Useful Log Rules:
- log(A*B) = log(A)+log(B) .......... log rule 1
- log(A/B) = log(A) - log(B) .......... log rule 2
- log(A^B) = B*log(A) ................... log rule 3
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Part (a)
All logs shown below are base 3.
log(500) = log(5*100)
log(500) = log(5*10^2)
log(500) = log(5)+log(10^2) .... use log rule 1
log(500) = log(5) + 2*log(10) .... use log rule 3
log(500) = 1.4650 + 2*2.096 ....... substitution
log(500) = 5.657
<h3>Answer: 5.657</h3>
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Part (b)
All logs shown below are base 3.
log(2) = log(10/5)
log(2) = log(10) - log(5) .... use log rule 2
log(2) = 2.096 - 1.4650 ....... substitution
log(2) = 0.631
<h3>Answer: 0.631</h3>
Answer:
The probability is 0.97
Step-by-step explanation:
In this question, we are concerned with calculating the probability of a student spending time reading or watching TV.
To calculate this, we simply use a direct mathematical formula.
P( of spending time reading or watching tv) = P(of spending time reading) + P(spending time watching Tv) - P( of spending time watching Tv and reading)
From the question, we identify the probabilities as follows;
P(spending time reading) = 0.1
P(of spending time watching Tv) = 0.9
P(of spending time watching Tv and reading) = 0.03
Now, plugging these values, we have
P( of spending time reading or watching Tv) = 0.9 + 0.1 -0.03
= 1-0.03 = 0.97
Answer:
10 three-point questions and 14 five-point questions.
Step-by-step explanation:
x+y = 24
3x+5y = 100
We can solve this system of equations using elimination. In order to do this, let's first multiply the first equation by 3...
3x+3y=72
3x+5y=100
Now, subtract the first equation from the second equation...
2y=28
Divide both sides by 2
y=14
Plug this back into any of the equations to solve for x...
x+14=24
x=10
There were 10 three-point questions and 14 five-point questions
The factors of 4 are 1, 2, and 4 .
The factors of 9 are 1, 3, and 9 .
