Cos(A-B) = cosAcosB + sinAsinB
<span>
cos(</span>π/2 - θ) = cos(π/2)cosθ + sin(π/2)sinθ
π/2 = 90°
cos(π/2) = cos90° = 0. sin(π/2) = sin90° = 1
cos(π/2 - θ) = cos(π/2)cosθ + sin(π/2)sin<span>θ
</span>
= 0*cosθ + 1*sin<span>θ = </span>sin<span>θ
Therefore </span>cos(π/2 - θ) = sin<span>θ
QED </span>
Answer:
Step-by-step explanation:
In the equation y=kx+1, k is the slope and 1 is the y-intercept.
To find the slope, use the formula k=y2-y1/x2-x1. To use this formula, you need two points. The first point, point M, is given to you. The second point can be the y-intercept, point (0, 1). Now, apply the formula to find the slope: k=3-1/1-0
k=2/1
k=2
We now have the equation y=2x+1.
The next step is to graph the line.
First, graph the y-intercept. Should look something like this: (star represents point. the point is on (0, 1).)
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Then, use the slope to find your second point: (the point is on (1, 3)).
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Draw a line through those two points and you have your answer!
<h3>
The probability of student passing the quiz with at least 50% of the questions correct is 0.05457.</h3>
Step-by-step explanation:
Here, the total number of T/F question = 10
The minimum answers needed correctly answered = 8
So, student needs to answer at least 8 questions correctly.
Here, the possibility of answering a question correctly = 
= p = 0.5
Also, the possibility of answering a question wrong = = q = 0.5
Now, to pass he needs to answer 8 or more ( 8 , 9 or 10) answers correctly.
P(answering 8 correct answer) = 
P(answering 9 correct answer) = 
P(answering 10 correct answer) = 
So, the total Probability = P(8) + P(9) + P(10)
= (0.0439) + (0.0097) + (0.00097)
= 0.05457
Hence, the probability that the student passes the quiz with at least 8 of the questions correct is 0.05457.
The answer would be: D-100. The reasoning of this is because if you take 3 X 10 to the third power and did the exponent (10 to the third power in this case) and multiplied it you would obviously get 1,000 for an answer. Then would would do 1,000 X 3 to get 3,000.
Step-by-step explanation:
3x-5=8x-60
55=5x
x=11
