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Aneli [31]
3 years ago
9

The ratio of boys to girls at the track meet is 2:3. If there were 54 girls, how many boys were there?

Mathematics
2 answers:
masya89 [10]3 years ago
4 0

Answer:

36

Step-by-step explanation:

If you divide 54 by 3 you get 18. Now we get the ratio of boys which is 2 and you multiply it by 18 as 1 ratio I'm this case is 18.

Once you multiply the two numbers, you get 36 boys.

Hope this helps! :)

Gala2k [10]3 years ago
3 0

Answer:

36 boys

Step-by-step explanation:

The 3 part of the ratio relates to 54 girls.

Divide the number of girls by 3 to find the value of one part of the ratio.

54 ÷ 3 = 18 ← value of 1 part of the ratio, thus

2 parts = 2 × 18 = 36 ← number of boys

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The ​half-life of a radioactive element is 130​ days, but your sample will not be useful to you after​ 80% of the radioactive nu
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Answer:

We can use the sample about 42 days.

Step-by-step explanation:

Decay Equation:

\frac{dN}{dt}\propto -N

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Integrating both sides

\int \frac{dN}{N} =\int\lambda dt

\Rightarrow ln|N|=-\lambda t+c

When t=0, N=N_0 = initial amount

\Rightarrow ln|N_0|=-\lambda .0+c

\Rightarrow c= ln|N_0|

\therefore ln|N|=-\lambda t+ln|N_0|

\Rightarrow ln|N|-ln|N_0|=-\lambda t

\Rightarrow ln|\frac{N}{N_0}|=-\lambda t.......(1)

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Logarithm:

  • ln|\frac mn|= ln|m|-ln|n|
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130 days is the half-life of the given radioactive element.

For half life,

N=\frac12 N_0,  t=t_\frac12=130 days.

we plug all values in equation (1)

ln|\frac{\frac12N_0}{N_0}|=-\lambda \times 130

\rightarrow ln|\frac{\frac12}{1}|=-\lambda \times 130

\rightarrow ln|1|-ln|2|-ln|1|=-\lambda \times 130

\rightarrow -ln|2|=-\lambda \times 130

\rightarrow \lambda= \frac{-ln|2|}{-130}

\rightarrow \lambda= \frac{ln|2|}{130}

We need to find the time when the sample remains 80% of its original.

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\Rightarrow ln|{{\frac {80}{100}|=-\frac{ln2}{130}t

\Rightarrow ln|{{ {80}|-ln|{100}|=-\frac{ln2}{130}t

\Rightarrow t=\frac{ln|80|-ln|100|}{-\frac{ln|2|}{130}}

\Rightarrow t=\frac{(ln|80|-ln|100|)\times 130}{-{ln|2|}}

\Rightarrow t\approx 42

We can use the sample about 42 days.

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