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3 years ago

15

Can someone please help me with this one question?

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