Answer: 10/36
When a pair of fair dice are rolled , the total possible cases are (6 × 6) = 36. Out of these 36 cases the following 10 cases are favors(giving the sum > 8) for the happening of the event . These 10 cases are (3, 6), (4, 5), (4, 6),(5, 4), (5, 5), (5, 6) , (6, 3), (6, 4), (6, 5), & (6, 6)
Answer:
Step-by-step explanation:
y-x=0.7
y=x+0.7, so lets plug in that into the expressions instead of y
1)
(y-x)=
x+0.7-x=
x+0.7+(-x)=
x+(-x)+0.7=
x-x+0.7=
0.7
2)
(x-(x+0.7))/((x+0.7)-x)=
(x-x+0.7)/(x+0.7-x)=
(x-x+0.7)/(x+0.7+(-x))=
(x-x+0.7)/(x+0.7+(-x))=
(x-x+0.7)/(x+(-x)+0.7)=
(x-x+0.7)/(x-x+0.7)=
0.7/0.7=
1
Answer:
E(X) = 1.5
Var(X) = 2.325
Step-by-step explanation:
X - the number of pairs of cats (out of the 5 cats) to choose the same type of treat, can take values of:
X = (0, 1, 2, 3, 4, 5)
Also probability of choosing a treat, since they are all equally likely is: f(x) = 1/10
E(X) - expectation of x, is given by:
E(X) = Summation [X*f(x)]
E(X) = 0x(1/10) + 1x(1/10) + 2x(1/10) + 3x(1/10) + 4x(1/10) + 5x(1/10)
= (1/10) x (1+2+3+4+5)
E(X) = 3/2 = 1.5
Also, variance is:
Var(X) = Summation f(x)*[X - E(X)]^2
= (1/10)x(0-1.5)^2 + (1/10)x(1-1.5)^2 +(1/10)x(2-1.5)^2 +(1/10)x(3-1.5)^2 +(1/10)x(4-1.5)^2 +(1/10)x(5-1.5)^2
= (1/10)x[2.25 + 0.25 + 2.25 + 6.25 + 12.25]
Var(X) = 2.325
Answer:
a. The value of the constant k is 21
b. The equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.
Step-by-step explanation:
a.
<em>A proportional relationship satisfies the equation y = k * x, where k is a positive constant and is called a proportionality constant. In this case "x" is the number of terraced houses and "y" is the width of a row of identical houses.
</em>
The data you have is that the width of 5 townhouses are 105 feet. This means that the value of "x" is 5 houses and the value of "y" is 105 feet. By replacing in the equation y = k * x and isolating the constant k, you get:
<em>105=k*5
</em>
<em>k=21
</em>
<u><em>So the value of the constant k is 21.</em></u>
b.
<em>As mentioned, the equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.</em>
This means that just as "x" increases, "y" increases. And that if "x" decreases, "y" will decrease. And this relationship between "x" e "and" will always be the same, determined by the value of the constant "k".