Answer:
<u>Marge's</u> present age = 14 ; <u>Dan's</u> present age = 29
Step-by-step explanation:
Let Marge's present age be = M
Dan's present age [D] : 14 years elder than Marge = M + 14
Marge Age = M - 8
Dan's Age = D - 8 = (M + 14) - 8 = M + 6
{Given} : Dan's age = 3 times Marge's age
M + 6 = 3 (M - 8)
M + 6 = 3M - 24
6 + 24 = 3M - M
30 = 2M
M = 30/2
M = 15 [Marge's present age]
Dan's present age [D] = M + 14 = 29
Answer:
23rd term
Step-by-step explanation:
Plz mark as Brainliest!
Answer:
the expected value of Xn , E(Xn) = 0 and the variance σ²(Xn) = n*(1-2n)
Step-by-step explanation:
If X1= number of tails when n fair coins are flipped , then X1 follows a binomial distribution with E(X1) = n*p , p=0,5 and the number of heads obtained is X2=n-X1
therefore
Xn =X1-X2 = X1- (n-X1) = 2X1-n
thus
E(Xn) =∑ (2*X1-n) p(X1) = 2*∑[X1 p(X1)] -n∑p(X1) = 2*E(X1)-n = 2*n*p--n= 2*n*1/2 -n = n-n =0
the variance will be
σ²(Xn) = ∑ [Xn - E(Xn)]² p(Xn) = ∑ [(2X1-n) - 0 ]² p(X1) = ∑ (4*X1²-4*X1*n+n²) p(X1) = = 4*∑ X1²p(X1) - 4n ∑X1 p(X1) - n²∑p(X1) = 2*E(X1²) -4n*E(X1)- n²
since
σ²(X1) = n*p*(1-p) = n*0,5*0,5=n/4
and
σ²(X1) = E(X1²) - [E(X1)]²
n/4 = E(X1²) - (n/2)²
E(X1²) = n(n+1)/4
therefore
σ²(Xn) = 4*E(X1²) -4n*E(X1)- n² = 4*n(n+1)/4 - 4*n*n/2 - n² = n(n+1) - 2n² - n²
= n - 2n² = n(1-2n)
σ²(Xn) = n(1-2n)
PART 1: Identify the slope of the graphed line
To find the slope, I will use the slope formula: m = (y₂ - y₁) / (x₂ - x₁) using the points (0, 1) & (3, 0).
m = (0 - 1) / (3 - 0)
m = - 1 / 3
The slope of the graphed line is negative one-third: - 1/3.
PART 2: Identify the y-intercept of the graphed line
The y-intercept of a line is the point where the line crosses the y-axis. In this problem, the line crosses the y-axis at y = 1.
PART 3: Identify the slope of the line given by the equation
The given equation is written in the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. The slope of the line as shown by the equation is 1/2.
PART 4: Identify the y-intercept of the line given by the equation
As previously stated, the equation is written is the slope-intercept form, so to find the y-intercept in the equation, all we need to do is find the value for b. In this case, b = -1.
Hope this helps!
