1 Solve for <span>yy</span> in <span>-2x+y=1.3<span>−2x+y=1.3</span></span>How?
<span>y=1.3+2x<span>y=1.3+2x</span></span>
2 Substitute <span>y=1.3+2x<span>y=1.3+2x</span></span> into <span>2(0.5x-y)=4.6<span>2(0.5x−y)=4.6</span></span>How?
<span>2(-1.5x-1.3)=4.6<span>2(−1.5x−1.3)=4.6</span></span>
3 Solve for <span>xx</span> in <span>2(-1.5x-1.3)=4.6<span>2(−1.5x−1.3)=4.6</span></span>How?
<span>x=-2.4<span>x=−2.4</span></span>
4 Substitute <span>x=-2.4<span>x=−2.4</span></span> into <span>y=1.3+2x<span>y=1.3+2x</span></span>How?
<span>y=-3.5<span>y=−3.5</span></span>
5 Therefore,
<span>x=-2.4<span>x=−2.4</span></span>
<span>y=-3.5<span>y=−3.<span>5</span></span></span>
Question:
Alfie tossed a paper cup in the air 150 times and recorded the side it landed on.
Right side up = 60 Upside down = 53 Side = 37
If Alfie tosses the paper cup 100 more times what is the expected number of times the cup will land on its side?
Answer:
The expected number of times the cup will land on its side is 25 times
Step-by-step explanation:
Given
Required
First, we calculate the probability of landing on side
Next, we calculate the expected value; E(x) using:
When tossed 100 more times:
n = 100 and P(x) = P(Side) = 0.247
So:
--- approximated
<em>Hence, it is expected that it will land on its side 25 times</em>
We can set up an equation to solve this problem, but first we need to write out what we know.
$20 overall
$0.24 every minute
$13.52 remaining on the card
Now that we know our information, we can set it up in an equation.
20 - 0.24x = 13.52
The 20 represents $20 overall when she first got the phone card.
We are then subtracting $20 from how must it costs a minute (which is 24 cents). The 'x' indicates the number we are trying to find (how many minutes her call lasted). Lastly, 13.52 is the result of everything, since she has $13.52 remaining on the card.
We can now solve the equation:
20 - 0.24x = 13.52
-0.24x = 13.52 - 20 /// subtract 20 from each side
-0.24x = -6.48 /// simplify
x = 27 /// divide each side by -0.24
Our solution is: x = 27.
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An easier way to solve this problem would be to first, subtract the total amount of money she had on the card when she first got it, and then the remaining total she ended up with.
$20 - $13.52 = $6.48
So, she spent a total of $6.48 on long distance calls, but since we are looking for how many minutes, we need to divide the total she spent and how much it costs per minute.
6.48 ÷ 24 = 27
We receive the same amount of minutes spent just like we did the last way we solved.
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Salma spent 27 minutes on the phone.
cos(3x) = cos(2x+x)
= cos(2x) cos (x) -sin(2x)sin(x)
