Someone help me on this math problem

The average number of transactions made at an ATM in a 20 minute period is 10. Use an appropriate probability distribution to fi

krek1111 [17]

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

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

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

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

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

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

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

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

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

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

What number is 20% of 40?

VladimirAG [237]

Answer:

It would be 8

Step-by-step explanation:

20% of 40 is 8

6 0

3 years ago

Read 2 more answers

What is the slope of the line that passes through the points (-10, -8)(−10,−8) and (-8, -16) ?(−8,−16)? Write your answer in sim

photoshop1234 [79]

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.

3 0

3 years ago

Step 1: –10 + 8x < 6x – 4

Aleks04 [339]

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

6 0

2 years ago

Read 2 more answers

Someone help me on this math problem​

Someone help me on this math problem