Exercise 12.1 a. Consider the series 1.2+2·3+34+ ..+n· (n +1) = k(k + 1). k=1 Show that Ek(k +1) = n(n+ 1)(n + 2) 3 k=1 by induction.

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A: The given figure

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A: The equation is given by 12-19d=17

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Q: : : 2. Find the area above the x-axis bounded by the function f(x) = -x² + 2x + 3 and the x-axis.

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Q: 2x2 + 16x +30 Find the horizontal and vertical asymptotes of the curve y x2 +x - 20

A: Horizontal and vertical asymptotes

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A: Given- Consider the following data:  x -1.1 4.0 2.5 3.0 -1.3 1.1 5.1 y 2.1 4.6 3.2 1.9 12.1 8.1…

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A: Apply Vertical Line Test,

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A: In this question, we will see how many students brought both a backpack and a lunchbox.

Q: Show that the equality [r + y] = [2] + [y] is not valid for all real numbers r and y.

A: Consider the provided question, We first define ceiling function. The ceiling function maps x to the…

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Q: Show clear steps please.

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A: 6.1)Given  x P(x) 0 0.05 1 0.15 2 0.45 3 0.35

Q: 1. Factor. 27x3у — 8y

A: Given, 27x3y-8y  We have to factor it.

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A: Concept:

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.