Paper: Business Mathematics (1429)
Level: Bachelor's
Time: 03 Hours
Semester: Spring 2022
Total Marks: 100
Pass Marks: 50
Question 1 (a) - A patient in a hospital is required to have at least 84 units of drug A and 120 units of drug B each day (assume that an over dosage of either drug is harmless). Each gram of substance M contains 10 units of drug A and 8 units of drug B, and each gram of substance N contains 2 units of drug A and 4 units of drug B. How many grams of substances M and N can be mixed to meet the minimum daily requirements?
Step-by-Step Solution
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Define the variables:
- x: grams of substance M
- y: grams of substance N
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Set up inequalities:
- 10x + 2y ≥ 84
- 8x + 4y ≥ 120
-
Simplify inequalities:
- 5x + y ≥ 42
- 2x + y ≥ 30
-
Solve for x:
- Subtract inequalities: 5x + y - (2x + y) ≥ 42 - 30
- Result: 3x ≥ 12
- Divide by 3: x ≥ 4
-
Solve for y:
- Substitute x = 4 into 2x + y ≥ 30
- Result: 2(4) + y ≥ 30
- Simplify: 8 + y ≥ 30
- y ≥ 22
To meet the minimum daily requirements, mix 4 grams of substance M and 22 grams of substance N.
Question 1 (b) - Find the following:
- What is y-intercept and slope of the equation 5x + 2y = 10?
- Determine the equation of a straight line whose y-intercept is-3 and slope 4
- Find the slope intercept form of the equation that passes through (-8, -4) and perpendicular to the line 8x - 2y = 0
- Determine the equation of a straight line which has a slope of -5 and x y intercept of(0,15)
Question 2 (a) - Find a formula for the probability distribution of the number of boys in families with three children assuming equal probabilities for boys and girls.
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