Math Answers

c. Calculate the confidence level that would be required to have the mean

assembly time estimated up to ±15 seconds assuming the sample size

is 120 minutes.

Given that U

 is a function of x,y

 and z

 and A

 a vector field, prove that:

∇.(UA)=(∇U).A+U(∇.A).

The students of same age group from two different schools were compared for variability in their mathematical skill. A random sample of 25 pupils from one school had a variance of 16 marks while a random sample of 22 pupils from the other school had a variance of 8 marks. Examine if

the difference in variability is significant IF at (24.21) at 5% level of significance

a,Calculate the area under the curve 𝑦 = 𝑥3 + 4𝑥 + 1 from x=-3 to x=3. 5

b) Evaluate: ∫4 𝑥𝑒𝑥 dx.

a) Define tangent and normal of a curve with figure. Also find the equation of tangent and normal of the ellipse (x ^ 2)/4 + (y ^ 2)/16 = 1 at the point (- 1, 3) .

b) Explain maximum and minimum value of a function with graphically. Evaluate maximum and minimum value of the function f(x) = x ^ 3 - 3x ^ 2 + 3x + 1

Suppose we are given a Boolean function f(x, y, z)=(x+y)(x+y)(x+2). Find its DN form

Find the derivatives of the following functions with respect to x.

𝑥³ + 𝑦³ = 3                                                                                                                   

𝑦 = (sin 𝑥)^{𝑡𝑎𝑛𝑥}

Let S = [1,2,4,5,10,20, 25, 50, 100). Then show that 5 forms a lattice under divisibility.

Draw the Hasse diagram also.

Currently, Teddy Inc. manufactures part CD7 used in the production of its product, producing 8,000 units annually. An outside supplier is offering to sell the part to Teddy for RM16. The cost of manufacturing CD7 is as follows:

Direct materials RM9.00 , Direct labour = 3.00, Variable overhead=2.50, Fixed overhead=4.00 and the TOTAL=RM18.50

Of the total overhead assigned to CD7, RM28,000 is direct fixed overhead (i.e. the amount is not needed if the product line is dropped). The remaining fixed overhead is common fixed overhead. There is no alternative use for facilities currently used to produce the part.

a.     Should Teddy accept the offer from the outside supplier? What is the most that Teddy is willing to pay?

b.     Can direct material ever be irrelevant in a make-or-buy decision?

The students of same age group from two different schools were compared for variability in their mathematical skill. A random sample of 25 pupils from one school had a variance of 16 marks while a random sample of 22 pupils from the other school had a variance of 8 marks. Examine if the difference in variability is significant. [F at (24,21) at 5% level of significance is 2.05]