Find the value of m divided 9 when m=72

Answer:

This series is convergent. The partial sums of this series converge to [tex]\displaystyle \frac{2}{3}[/tex].

Step-by-step explanation:

The [tex]n[/tex]th partial sum of a series is the sum of its first [tex]n\!\![/tex] terms. In symbols, if [tex]a_n[/tex] denote the [tex]n\![/tex]th term of the original series, the [tex]\! n[/tex]th partial sum of this series would be:

[tex]\begin{aligned} S_n &= \sum\limits_{k = 1}^{n} a_k \\ &= a_1 + a_2 + \cdots + a_{k}\end{aligned}[/tex].

A series is convergent if the limit of its partial sums, [tex]\displaystyle \lim\limits_{n \to \infty} S_{n}[/tex], exists (should be a finite number.)

In this question, the [tex]n[/tex]th term of this original series is:

[tex]\displaystyle a_{n} = \frac{{(-1)}^{n+1}}{{2}^{n}}[/tex].

The first thing to notice is the [tex]{(-1)}^{n+1}[/tex] in the expression for the [tex]n[/tex]th term of this series. Because of this expression, signs of consecutive terms of this series would alternate between positive and negative. This series is considered an alternating series.

One useful property of alternating series is that it would be relatively easy to find out if the series is convergent (in other words, whether [tex]\displaystyle \lim\limits_{n \to \infty} S_{n}[/tex] exists.)

If [tex]\lbrace a_n \rbrace[/tex] is an alternating series (signs of consecutive terms alternate,) it would be convergent (that is: the partial sum limit [tex]\displaystyle \lim\limits_{n \to \infty} S_{n}[/tex] exists) as long as [tex]\lim\limits_{n \to \infty} |a_{n}| = 0[/tex].

For the alternating series in this question, indeed:

[tex]\begin{aligned}\lim\limits_{n \to \infty} |a_n| &= \lim\limits_{n \to \infty} \left|\frac{{(-1)}^{n+1}}{{2}^{n}}\right| = \lim\limits_{n \to \infty} {\left(\frac{1}{2}\right)}^{n} =0\end{aligned}[/tex].

Therefore, this series is indeed convergent. However, this conclusion doesn't give the exact value of [tex]\displaystyle \lim\limits_{n \to \infty} S_{n}[/tex]. The exact value of that limit needs to be found in other ways.

Notice that [tex]\lbrace a_n \rbrace[/tex] is a geometric series with the first term is [tex]a_0 = (-1)[/tex] while the common ratio is [tex]r = (- 1/ 2)[/tex]. Apply the formula for the sum of geometric series to find an expression for [tex]S_n[/tex]:

[tex]\begin{aligned}S_n &= \frac{a_0 \cdot \left(1 - r^{n}\right)}{1 - r} \\ &= \frac{\displaystyle (-1) \cdot \left(1 - {(-1 / 2)}^{n}\right)}{1 - (-1/2)} \\ &= \frac{-1 + {(-1 / 2)}^{n}}{3/2} = -\frac{2}{3} + \frac{2}{3} \cdot {\left(-\frac{1}{2}\right)}^{n}\end{aligned}[/tex].

Evaluate the limit [tex]\displaystyle \lim\limits_{n \to \infty} S_{n}[/tex]:

[tex]\begin{aligned} \lim\limits_{n \to \infty} S_{n} &= \lim\limits_{n \to \infty} \left(-\frac{2}{3} + \frac{2}{3} \cdot {\left(-\frac{1}{2}\right)}^{n}\right) \\ &= -\frac{2}{3} + \frac{2}{3} \cdot \underbrace{\lim\limits_{n \to \infty} \left[{\left(-\frac{1}{2}\right)}^{n} \right] }_{0}= -\frac{2}{3}\end{aligned}}_[/tex].

Therefore, the partial sum of this series converges to [tex]\displaystyle \left(- \frac{2}{3}\right)[/tex].

Answer:

what's the question

Step-by-step explanation:

lol but u could mark me brainlyist

Answer:

.....................................

Step-by-step explanation:

Answer:

[tex] {x}^{2} + {x}^{2} = {(8 \sqrt{2}) }^{2} \\ 2 {x}^{2} = 128 \\ {x}^{2} = 64 \\ \boxed{x = 8}[/tex]

Answer: 3.2x = 48

Step-by-step explanation: So that means x = 15.

Answer:

k = 10

Step-by-step explanation:

X progresses by 25, while y progresses by 250.

So divide 250 ÷ 15 and your answer is 10.

Answer:

Amount contributed by Oscar = $8

Step-by-step explanation:

Given that:

Amount spent on gift = $36

Amount contributed by Moriah = $12

Let,

x be the amount contributed by each of them.

Thus,

Gift total = Contribution of all

36 = x+x+x+12

36 = 3x+12

3x+12 = 36

3x=36-12

3x=24

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{24}{3}\\x=8[/tex]

Hence,

Amount contributed by Oscar = $8

Answer:

0.084 , 8.4, 0.84, 84     sorry if im wrong

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It is letter A I got 100!

Answer:

A

Step-by-step explanation:

EDGE 2021

Answer:

Rounding to the nearest number, the answer would be 12 units

Step-by-step explanation:

I hope this helped! Please mark me as brainliest if you can!

apply distributive property AKA (A • 9b)+(A • 13)

9Ab + 13A

I hope this helps :)

Answer:

10h=200

h=20

Step-by-step explanation:

10h=200

10h/10=200/10

h=20

Multiply the number of hours worked (h) by earnings per hour $10 to get

10h

This needs to be more than ( Greater than) 200

Now you have 10h > 200

Solve for h by dividing both sides by 10:

h >20

This means she needs to work more than 20 hours this week.

Answer:

a number 12

Step-by-step explanation:

duh bro

Step-by-step explanation:

Sum of interior angles in a polygon

= 180°(n - 2), where n is the number of sides.

Hence a convex polygon with 6 sides

=> 180°(6 - 2) = 720°.

Answer:

Hey

Step-by-step explanation:

Write the fraction in simplest form

[tex] - \frac{29}{18} [/tex]

[tex] \frac{8}{9} - \frac{5}{2} [/tex]

Find the difference between 8/9 and 5/-2

[tex] \frac{8}{9} - \frac{5}{2} [/tex]

[tex] \frac{8 \times 2}{9 \times 2} - \frac{5 \times 9}{2 \times 9} [/tex]

[tex] \frac{16}{18} - \frac{45}{18} [/tex]

[tex] \frac{16 - 45}{18} [/tex]

[tex] \frac{ - 29}{18} [/tex]

[tex] - \frac{29}{18} [/tex]

Solution :

Let the three places be 1, 2, 3, 4, 5, 6, 7, 8

a). Number of the cases when a general manager is the next to a vice president is equal to 7 and the these 2 can be arranged in 21 ways. So the total number of ways = 7 x 2

                  = 14

[(1,2)(2,1) (2,3)(3,2) (3,4)(4,3) (4,5)(5,4) (5,6)(6,5) (6,7)(7,8) (8,7)(7,6)]

Therefore the required probability is

  [tex]$=\frac{14}{8!}$[/tex]

 = [tex]$\frac{14}{40320} = 0.000347$[/tex]

b). The probability that the marketing director to be placed in the leftmost position is

   [tex]$=\frac{7!}{8!}$[/tex]

  [tex]$=\frac{1}{8} = 0.125$[/tex]

c). The two events are not independent because

   [tex]$P(A \cap B) \neq P(A) \times P(B)$[/tex]

  [tex]$\frac{12}{8!} \neq \frac{14}{8!} \times \frac{1}{8}$[/tex]

where A is the case a and B is the case b.

(a) The possibility of the general manager is next to the vice president is [tex]\frac{1}{4}[/tex].

(b) The possibility of the marketing director is in the leftmost position is [tex]\frac{1}{8}[/tex].

(c) So, the two events are dependent on each other.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. The probability of all the events in a sample space adds up to 1.

Total people in company A and company B is [tex]=8[/tex]

Overall ways in which these [tex]8[/tex] people can be lined up[tex]=8![/tex]

                                                                                        [tex]=40320[/tex]

(a) The probability that the general manager is next to the vice president is[tex]=P(A)[/tex]

Now, we can combine the general manager and vice president as one, then the total people in both the company will become [tex]7[/tex].

by arranging these [tex]7[/tex] people in one line [tex]=7![/tex]

                                                                [tex]=5040[/tex]

Again, combine the general manager and vice president in one line[tex]=2![/tex]

                                                                                                                [tex]=2[/tex]

Therefore, [tex]P(A)=\frac{5040\times 2}{40320}[/tex]

                          [tex]=\frac{10080}{40320}[/tex]

[tex]P(A)=\frac{1}{4}[/tex]

(b) The probability that the marketing director is in the leftmost position is[tex]=P(B)[/tex]

Now, fixing the position of marketing director in the leftmost.

arranging the [tex]7[/tex] other people in [tex]7![/tex] ways [tex]=5040[/tex]

Therefore,[tex]P(B)=\frac{5040}{40320}[/tex]

                          [tex]=\frac{1}{8}[/tex]

[tex]P(B)=\frac{1}{8}[/tex]

(c) Assuming event B already occurred which means that the position of marketing director is already fixed in the leftmost position.

Now, trying to find out the probability of the general manager next to the vice president is event A. it comes different because we are not allowed to arrange rest [tex]7[/tex] people, we have to fix the position of one person that causes the repetition of probability.

So, the two events are dependent on each other.

Learn more about the topic of Probability: https://brainly.com/question/26959834

Answer:

51/100

Step-by-step explanation:

Answer:

im sure its D.)

Step-by-step explanation:

Answer:

Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. Often we will solve a trigonometric equation over a specified interval. However, just as often, we will be asked to find all possible solutions, and as trigonometric functions are periodic, solutions are repeated within each period. In other words, trigonometric equations may have an infinite number of solutions. Additionally, like rational equations, the domain of the function must be considered before we assume that any solution is valid. The period of both the sine function and the cosine function is 2π. In other words, every 2π units, the y-values repeat. If we need to find all possible solutions, then we must add 2πk, where k is an integer, to the initial solution. Recall the rule that gives the format for stating all possible solutions for a function where the period is 2π:

sinθ=sin(θ±2kπ)

There are similar rules for indicating all possible solutions for the other trigonometric functions. Solving trigonometric equations requires the same techniques as solving algebraic equations. We read the equation from left to right, horizontally, like a sentence. We look for known patterns, factor, find common denominators, and substitute certain expressions with a variable to make solving a more straightforward process. However, with trigonometric equations, we also have the advantage of using the identities we developed in the previous sections.

Step-by-step explanation:

Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. Often we will solve a trigonometric equation over a specified interval.  

Answer:

quadrant 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]

Suppose [tex]5x^4 + 1 = f[/tex]

by differentiation;

[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]

Suppose n = 3

Then, the integral

[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]

[tex]= \int e^f \ \dfrac{df}{20}[/tex]

[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]

[tex]= \dfrac{1}{20} e^f + C[/tex]

recall that [tex]f = 5x^4 + 1[/tex]

Then;

[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]

(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]

suppose; [tex]\dfrac{1}{x^3} = f[/tex]

[tex]x^3 = f[/tex]

[tex]\implies -3x^{-4} \ dx = df[/tex]

[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]

If n = u, then the integration is:

[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]

[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]

Since;  [tex]x^3 = f[/tex]

Then;

[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]

(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]

Suppose  [tex]x^2 + 8x - 4 = f[/tex]

Then, by differentiation of both sides

[tex](2x + 8) \ dx = df[/tex]

[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]

Suppose n = 4 in integration, then:

[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]

By substitution;

[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]

[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]

[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]

The suitable substitutions of n are 3,4,4 respectively.

The process of finding integrals is called integration.

a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

Suppose

[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]

So, we need n=3 for easy integration.

[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]

[tex]I=\frac{e^{t} }{20}[/tex]

[tex]I = e^{5x^{4}+1 }/20 +c[/tex]

b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]

n=4 is needed for easy integration.

I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]

c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]

n=4 is needed for easy integration.

[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]

Hence, the suitable substitutions of n are 3,4,4 respectively.

To get more about integration visit:

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Answer:

These two corners are [tex]\sqrt{13}[/tex] units apart.

Step-by-step explanation:

Distance between two points:

Suppose we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Approximately how far apart are the two corners?

We have to find the distance between the points (-5,-2) and (-8-3). So

[tex]D = \sqrt{(5-(-8))^2+(-2-(-3))^2} = \sqrt{13}[/tex]

These two corners are [tex]\sqrt{13}[/tex] units apart.

Answer: It's the third one down

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex] \tan(30°) = \frac{12}{r} \\ \frac{1}{ \sqrt{3} } = \frac{12}{r} \\ \boxed{r = 12 \sqrt{3} }[/tex]

and,

[tex] \sin(30°) = \frac{12}{t} \\ \frac{1}{2} = \frac{12}{t} \\ \boxed{t = 24}[/tex]

Answer:

15 students

Step-by-step explanation:

25% = 1/4, so you can just do 1/4 of 60 or 1/4 * 60. 60/4 = 15 students.