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y = -4 - 2/3x, so the slope would be -2/3, and the y-intercept would be -4.
x2 + y2 = r2 describes a circle, radius r, centred on the origin. r is thus sqrt(25 + 144) ie 13 units.
4y + 4 = 2y + 12Subtract 4 from each side of the equation:4y = 2y + 8Subtract 2y from each side:2y = 8Divide each side by 2 :y = 4
The sum of four numbers equals 40: a+b+c+d=40 Those same four numbers, along with another number (e), give the set a mean of 12: (a+b+c+d+e)/5=12 Use these two facts to determine e as follows: (a+b+c+d+e)/5=12 a+b+c+d+e=60 (a+b+c+d)+e=60 40+e=60 e=20
2 out of 12Ans:1 2 3 4 5 6 1 2 3 4 5 6total no N of sums of two numbers assuming dice are indistinguishable:N = 36ways to get 7:1 and 6 with a chance of (1/6)*(1/6) = 1/362 and 5 wih a chance of 1/364 and 3 with a chance of 1/36whats the chance of getting 7 with either of these combinations:1/36 + 1/36+ 1/36 = 1/12what about 11:6 and 5, which is the only way to get an 11:the prob of this is (1/6)*(1/6) = 1/36the prob of getting a 7 or an 11, with two dice:1/36 + 1/12 = 1/9!Hopefully someone will jump in if I've made a mistake.OK, I've been told the answer is 2/9. If you do the same working as above, but you'll have to assume there are two ways to get each sum:example, if you get a 7 from 2 and 5, then you can also get 7 from a 5 and 2. This means the dice are distinguishable!
Both of these equations describe straight lines in the xy-plane. At the y-axis x=0 and at the x-axis y=0. So, by substituting in x=0, we can find where the two lines cross the y-axis and, by substituting in y=0, we can find where they cross the x-axis. For the first line:x - 3y = -3 (sub in x=0)0 - 3y= -3(divide both sides by -3)y=1 ----> so this line crosses the y-axis at y=1 only.By following a similar process we can find that this line crosses the x-axis at x=-3 and that the second line, 6x + 2y = -12, crosses the x and y axes at x=-2 and y=-6respectively.If the two lines cross each other then, at some point in the xy-plane, their x and y values will be equal, meaning we can rearrange one equation and substitute it into the second one:Rearrange x - 3y = -3 to give:x = 3y - 3So we can substitute 3y - 3 into the second equation, 6x + 2y = -12, giving:6(3y - 3) + 2y = -12(multiply out the bracket and collect terms)20y - 18 = -12(add 3 to both sides and then divide both sides by 20)y= 6/20 = 0.3(sub this back into x= 3y - 3 to find x)x=-2.1So, the two lines cross each other at the point (-2.1, 0.3)
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