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irina1246 [14]
3 years ago
11

How do you do this question?

Mathematics
1 answer:
Luda [366]3 years ago
8 0

Answer:

∫ₑ°° 1 / (x (ln x)¹⁰) dx

∫₁°° x⁻³ dx

Step-by-step explanation:

A p-series 1 / xᵖ converges if p > 1.

∫ₑ°° 1 / (x (ln x)¹⁰) dx

If u = ln x, then du = 1/x dx.

When x = e, u = 1.  When x = ∞, u = ∞.

= ∫₁°° 1 / (u¹⁰) du

p = 10, converges

∫₁₀°° x^(-⅔) dx

= ∫₁₀°° 1 / (x^⅔) dx

p = ⅔, diverges

∫₁°° 2 / x^0.5 dx

= 2 ∫₁°° 1 / x^0.5 dx

p = 0.5, diverges

∫₁°° x⁻³ dx

= ∫₁°° 1 / x³ dx

p = 3, converges

∫₂°° 1/(3x) dx

= ⅓ ∫₂°° 1/x dx

p = 1, diverges

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a) For this case we can use the definition of weighted average given by:

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Step-by-step explanation:

Assuming the following question: "One sample has a mean of M=8 and a second sample has a mean of M=16 . The two samples are combined into a single set of scores.

a) What is the mean for the combined set if both of the original samples have n=4 scores "

For this case we can use the definition of weighted average given by:

M = \frac{ \bar X_1 n_1 + \bar X_2 n_2}{n_1 +n_2}

And if we replace the values given we have:

M = \frac{8*4 + 16*4}{4+4}= 12

b) what is the mean for the combined set if the first sample has n=3 and the second sample has n=5

Using the definition we have:

M = \frac{8*3 + 16*5}{3+5}= 13

c) what is the mean for the combined set if the first sample has n=5 and the second sample has n=3

Using the definition we have:

M = \frac{8*5 + 16*3}{5+3}= 11

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