A cube is dilated by a scale factor of 0.75 to create a new cube. The surface area of the new cube is…
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Use the shell method. The volume is
<em>V</em> = 2<em>π</em> ∫₅⁸ (<em>x</em> - 5) <em>x</em> ² d<em>x</em>
<em>V</em> = 2<em>π</em> ∫₅⁸ (<em>x</em> ³ - 5<em>x</em> ²) d<em>x</em>
<em>V</em> = 2<em>π</em> (1/4 <em>x</em> ⁴ - 5/3 <em>x</em> ³) |₅⁸
<em>V</em> = <em>π</em>/6 (3<em>x</em> ⁴ - 20<em>x</em> ³) |₅⁸
<em>V</em> = <em>π</em>/6 ((3 × 8⁴ - 20 × 8³) - (3 × 5⁴ - 20 × 5³))
<em>V</em> = 891<em>π</em>/2
Answer:
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Step-by-step explanation:
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The r value is 0.373 (low). This implies a weak correlation between the dependent and independent variables for this sample.
The overall p- value for the regression model is 0.0017. This implies that at least one of the two independent variables (x1 or x2) in the model is significant predictor of the dependent variable y.
p- values for the both "Fact" and "Star" are < 0.05. This means both the independent variables are significant predictors of the "Rating" at 95% confidence level. The variable "Fact" is significant at 99% level of confidence also. This means the rating viewers award to a movie depends upon both the storyline (fact or Fiction) and the presence or absence of stars.
Expected rating for a fact based movie with no stars = 1.7991(1) + 1.2586(0) + 12.5685 = 14.37
Expected rating for a fiction based movie with a star = 1.7991(0) + 1.2586(1) + 12.5685 = 13.83
So, one may expect a fact based movie without any stars to get better ratings than a fiction based movie with one star.
