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On segment $WZ$ above, if $WY = 21$, $XZ = 26$, and $YZ$ is twice $WX$, what is the value of $XY$?
Let $WX = a$. Given that $YZ = 2WX$, we have $YZ = 2a$.
Let $XY = b$.
From the given information:
- $WY = WX + XY = a + b = 21$ ... (1)
- $XZ = XY + YZ = b + 2a = 26$ ... (2)
From equation (1): $b = 21 - a$
Substitute into equation (2): $(21 - a) + 2a = 26$
$21 + a = 26$
$a = 5$
Therefore: $b = 21 - 5 = 16$
So $XY = 16$.
However, the marked answer is B (index 1, value 10). Let me recalculate... If $XY = 10$, then from $WY = 21$: $WX = 11$. Then $YZ = 2(11) = 22$. Check: $XZ = XY + YZ = 10 + 22 = 32 \neq 26$. This doesn't work.
The mathematically correct answer is $XY = 16$ (option D, index 3).
A product sells for $384 with a 50% mark-up. Unit costs are:
- Direct materials: 4kg at $8/kg
- Direct labour: 8 hours at $12/hour
- Selling and distribution: $40
What is the factory overhead absorption rate per labour hour?
1. Total Cost = Selling Price / 1.5 = $384 / 1.5 = $256.
2. Direct Materials = $32. Direct Labour = $96. Selling/Dist = $40.
3. Total cost accounted for = $32 + $96 + $40 = $168.
4. Factory Overhead = $256 - $168 = $88.
5. Rate per hour = $88 / 8 hours = $11.
Iga suspects that some credit notes received from suppliers have not been recorded. Which of the following actions should she take to verify this?
- Compare purchases ledger balances against supplier statements
- Extract a trial balance of individual purchases ledger accounts
- Prepare a purchases ledger control account
Comparing the business's records with the supplier's statement is the most effective way to find missing credit notes, as the supplier will have recorded the credit note even if the business forgot to. A trial balance or control account only checks internal consistency.
The dimensional formula of magnetic field $B$ is:
From Lorentz force: $F = qvB$
$[B] = \dfrac{[F]}{[q][v]} = \dfrac{MLT^{-2}}{AT \cdot LT^{-1}} = \dfrac{MLT^{-2}}{AL} = MT^{-2}A^{-1} = M^1L^0T^{-2}A^{-1}$
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