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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.
Language Development Milestones:
| Age | Expected Language |
|---|---|
| 2 months | Coos, social smile |
| 6 months | Babbles (ba, da, ma) |
| 9 months | Mama/dada (non-specific) |
| 12 months | 1โ3 meaningful words (mama, dada specific) |
| 18 months | Minimum 10โ20 words; points to body parts |
| 24 months | 2-word phrases; 50+ words |
| 3 years | 3-word sentences; strangers understand ~75% |
Red flag at 18 months: No single words = speech delay โ requires formal evaluation.
Critical distinction:
- This child maintains eye contact, points, plays peek-a-boo = social development intact โ less likely autism
- Speech delay without social communication deficits suggests: hearing loss, expressive language delay, bilingual exposure, or oral-motor issues
First step: Formal hearing test (audiometry) โ hearing loss is the most common correctable cause of speech delay. Concurrent speech-language evaluation.
Reassurance without evaluation at 18 months is inappropriate โ early intervention improves outcomes significantly.
A stone is dropped from rest from the top of a $20\text{ m}$ tower. Its speed on hitting the ground is ($g = 10\text{ m/s}^2$):
Using $v^2 = u^2 + 2gh = 0 + 2(10)(20) = 400$
$v = \sqrt{400} = \mathbf{20\text{ m/s}}$
For a projectile launched along a smooth inclined plane, the range along the incline is: $x = \dfrac{2u^2\sin(\theta-\alpha)\cos\theta}{g\cos^2\alpha}$, where $\alpha$ is the incline angle and $\theta$ the launch angle from horizontal.
When the projectile is fired along the incline: $\theta = \alpha$, so $\sin(\theta-\alpha) = 0$... Using the general formula and applying both cases gives $x_1 : x_2 = \mathbf{1:\sqrt{3}}$.
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