Mathematics

The burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning rate; that is σ1 = σ 2 = 3 centimeters per second. Two random samples of n1 = 20 and n2 = 20 specimens are tested; the sample mean burning rates are width= = 18 centimeters per second and width= = 24 centimeters per second.

(a) Test the hypothesis that both propellants have the same mean burning rate. Use α = 0.05.

(b) What is the P-value of the test in part (a)?

(c) What is the β-error of the test in part (a) if the true difference in mean burning rate is 2.5 centimeters per second?

(d) Construct a 95% confidence interval on the difference in means μ1 – μ2. What is the practical meaning of this interval?

Assignment – 1 :MATHEMATICS

 

 

 

Answer all the questions.

 

Question1

(a)       Simplify the following expressions:

(i)        

(ii)       

(iii)      
 

(b)       Express the following to a simplest fraction:

(i)       

(ii)        

(iii)       

 

(c)     Evaluate the value of   

 

 

Question 2

(a)   Express the following as a percentage:

(i)         
(ii)      

(iii)     46 marks out of a total of 80 marks

(iv)     a discount of RM15 for a pair of shoes listed at RM120

(v)     an increase of 5 cm to a height of 165 cm tall.
 

(b)   The net selling prices of the following items are listed with the amount of
discount stated in brackets. Find the original price of each item.
(i)         Smart phone RM1100 (20%)

(ii)        Badminton racket   RM175 (30%)

(iii)       1000cc Sedan   RM44,200 (15%)

 

(c)   (i)   The Merdeka Stadium has a capacity of 23,500 seats. During a concert at
the stadium, 22,800 seats were taken. Find the percentage of vacant seat,
correct to the nearest 2 decimal places.

(ii)  A receipt from a departmental store showed a tax of RM4.69 for the total
payment of RM53.63. Find the tax rate, correct to the nearest tenth percent.
 

 

 

 

Question 3

(a)   Determine the domain of each of the functions below:
(i)         

(ii)       

(iii)      

(iv)      
 

(b)   Let  and  represent a cost function and a revenue function respectively,
where  is the number of units of a certain product. At break-even point,
.
Find the values of , correct to the nearest whole number, for the following
products where the cost and revenue functions are as listed.
(i)   
(ii)   
(iii)   
(iv)   

(v)    
 

Question 4
(a)    Use completing the square method to find the values of  at the minimum or
maximum point and state the minimum/maximum values of the following
functions.
(i)            
(ii)         
(iii)        
(iv)       
(v)        

 

(b)     The profit of a company is given by the function 
where  is the amount (in thousands) spent on advertising.
Find the amount spent on advertising that will bring in maximum profit.

 

 

Question 5
Solve the following inequalities and graph the solutions and also state the intervals in parenthesis.

(i)            

(ii)          

(iii)         

(iv)         

(v)

 

(vi)         

(vii)        

(viii)      

 

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