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Ivahew [28]
3 years ago
8

In the small hamlet of abaze, two base systems are in common use. also, everyone speaks the truth, and no one changes which base

they are using in mid-sentence. one resident said, "26 people use my base, base 10, and only 22 people speak base 14." another said, "of the 25 residents, 13 use both bases and 1 can't use either base." how many residents are there? (use base 10, please!)
Mathematics
2 answers:
meriva3 years ago
8 0
Alright, "<span>of the 25 residents", bingo, we have it, 25
wait, 26 people use my base?, wat

ok, so um

anyway, 13 use both, so 13 of the 26 using base 10 are also in the 22 using base 14
so
26+22-13=35 people using bases
and then there is 1 resident not using anything
35+1=36

36 residents



wait, we had 'of the 25 residents, 13 use both and 1 can't use either'
what happened to the other 11, maybe they are using one or the other?

I say 36 residents
</span>
ollegr [7]3 years ago
8 0

Suppose that the first resident speaks in base $B$. Converting to base $10$, his statement implies that $2B + 6$ people uses base $B$ (notice that base $10$ is actually base $1 \cdot B + 0 = B$), and that $2B+2$ people speak using base $B + 4$. Clearly, the second resident is not talking in base $B$, so he must speak base $B + 4$. Then we can also write all of his statements in terms of the variable $B$. It follows that there are $2(B+4) + 5 = 2B + 13$ total residents, of which $(B+4)+3 = B+7$ are bilingual and $1$ cannot use either base. By the Principle of Inclusion-Exclusion, there are $$(2B + 6) + (2B+2) + 1 - (B+7) = 3B + 2$$total people, and setting this equal to $2B + 13$, it follows that $3B + 2 = 2B + 13 \Longrightarrow B = 11$. Thus, the answer is $2B + 13 = 2 \cdot 11 + 13 = \boxed{35}$.

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Answer:

27.0000

Step-by-step explanation:

27.2163 rounded to the nearest hundredth is 27.0000 or 27 because the hundredth place held a 1 and 5 or above rounds up and 4 or below rounds down. The .2163 turned into zeros because the second number (the hundredths place) was a 1 so it rounded down, and hen it rounds down, all the numbers round to 0.

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Answer:

1.5 gallons of juice

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Step-by-step explanation:

4 0
3 years ago
Find three consecutive even integers such that the sum of the first, twice the second, three times the third is -76. What is the
ss7ja [257]

Answer:

The numbers are -14,-13 and -12

Step-by-step explanation:

<u><em>The correct question is </em></u>

Find three consecutive integers such that the sum of the first, twice the second and three times the third is -76. What is the number?

Let

x ----> the first consecutive integer

x+1 ---> the second consecutive integer

x+2 ---> the third consecutive integer

we have that

x+2(x+1)+3(x+2)=-76

solve for x

apply distributive property

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Combine like terms

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subtract 8 both sides

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so

x+1=-14+1=-13

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okok so the answer is

Step-by-step explanation:

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Hope this helps :)

4 0
3 years ago
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