Search
Qn 5. In a scalene triangle whose sides have lengths a, b and c, consider
the bisector r of the angle formed by a and b. Compute, providing your
working based on Euclidean geometry, the ratio between the lengths of the
two segments that the bisector r determines on the side of length c when
intersecting it.
A firm employs 300 women and 100 men. The mean number of days absent last year for the women was 5.3 with a s.d. of 2.2 and for the men the corresponding figures were 6.2 and 2.9. Is the difference between the means significant at 5% level of significance?
Qn 1. An integer N has digital representation a1a2a3. Moreover,
None of the digits a1, a2, or a3 and none of the numbers with digital
representation a1a2, a1a3, or a2a3 is divisible by 3.
N is odd.
N is divisible by 9.
a1 ≥ a2 ≥ a3.
Determine all possible numbers N.
Qn 6. Let A, B, C and D be four points on a circle, taken in such a way that
the segments AC and BD have an intersection E. If AE = πDE, compute,
providing your working, the ratio between the areas of the triangles △AEB
and △CED, that is,
A(△AEB)
A(△CED)
find the angle of qrts in parallelogram if q is 104 degrees and s is 49
1. Each main bearing cap in an engine contains 4 bolts. The bolts are selected at random without replacement from a parts bin that contains 30 bolts from one supplier and 70 bolts from another.
a.
b. What is the probability that a main bearing cap contains all bolts from the same supplier?
c. What is the probability that exactly 3 bolts are from the same supplier?
1. The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes.
a. What is the probability that a battery lasts more than four hours?
b. What are the quartiles (the 25% and 75% values) of battery life?
c. What value of life in minutes is exceeded with 95% probability?
Let T be a random variable giving the number of heads plus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value.
Two cards are drawn from a deck. How many possible values can each of the following variables take?
1. sum of the numbers on the cards ___________
2. number of times both cards are black ________
3. Number of times both cards are 7s ___________
4. Number of times the first card is six and the second card is red _____
5. Number of times the first card is face card and the second card is not
a face card _______
