Answer:
Step-by-step explanation:
In probability,
"AND" means "multiplication"
"OR" means "ADDITION"
We want probability of Blue Pen and Yellow Highlighter. So we find individual probabilities and "MULTIPLY" them.
Let P(b) be probability of blue pen
Let P(y) be probability of yellow highlighter
We know probability of event is that event divided by total number of that
So,
There are 4 + 2 = 6 pens
Blue pen = 2
Hence,
P(b) = 2/6 = 1/3
And,
There are 5 highlighters
Yellow highlighter = 1
Hence,
P(y) = 1/5
Now,
P(b and y) = 1/3 * 1/5 = 1/15
Hence,
probability of grabbing blue pen and a yellow highlighter is
The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>
Answer:
Step-by-step explanation:
As
(g/f)(x) = g(x) / f(x)
Therefore,
Answer:
Probability that the proportion in our sample of red candies will be less than 20% is 0.5 .
Step-by-step explanation:
We are given that 20% of the candy produced are red. A random sample of 100 bags of Skittles is taken.
The distribution we can use here is;
~ N(0,1)
where, p = 0.20 and n = 100
Let 
= proportion of red candies in our sample
So, P( < 0.20) = P( < 
) = P(Z < 0) = 0.5
Therefore, probability that the proportion in our sample of red candies will be less than 20% is 0.5 .
Answer:no
Step-by-step explanation:
Because on a graph (2,3) means that the point is two along and three up while (3,2) means it is 3 along and two up.
