Other Math Answers

Consider arterial blood viscosity µ = .0 025 poise. If the length of the artery is 5.1 cm, radius
3
8 10−
× cm. and 3
1 2 P = P − P = 4×10 dynes/ 2
cm then find (i) maximum peak velocity of
blood and (ii) the shear stress at the wall.

Give one example each, with justification, to support the following statements. (6)
i) For developing mathematical ability, children should pose problems and not
merely answer them
ii) Children know some mathematics before they enter formal school.
iii) Children learn by experiencing things.

The huge volcanic eruption on the island of Krakatoa, Indonesia, in 1883 was heard on Rodrigues Island, 4,782 km (2,970 miles) away. How long did it take the sound to travel to Rodrigues? (Assume the air temperature is 20°C.)

Bureau of labor statistics wants to use statistics to determine whether there is difference between two countries on some measure of labor or between time periods for one country. The bureau reports that hourly compensation rates in US dollars for manufacturing production workers in country ‘A’ in 2015 and 2019 were $25.96 and $28.29 respectively. Hourly compensation rates for country ‘B’ over same period of time were $19.26 in 1995 and $23.89 in 2004. According to the survey by labor department the hours actually worked by employees per week in country A in 2015 were 36.1 and were 35.5 in 2019. For country B the figures were 37.1 in 2015 and 35.9 in 2019.
ii. How will you help the department statistically to find whether the difference between the two countries’ average workweek is significant or not?(7marks)

in the olden days, type was set by hand using lead pieces. the type had to be carefully put together. the printer wants to print a list of whole numbers from 1 to 1,000 in order to find the primes under 1,000. if he had 100 of each of the digits from 0 to 9 , how many numbers could he set before he ran out of some digits?

Given one example each from the real world for the following, along with justification, for your
example
i) A non-linear model
ii) A linear, deterministic model.

Two firms X and Y produce the same commodity. Due to production constraints, each firm is
able to produce ,1 3 and 5 units. The cost of producing qx units for firm X is Rs.[6+qx^2-2q+5] and firm Y has identical cost function Rs.[6+qy^2-2qy+5] for producing qy units. p is the price of one unit for firm X . We assume that the market is in equilibrium.
The outcomes are the profits of the firm shown in the form of a matrix A {aij } Write (i) a11
(ii) a22 (iii) a21 , if demand function D( p) is given as D( p) = 50 − p .

Bureau of labor statistics wants to use statistics to determine whether there is difference between two countries on some measure of labor or between time periods for one country. The bureau reports that hourly compensation rates in US dollars for manufacturing production workers in country ‘A’ in 2015 and 2019 were $25.96 and $28.29 respectively. Hourly compensation rates for country ‘B’ over same period of time were $19.26 in 1995 and $23.89 in 2004. According to the survey by labor department the hours actually worked by employees per week in country A in 2015 were 36.1 and were 35.5 in 2019. For country B the figures were 37.1 in 2015 and 35.9 in 2019.
How will you help the department statistically to find whether the hourly labor cost in country A in 2019 was significantly higher than the 2019 hourly labor cost in country B based on given figures? (8marks)

An advertising agency whishes to reach two types of audiences: customers with annual income greater than one lakh rupees (target audience A) and customers with annual income of less than one lakh rupees (target audience B). The total advertising budget is ` 2,00,000. One programme of TV advertising costs ` 50,000; one programme of radio advertising costs ` 20,000. For contract reasons, at least three programmes should to be on TV and the number of radio programmes must be limited to 5. Surveys indicate that a single TV programme reaches 4,50,000 propective customers in target audience A and 50,000 in target audience B. One radio programme reaches 20,000 prospective customers in target audience A and 80,000 in target audience B. Formulate it as a LPP and solve it graphically to maximize the total reach for the programmes

An advertising agency whishes to reach two types of audiences: customers with annual income greater than one lakh rupees (target audience A) and customers with annual income of less than one lakh rupees (target audience B). The total advertising budget is ` 2,00,000. One programme of TV advertising costs ` 50,000; one programme of radio advertising costs ` 20,000. For contract reasons, at least three programmes should to be on TV and the number of radio programmes must be limited to 5. Surveys indicate that a single TV programme reaches 4,50,000 propective customers in target audience A and 50,000 in target audience B. One radio programme reaches 20,000 prospective customers in target audience A and 80,000 in target audience B. Formulate it as a LPP and solve it graphically to maximize the total reach for the programmes