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QUESTION TWO a) Solve for \( x, y \) and \( z \) using matrix inversion: \( -9 x+4 y-6 z=16 \) \( \begin{array}{l}17 x-14 y-2 z=-16 \\ x-16 y-2 z=-56\end{array} \)
Algebra Jan 18, 2025
UESTION ONE Faculty or a School in a University is offering 3 courses. One is a minor if the name appears in all the hree registers, major if two and specialist if one. In one certain year the School had 200 finalists listributed in registers as follows; 130 Chemistry, 128 Mathematics and 134 Zoology. Some additional nformation indicated that 80 students were registered for Zoology and Chemistry, 68 registered for Mathematics and Zoology and 86 registered for Chemistry and Mathematics. Using the Venn diagram as an illustration determine the number of students that: \( \begin{array}{ll}\text { a) Were minor, major and specialist } & \\ \text { b) Never registered for Chemistry } & \text { (04 marks) } \\ \text { c) Never registered for Mathematics } & \text { (02 marks) } \\ \text { d) Failed to specialized in Chemistry even though registered for it } & \text { (02 marks) } \\ \text { e) Were either specialist or major but not in Chemistry } & \text { (02 marks) }\end{array} \)
Statistics Jan 18, 2025
a) Solve for \( x, y \) and \( z \) using matrix inversion: \( -9 x+4 y-6 z=16 \) \( 17 x-14 y-2 z=-16 \) \( x-16 y-2 z=-56 \) ( 05 marks) \( \begin{array}{l}\text { b) A consumer survey among } 2000 \text { consumers conducted by CCK during the month of February } 2020 \\ \text { revealed the following switching pattems among } 800 \text { users of Safaricom, } 100 \text { consumers shifted their } \\ \text { loyalty to Airtel and } 200 \text { consumers shifted their loyalty to Telkom, the rest remained loyal to Safaricom. } \\ \text { Among } 600 \text { users of Airtel } 250 \text { consumers shifted their loyalty to Safaricom, } 150 \text { consumers shifted to } \\ \text { Telkom while the rest remained steadfast to Airtel. Among } 600 \text { users of Telkom, } 300 \text { consumers shifted } \\ \text { their loyalty to Safaricom and } 150 \text { consumers migrated to Airtel while the rest were hardeore royals to } \\ \text { Telkom. } \\ \text { Required: } \\ \text { i) Transition matrix representing the above switching patterns } \\ \text { ii) Respective market shares two months later } \\ \text { iii) Market share in long run }\end{array} \)
Algebra Jan 18, 2025
Exprear the falluwing equatoms internes of \( y \) \( y+z=15 \)
Algebra Jan 18, 2025
3. Calculate the SA of a closed cylinder whose radus is 7 cm and heigit of 26 cm
Geometry Jan 18, 2025
3. Calculate the SA of a closed cylinder whose radus is 7 cm and reigitt of 2 tcom
Geometry Jan 18, 2025
Given that \( Y \sim \mathrm{~B}(11,0.23) \), calculate: \( \begin{array}{ll}\text { a } \mathrm{P}(Y \neq 3) & \text { b } \mathrm{P}[Y<\mathrm{E}(Y)]\end{array} \)
Probability Jan 18, 2025
Given that \( Y \sim \mathrm{~B}(11,0.23) \), calculate: \( \begin{array}{ll}\text { a } \mathrm{P}(Y \neq 3) & \text { b } \mathrm{P}[Y<\mathrm{E}(Y)]\end{array} \)
Probability Jan 18, 2025
3 Given that \( Y \sim \mathrm{~B}(11,0.23) \), calculate: \( \begin{array}{ll}\text { a } \mathrm{P}(Y \neq 3) & \text { b } \mathrm{P}[Y<\mathrm{E}(Y)]\end{array} \)
Probability Jan 18, 2025
Solve \( 7 \frac{2}{3}-3 \frac{1}{6} \)
Arithmetic Jan 18, 2025
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