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Using Benford's law, based on the probability that amount's first digit of a randomly chosen invoice is an 8 or a 9 is 0.097, a) you expect to examine 10.309 invoices until you get one that begins with an 8 or 9. b) If you don't get an amount starting with an 8 or 9 until the 40th invoice, then the probability of this happening is 0.0000124, which is a very low probability, which suggests that the invoice amounts may not be genuine.

According to Benford's law, the given probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097.

(a) The expected number of invoices to examine until you get one that begins with an 8 or 9 can be calculated using the formula

E(X) = 1/p, where p is the probability of the desired outcome.

In this case, p = 0.097, so E(X) = 1/0.097 = 10.309. Therefore, you can expect to examine about 10 invoices until you get one that begins with an 8 or 9.

(b) If you don't get an amount starting with an 8 or 9 until the 40th invoice, you may suspect that the invoice amounts are not genuine.

To compute an appropriate probability to support your answer, you can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

In this case, n = 39, k = 0, and p = 0.097. So, P(X = 0) = (39 choose 0) * 0.097^0 * (1-0.097)^(39-0) = 0.023. This means that the probability of not getting an amount starting with an 8 or 9 in the first 39 invoices is 0.023, which is quite low. This supports the suspicion that the invoice amounts may not be genuine.

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By determining the value of x when y = 0, (x, 0), and the value of y when x = 0, respectively, the x-intercept and y-intercept are determined (0, y).

A two-variable equation with a line-shaped graph is referred to as a linear equation. A collection of coordinate plane points that are all the solutions to the linear equation make up the graph. If all of the variables have true numerical values, the equation can be graphed by first drawing a sufficient number of points to identify a pattern, then connecting those points to include all of the points.

A linear equation is represented in standard form as

Ax+By=C,A,B≠0

The equation for y must first be solved before you may graph a linear equation in its usual form.

The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).

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Using Definition 1 of the Laplace transform, we have determined the Laplace transforms of the given functions as mentioned above.

Definition 1 of the Laplace transform states that for a function f(t) defined for t ≥ 0, its Laplace transform F(s) is given by F(s) = L{f(t)} = ∫[0,∞] e^(-st) f(t) dt. Using this definition, we can determine the Laplace transforms of the given functions:

1. The Laplace transform of t is given by L{t} = 1/s².

2. The Laplace transform of t² is given by L{t²} = 2/s³.

3. The Laplace transform of e^(6t) is given by L{e^(6t)} = 1/(s - 6).

4. The Laplace transform of te^(3t) requires applying the property of the Laplace transform for the derivative of a function. The Laplace transform of te^(3t) is given by L{te^(3t)} = -d/ds (1/(s - 3)²).

5. The Laplace transform of cos(2t) requires using the trigonometric property of the Laplace transform. The Laplace transform of cos(2t) is given by L{cos(2t)} = s/(s² + 4).

In conclusion, using Definition 1 of the Laplace transform, we have determined the Laplace transforms of the given functions as mentioned above.

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To verify the parallelogram law for vectors u and v in R^n, we will follow these steps:
1. Write the given equation: ||u+v||^2 + ||u-v||^2 = 2||u||^2 + 2||v||^2
2. Use the definition of the norm in terms of the inner product: ||u+v||^2 =  and ||u-v||^2 =
3. Use properties of inner product.

Now, let's apply these steps:
Step 1: We have the equation ||u+v||^2 + ||u-v||^2 = 2||u||^2 + 2||v||^2.
Step 2: Replace the norms with their corresponding inner products:
+  = 2 + 2
Step 3: Apply properties of inner products and expand the terms:
(u⋅u + 2u⋅v + v⋅v) + (u⋅u - 2u⋅v + v⋅v) = 2(u⋅u) + 2(v⋅v)
Now, observe that the terms "2u⋅v" and "-2u⋅v" cancel each other out: 2(u⋅u) + 2(v⋅v) = 2(u⋅u) + 2(v⋅v)
As the equation holds true, we have successfully verified the parallelogram law for vectors u and v in R^n using the definition of the norm in terms of the inner product and properties of inner product.

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The probabilities for the hypergeometric distribution with the given parameters are:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To determine the probabilities for the hypergeometric distribution with the given parameters, we can use the following formula:

P(X = k) = (choose(K, k) * choose(N-K, n-k)) / choose(N, n)

where "choose(a, b)" represents the binomial coefficient, calculated as a! / (b! * (a - b)!)

Let's calculate the probabilities:

a. P(X = 1):

P(X = 1) = (choose(20, 1) * choose(100-20, 4-1)) / choose(100, 4)

        = (20 * 80) / 3921225

        ≈ 0.000407

b. P(X = 6):

P(X = 6) = (choose(20, 6) * choose(100-20, 4-6)) / choose(100, 4)

        = (38760 * 0) / 3921225

        = 0

c. P(X = 4):

P(X = 4) = (choose(20, 4) * choose(100-20, 4-4)) / choose(100, 4)

        = (4845 * 80) / 3921225

        ≈ 0.098117

d. P(X = 0):

P(X = 0) = (choose(20, 0) * choose(100-20, 4-0)) / choose(100, 4)

        = (1 * 77) / 3921225

        ≈ 1.97e-05

Therefore:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

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The complete question is:

Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. P(X = 0).

Answer:

what is P'Q'R'S

Step-by-step explanation:

Answer:

A = x² + 22x + 120

Step-by-step explanation:

Since the ball pit was originally 10 feet by 12 feet and each side is increased by the same amount which we would call x, the new length of sides are thus 10 + x and 12 + x respectively.

The area of the new pit is thus A = (10 + x)(12 + x), since it is a rectangle.

Expanding the brackets, we have

A = 10 × 12 + 10x + 12x + x²

collecting like terms, we have

A = 120 + 22x + x²

A = x² + 22x + 120

The hexadecimal system, commonly used in computing and mathematics, consists of 16 digits. These digits are represented by the numbers 0 to 9 and the letters A to F.

This means that there are a total of 16 possible values for each digit in the hexadecimal system. The inclusion of the letters A to F allows for the representation of values greater than 9. Each digit in the hexadecimal system represents a multiple of a power of 16, with the rightmost digit representing 16^0, the next digit representing 16^1, and so on.

The hexadecimal system is widely used in computer programming and digital systems, where it provides a convenient way to represent and manipulate binary data.

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Answer:

2 now mqrk MEEEE

Step-by-step explanation:

Answer:

ABC is isosceles

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hndnenenennjejejejekwkkwnwbfnfn

Answer:

????????????????????????????????

Step-by-step explanation:

The first case given is a deigned experiment and the second case is an observational study.

i. This is a designed experiment because the tunas were randomly assigned to two different treatments (polluted and non-polluted water) in an attempt to determine the effect of the treatment (methyl mercury) on the outcome (survival times). The experiment was intentionally designed and carried out to test a hypothesis.

ii. This is an observational study because the data was collected by simply observing the natural occurring relationship between increasing amounts of phosphorus in the lake and decreasing number of lake trout over time, without any manipulation or intervention by the biologist. The purpose is to describe or understand the relationship between two variables rather than to test a hypothesis.

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As described in statistics the mean standard deviation of the headway is 0.890

what is the statistics ?

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to a problem in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

solution:

P(0.995 ≤ x ≤ 1.445) = F(1.445) - F is the given mean value (0.995).

The distribution's cdf is

f(x) = { (1 - 1/x⁶ , x > 1) (0. x ≤ 1)

F(1.445) = 1 - (1/(1.445)⁶)

F(0.995) = 0

Now, using the values of F(1.445) and F(0.995) in P( 0.995 ≤ x ≤ 1.445) to get F(1.445) - F(0.995):

P( 0.995 ≤ x ≤ 1.445)

=1 - (1/(1.445)⁶) - 0

=0.890

Therefore the mean value of standard deviation is 0.890

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In scientific notation, a number is written as the base number times ten raised to a power. The base number, known as the significand, is also referred to as the mantissa.

The term mantissa is used for the fractional part of a common logarithm as well.

The mantissa is the fractional part of a logarithm. In the context of scientific notation, the mantissa refers to the base number, which is multiplied by 10 raised to a certain power to represent a number.

In other words, the mantissa is the significant digits of a number, excluding the leading and trailing zeros, expressed as a decimal fraction between 1 and 10. For example, in the number 3.24 x 10^5, the mantissa is 3.24.

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general equation of a population is

where a is the initial population and b the percent of growing

then replacing a=6 and b=12

and simplify

A scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.

Therefore, a scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.

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\(\\ \rm\Rrightarrow (5x+1)(5x-1)\)

\(\\ \rm\Rrightarrow (5x)^2-(1)^2\)

\(\\ \rm\Rrightarrow 25x^2-1\)

Answer: 25x²-1

i have attached a graph of it if you need it :)

The authors of "The Randomness of the National Lottery" completed in 2002 hit a snag when they found that one numbered ball, 38, was drawn so often that they believed there was bias in the selections.

Haigh and Goldie found that over 637 draws, each number should be drawn between 70 and 86 times. But they found that 38 came up 107 times, 14 times more than the next most drawn ball. The chance that a particular number was drawn more than 107 times in 637 draws was less than 1%.

Therefore, the authors were correct that the chance is under 1%.A spokesperson defending the lotteries randomness criticized the author's conclusion by saying that if you travel through an awful lot of data, you are always going to uncover patterns somewhere in her statement. Her statement is consistent with the decision-making processes of the hypothesis testing.

Therefore, it is entirely reasonable to suggest that the authors' approach was correct. There are always going to be anomalies in a lottery drawing that may or may not be a result of some kind of fraud. However, the fact that 38 was drawn more often than expected is highly suggestive of something that is out of the ordinary.

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In statics the mode is the data/value that occurs most often.

Now, we have the next set of data:

-7 -6 -6 -6 -7

The number -6 occurs 3 times and the number -7 occurs twice.

Therefore, the mode is given by the number -6.

Answer: -6

Mode: The most frequent number

Step-by-step explanation:

-6 is the most frequently used number

Answer:

−2

Step-by-step explanation:

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

The phase of inferential statistics which is sometimes considered to be the most crucial because errors in this phase are the most difficult to correct is "data gathering".

Inferential statistics are frequently employed to compare treatment group differences.

Some characteristics of inferential statistics are-

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The probability that greater than 99 out of 160 students will graduate on time is 0.1011, or 10.11%

To approximate the probability that greater than 99 out of 160 students will graduate on time given that the probability for a single student is 57%, we will use the normal distribution follow the given steps:

1. Determine the mean (μ) and standard deviation (σ) of the binomial distribution.
  μ = n * p = 160 * 0.57 = 91.2
  σ = sqrt(n * p * (1-p)) = sqrt(160 * 0.57 * 0.43) ≈ 6.498

2. Convert the problem to a standard normal distribution (Z-distribution) by finding the Z-score:
  Z = (X - μ) / σ
  Since we want to find the probability of more than 99 students graduating, we will use 99.5 (continuity correction).
  Z = (99.5 - 91.2) / 6.498 ≈ 1.276

3. Look up the Z-score in a standard normal (Z) table or use a calculator to find the area to the right of Z. The area to the left of Z is 0.8989.

4. Subtract the area to the left of Z from 1 to find the area to the right (our desired probability):
  P(X > 99) = 1 - 0.8989 = 0.1011

So, the probability that greater than 99 out of 160 students will graduate on time is approximately 0.1011, or 10.11% when rounded to four decimal places.

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Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

a. Yes, the individual scores can be rediscovered.

b. No, this is not possible with four players because there will not be enough information to solve the equations.

a. Let the individual scores of the three players be a, b, and c respectively. Since we know the total of the scores for players 1 and 2 is x, the total of the scores for players 2 and 3 is y, and the total of the scores for players 3 and 1 is z,

\(a + b = xb + c = yc + a = z2a + 2b + 2c = x + y + zWe can subtract x + y + z from both sides of the equation to get:2a + 2b + 2c - x - y - z = 02(a + b + c) - (x + y + z) = 02*(total of all 3 scores) - (total of 1 & 2 + total of 2 & 3 + total of 3 & 1) = 0a + b + c = (x + y + z)/2Then subtract x and y from both sides a + b - x - y = (z - x - y)/2a = (z - x - y)/2 + x\)

Since we know z, x, and y, we can plug these values in to solve for a. Similarly, we can use the same method to solve for b and c.

b. With three players, there were three equations with three unknowns. With four players, there will be four equations with four unknowns, so the equations will be underdetermined and there will not be enough information to solve them.

Therefore, it is possible to rediscover individual scores in a certain scenario. However, it is not feasible to do so with four players,

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The radius of the hoop is 8 inches.

We have,

The circumference of a circle is given by the formula C = 2πr

Where C is the circumference and r is the radius.

Rearranging the formula.

r = C / (2π)

Substituting the given value for the circumference of the hoop.

r = 50.24 in / (2 × 3.14)

r = 8 in (rounded to the nearest whole number)

Therefore,

The radius of the hoop is 8 inches.

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Answer:

B- 19.84

Step-by-step explanation:

To find the length of a side of a square from the area, find the square root of the area.

side length = sqrt (36)

side length = 6 inches