Answer: x=0
Step-by-step explanation:
The line has an undefined slope and has infinitely many solutions as it passes through the y-axis
Therefore the equation of the line is x=0
An= mth term.
an=a₁+(n-1)*d
a₁₂=41
a₁₅=140
a₁₂=41
41=a₁+(12-1)*d
41=a₁+11d
a₁+11d=41 (1)
a₁₅=140
140=a₁+(15-1)*d
140=a₁+14d
a₁+14d=140 (2)
With the equiations (1) and (2) build a system of equations
a₁+11d=41
a₁+14d=140
we solve it.
-(a₁+11d=41)
a₁+14d=140
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3d=99 ⇒d=99/3=33
a₁+11d=41
a₁+(11*33)=41
a₁+363=41
a₁=41-363=-322
an=a₁+(n-1)*d
an=-322+(n-1)*33
an=-322+33n-33
an=-355+33n
an=-355+33n
To check:
a₁₂=-355+33*12=-355+396=41
a₁₅=-355+33*15=-355+495=140.
Answer:
<em>On time: 0.67</em>
<em>Late: 0.33</em>
Step-by-step explanation:
<u>Probabilities</u>
One approach to estimating the probability of occurrence of an event is to record the number of times that event happens (e) and compare it with the total number of trials (n).
The probability can be estimated with the formula:

And the probability that the event doesn't occur is
Q = 1 - P
Paulo arrives on time to school e=53 times out of n=79 times. The probability that he arrives on time is:

P = 0.67
And the probability he arrives late is:
Q = 1 - 0.67 = 0.33
Answer:
a) True
<em> </em>
<em></em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given that the definite integration</em>
<em> </em>
<em></em>
<em>we know that the trigonometric formula</em>
<em> sin²∝+cos²∝ = 1</em>
<em> cos²∝ = 1-sin²∝</em>
<u><em>step(ii):-</em></u>
<em>Now the integration</em>
<em> </em>
<em></em>
<em> = </em>
<em></em>
<em>Now, Integrating </em>
<em> </em>
<em></em>
<em> = sin π - sin 0</em>
<em> = 0-0</em>
<em> = 0</em>
<u><em>Final answer:-</em></u>
<em> </em>
<em></em>
<em></em>
<em></em>