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Igoryamba
3 years ago
13

In how many ways can the letters of the word ``COPYRIGHT'' be arranged?

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
4 0

Answer:

362,880 ways

Step-by-step explanation:

There are 9 letters so 9!

And none of them are repeated so 9!/0!

9! = 362,880

I hope this helps, and plz mark me brainliest!!

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An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a
LekaFEV [45]

Let Xb be the number of reservations that are accommodated. Xb has the binomial distribution with n trials and success probability p = 0.94

In general, if X has the binomial distribution with n trials and a success probability of p then
P[Xb = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[Xb = x] = 0 for any other value of x.

To use the normal approximation to the binomial you must first validate that you have more than 10 expected successes and 10 expected failures. In other words, you need to have n * p > 10 and n * (1-p) > 10.

Some authors will say you only need 5 expected successes and 5 expected failures to use this approximation. If you are working towards the center of the distribution then this condition should be sufficient. However, the approximations in the tails of the distribution will be weaker espeically if the success probability is low or high. Using 10 expected successes and 10 expected failures is a more conservative approach but will allow for better approximations especially when p is small or p is large.

If Xb ~ Binomial(n, p) then we can approximate probabilities using the normal distribution where Xn is normal with mean μ = n * p, variance σ² = n * p * (1-p), and standard deviation σ

I have noted two different notations for the Normal distribution, one using the variance and one using the standard deviation. In most textbooks and in most of the literature, the parameters used to denote the Normal distribution are the mean and the variance. In most software programs, the standard notation is to use the mean and the standard deviation.

The probabilities are approximated using a continuity correction. We need to use a continuity correction because we are estimating discrete probabilities with a continuous distribution. The best way to make sure you use the correct continuity correction is to draw out a small histogram of the binomial distribution and shade in the values you need. The continuity correction accounts for the area of the boxes that would be missing or would be extra under the normal curve.

P( Xb < x) ≈ P( Xn < (x - 0.5) )
P( Xb > x) ≈ P( Xn > (x + 0.5) )
P( Xb ≤ x) ≈ P( Xn ≤ (x + 0.5) )
P( Xb ≥ x) ≈ P( Xn ≥ (x - 0.5) )
P( Xb = x) ≈ P( (x - 0.5) < Xn < (x + 0.5) )
P( a ≤ Xb ≤ b ) ≈ P( (a - 0.5) < Xn < (b + 0.5) )
P( a ≤ Xb < b ) ≈ P( (a - 0.5) < Xn < (b - 0.5) )
P( a < Xb ≤ b ) ≈ P( (a + 0.5) < Xn < (b + 0.5) )
P( a < Xb < b ) ≈ P( (a + 0.5) < Xn < (b - 0.5) )

In the work that follows X has the binomial distribution, Xn has the normal distribution and Z has the standard normal distribution.

Remember that for any normal random variable Xn, you can transform it into standard units via: Z = (Xn - μ ) / σ

In this question Xn ~ Normal(μ = 0.94 , σ = sqrt(0.94 * n * 0.06) )

Find n such that:

P(Xb ≤ 160) ≥ 0.95

approximate using the Normal distribution
P(Xn ≤ 160.5) ≥ 0.95

P( Z ≤ (160.5 - 0.94 * n) / sqrt(0.94 * n * 0.06)) ≥ 0.95

P( Z < 1.96 ) ≥ 0.95

so solve this equation for n

(160.5 - 0.94 * n) / sqrt(0.94 * n * 0.06) = 1.96

n = 164.396

n must be integer valued so take the ceiling and you have:

n = 165.

The air line can sell 165 tickets for the flight and accommodate all reservates at least 95% of the time

If you can understand that...

7 0
3 years ago
2 The length of Rectangle A is 7x +11. The
MakcuM [25]

Answer:

Step-by-step explanation:

If congruent the sides are equal

15x-9=7x+11

8x=20

x=20/8=2.5

8 0
2 years ago
Find the slope of the line between points A and B. Simplify your answer.
Taya2010 [7]

Answer:

-2

Step-by-step explanation:

From the given graph, the point A(1, -4) and B(-1, 0)

Slope (m) = (y2 - y1) / (x2 - x1)

x1 = 1, y1 = -4, x2 = -1 and y2 = 0

Slope (m) = (0 - (-4))/(-1 - 1)

= 4/-2

Slope = -2

Thank you.

6 0
3 years ago
Read 2 more answers
In the formula A(t) = A0ekt, A(t) is the amount of radioactive material remaining from an initial amount A0 at a given time t an
Alenkasestr [34]

Answer:  693 years

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

A(t) =A_0e^{kt}

k = rate constant

t = time taken for decomposition = 1

A_0 = Initial amount of the reactant

A_t = amount of the reactant left =A_0-\frac{0.1}{100}\times A_0=0.999A_0

0.999A_0=A_0e^{k\times 1}

0.999=e^k

k=-0.001year^{-1}

for half life : t=t_\frac{1}{2}

A_t=\frac{1}{2}A_o

Putting in the values , we get

\frac{1}{2}A_0=A_0e^{-0.001\times t_\frac{1}{2}

t_\frac{1}{2}=693 years

Thus half life of this isotope, to the nearest year is 693.

8 0
3 years ago
A triangular flag has an area of 444 square meters and a height of 74 meters. What is the length of the base
Serjik [45]
Yes because 74*12 is 888 and because it is a triangular flag, the area would be 444.
5 0
3 years ago
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