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Natalka [10]
3 years ago
14

If 6 burgers cost $7.74 how many can you buy for $19.35

Mathematics
1 answer:
xeze [42]3 years ago
6 0

Answer:

15 burgers!

Step-by-step explanation:

The trick is to get rid of the decimal point from the number we are dividing by.

How? We can "shift the decimal point" out of the way by multiplying by 10, as many times as we need to.

But we must do the same thing to both numbers in the division.

Example: 15 divided by 0.2

Let us multiply the 0.2 by 10, which shifts the decimal point out of the way:

0.2 × 10 = 2

But we must also do it to the 15:

15 × 10 = 150

So 15 ÷ 0.2 has become 150 ÷ 2 (they are both 10 times larger):

150 ÷ 2 = 75

And so the answer is:

15 ÷ 0.2 = 75

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums
gtnhenbr [62]

I'm guessing the sum is supposed to be

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}

Split the summand into partial fractions:

\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}

1=a(5k+4)+b(5k-1)

If k=-\frac45, then

1=b(-4-1)\implies b=-\frac15

If k=\frac15, then

1=a(1+4)\implies a=\frac15

This means

\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}

Consider the nth partial sum of the series:

S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)

The sum telescopes so that

S_n=\dfrac2{14}-\dfrac2{5n+4}

and as n\to\infty, the second term vanishes and leaves us with

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17

7 0
3 years ago
The amount of carbon-14 in animal bones after t years is given by P(t)=P[0]e^(-0.00012097t). A bone has lost 37% of its carbon-1
Vesna [10]
63 years :) Hope this helps ;D
8 0
3 years ago
Help please this is also do very very soon thank you!!!
stepan [7]

Answer:

700

Step-by-step explanation:

100:2

???:14

14*100

=1400

1400/2

=700

3 0
3 years ago
Read 2 more answers
4.5<br>-<br>17 - X 8<br><br>I need help! <br>10 pts​
sesenic [268]

Answer:

x = -1.5625

Step-by-step explanation:

Solve for x:

-8 x - 12.5 = 0

Add 12.5` to both sides:

(12.5 - 12.5) - 8 x = 12.5

12.5 - 12.5 = 0:

-8 x = 12.5

Divide both sides of -8 x = 12.5 by -8:

(-8 x)/(-8) = 12.5/(-8)

(-8)/(-8) = 1:

x = 12.5/(-8)

12.5/(-8) = -1.5625:

Answer: x = -1.5625

7 0
3 years ago
PLEASE ANSWER QUICKLY
wel

Answer:

65 passengers

6 0
3 years ago
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