Answer:
The probability that exactly 6 transactions will be made at an ATM in the next 20 minutes = 0.06306 = 0.0631 to 4d.p
Step-by-step explanation:
This is a Poisson distribution problem
The Poisson distribution formula is given as
P(X = x) = (e^-λ)(λˣ)/x!
where λ = mean = 10 transactions per 20 minutes
x = variable whose probability is required = 6 transactions in the next 20 minutes
P(X = 6) = (e⁻¹⁰)(10⁶)/6! = 0.06306
Let

where we assume |r| < 1. Multiplying on both sides by r gives

and subtracting this from
gives

As n → ∞, the exponential term will converge to 0, and the partial sums
will converge to

Now, we're given


We must have |r| < 1 since both sums converge, so


Solving for r by substitution, we have


Recalling the difference of squares identity, we have

We've already confirmed r ≠ 1, so we can simplify this to

It follows that

and so the sum we want is

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Answer:
It would be 8
Step-by-step explanation:
20% of 40 is 8
The slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.
<u>Explanation:</u>
Points given = ( -10, -8) and ( -8, -16)
Slope = ?
( -10, -8 ) : x1 = -10 and y1 = -8
( -8, -16 ) : x2 = -8 and y2 = -16
We know,
slope = y2 - y1 / x2 - x1
Slope = -16 - ( -8) / -8 - (-10)
slope = -16 + 8 / -8 + 10
slope = -8 / 2
slope = -4
Therefore, slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.
Answer:
3 > x
Step-by-step explanation:
–2(5 – 4x) < 6x – 4
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: divide each side by by -2, remembering to flip the inequality
-6/-2 > -2/-2
3 > x