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Goshia [24]
3 years ago
7

Tom was selling his old games. He started out with 57 but sold 37 of them. He put the rest in boxes with 5 games in each. How ma

ny boxes did Tom have to use?
Mathematics
1 answer:
eduard3 years ago
8 0

Answer:

Tom started out with 57 games but sold 37 of them.

=> Now, Tom has: 57 - 37 =20 games

He put the rest in boxes with 5 games in each.

=> The number of boxes: 20/5 = 4 box

Hope this helps!

:)

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Find the sum of the positive integers less than 200 which are not multiples of 4 and 7​
taurus [48]

Answer:

12942 is the sum of positive integers between 1 (inclusive) and 199 (inclusive) that are not multiples of 4 and not multiples 7.

Step-by-step explanation:

For an arithmetic series with:

  • a_1 as the first term,
  • a_n as the last term, and
  • d as the common difference,

there would be \displaystyle \left(\frac{a_n - a_1}{d} + 1\right) terms, where as the sum would be \displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n).

Positive integers between 1 (inclusive) and 199 (inclusive) include:

1,\, 2,\, \dots,\, 199.

The common difference of this arithmetic series is 1. There would be (199 - 1) + 1 = 199 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}.

Similarly, positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 4 include:

4,\, 8,\, \dots,\, 196.

The common difference of this arithmetic series is 4. There would be (196 - 4) / 4 + 1 = 49 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}

Positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 7 include:

7,\, 14,\, \dots,\, 196.

The common difference of this arithmetic series is 7. There would be (196 - 7) / 7 + 1 = 28 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}

Positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 28 (integers that are both multiples of 4 and multiples of 7) include:

28,\, 56,\, \dots,\, 196.

The common difference of this arithmetic series is 28. There would be (196 - 28) / 28 + 1 = 7 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}.

The requested sum will be equal to:

  • the sum of all integers from 1 to 199,
  • minus the sum of all integer multiples of 4 between 1\! and 199\!, and the sum integer multiples of 7 between 1 and 199,
  • plus the sum of all integer multiples of 28 between 1 and 199- these numbers were subtracted twice in the previous step and should be added back to the sum once.

That is:

19900 - 4900 - 2842 + 784 = 12942.

8 0
3 years ago
Five members of the soccer team and five members of the track team ran the 100-meter dash. Their times are listed in the table b
Sonbull [250]
Soccer : (12.3 + 13.2 + 12.5 + 11.3 + 14.4) / 5 = 63.7 / 5 = 12.74
track : (12.3 + 11.2 + 11.7 + 12.2 + 13.7) / 5 = 61.1 / 5 = 12.22

difference is : 12.74 - 12.22 = 0.52 <=
3 0
3 years ago
Read 2 more answers
Can u pls help me with this thanks
aleksandrvk [35]

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7 0
3 years ago
Which is larger?<br> 7% or 0.7 and explain how you know.
disa [49]
They are equal because you can measure the percentage as a decimal with a maximum of 1.
7 0
3 years ago
Read 2 more answers
Solve using elimination. –8x + 6y = –16 –8x + 9y = 8
stira [4]
I think this is right

5 0
3 years ago
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