In 1, t<span>here are 6 outcomes for each die, so for three dice, the total combination is 6 x 6 x 6 = 216 outcomes. Hence, t</span><span>he probability of any individual outcome is 1/216 </span>
The outcomes that will add up to 6 are
<span>1+1+4 </span>
<span>1+4+1 </span>
<span>4+1+1 </span>
<span>1+2+3 </span>
<span>1+3+2 </span>
<span>2+1+3 </span>
<span>2+3+1 </span>
<span>3+1+2 </span>
<span>3+2+1 </span>
<span>2+2+2 </span>
<span>Hence the probability is </span><span>10/216 </span>
In 3, the minimum sum of the three dice is 3. so we start with this
<span>P(n = 3) </span>
<span>1+1+1 ; </span><span>1/216 </span>
<span>P(n = 4) </span>
<span>1+1+2 </span>
<span>1+2+1 </span>
<span>2+1+1 ; </span><span>3/216 </span>
<span>P(n = 5) </span>
<span>1+1+3 </span>
<span>1+3+1 </span>
<span>3+1+1 </span>
<span>1+2+2 </span>
<span>2+1+2 </span>
<span>2+2+1; </span><span>6/216
The sum in 3 is 10/216 or 5/108</span>
The side of the square is 4 cm since 4x4= 16
Beginning with the function y = sin x, which would have range from -1 to 1 and period of 2pi:
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
Answer:
Step-by-step explanation:
(1) 2x - 6y = -12
(2) x + 2y = 14
There is a -6y and a +2y. Since they have opposite signs, I'll try to eliminate the y terms. (That's my choice. There is more than one way to solve these.)
Multiply eq. (2) by 3:
3x + 6y = 42
Then add the result to eq. (1) to eliminate the y terms:
2x - 6y = -12
3x + 6y = 42
------------------
5x = 30, so x = 6
Now plug the value of x into eq. (2) and solve for y:
6 + 2y = 14
2y = 8
y = 4
Why did I use eq. (2) to solve for y? Because it's less work. I could have used eq. (1) instead:
2(6) - 6y = -12
12 - 6y = -12
-6y = -24
y = 4
More than one way to solve.
<span>Extrapolating.
Extrapolating is making inferences that beyond the data range. In contrast to this, interpolating is using the data set to make estimates as to what would happen in the data range.</span>
