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Tay-Sachs disease is an inherited disease that is caused by a recessive allele. If a man and his wife, who are both carriers, have three children, what is the probability of each of the following? Show your calculations and give your answers as fractions.




a) All their three children do not have the disease.




d) At least one child is phenotypically normal without the disease.




b) One or more of their three children have Tay-Sachs disease.




c) All three children have the Tay-Sachs disease.

A CAPE Chemistry student sought to determine the solubility product, Ksp of calcium hydroxide by titrating saturated solution of Ca(OH)2 against standardized hydrochloric acid solution, HCl. The saturated Ca(OH)2 solution was filtered, to remove excess solute, and 25mL aliquots were titrated against 0.10M HCl solution using bromothymol blue indicator.


State the colour change the student observed as the end-point was reached. 

Calculate the concentration of Calcium Hydroxide.


Write the Ksp expression for Ca(OH)2.

Use the equilibrium expression for the dissolution of Ca(OH)2 to determine the concentration of Ca2+ and OH–.


Calculate the Ksp for calcium hydroxide (state the units).


The value the student calculated deviated significantly from the accepted value. The reason given was 

‘some of the excess solute got into the filtrate during filtration of the saturated calcium hydroxide’.


State how this could have affected the Ksp value.


State one other factor that could have affected the Ksp value.



Given the following function in two variables x and y


f(x, y) = x3y + 2x4 + y5


a. Find the Jacobean determinant at points P (3,2)

b. Find the Hessian determinant at points P (1,3)


One of the psychological tests conducted by the guidance counselors in a public school is the Survey of Study Habits and Attitudes (SSHA) that measures student’s attitudes toward studying. The mean score of Senior High students is with standard deviation of . Mrs. Suacillo suspects that older students have better attitudes toward school. He randomly selects Grade students who are at least years old and gives them SSHA. The test result has a mean score of points. Is there a reason to believe that the claim of the guidance counselors is correct? Assume that the population mean score is normally distributed. Carry out a significance test at level. \


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Evaluate the following integrals using residue theorem: (a) ∫∞−∞ x² /(x² +9)(x² +4)²dx

The daily net profit for spaza shop follows a normal distribution with a mean of R220 and a standard deviation of R175.

a) The probability that the daily net profit exceeds R250 is (answer to 2 decimal places)   

b) The cut-off value for lowest 40 % of daily net profits is (in Rands and cents) 

 


The monthly amount spent on stationery in a large company has a normal distribution with mean R2500 and standard deviation R150. How much should the company budget for stationery if the chance of exceeding the budget has to be only 2.5%?


A pizza parlour will deliver a pizza take-away order to the customer if s/he lives within a 5 kilometre radius from the pizza parlour. If the customer lives within this radius, it is found that the time taken to receive the pizza is normally distributed with a mean time of 45 minutes and a standard deviation of 8 minutes. Paul has relocated and now lives within the 5 kilometre radius. He orders a pizza from the pizza parlour. The probability that it takes between 43 and 49 minutes for him to receive his pizza is (correct to 2 decimal places)

 


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