Math Answers

the weights of 1000 children have average of 45 kilograms and a standard deviation of 5 kilograms, how many children weight 35 kg to 55 kg

A sample of 25 elements from a normally distributed population is selected.the sample mean is 10.assuming a population standard deviationog 4, determine the 95%confidence interval for mean ?

A wallet contains a Php 20-bill, a Php 50-bill, and a Php 100-bill. A bill is taken out from the wallet and then replaced with a bill of the same amount that was taken away. If a bill is taken out from the wallet, what is the probability that the sum of the bill is more than Php 40?

a)     A sole trader fixes his prices to achieve a gross profit percentage on sales revenue of 40%. All his sales are

for cash.  He suspects that one of his sales assistants is stealing cash from sales revenue.

His trading account for the month of June 20X3 is as follows:

$

Recorded sales revenue 181,600

Cost of sales 114,000

Gross profit    67,600

Assuming that the cost of sales figure is correct, how much cash could the sales assistant have taken?  (3 marks)

b) The profit earned by a business in 20X7 was $72,500. The proprietor injected new capital of $8,000 during

the year and withdrew goods for his private use which had cost $2,200.

If net assets at the beginning of 20X7 were $101,700, what were the closing net assets? (3 marks)

c) Explain the uses of cash flow statements. (4 Marks)

d) Outline and explain the three types of capital reserves. (6 Marks)

e) Explain using examples the various categories of financial ratios. (4 Marks)

13.Solve the recurrence relation using generating function , a_n-9a_n-1+20a_n-2=0 for n greater than or equals to 2 with initial values a₀=-3, a₁=-10.

John is offering chocolates at a Plaza. The experimental probability of a randomly chosen shopper accepting a sample is 10%. The conditional probability of a customer purchasing some chocolates given that he/she tried the sample is 18%. No one buys the chocolate without trying the sample. IF John offers 600 people chocolate samples, how many sales will he make?

12. Solve the recurrence relation a_n=a_n-1+n²,where a₀=7 by substitution

11. For arbitrary constants c₁,c₂, And c₃ show that a_n=c₁2ⁿ+c₂5ⁿ+c₃n5ⁿ satisfies the recurrence relations a_n-12a_n-1+45a_n-2-50a_n-3=0

8. Find a generating function for the sequence (a₀, a₁,....a_r.....), where ar=the number of non negative integral solutions to e₁+e₂ +....e_n=r where 0 less than or equal to e₁ less than or equal to 1 for each i=1,2,3,.....n

Convert to the following decimal fractions to the form a\b where a and b€Z`b

1.3.1 0.1250

1.3.2 0.5

1.3.3 1.25

1.3.4 0.31