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NEW QUESTION 30
Identify which of the following is not true about the population variance of a set of data.

Its positive square root gives the standard deviation

It can be calculated as

It is represented by the symbol

It can be calculated as

NEW QUESTION 31
Calculate

399.68

58.88

951.84

337.84

NEW QUESTION 32
Consider the function f(x) =x2- 5x – 3
The value of one of the roots of the above equation can be obtained by using the iteration formula

Apply the iteration formula to determine the value of the root.

0.54

4.40

5.53

1.54

NEW QUESTION 33
Determine the stationary point(s) for the following function

Minimum at x = -1 and maximum at x = -3.

Maximum at x = 1 and maximum at x = 3.

Minimum at x = -3 and maximum at x = -1.

Minimum at x = 1 and minimum at x = 3.

NEW QUESTION 34
Consider the function f(x)x2 6x=20. This functions has a stationary point at x=3.
Determine the nature of this stationary point and how we know this to be true.

It is a minimum stationary point because the second derivative of the function with respect to x takes the value 2 which is positive.

It is a maximum stationary point because the value of the function at x = 3 is 11, which is positive.

It is a minimum stationary point because the value of the function at x = 3 is 11, which is positive.

It is a maximum stationary point because the second derivative of the function with respect to x takes the value 2, which is positive.

NEW QUESTION 35
The volume of a cone can be determined by summing up the infinitesimal circular cross-sections of the cone across the length of the cone Consider the function f(x) = x2 for x contained in [0,1].

Now consider an infinitesimal circular cross-sectional element of width dx and radius r = f(x) Determine the volume of the cone enclosedby the function f(x) by considering the volume of each circular cross-sectional element (Recall thatthe sum of infinitesimal elements can be represented as an integral Recall also that the area of a

circle is
A)

B)

C)

D)
1

Option A

Option B

Option C

Option D

NEW QUESTION 36
Evaluate

NEW QUESTION 37
The distribution of test scores from a recent clinical drug study have been tabulated below.
Determine i) whether the distribution of test scores are symmetric positively skewed or negatively skewed, and ii) the sample median value.

i) Positively skewed, ii)

i) Symmetric, ii) 4

i) Positively skewed, ii) 3

i) Negatively skewed, ii) 3

NEW QUESTION 38
Two real numbers, x and y, satisfy the following inequalities:

Determine which statement is true.

y must be positive.

y can be negative.

y cannot be negative.

y cannot be zero.

NEW QUESTION 39
Differentiate with respect to X:

A)

B)

C)

D)

Option A

Option B

Option C

Option D

NEW QUESTION 40
Identify which of the following statements is correct.

x in(n)

In(x)+ in(n)

n in (x)

In (nx)

NEW QUESTION 41
The particular solution of the second-order difference equation

Determine the values of(A, B).

(-2,5)

(5,-2)

(-2, 3)

(-3, 2)

NEW QUESTION 42
Identify the necessary and sufficient condition under which the quadratic equation ax2+ 2a2x + a3= 0 hasone repeated real root.

a>0

a = 0

a<0

NEW QUESTION 43
Let a and b be two positive numbers and let m and n be two positive integers.
Identify which of the followingequalities is false.
A)

B)

C)

D)

Option A

Option B

Option C

Option D

NEW QUESTION 44
Identify which of the following non-terminating geometric series converge, for values of x such that 1 < x < 2.

I, II and IV

II and IV

II, III and IV

I and IV

NEW QUESTION 45
Calculate the sum of the following series: 3, -6,12, -24,…, -1.536.

3,069

-1,023

-3,833

-60

NEW QUESTION 46
A set of 17 observed values is being studied.
Identify which of the following statements is/are true.
I The median must be equalto one of the observed values.
II. The mean could be different from all of the observed values.
Ill If the observations are positively skewed, then the mean is less than the median IV. More than one mode is not possible.

II and IV only

I and II only

III only

I only

NEW QUESTION 47
A national newspaper wants to publish the results of a survey showing people’s preferences for different types of sandwiches. Identify which of the following ways of publishing the survey results is likely to be the least useful to its readers.

Table of data

Pie chart

Bar chart

Box plot

NEW QUESTION 48
Identify which of the following statements is correct.

is greater than x

is less than x

is equal to x.

can be greater than or less than x.

NEW QUESTION 49
Identify which of the following statements is not true about the probability density function of a continuous random variable.

It could be greater than 1.

It must be non-negative.

Integrating it across its domain must produce an answer of 1.

Differentiating it gives the cumulative distribution function.