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All of the previous questions used what we know as Euclidean geometry.
There are other geometries. One such is spherical geometry.
What can you say about the sum of the interior angles of a triangle in spherical geometry?
TOTAL
This question is concerning the completion of the square by using plane geometry
The area of a square of length x is : x
2
The area of a rectangle of sides x and y is : xy
Consider the expression : x
2 + 10x
Such can be considered as the sum of two areas viz square x
2 and a rectangle 10x
Now do the following (sketch essential)
Divide the rectangle into two equal areas viz 5x and 5x
Next to the square place the two rectangles with the side x in common. One to the RHS and the other below.
You will now have a ’nearly complete’ square
a) What is the length of each side of the ’missing square’ in your diagram
b) If you add the area of the missing square to make a big square, what is the area of the complete (big) square
c) By using the areas from your sketch, find the expressions ? and ?? in the following:
x
2 + 10x + (?)2 = (??)2
A travel agency receives an average of 150 calls per hour (time between calls are exponentially distributed). It takes an operator an average of 5 minutes to handle a call (exponentially distributed). If a caller gets a busy signal, the travel agency assumes that he or she will call a competitor, and the travel agency will lose an average of $50 in profit. The cost of keeping a phone line open is $12 per hour. How many operators should the travel agency have on duty?
i. Suppose that a unit of sugar is priced at R5 and the price of a unit of salt is R10.
Compute the weighted marginal-utility for sugar and salt and enter these values in
the table.
[04]
ii. Given Kagiso’s R30 budget, how many units of sugar and salt will be purchased?
Explain how you arrived at this answer.
[02]
iii. Suppose the price of salt stays constant at R10 and the price of sugar falls to R3.
How many units of sugar will be demanded at this price? Carefully explain your
reasoning.
[03]
Sonja Cc is a small firm that makes outfits for customers tailored for their functions, in May 2021 she has ordered for a bridal party (BP)
The details for the job (BP) are as follow:
Direct materials: 10 units at N$108.
Direct labour: 16 hours for department A
10 hours for department B
14 hours for department C
The labour hours are budgeted at 40, 25 and 30 in departments A, B and C respectively.
The firm expect a profit of 40% on the total cost of BP.
Required:
a)Calculate the predetermined overhead allocation rate (OAR) for each department using labour hours as a base for such allocation.
b)Calculate the cost of a bridal party (BP)
c)Calculate the selling price of the bridal party (BP).
Calculate the potential of a cell where the Al3+ concentration is only 0.10 M.
2 Al (s) + 3 Cu2+ (aq, 1.0 M) → 2 Al3+ (aq, 1.0 M) + 3 Cu (s)
A store donated a lot of 8 computer sets that includes 3 which are malfunctioning or defective. If 4 of this computer sets are chosen at random for delivery to a school.
i) What will be the probability mass function of a random variable 𝑌?
ii) What will be the expected value of 𝑌?
For each fixed λ > 0, let X have a Poisson distribution with parameter λ. Suppose λ
itself is a random variable with the gamma distribution
f(λ) =
1
Γ(n)
λ
n−1
e
−λ
, λ ≥ 0
0, λ < 0
where n is a fixed positive constant. Show that
P(X = k) = Γ(k + n)
Γ(n)Γ(k + 1)
1
2
k+n
, k = 0, 1, 2
I’m economic theory, a clear distinction is made between a movement along the demand curve and a movement of the demand curve. I’m light of this statement, provide the correct graph to illustrate and explain an increase in the price of the product
What's the best way of finding percentage composition of a substance contributed by each element?
