Answers to assignments 323
spend up to $50.29 without increasing
the bill.
3 D is not possible as there is no subject
from the third column.
4 34¢ can be made up as 22¢ + 9¢ + 2¢ + 1¢;
any other combination needs at least one
more denomination. 67¢ can be made up
as 3 × 22¢ + 1¢, so no extras are needed.
$1.43 can be made up as 6 × 22¢ + 9¢ +
2¢, so four denominations are needed in
total: 22¢, 9¢, 2¢ and 1¢.4.1 Inference
2 There are a number of clues that you
could have noted. One is that the
two people are walking in opposite
directions. Look at their knees if you
missed this point. This fact makes D
quite implausible. C is not impossible,
i.e. that the contact between L’s hand
and the bag is accidental; but if you look
closely at L’s fingers, it would be unlikely
that his or her hand would be in that
position unintentionally. The position
of L’s fingers also make it less likely
that L was reaching into the bag; more
likely that he or she was grasping it. A is
therefore a more plausible explanation
than B.
A is probably the most plausible of
the four suggestions, but is it the best
possible explanation? It is hard to see
what else might be going on, and A is
not far-fetched. People do, unfortunately,
snatch bags. R is carrying the bag
carelessly, and it would be very easy
for L to pull it off R’s shoulder and run.
R has no grip on it that we can see.
Our answer is, therefore, that A is a
reasonable conclusion to draw. However,
you may have a better explanation.
There is no right or wrong answer:
what matters is that you made full use
of the information, and did not jump
to conclusions without being able to
give good reasons using the evidence
available.It is not trivial to generate a mathematical
formula or rule from a graph, but a useful first
step would be to reverse the above process and
generate the table from the graph. We can
then identify what the price of one item is,
and then the unit price of each subsequent
item bought. Offers such as ‘buy two, get one
free’ will generally produce cyclic graphs like
that shown in the first example. Offers such as
‘20% off if you spend over $20’ will give a
discontinuity in either the value or the
gradient of the graph. Such observations may
help to identify the nature of the offer.
3.12 Making choices and decisions
1 If you have a score of 17, the possible
outcomes (only allowing one more
throw) are:
No extra throw Win 3One extra throw 1 Win 32 Win 63 Win 84 Win 105 Lose 46 Lose 4Averaging the outcomes with the extra
throw (all scores are equally possible):
(3 + 6 + 8 + 10 − 4 − 4)/6 =^196 , so the
average is a win of just over 3. The score
with no extra throw is a win of 3, so it is
marginally better to throw again.
2 If Clyde spends $29.99, he will get a 2¢
voucher that will save him 60¢ on petrol,
so his effective spend is $29.39. Any
spend over $30 in the shop will get him
a 3¢ voucher, saving him 90¢ on petrol,
so he can spend up to $30.29 (an extra
30¢) without increasing his overall bill.
Similarly, if he spends $49.99, he could