Quantitative Methods Answers

Determine the amount of an immediate annuity of N$200 per annum left unpaid for 10 year at 7% p.a compounded interest.

Consumption of sugar-sweetened beverages has increased over the years. Individuals aged 17-20, were surveyed in 2020 across the 10 provinces to determine the number of calories consumed by sugar-sweetened beverages. The average consumption for 17-20-year-old in Canada is 298 calories. You decide to test if the average calorie consumption for students at John Abbott will be less than the national average. You select a random sample of 35 students and your results show that the average sugar-based calorie consumption is 𝑋" = 280, s=18. Do John Abbott students consume significantly fewer sugar-sweetened calories? Set alpha to 0.01 Find Null and research hypothesis 1 or 2 tailed? Find critical value? find test statistic?

Find the inverse of the following Matrix using Gauss Jordan method

1 2 3 0

2 4 3 2

3 2 1 3

6 8 7 5

Find the smallest positive root by using the bisection method

2sin(2x)+2x^3-5

with 3 decimal plates

2- The longitudinal extension of metal bar in direction of an applied force is

given by

y = LKeF×1×10−3

Where y is the longitudinal extension in m, L is the length of the bar in m which

is L= 0.15 (m), K is a constant depends on the material and is K= 1, and F is applied

force in N.

a) Find the work done if the force increases from 100 N to 500 N using:

i) An analytical integration technique

ii) A numerical integration technique (n=8 intervals)

[Note: the work done is given by the area under the curve]

b) Using a computer spreadsheet and recalculates step (ii) by increasing

the number of intervals to n=10 and compare your obtained results

with (i) and (ii)

c) Using Simpson’s rule to find the work done (n=8).

d) Analyse whether the size of numerical steps has effect on the obtained

result and explain why.

Determine numerically the first derivative of function tabulated below,

at the point x=4

x: 1 2 4 8 10

y=f(x):0 1 5 21 27

The difference in hours between​ full-timers and the​ part-timers who work 6 hours a day is 5 working hours. How many hours per day do​ full-timers work?

For a p-value of 0.0052, test your hypothesis using .01 as the level of significance

Select one:

a. I reject Hnull

b. I fail to reject Hnull

c. Neither

x2-2x-3=0 for the positive root by iteration method.

solve the following question by using bisection method.

correct to the four decimal places.

x² ⁻ 3 = 0