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2 years ago

7

Larry makes sandwiches for lunch everyday. he can make 5 sandwiches with every 3 tomatoes he buys. if he bought 9 tomatoes, how

many sandwiches could he make?

1 answer:

tangare [24]2 years ago

6 0

15 sandwiches
3 tomatoes= 5 sandwiches.
So if there's 9, that makes 3 groups of 3 tomatoes which would make 3x5 or 5+5+5 ;-;
15.

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A bag contains pennies, nickles, dimes, and quarters.There are 50 coins in all. Of the coins, 10% are pennies and 32% are dimes.

ikadub [295]

10 pennies, 16 dimes, 19 nickles.
Sorry I'm not from US so I don't know your currency. Sorry about that. Hope what I have given you is enough. :)

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2 years ago

Lim (n/3n-1)^(n-1)<br> n<br> →<br> ∞

n200080 [17]

Looks like the given limit is

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}$

With some simple algebra, we can rewrite

$\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)$

then distribute the limit over the product,

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}$

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, <em>e</em> :

$\displaystyle e = \lim_{n\to\infty} \left(1+\frac1n\right)^n$

To make our limit resemble this one more closely, make a substitution; replace 9/(<em>n</em> - 9) with 1/<em>m</em>, so that

$\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1$

From the relation 9<em>m</em> = <em>n</em> - 9, we see that <em>m</em> also approaches infinity as <em>n</em> approaches infinity. So, the second limit is rewritten as

$\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}$

Now we apply some more properties of multiplication and limits:

$\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9$

So, the overall limit is indeed 0:

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}$

7 0

2 years ago

A photographer uses an online service to sell some of his work. The amount of money he will make from selling 10 copies of the s

VLD [36.1K]

Answer:

Step-by-step explanation:

The expression representing the amount of money that the photographer would make from selling 10 copies is given as

10(0.75p - 0.5)

where p represents the price determined for each copy. Assuming the price charged per copy is $5, then the amount made from 10 copies is

10(0.75 × 5 - 0.5) = $32.5

It could have been

10(5 - 0.5) = $45

The price is being reduced by 25%(100 - 75)

Therefore, the option that most likely describes the agreement between the online service company and the photographer is

A. The company keeps 25% of the amount paid for each copy and charges the photographer $0.50 for every copy purchased.

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2 years ago

What is the y-intercept of the function y = –2(2)^x+ 2?

NISA [10]

Y=mx+b
so is 2
the last number of the equation

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2 years ago

keisha made $396 for 18 hours of work at the same rate how many hours would she have to work to make the 242

love history [14]

Answer:

hahaha I stole your points lololoooooooooooollllllllllolololol

Step-by-step explanation:

JK, if you are asking how many hours it would take to make 242 dolla then the answer is 11

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1 year ago

Read 2 more answers