Evaluate the Following Iterated Integral $\int_{0}^{\pi /15}\int_{0}^{\pi/15}\int_{0}^{cos\theta}\rho^{2} \sin \phi \cos \phi d \rho d \theta d \phi$

question 46

Multiple Choice

Evaluate the following iterated integral.
$\int_{0}^{\pi /15}\int_{0}^{\pi/15}\int_{0}^{cos\theta}\rho^{2} \sin \phi \cos \phi d \rho d \theta d \phi$

• A) \(\frac { 1 } { 36 } \left( 5 + \cos \frac { 2 \pi } { 15 } \right) \sin ^ { 3 } \frac { \pi } { 15 }\)
• B) \(\frac { 1 } { 6 } \left( 5 + \cos \frac { 2 \pi } { 15 } \right) \sin ^ { 3 } \frac { \pi } { 15 }\)
• C) \(\frac { 1 } { 6 } \left( 3 + \cos \frac { 2 \pi } { 15 } \right) \sin ^ { 2 } \frac { \pi } { 15 }\)
• D) \(\frac { 1 } { 36 } \left( 5 + \cos \frac { \pi } { 15 } \right) \sin ^ { 3 } \frac { \pi } { 15 }\)
• E) \(\frac { 1 } { 36 } \left( 5 + \cos \frac { 2 \pi } { 15 } \right) \sin ^ { 2 } \frac { \pi } { 15 }\)

Understand the purpose and application of one-way ANOVA in testing whether the means of several groups are equal.

Calculate and interpret the F-test statistic and the corresponding p-value in one-way ANOVA.

Identify the conditions under which one-way ANOVA is appropriate to use.

Explain the role of treatment and error sum of squares in one-way ANOVA.

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