A female cockroach makes 9 oothecae in her life…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A female cockroach makes oothecae in her life. Each ootheca holds eggs. In a model, of the eggs become adults.
- How many eggs does she lay?
- How many adults do you expect from these eggs?
- What is the smallest whole number of oothecae, with eggs each, that gives at least eggs?
Need a reminder? The key ideaShow
The cockroach has separate sexes. The male has a pair of testes, vasa deferentia, a seminal vesicle and an ejaculatory duct. The sperms are packed in bundles called spermatophores. The female has a pair of ovaries, each with eight ovarioles, a genital chamber and a pair of spermathecae. The fertilised eggs are enclosed in capsules called oothecae. A female produces about nine to ten oothecae, each with about fourteen to sixteen eggs. The young nymph resembles the adult and grows by moulting about thirteen times. The earthworm is hermaphrodite with a closed blood system and breathes through its moist skin. The frog has a three-chambered heart, breathes through skin, mouth and lungs, and fertilises its eggs outside the body.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. oothecae, eggs in each, and a survival share of (a made up value).
Plan. Count the eggs. Take the share. Find the smallest whole number of capsules.
Step 1. Eggs. .
Step 2. Adults. . This is an expected value, so it need not be a whole number.
Step 3. The fewest capsules. , so capsules are needed. Check: is too few, and is enough.
Answer: eggs; adults; oothecae.
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