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PtichkaEL [24]
3 years ago
14

20 POINTS PLEAE HELP!!!!!!!!!!!!!!!

Mathematics
2 answers:
Alina [70]3 years ago
5 0
His first payment is $100, thus a₁ = 100.

the next "term", month will be 1.1 times more than the one before, namely r = 1.1, the common ratio.

\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=100\\
r=1.1\\
n=20
\end{cases}

\bf \sum\limits_{i=1}^{20}~100(1.1)^{i-1}\qquad \qquad\qquad  \qquad S_{20}=100\left( \cfrac{1-1.1^{20}}{1-1.1} \right)
\\\\\\
S_{20}=100\left( \cfrac{1-\stackrel{\approx}{6.727499949}}{-0.1} \right)\implies S_{20}\approx 100(57.27499949)
\\\\\\
S_{20}\approx 5727.4999493256

is the serie divergent or convergent?

well, to make it short, when the common ratio is 0 < | r | < 1, namely a fraction between 0 and 1, only then the serie is convergent, namely it reaches a fixed value, now in this case, 1.1 is a value larger than anything between 0 and 1, so no dice.
frozen [14]3 years ago
5 0
The easiest way to get the answer is to use a spreadsheet. That will allow you to look at ways of getting the answer if you are not certain.

Step One
This is an exponential function and as such you have to make a built in correction factor. To get tn you need to use
tn = 100* [(1.1)^(1/20) ] ^ (20*(n - 1) )
1.1^(1/20) = 1.004776882
tn = 100 * (1.004776882)^(20*(n - 1) )  So if you want the 18th term, you do it like this.
t18 = 100*(1.004776882)^(20*(18 - 1)) 
t18 = 100*(1.004776882)^ 340
t18 = 100 * 5.0545
t18 = 505.45  Does that agree with what the spreadsheet gives? Amazingly enough it does!

Now we have to figure out how to get the sum of all those terms. 
Oddly, you go back to 1.1

\frac{100*(1 - (1.1)^{20})}{1 - 1.1} The answer can be made closer by using the adjustment we used for each term, but as you can see, the sum is within pennies of agreement.

I don't know how to represent this using sigma notation. I could if I knew the latex for it.

It is definitely a divergent series.

You might be interested in
Find the 44th percentile, P44, from the following data! pls help
irina [24]

Answer:

P_{44} = 29.9

Step-by-step Explanation:

The 44th percentile, P_{44}, of the given data can be calculated using the kth formula for percentile given as:

i = \frac{k}{100}(n + 1)

where,

i = the ranking or the position of the percentile = ?

k = the percentile = 44

n = total number of the given data values = 23

Plug in the values into the formula to find "i"

i = \frac{44}{100}(23 + 1)

i = \frac{44}{100}(24)

i = \frac{1,056}{100}

i = 10.56

Since "I", 10.56, is not an integer, round the number down, and round it up to the nearest integer, then look for the position each occupy in the ordered data set, and find their average.

Thus,

i_{down} = 10.56 = 10

i_{up} = 10.56 = 11

The data occupying the 10th position on the data set = 28.7

11th = 31.1

P_{44} = \frac{28.7 + 31.1}{2} = \frac{59.8}{2}

P_{44} = 29.9

6 0
3 years ago
Which angles are supplementary to each other?
Rus_ich [418]

Answer:

Angle 4 and Angle 1 are supplementary to each other.

Step-by-step explanation:

A line is 180°. Because angle 4 and angle 1 and right next to each other and they share a straight line, both of their angles should add up to 180°, making these two angles supplementary.

I hope this was helpful to you! If it was, please rate and press thanks! Have a fantastic day!

6 0
2 years ago
00:00
vaieri [72.5K]

Answer:

(D)What did Micah eat for lunch yesterday?

Step-by-step explanation:

A statistical question is a question for which the expected response varies. That is, we do not expect to get a single answer. Out of the given options,

Option D is not a valid statistical question as the response to the question will always be the same for a particular day,

If Micah ate cheesecakes for lunch yesterday, asking repeated times will not change the response.

6 0
3 years ago
Proving the Converse of the Parallelogram Side Theorem
Brrunno [24]

Answer:

do it yourself

Step-by-step explanation:

6 0
2 years ago
Not sure what to do here can someone please help
kumpel [21]

Answer:

  x = 2

Step-by-step explanation:

These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.

__

<h3>Squaring</h3>

The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.

  \sqrt{x+2}+1=\sqrt{3x+3}\qquad\text{given}\\\\(x+2)+2\sqrt{x+2}+1=3x+3\qquad\text{square both sides}\\\\2\sqrt{x+2}=(3x+3)-(x+3)=2x\qquad\text{isolate the root term}\\\\x+2=x^2\qquad\text{divide by 2, square both sides}\\\\x^2-x-2=0\qquad\text{write in standard form}\\\\(x-2)(x+1)=0\qquad\text{factor}

The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.

  x = -1: √(-1+2) +1 = √(3(-1)+3)   ⇒   1+1 = 0 . . . . not true

  x = 2: √(2+2) +1 = √(3(2) +3)   ⇒   2 +1 = 3 . . . . true . . . x = 2 is the solution

__

<h3>Substitution</h3>

Another way to solve this is using substitution for one of the radicals. We choose ...

  u=\sqrt{x+2}\qquad\text{requires $u\ge0$}\\\\u^2-2=x\qquad\text{solve for x}\\\\u+1=\sqrt{3(u^2-2)+3}\qquad\text{substitute for x in the original equation}\\\\(u+1)^2=3u^2-3\qquad\text{square both sides, simplify a little}\\\\2u^2-2u-4=0\qquad\text{subtract $(u+1)^2$}\\\\2(u-2)(u+1)=0\qquad\text{factor}

Solutions to this equation are ...

  u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution

The value of x is ...

  x = u² -2 = 2² -2

  x = 2 . . . . the solution to the equation

_____

<em>Additional comment</em>

Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.

6 0
2 years ago
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