2x + 3y = 16<br> 4x

Write out the first few terms of the series Summation from n equals 0 to infinity (StartFraction 2 Over 3 Superscript n EndFract

anyanavicka [17]

Answer:

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = 15/8$

Step-by-step explanation:

The sum you are trying to understand is this.

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}$

Remember that in general when you have a geometric series

$\sum\limits_{n = 0}^{\infty} a*r^n$ you have that

$\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}$ and that equality is true as long as $|r| < 1$ .

Therefore here we have

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n$ and $\big|\frac{-1}{15} \big| = \frac{1}{15} < 1$

Therefore we can use the formula and

$\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n = \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16 = 15/8$

5 0

3 years ago

Estimate 53.83-36.464 by first rounding each number to the nearest whole number.

Free_Kalibri [48]

Answer:

18

Step-by-step explanation:

53.83 rounds to 54

36.464 rounds to 36

54-46=18

7 0

3 years ago

Read 2 more answers

I NEED HELP ASAP PLEASE!!!

Artemon [7]

Answer:

-3x+1y=-1

or

3x-1y=1

or

by multiplying with 1/3 the first equation we get

-1x+1/3y=-1/3

or from second equation

1x-1/3y=1/3

Step-by-step explanation:

y-y1=m(x-x1)

y1=-7

x1=-2

m=3

so

y-(-7)=3(x-(-2))

y+7=3(x+2)

y+7=3x+6

-3x+y=6-7

-3x+ 1y= -1

8 0

3 years ago

Help me with this pls!!! You need to fill in the blanks with the words given above 99 Points!

sweet-ann [11.9K]

A simulation is a mathematical model used to represent a situation.

A simulation can be a program or a physical test to "simulate" a situation to predict the outcomes.

When we combine two or more simple events we have a compound event

"Compound" means to combine, like a compound word would be a combination of two words

A Tree Diagram is a diagram that shows all the possible outcomes of an event

In a tree diagram, each possible outcome "branches" off the main stem, making the final diagram look like a tree with many separating branches.

All the possible outcomes or results is called the sample space

The outcomes are each different samples, and a sample space is a space that collects each of these samples

When an event is not affected by a previous outcome we have an independent event

This event is "independent", not affected by other factors, making it an independent event

Let me know if you need any clarifications, thanks!

~ Padoru

8 0

3 years ago

Consider a single spin of the spinner. Which events are mutually exclusive? Choose all that apply. a)landing on a shaded sector

denis23 [38]

Answer: the correct options are b and d.

Step-by-step explanation:

Let us first define what mutually exclusive events are. If two events are mutually exclusive, it means that they cannot happen at the same time. For example, getting a head and a tail at the same time are mutually exclusive.

Considering a single spin of the spinner, the events that are mutually exclusive are

b)landing on a shaded sector and landing on a 3. This is because 3 is unshaded. You can either land on 3 or an unshaded sector at a time

d)landing on an unshaded sector and landing on a number less than 2. This is because the numbers in the unshaded sectors are greater than 2.

3 0

3 years ago

2x + 3y = 16 4x - 3y =-4