john gray bought a basic car for $32,750.00, with options that cost $375.00. there's a 6% sales tax in his state and a combined
1 answer:
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Answer:
1.5 feet
Step-by-step explanation:
Bob wants to plant a 7 foot by 10 foot garden.
Area = square feet
He wants to make a uniform border of petunias around the outside and still have 28 square feet to plant tomatoes and roses in the middle.
Means we have to factor 28 in a way that the length and width is less than 10 and 7.
28 = 2 x 2 x 7
Means 4 feet can be width and 7 feet the length of the area where tomatoes need to be planted.
So, we have feet less than outer garden means at each side
feet decreases.
Similarly, we have feet less width and at each side it is 1.5 feet.
Therefore, the border of petunias will be 1.5 feet wide on all sides.
Answer:
I.
CORRECT.
II.
CORRECT.
III.
CORRECT.
IV.
CORRECT.
V.
INCORRECT.
VI.
CORRECT
Step-by-step explanation:
To understand let us restate the comparison test in simple terms.
Comparison test :
Given and
such that
, then
1. If converges then
converges as well.
2. If diverges then
diverges as well.
Now to give you a more intuitive idea of what is going on, think about it like this. When the series on top converges it is like an "upper bound" for what you have on the bottom, therefore what you have on the bottom has to converge as well.
Similarly if what you have on the bottom explotes, then what you have on top will explote as well.
That's how I like to think about that intuitively.
Now, using those results let us examine the statements.
I.
Since the infinite sum of 1/n diverges in fact the infinite sum of ln(n)/n does not converge.
Therefore, CORRECT.
II.
Since the infinite sum of is in fact convergent then
converges as well using the comparison theorem. Therefore
CORRECT.
III.
Once again does converge so what you have on the bottom converges as well. Therefore
CORRECT.
IV.
Once again converges therefore since it is on top what is on the bottom converges as well. Therefore.
CORRECT.
V.
Now the fact that diverges does not necessarily imply that what you have on the bottom diverges. Therefore
INCORRECT.
VI.
That is correct as well since what you have on top converges therefore what you have on the bottom converges as well.