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astraxan [27]
3 years ago
15

Can someone please help me with this one question?

Mathematics
1 answer:
Scilla [17]3 years ago
8 0
It's been awhile since I've worked with infinite series and partial sums, but here are my thoughts:
A. the first 4 terms:  -4, - \frac{4}{3}, -\frac{4}{9}, - \frac{4}{27}
B. In examining the partial sums of the series, it appears that the sequence produced has a limit and therefore the series would be convergent.
C. the limit or sum of the series looks to be -5    Below look at the sequence of partial sums:  
-4, -5 \frac{1}{3}, -5 \frac{7}{9}, -5 \frac{25}{27}

So you can see we're getting closer and closer to -5
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A special type of door lock has a panel with five buttons labeled with the digits 1 through 5. This lock is opened by a sequence
belka [17]

There are several ways the door can be locked, these ways illustrate combination.

There are 3375 possible combinations

From the question, we have:

\mathbf{n = 5} --- the number of digits

\mathbf{r = 3} ---- the number of actions

Each of the three actions can either be:

  • <em>Pressing one button</em>
  • <em>Pressing a pair of buttons</em>

<em />

The number of ways of pressing a button is:

\mathbf{n_1 = ^5C_1}

Apply combination formula

\mathbf{n_1 = \frac{5!}{(5-1)!1!}}

\mathbf{n_1 = \frac{5!}{4!1!}}

\mathbf{n_1 = \frac{5 \times 4!}{4! \times 1}}

\mathbf{n_1 = 5}

The number of ways of pressing a pair is:

\mathbf{n_2 = ^5C_2}

Apply combination formula

\mathbf{n_2 = \frac{5!}{(5-2)!2!}}

\mathbf{n_2 = \frac{5!}{3!2!}}

\mathbf{n_2 = \frac{5 \times 4 \times 3!}{3! \times 2 \times 1}}

\mathbf{n_2 = 10}

So, the number of ways of performing one action is:

\mathbf{n =n_1 + n_2}

\mathbf{n =5 + 10}

\mathbf{n =15}

For the three actions, the number of ways is:

\mathbf{Action = n^3}

\mathbf{Action = 15^3}

\mathbf{Action = 3375}

Hence, there are 3375 possible combinations

Read more about permutation and combination at:

brainly.com/question/4546043

4 0
2 years ago
PLEASE HURRY ;-;
katovenus [111]

Answer:

do you go to palcs too?

Step-by-step explanation:

3 0
2 years ago
A paraboloid container is being filled with fluid at the rate of 4.5 cubic feet per minute. At what rate is the level of fluid c
docker41 [41]

Answer:

2.62 ft./min

Step-by-step explanation:

Just took the test.

7 0
3 years ago
Please help me!! thank you!!
I am Lyosha [343]

Answer:

A. 106 + 2x + 50 = 180

Step-by-step explanation:

A. 106 + 2x + 50 = 180. Correct.

B. 2x + 50 = 180. Incorrect. Angle is not a Straight Angle.

C. 2x + 50 = 106. Incorrect. That equals the first angle.

hope this helps.

4 0
3 years ago
Please answer both question fully.
BARSIC [14]

Step-by-step explanation:

<h3>Part A</h3>

<u>Angle measures:</u>

  • a = x = z = 51° (as vertical angles and corresponding angles)
  • b = d = y = w = 180° - 51° = 129° (as supplementary angles and corresponding angles)
<h3>Part B</h3>

Supplementary angles for a linear pair and sum to 180°.

<u>Examples are:</u>

  • a and b or
  • a and d or
  • x and y etc.
7 0
2 years ago
Read 2 more answers
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