Answer:
1 1/4
Step-by-step explanation:
1/2 = 2/4
1 3/4 - 2/4 = 7/4 - 2/4 = 5/4 = 1 1/4
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Tripod will not tip over because: a plane contains at least 3 noncollinear points .
Answer: B )
<h3>
Answer: Choice A. P = 1000M</h3>
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Explanation:
Use the log rule
log(A/B) = log(A) - log(B)
this works for any valid log base
So we can say
- log(P/N) = log(P) - log(N)
- log(M/N) = log(M) - log(N)
meaning that
- log(P/N) = 8 turns into log(P) - log(N) = 8
- log(M/N) = 5 turns into log(M) - log(N) = 5
We have this system of equations
Subtract the equations straight down. You'll find the log(N) terms cancel out and we have the new equation log(P) - log(M) = 3 which transforms into log(P/M) = 3
Lastly, convert the log equation into its exponential equivalent form using the idea that log(b,x) = y turns into y = b^x, where b is the base
Throughout this problem, the base wasn't given. Instead its implied we're talking about base 10.
So,
log(P/M) = 3
P/M = 10^3
P/M = 1000
P = 1000M
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Alternatively,
log(P/N) = 8 turns into P/N = 10^8
log(M/N) = 5 turns into M/N = 10^5
meaning that we can divide the two equations to get P/M = (10^8)/(10^5). That simplifies to P/M = 1000 and rearranges to P = 1000M
The margin of error can be calculated using the t
statistic. The formula for margin of error is given as:
<span>Margin of error = t * s / sqrt (n) ---> 1</span>
Where,
t = the t score based on the given confidence level and
degrees of freedom
n = number of samples = 21
s = standard deviation = 7.1
Degrees of freedom = n – 1 = 21 – 1 = 20
Based on the standard probability tables for t, the t
score is:
t = 0.860
Substituting into equation 1:
margin of error = 0.860 * 7.1 / sqrt (21)
margin of error = 1.33
The range is:
range = 30.1 ± 1.33
range = 28.77, 31.43
Therefore the commute time to work is between 28.77 minutes
and 31.43 minutes.