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2 years ago

3. Jorge used 2 packs of pencils in the first 1/3 of the year. At what rate is Jorge using pencils?

Mathematics

1 answer:

ANTONII [103]2 years ago

7 0

Answer:

Jorge is using pencils at a rate of 6 packs a year or a rate of 2 packs every four months.

Step-by-step explanation:

1/3 of a year is four months so that would be 2 packs every four months and if you multiply that by three you’d get 12 month, or one year, and 6 packs of pencils.

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. Katie withdrew a total of $300 from her bank account over the last 5 weeks. How much money did she withdraw each week? Write a

Elodia [21]

Answer:

300/5=60

Step-by-step explanation:

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3 years ago

The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i

kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.

Recall the formula for the sum of consecutive positive integers,

$\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2$

Now,

$1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016$

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

$\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224$

numbers, and their sum is

$\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400$

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1 year ago

Solve the simultaneous equations 5y−4x=8 y+x=7 x= ? y= ?

inna [77]

Answer:

x=3 y=4

Step-by-step explanation:

5(4)=20

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20-12=8

4+3=7

4 0

3 years ago

Read 2 more answers

Raoul has to finish a 473-page book in a week. He decides to read the same number of pages each weekday and 30 extra pages on Sa

hodyreva [135]

Answer:

$59$ pages

Step-by-step explanation:

Variable:

x = number of pages he has to read on a weekday

x + 30 = The number of pages read on Saturday and Sunday

$5x+2(x+30) = 473$

$==> 5x + 2x + 60 = 473$

$==> 7x =413$

$==> x = 59$

Meaning that Raoul has to read 59 pages on Wednesday

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3 years ago

11. If Sally

Delvig [45]

Answer:

0.2

Step-by-step explanation:

Multiply 4/5 and 1/4: Decimal form

.8 • .25

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3 years ago

3. Jorge used 2 packs of pencils in the first 1/3 of the year. At what rate is Jorge using pencils?​

3. Jorge used 2 packs of pencils in the first 1/3 of the year. At what rate is Jorge using pencils?