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NISA [10]
3 years ago
5

Does the following infinite series converge or diverge?

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0
The nth term is (presuming the denominator on the first is a typo)

-\dfrac{n}{(-3)^n}

The ratio of successive terms is

\dfrac{ \frac{n+1}{(-3)^(n+1)}}{\frac{n}{(-3)^n}} = \frac{n+1}{-3n}

The limit is -1/3, absolute value less than 1, so the series converges.  It has a sum -- that's what converges means.

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There are 12 face cards in a deck, and one you draw the first face card there will be 11 left so:
(12/52)*(11/51)=132/2652=11/221
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Machine A and machine B both make car parts.
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504+640=1144 hope this helps!
5 0
2 years ago
Identify the graph of the inequality 2(2x – 1) + 7 < 13 or –2x + 5 < –10.
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Answer:

–2x + 5 < –10.

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3 0
2 years ago
Help me please. <br>Help me please. <br>Help me please.
Gnesinka [82]
A)
To be similar triangles have to have equal angles
triangle ZDB' 
1)angle Z=90 degrees
triangle B'CQ
1) angle C 90 degrees

angle A'B'Q=90
DB'Z+A'B'Q+CB'Q=180, straight angle
DB'Z+90+CB'Q=180
DB'Z+CB'Q=90

triangle ZDB'
DZB'+DB'Z=180-90=90

DB'Z+CB'Q=90
DZB'+DB'Z=90
DB'Z+CB'Q=DZB'+DB'Z
2)CB'Q=DZB' (these angles from two triangles ZDB' and B'CQ )
3)so,angles DB'Z and B'QC are going to be equal because of sum of three angles in triangles =180 degrees and 2 angles already equal.
so this triangles are similar by tree angles
b)
B'C:B'D=3:4
B'D:DZ=3:2
CQ-?
DC=AB=21
DC=B'C+B'D (3+4= 7 parts)
21/7=3
B'C=3*3=9
B'D=3*4=12
B'D:DZ=3:2
12:DZ=3:2
DZ=12*2/3=8
B'D:DZ=CQ:B'C
3:2=CQ:9
CQ=3*9/2=27/2

c)
BC=BQ+QC=B'Q+QC
BQ' can be found by pythagorean theorem



3 0
3 years ago
A random sample of 121 automobiles traveling on an interstate showed an average speed of 73 mph. from past information, it is kn
tatiyna

121 is big enough to assume normality and not worry about the t distribution. By the 68-95-99.7 rule a 95% confidence interval includes plus or minus two standard deviations. So 95% of the cars will be in the mph range


(73 - 2 \cdot 11, 73 + 2 \cdot 11) = (51,95)


The question is a bit vague, but it seems we're being asked for the 95% confidence interval on the average of 121 cars. The 121 is a hint of course.


The standard deviation of the average is in general the standard deviation of the individual samples divided by the square root of n:


\sigma = \dfrac{ 11}{\sqrt{121}} = 1


So repeating our experiment of taking the average 121 cars over and over, we expect 95% of the averages to be in the mph range


(73 - 2 \cdot 1, 73 + 2 \cdot 1) = (71,75)


That's probably the answer they're looking for.



4 0
3 years ago
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