6 and 15 have 3 as a common factor. Thus 6:15 is 2:5. The other ratios are also the same as given in the question. Since the numbers in the second column increase in 15s, the numbers in the first row should increase in sixes (12:30 is the same as 6:15 and 2:5). Thus the answers are:
- 6:15
- 12:30
- 18:45
- 24:60
- 30:75
Answer: For 18 months the last term is 18 and the sum is 171. For 24 months the last term is 24 and the sum is 300. For 30 months the last term is 30 and the sum is 465.
Explanation:
For the Rule of 78, for a 12 month period, the last term in the sequence is 12 and the series sums to 78. It is also defined as,
It is an AP with first term 1 and common difference 1.
The formula for sum of n terms is,
Similarly, for 18 months the last term is 18 and its sum is,
Similarly, for 24 months the last term is 24 and its sum is,
Similarly, for 300 months the last term is 30 and its sum is,
Therefore, the last term for 18 month is 18 and its sum is 171. The last term for 24 month is 24 and its sum is 300. The last term for 30 month is 30 and its sum is 465.
Find attached the document with both graphs.
The remarks are:
- both graphs have the same shape: open downward, same symetry axis, same, x-coordinate of the vertex.
- the maximum value of -2x^2 is 0
- the maximum value of -2x^2 + 4 is 4
- the graph of y = -2x^2 + 4 is the graph -2x^2 shifted 4 units upward as consecuence of having summed 4 to the function.
Answer:
b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.
See explanation below.
Step-by-step explanation:
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the means for the two groups are different (men have longer mean nose length than women), the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Assuming that we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:
(1)
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Let's assume that the calculated statistic is
Since is a right tailed test test the p value would be:
And we know that the p value is 0.225. If we select a significance level for example 0.05 or 0.1 we see that
And on this case we have enough evidence to FAIl to reject the null hypothesis that the means are equal. So then the best conclusion would be:
b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.
Answer:
L(xyz) = ( 1 , 3 , -7 )
L = x + 3y - 7z -3
Step-by-step explanation:
f (x,y,z) = xy + 2yz - 3xz
f (3,1,0) = (3) (1) + 2 (1) (0) - 3 (3) (0)
f (3,1,0) = 3
fx = y - 3z
f (3,1,0) = (1) - 3 (0)
fx = 1
fy = x + 2z
f (3,1,0) = (3) - 2 (0)
fy = 3
fz = 2y - 3x
f (3,1,0) = 2 (1) - 3 (3)
fz = -7