x + 3) - 1(x + 3)
Now what's common is (x + 3), so we can factor THAT out and what is left over is 2x - 1:
(x + 3)(2x - 1) = 0
If x + 3 = 0, then x = -3
and if 2x - 1 = 0, then 2x = 1 and x = 1/2