3 years ago

Someone help me out pleaaase

Mathematics

1 answer:

alexdok [17]3 years ago

6 0

The answer to number one is A

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Please help me solve this

Viktor [21]

You can factor the 32 out of the sum:

$\displaystyle \sum_{m=1}^\infty 32 \cdot \left(\dfrac{1}{2}\right)^{m-1} = 32\sum_{m=1}^\infty \left(\dfrac{1}{2}\right)^{m-1}$

We can also change the index as follows

$\displaystyle 32\sum_{m=1}^\infty \left(\dfrac{1}{2}\right)^{m-1} = 32\sum_{m=0}^\infty \left(\dfrac{1}{2}\right)^{m}$

Now, we have a theorem that states that the series

$\displaystyle \sum_{m=1}^\infty a^m$

converges if and only if $|a|$ , and in this case we have

$\displaystyle \sum_{m=1}^\infty a^m = \dfrac{1}{1-a}$

This is your case, because you have

$|a|=\dfrac{1}{2}$

which implies that your series converges, and the value is

$\displaystyle 32\sum_{m=0}^\infty \left(\dfrac{1}{2}\right)^{m} = 32 \cdot \dfrac{1}{1-\frac{1}{2}} = 32\cdot 2 = 64$

3 0

3 years ago

The Sanchez family uses 2 3/4 tubes of tooth paste each month. How many tubes of toothpaste does the Sanchez family use each yea

Licemer1 [7]

2.75 * 12 = 33.

If the Sanchez family is using 2 3/4 (or 2.75) tubes of toothpaste and there are 12 months in a year, we use the equation above and get 33 as our answer.

8 0

3 years ago

Read 2 more answers

Express 81 as the sum of first nine consecutive odd numbers

matrenka [14]

Answer:

see explanation

Step-by-step explanation:

The sum of the first 9 consecutive odd numbers is

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81

3 0

3 years ago

A landscaper mowed 2 1/4 yards in 1 1/2 hours. How much did she mow in 1 hour? How many hours does it take to mow one yard?

ioda

Answer:

1.5 or 1 1/2 of a lawn in one hour. about one hour to mow one yard.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

How do you simplify this

katen-ka-za [31]

It's 2/5 in decimal form it is 0.4.

5 0

3 years ago