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The smallest value of x in the Poisson distribution is 0, which means that no cars can pass through the intersection in a given minute.

For explain further, a Poisson distribution is a statistical model that describes the probability of a given number of events occurring in a fixed period of time, such as cars passing through an intersection in a minute.

In a Poisson distribution, the probability of x events occurring in a given minute is given by the equation P(x) = e-λλx/x!, where λ is the average number of events in a given minute. In this case, λ would be the average number of cars that pass through the intersection per minute.

The probability of 0 cars passing through the intersection in a given minute is e-λλ0/0! = 1, which is the highest probability in the distribution. Therefore, the smallest value of x in a Poisson distribution is 0.

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Explanation

Opposite sides are 5 miles each and for each semicircle we have:

Then the lenght of the track is:

Approximately 13.1416 miles

a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).

(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.

Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.

Now, let's find the expected value of X:

E[X] = E[Y/n] = E[Y]/n = np/n = p.

Therefore, X is an unbiased estimator of p.

(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.

Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.

(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:

E[X(1-X)] = E[X - X²] = E[X] - E[X²].

We already know that E[X] = p from part (a).

Now, let's find E[X²]:

E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².

Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:

E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.

Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].

(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.

E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].

For unbiasedness, we want this to be equal to p(1-p)/n:

c[(n-1)[p(1-p)/n]] = p(1-p)/n.

Simplifying, we have:

c(n-1)p(1-p) = p(1-p).

Since this should hold for all values of p, (n-1)c = 1.

Therefore, the value of c is c = 1/(n-1).

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Answer:

1548.66 feet

Step-by-step explanation:

We can draw a straight line down the middle to form two right triangles

This will split the 70 degree angle into two 35 degree angles

We now have two 90-35-55 right triangles

Now we can use cos(55) * the hypotenuse on both sides to get the distance across the lake

Thus we have:

1200cos(55 = 688.29

1500cos(55 = 860.36

Best of luck

Answer: 28282

Step-by-step explanation:

I think

Answer:

d. 7/9

Step-by-step explanation:

The total points earned by both Joy and Denise: 5/9 + 2/9 = 7/9

Answer:7/9

Step-by-step explanation:U basically add 2/9 and 7/9 coz they have the same denominators

Answer:

D). The distribution of the data is symmetrical, so the mean and median are within the "2.1-3 mile" category.

Step-by-step explanation:

The last statement i.e. 'The distribution..."2.1-3 mile" category' correctly asserts a true claim regarding the data provided in the given histogram. It aptly states that the dissemination of the data is uniform(2, 4, 5, 4, 2(no. of students) live between the distance of 0.1 to 5 miles from the school) and this causes both the mean, as well as, the median of the distribution to fall in the category between '2.1 to 3 mile.' Thus, option D is the correct answer.

Yes, according to the Central Limit Theorem, when the sample size is large enough (typically n ≥ 30), the sampling distribution of the sample mean tends to follow a normal distribution, regardless of the shape of the population distribution.

In this case, since the sample sizes are n = 33 and n = 66, which are both larger than 30, we can conclude that the sampling distribution of the sample mean will be approximately normally distributed.

To clarify, the Central Limit Theorem states that as the sample size increases, the distribution of sample means becomes increasingly close to a normal distribution, even if the population distribution is not normally distributed. This is a fundamental concept in statistics that allows us to make inferences about population parameters based on sample statistics.

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The graph of f(x) consists of four line segments that can be represented by four equations, each describing a different section of the graph. Let's call these equations f1(x), f2(x), f3(x), and f4(x). To find g(x), we need to integrate f(t) with respect to t from some lower limit a to x, where a is the left endpoint of the interval on which f(x) is defined.

For example, suppose that f(x) is defined on the interval [0, 4] and is given by the following equations:

f1(x) = 0 for 0 ≤ x < 1
f2(x) = 2x - 2 for 1 ≤ x < 2
f3(x) = -2x + 6 for 2 ≤ x < 3
f4(x) = 0 for 3 ≤ x ≤ 4

Then, g(x) = x - 4f(t)dt for a = 0 and x between 0 and 4. We can break this integral into four parts corresponding to each of the line segments in f(x). For example, to find the first part of g(x), we integrate f1(t) from 0 to x:

g1(x) = x - 4(∫₀ˣ 0 dt) = x

Similarly, we can find the other parts of g(x) by integrating the corresponding line segments:

g2(x) = x - 4(∫₁ˣ (2t - 2) dt) = x² - 8x + 12
g3(x) = x - 4(∫₂ˣ (-2t + 6) dt) = -x² + 10x - 20
g4(x) = x - 4(∫₃ˣ 0 dt) = x

So, the function g(x) is a piecewise-defined function consisting of four different quadratic equations. It requires breaking down the problem into different parts, describing the equations for each section of the graph, and then finding the integral for each part to determine the function g(x).

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Answer: The answer is 500 hope this helps!

Step-by-step explanation:

The probability of drawing two yellow balls if they're not replaced exists 1/45.

The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.

Number of yellow marbles be 2

Number of pink marbles be 3

Number of blue marbles be 5

Total number of marbles = 2+3+5 = 10

The probability of removing the first yellow ball = 2/10

Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.

Probability of drawing the second yellow ball = 1/9.

Probability of drawing two yellow balls if they're not replaced

= 2/10 × 1/9

= 2/90

= 1/45

The probability of drawing two yellow balls if they're not replaced exists 1/45.

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if it wants to reduce the dollars flowing out of the country, the United States can limit the number of Japanese cars being imported by imposing an Import Quota.

Import Quota:

An import quota is a type of trade restriction that places a physical limit on the amount of goods that can be imported into a country during a specific period of time. Like other trade restrictions, quotas are generally used to the benefit of commodity producers in a given economy (protectionism). The essence of import quotas is to limit the amount of foreign goods that can be brought into a country. Quotas work by allowing only those authorized through a license or government contract to bring in the amount specified in the contract. When the quantity specified in the quota is reached, no more goods can be imported during this period.

There are also quota insurance programs where liability and premiums are distributed proportionately among insurers. For example, three companies have a $1,000,000 fire insurance policy per quota, Company A receives 50% ($500,000), Company B receives 30% ($300,000), and Company C receives 20% ($200,000). If the annual bonus is $5,000, Company A will receive $2,500, Company B will receive $1,500 and Company C will receive $1,000. Company A pays 50%, company B 30% and company C 20% for each claim.

Complete Question:

To reduce dollars flowing out of the country, the United States can take measures to limit the number of foreign cars imported from Japan by imposing a(n).

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Answer:

=5x2+5x

Step-by-step explanation:

Let's simplify step-by-step.

3x+3x2+2x2+2x

Answer:

u kqmnwnb jwkoajh wmkn.q

Answer:

8.50 divided by 1.25 then when u get the answer subtract 40

Answer:

25

Step-by-step explanation:

so instantly 40-8.50=31.5

The question is very vague because it doesn't state the number of rides he wants to go on in minimum.

if you do 1.25x25=31.25

According to that, he will leave with a change of 0.25 and obv u cannot go on half a ride...

So in about 2 mins i guess it is 25???

Add me on instagram: vnshl

Answer: (4x5) / 10 - 5 = 5

Step-by-step explanation: 20/10 = 10

10-5 = 5

Answer: 90 degrees

Step-by-step explanation:

The hypotenuse is opposite the right angle, which is created by the two shortest sides.

The coordinates of the ice cream shop, where Michael and Emma plan to meet before going to the library located at point (2, -3), can be determined by considering a specific location that is convenient for both of them.

Since the question does not provide any specific information about the location of the ice cream shop, we can assume that it can be any point in the vicinity of the library. Therefore, we have the freedom to choose the coordinates of the ice cream shop based on convenience or other factors.
For example, one possible set of coordinates for the ice cream shop could be (1, -2), which is one unit to the left and one unit higher than the library. However, it is important to note that without additional information, the exact coordinates of the ice cream shop cannot be determined.

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The exact value of tan 120° is -√3. This means that at the angle of 120 degrees, the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle is equal to the negative square root of 3.

To find the exact value of tan 120° using a double-angle identity, we can utilize the tangent double-angle identity, which states:

tan(2θ) = (2tanθ) / (1 - tan^2θ)

In this case, we want to find the value of tan 120°, so we can rewrite it as tan(2 * 60°), since 2θ is equal to 2 * 60°.

Let's substitute θ = 60° into the double-angle identity:

tan(2 * 60°) = (2 * tan 60°) / (1 - tan^2 60°)

We know that the tangent of 60° is equal to the square root of 3 (√3). Therefore, we can substitute tan 60° with √3:

tan(2 * 60°) = (2 * √3) / (1 - (√3)^2)

Now, we simplify the expression further:

tan(2 * 60°) = (2√3) / (1 - 3)

                  = (2√3) / (-2)

                  = -√3

Therefore, the exact value of tan 120° is -√3.

In summary, using the tangent double-angle identity, we found that the exact value of tan 120° is -√3. This means that at the angle of 120 degrees, the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle is equal to the negative square root of 3.

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Answer:

for this problem we use the sine function

\( \sin(x) = \frac{opp}{hyp} \\ \sin(38 ) = \frac{x}{100} \)

multiply both sides of the equation by 100

\(100 \sin(38) = \frac{100x}{100} \)

100 cancels on the right hand side of the equation

\(100 \sin(38) = x \\ x = 61.566\:ft\)

Answer:

Step-by-step explanation:

3.733333333

76%.

To find the proportion of students who participate in either sports or academic clubs at Cityville High School,

add together the percentages of students who participate in sports (35%) and academic clubs (43%),

and subtract the percentage of students who participate in both (12%).

The result is the proportion of students who participate in either sports or academic clubs, which is 76%.

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After 1st Translation  (x,y) → (x-6.y) = X(-4,4), Y(0,0), Z(1,2)

After 2nd Translation (x, y) → (x+2y+7) = X(4,11), Y(8,7), Z(9,9)

What is translation?

And image After Composition means resultant image after you plot the translated points.

So, Given Vertices are X(2,4), Y(6,0), Z(7,2)

Then after 1st Translation = X(-4,4), Y(0,0), Z(1,2)

After 2nd Translation = X(4,11), Y(8,7), Z(9,9)

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Answer:

going in the order top to bottom

i)

2

2

2

2 and 2

ii)

2 and 2

2

2

2 and 2

iii)

2

2

2 and 2

2 and 2

Step-by-step explanation:

you have to find out what number you times to get the number they have given you (eg: you have to get 4 and they have given you the number 2, 2 times what makes 4? the answer is 2)

Answer:

Can you add if you can add you have to add up every thing and the answer will be

we can solve for the coefficients a₀, a₁, a₂, and a₃ by equating the corresponding terms in the power series expansion to the derivatives obtained from the differential equation.

Start by assuming a power series form for the general solution: y(x) = Σ[ n=0 to ∞ ] (a_n * (x - x0)^n). Substitute this power series into the differential equation and expand it using the binomial theorem. Equate the coefficients of like powers of (x - x0) to zero.

This will give you a system of equations. Solve the system of equations to find the values of a_0, a_1, a_2, and a_3 (the coefficients of the first four nonzero terms). Substitute these coefficients back into the power series to obtain the desired expansion.

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Answer:

Step-by-step explanation:

Wei will be represented by the variable 'w', and Nora 'n'

a:

Wei starts with $50, and will add $150 to it every month (x)

So, here is our equation:

W = 50 + 150x

b:

Likewise, Nora starts with $200 and will add $150 to it every month (x)

So, here is the equation of that:

N = 200 + 150x

c:

see attached screenshot

There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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