Out of 100 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:
(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.
(ii) Mix the samples within each set and test the mixed sample for covid.
(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.
(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.
Given this strategy, no more than __________ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.
A 100 cm $$\times$$ 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm $$\times$$ 1 cm.
The total number of creases visible when the sheet is unfolded is __________.
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.
The ratio of the area of the regular convex to the area of the original equilateral triangle is