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Maneet Kaur B.

Tutor for eight years having expertise in Statistics

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ACT

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Question:

Given x = 2 and y = 4, by how much does the value of (5x^2 - 2y) exceed the value of (2x^2 - 5y) Option1: 12 Option2: -12 Option3: 24 Option4: -24

Maneet Kaur B.

Answer:

When x = 2 and y = 4, (5x^2 - 2y) = (5*(2^2) - 2*4) = 5*4 - 8 = 20 - 8 = 12 ………(1) When x = 2 and y = 4, (2x^2 - 5y) = (2*(2^2) - 5*4) = 2*4 - 20 = 8 - 20 = -12 ………(2) Ans. Difference (1) - (2) = 12 - (-12) = 12 + 12 = 24 Ans. 24 ( c)

Statistics

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Question:

Calculate the Mean and MAD for the following data: Data set: 3, 4, 2, 1

Maneet Kaur B.

Answer:

We calculate the MAD as considering the average of the differences of the data values from its mean. Mean = (3 + 4 + 2 + 1)/ 4 = 2.5 MAD = (|3 - 2.5| + |4 - 2.5| + |2 - 2.5| + |1 - 2.5|)/ 4 = (0.5 + 1.5 + 0.5 + 1.5)/ 4 = 1 Thus, MAD = 1 Ans. Mean = 2.5 MAD = 1

Algebra

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Question:

The equation is given to be: 4 . (x - 3) + 2x = 6x + a. Find 'a' so that the equation has infinitely many solutions.

Maneet Kaur B.

Answer:

An equation with infinitely many solutions should have the same things on both the sides, regardless of what x should have as the value. We simplify the equation first: 4x - 12 + 2x = 6x + a 6x - 12 = 6x + a 6x - 12 - 6x = 6x + a - 6x -12 = a Thus, a = -12. Ans No matter what x variable would take the value as, a = -12 so that the equation has infinitely many solutions.

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