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3 years ago

When the smaller of two consecutive integers is added to two times the larger, the result is 35. Find the integers.

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

4 0

x+2(x+1)=35

x+2x+2=35

3x=35-2=33

x=33/3=11

smaller number=11

larger number=11+1=12

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Answer:

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Step-by-step explanation:

The (1 - α)% confidence interval for the population standard deviation is:

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The information provided is:

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$\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.10/2, (26-1)}=\chi^{2}_{0.05, 25}=37.652$

$\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.10/2, (26-1)}=\chi^{2}_{0.95, 25}=14.611$

*Use a Chi-square table.

Compute the 90% confidence interval for the population standard deviation waiting time for an oil change as follows:

$CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}$

$=\sqrt{\frac{(26-1)\times 4.8^{2}}{37.652}}\leq \sigma\leq \sqrt{\frac{(26-1)\times 4.8^{2}}{14.611}}\\\\=3.9113\leq \sigma\leq 6.2787\\\\\approx 3.9 \leq \sigma\leq6.3$

Thus, the 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).

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When the smaller of two consecutive integers is added to two times the​ larger, the result is 35. Find the integers.

When the smaller of two consecutive integers is added to two times the larger, the result is 35. Find the integers.