Question
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  1. Out of 70 schools 42 of them can be attended by boys and 35 can be attended by girls, If a pupil is selected at random from these schools, find the probability that he/she is from a mixed school.
    (A)
    (B)
    ©
    (D)
  2. Given that and , calculate .
    (A)
    (B)
    ©
    (D)
  3. What is the probability of obtaining a head and a six when a fair coin and a die are tossed together?
    (A)
    (B)
    ©
    (D)
  4. If and , find .
    (A)
    (B)
    ©
    (D)
  5. Factorize
    (A)
    (B)
    ©
  6. Solve the equation .
    (A)

Ask by Hammond May. in Nigeria
Jan 05,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Solutions:
  1. Question 32:
    • Answer:
    • Option: (B)
  2. Question 33:
    • Answer:
    • Option: (B)
  3. Question 34:
    • Answer:
    • Option: (A)
  4. Question 35:
    • Answer:
    • Option: (D)
  5. Question 36:
    • Answer: The polynomial does not factor neatly with the given options.
    • Option: None of the provided options are correct.
  6. Question 37:
    • Answer:
    • Option: (A)

Solution

Let’s solve each of the given questions step by step:

Question 32

Out of 70 schools, 42 can be attended by boys and 35 can be attended by girls. Find the probability that a randomly selected pupil is from a mixed school.
Options:
  • (A)
  • (B)
  • ©
  • (D)
Solution:
To find the number of mixed schools (schools attended by both boys and girls), we use the principle of inclusion:
Probability:
Answer:
Option (B)

Question 33

Given vectors , , and , calculate .
Options:
  • (A)
  • (B)
  • ©
  • (D)
Solution:
First, find :
Now, compute the magnitude:
Answer:
Option (B)

Question 34

What is the probability of obtaining a head and a six when a fair coin and a die are tossed together?
Options:
  • (A)
  • (B)
  • ©
  • (D)
Solution:
  • Total possible outcomes: (coin) (die)
  • Favorable outcome: Getting a head and a six
Probability:
Answer:
Option (A)

Question 35

If and , find .
Options:
  • (A)
  • (B)
  • ©
  • (D)
Solution:
Calculate :
However, this exact option isn’t listed. It appears the question might be asking for :
Answer:
Option (D)

Question 36

Factorize .
Options:
  • (A)
  • (B)
  • ©
  • (D)
Solution:
We need to find two binomials that multiply to .
Let’s test Option (A):
Next, Option (B):
Continue with Option ©:
Finally, Option (D):
Conclusion:
The polynomial does not factor neatly into integer coefficients based on the provided options. However, none of the given options correctly factorize the polynomial. It appears there might be an error in the options provided.
Answer:
None of the provided options correctly factorize the polynomial.

Question 37

Solve the equation .
Options:
  • (A)
Solution:
Answer:
Option (A)

Answered by UpStudy AI and reviewed by a Professional Tutor

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Bonus Knowledge

When it comes to probability and mathematics, it’s fascinating to see how much real-world application stems from these concepts. For instance, understanding probability helps us make informed decisions every day—be it planning for rainy days or deciding which lottery ticket to buy! Every time you flip a coin or roll a die, remember you’re diving into the rich world of outcomes that can guide choices and predictions.
Now, if you’re intrigued by the nuances of factoring polynomials, you’ll be pleased to know that factoring is fundamental in various fields, including engineering and computer science! Mastering factoring techniques not only simplifies calculations but also aids in solving complex equations that can model real-world phenomena, like projectile motion. So next time you encounter a polynomial, recall it’s about untangling the mysteries hidden within those numbers!

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