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4 years ago

Please Help, answer 4 and 5

Mathematics

1 answer:

JulijaS [17]4 years ago

4 0

4. P(25-44) = ((# 25-34) +(#35-44))/(total # 15 and older)
.. = (3714 +4074)/(1313 +3714 +4074 +7757 +9747)
.. = 7788/26605
.. ≈ 0.293

5. Prime numbers in the range 2-12 are 2, 3, 5, 7, 11. Their respective probabilities are 1/36, 2/36, 4/36, 6/36, 2/36. The sum of these is 15/36, ≈ 0.417

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Answer:

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Step-by-step explanation:

Let $\dfrac{a}{b}$ be the original fraction.

If the numerator of a fraction is increased by six, the value of the fraction will increase by one. Hence,

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If the denominator of the original fraction is increased by 36, the value of the original fraction will decrease by one. Hence,

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Add these two equalities:

$\dfrac{a+6}{b}+\dfrac{a}{b+36}=\dfrac{a}{b}+1+\dfrac{a}{b}-1\\ \\\dfrac{a+6}{b}+\dfrac{a}{b+36}=2\dfrac{a}{b}\\ \\\dfrac{a}{b+36}=\dfrac{2a-(a+6)}{b}\\ \\\dfrac{a}{b+36}=\dfrac{a-6}{b}\\ \\ab=(a-6)(b+36)\\ \\ab=ab+36a-6b-216\\ \\36a-6b-216=0\\ \\6a-b-36=0\\ \\b=6a-36$

Substitute it into the first equation:

$\dfrac{a+6}{6a-36}=\dfrac{a}{6a-36}+1\\ \\\dfrac{a+6}{6(a-6)}=\dfrac{a}{6(a-6)}+1\\ \\a+6=a+6(a-6)\\ \\a+6=a+6a-36\\ \\6a=6+36\\ \\6a=42\\ \\a=7\\ \\b=6\cdot 7-36=42-36=6$

Thus, the initial fraction was

$\dfrac{7}{6}$

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