MATHEMATICS HIGH SCHOOL

identify whether the series infinity sigma i=1 8(5/6)^i-1 is a convergent or divergent geometric series and find the sum if possible

Answers

Answer 1

Answer:

Answer:

The sum of infinite geometric series is:

Step-by-step explanation:

We have to find the sum of the geometric series which is given as:

$\sum^(\infty)_(i=1) 8* ((5)/(6))^i$

which could also be written as:

$8\sum^(\infty)_(i=1) ((5)/(6))^i$

As we know that any infinite series of the form:

$\sum^(\infty)_(i=1)x^i$

is convergent if |x|<1

Here we have:

x=5/6<1

Hence,the infinite series is convergent.

Also we know that for infinite geometric series the sum is given as:

$S=(a)/(1-r)$

Here we have:

a=5/6 and common ration r=5/6

Hence, the sum of series is:

$8\sum^(\infty)_(i=1) ((5)/(6))^i=8* (((5)/(6))/(1-(5)/(6)))\n\n=8* (((5)/(6))/((1)/(6)))\n\n=8* 5\n\n=40$

Hence, the sum of series is:

Answer 2

Answer: The sum is convergent. I'll assume the 8 isn't an attempt at using the infinity symbol, so that you have

$\displaystyle\sum_(i=1)^\infty 8\left(\frac56\right)^(i-1)$

This converges because the common ratio between terms is smaller than 1.

The sum is

$\frac8{1-\frac56}=48$

since

$\displaystyle\sum_(i=1)^\infty ar^(i-1)=a\lim_(n\to\infty)\sum_(i=1)^nr^(i-1)=a\lim_(n\to\infty)(1-r^n)/(1-r)=\frac a{1-r}$

if $|r|<1$ .

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Find the additive inverse of each number
1.) 3-7i
2.) -2 + i

Answers

$The\ additive\ inverse\ of\ a\ is\ -a.\n\n1)\nthe\ additive\ inverse\ of\ 3-7i is\ -(3-7i)=-3+7i\n\n2)\nthe\ additive\ inverse\ of\ -2+i is\ -(-2+i)=2-i$

Write a real world situation for the following equations:1. 30x = 48 + 22x
2. 120 + 25x = 45x
3. 100 - 6x = 160 - 10x
plz help me.

Answers

2. Snap gym costs $120 for registration fee and $25 each month. Awesome gym costs $45 each month with no registration fee. After how many months will the cost of the two gyms be equal ?3. Awesome video game has a total of 100 points. If you are out, you miss 6 points. Cool video game has a total of 160 points. If you are out, you miss 10 points. After how many times of getting out will you have the same number of points on both the games ?

What is the answer? Pls helpp

Answers

There would be 18 separate outcomes, since the spinner has three numbers and the dice has six numbers. Since the spinner has all odd numbers then an even number must be rolled on the dice for the answer to be odd. And since half of the numbers on a dice are even then half of the answers will be odd, aka 50%

A cell phone company orders 500 new phones from a manufacturer. If the probability of a phone being defective is 2.6%, predict how many of the phones are likely to be defective. Round to the nearest whole number.

Answers

First turn 2.6% into a decimal which is 0.026 then times by 500 too get.... ? do you know the answer?

Answer:

13 phone would be defective

Step-by-step explanation:

36x^2-21x-30 factor

Answers

Easy...

to even begin to factor..you must factor out a 3, to simplify your answer.

3(12 $x^(2)$ -7x-10)

Now, you can factor.

$3(12 x^(2) -7x-10)$

So..to find the answer...

12*-10=-120x
and
you would use -7x

What multiplies to -120..but adds to -7?

-15*8=-120
and
-15+8=-7

To find the answer, plug in what you know..

3(3x+2)(4x-5)

Thus, your answer.

$800 is deposited in an account that pays 9% compounded semi-annually. Find the balance after 4 years.

Answers

The formula for compound interest is the following:

A=P(1+r/n)^nt
A=accumulated amount (what we're looking for)
P=Principal amount (initial amount). $800 in this case
r=rate. 0.09 in this case which we get from converting 9% to decimal by dividing by a 100.
n=number of times interest is compounded. In this case semi-annually which means 2
t=time. In this case 4 years
Let's calculate:
A=800(1+0.09/2)^(2*4)
A=800(1+0.045)^8
A=800(1.045)^8
A=800(1.42210061284)
A=1137.68049027
Let's round to the hundredth place (to represent cents) since the amount represents money.
Answer=The balance after 4 years will be $1,137.68

Answer:

Principal = $ 800

Time = 4 years

Rate of Interest = 9% compounded Semi Annually

$=(9\pr)/(2)$

Time = 4× 2=8 periods

As, we have to find balance after 4 years, so we will use the formula for amount in terms of Compound interest.

Amount(A)

$A=P[1+(R)/(100)]^n\n\n A=800* [1+(9)/(200)]^8\n\n A=800 * [(209)/(200)]^8\n\n A=800 * (1.045)^8\n\n A=800 * 1.422\n\n A=1137.680$

Balance after 4 years = $ 1137.68

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