Answer:
a) 3.5
b) 3.33
c) 
Step-by-step explanation:
As given,
A fair die is rolled 10 times
a)
Expected value of Sum of the number in 10 rolls = 
= 3.5
∴ we get
Expected value of Sum of the number in 10 rolls = 3.5
b)
Ley Y : number of multiples of 3
Y be Binomial
Y - B(n = 10, p = 
)
Now,
Expected value = E(Y) = np = 10× = 3.33
c)
Let m = total number of faces in a die
⇒m = 6
As die is roll 10 times
⇒n = 10
Now,
Let Y = number of different faces appears
Now,
Expected value, E(Y) = m - m
= 
Answer:
x = -2
x= -3
Step-by-step explanation:
x 2+5x+6=0
To solve the equation, factor x^2+5x+6 using formula x^2+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.
a+b=5
ab=6
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 6.
1,6
2,3
Calculate the sum for each pair.
1+6=7
2+3=5
The solution is the pair that gives sum 5.
a=2
b=3
Rewrite factored expression (x+a)(x+b) using the obtained values.
(x+2)(x+3)
To find equation solutions, solve x+2=0 and x+3=0.
x=−2
x=−3
Answer:
true, yes
Step-by-step explanation:
Setup
0.8x + 0.4y = 50
0.1x + 0.2y = 10 - Multiply by -2 and add
get
0.6x = 30
x = 50 mg compound A
.1 (50) + .2y = 10
5 + .2y = 10
.2y = 5
y = 25 mg compound B
Answer:
The even numbers between 0 and X represents an arithmetic sequence with a common difference of 2
The rule of arithmetic sequence = a + d(n - 1)
Where a is the first term and n is the number of terms
So, for the even numbers between 0 and X
The first term = a = 0
d = 2
So, we need to find n at the last term which is X
∴ X = 0 + 2 ( n -1 )
∴ n - 1 = X/2
∴ n = X/2 + 1
The sum of the arithmetic sequence = (n/2) × (2a + (n−1)d)
Substitute with a and d and X
So, the sum = (n/2) * (2*0 + (n−1)*2)
= (n/2) * ((n−1)*2)
= n(n-1)
= (X/2 + 1) * (X/2)
= X/2 by (X/2 + 1)
So, The quick way to add all even numbers between 0 and X always works.
