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Answer:

dark blue

Step-by-step explanation:

The second Borel-Cantelli lemma, we have P(lim sup Sn < ∞) = 0, which implies that Sn converges almost surely.

Let {Xn} be a sequence of random variables, and let Sn = X1 + X2 + ... + Xn be the corresponding sequence of partial sums. We want to show that if E(Xn²) is finite for all n, then Sn converges almost surely.

Let Yn = Xn^2. Then E(Yn) = E(Xn²) < ∞ for all n, since we are given that the second moments are finite. By the second Borel-Cantelli lemma, it suffices to show that the series ∑ P(Yn > ε) converges for every ε > 0.

Since Yn = Xn² ≥ 0, we have P(Yn > ε) ≤ P(|Xn| > √ε). Using Markov's inequality, we have:

P(|Xn| > √ε) ≤ E(|Xn|²)/ε = E(Yn)/ε.

Therefore, we have:

∑ P(Yn > ε) ≤ ∑ E(Yn)/ε = (1/ε) ∑ E(Yn) = (1/ε) ∑ E(Xn²) < ∞.

The last inequality follows from the fact that the second moments are assumed to be finite.

Thus, by the second Borel-Cantelli lemma, we have P(lim sup Sn < ∞) = 0, which implies that Sn converges almost surely.

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Answer:

[tex]0.1212...=\dfrac{4}{33}[/tex]

Step-by-step explanation:

A repeating decimal is a decimal number with a digit (or group of digits) that repeats forever.

There are three ways to show a repeating decimal:

0.1212... is a repeating decimal as there are two duplicates of the repeating block of digits "12" followed by an ellipsis.

To express a repeating decimal as a rational number, begin by assigning the decimal to a variable:

[tex]x=0.1212...=0.\overline{12}[/tex]

Multiply both sides by 100:

[tex]\implies x \cdot 100=0.\overline{12}\cdot 100[/tex]

[tex]\implies 100x=12.\overline{12}[/tex]

Subtract the first equation from the second to eliminate the part after the decimal:

[tex]\begin{array}{crcr}& 100x & = & 12.\overline{12}\\- & x & = & 0.\overline{12}\\\cline{2-4} & 99x & = & 12\phantom{.12}\\\end{array}[/tex]

Divide both sides of the equation by 99:

[tex]\implies \dfrac{99x}{99}=\dfrac{12}{99}[/tex]

[tex]\implies x=\dfrac{12}{99}[/tex]

Reduce the fraction to is simplest form by dividing the numerator and denominator by 3:

[tex]\implies x=\dfrac{12 \div 3}{99 \div 3}=\dfrac{4}{33}[/tex]

[tex]\textsf{Therefore, $0.1212...$ expressed in the form of a rational number is\;$\dfrac{4}{33}$}.[/tex]

After the battery is fully charged, Car B can go further than Car A.  Car B, as compared to Car A, had lower variability measurements. After the battery is completely charged, Car B can go further than Car A since Car A has a lower mean and median. Option D is Correct.

The median splits the data in half. A lower median indicates that Car A has less mileage than Car B.

Two measurements exist.

The measure of centre reveals how closely or widely the data are dispersed around the centre.

The measurements of centre are mean, median, and mode.

Car A travelled less since it had a lower mean and median.

We can find out how data changes with a single value using the measure of variability. The data is denser at the mean when the MAD is less. The MAD in Car B is lower. Data that is closer to the centre of the data set has a smaller IQR.

IQR is lower in Car B.

Consequently, automobile B travelled steadily since its IQR and MAD were lower. Option D is Correct.

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Correct Question:

Annabel is comparing the distances that two electric cars can travel after the battery is fully charged. Car A (miles) Car B (miles) Mean 145 200 Median 142 196 IQR 8 4 MAD 6 2 Part A Use the measures of center to make an inference about the data. Use the drop-down menus to complete your answer. Car A can travel further than Car B after the battery is fully charged. Part B Based on the data, which car performs most consistently? Explain. A. Car A because the measures of center are smaller for Car A than for Car B. B. Car B because the measures of center are smaller for Car B than for Car A. C. Car A because the measures of variability are smaller for Car A than for Car B. D. Car B because the measures of variability are smaller for Car B than for Car A.

The value of θ from the given right triangle is 50 degree.

The legs of given right angle triangle are 6 units and 5 units.

Here, opposite side = 6 units and adjacent side = 5 units

We know that, tanθ= Opposite/Adjacent

tanθ= 6/5

tanθ= 1.2

θ=50.19

θ≈50°

Therefore, the value of θ from the given right triangle is 50 degree.

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The probability of choosing a black chip and then another black chip is,

⇒ 1/3

Since, There are 4 + 6 = 10 chips in the bag.

And, 6 of them are black .

Hence, The probability that the first chip chosen will be black is,

⇒ 6/10

⇒ 3/5.

After that, there is one black chip less in the bag, so there are 9 chips in the bag, 5 of them are black.

Hence, The probability that the second chip chosen will be black is,

⇒ 5/9

Now, Multiply the probabilities to find the probability that the first chip will be black and the second chip will be black:

⇒ 3/5 × 5/9

⇒ 1/3

Thus, The probability of choosing a black chip and then another black chip is,

⇒ 1/3

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Based on the information provided, only one of the independent variables can be an indicator (dummy) variable, which is:

- The player was traded in the last 5 years

Based on the information provided, only one of the independent variables can be an indicator (dummy) variable, which is:

- The player was traded in the last 5 years

This variable can take on a value of 0 or 1, where 0 represents that the player was not traded in the last 5 years, and 1 represents that the player was traded in the last 5 years. The other independent variables are continuous variables (e.g., player's age, player's height, career free throw percentage, average points per game) or categorical variables that do not need to be represented as dummy variables (e.g., the team had greater than 45 wins in the previous season).

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The coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x) is 1/15.

To find the coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x), we need to write the Taylor series for [tex]e^x[/tex] and sin(x) and then multiply them to get the Taylor series for f(x). The Taylor series for e^x is:

[tex]e^x[/tex] = 1 + x + (x²/2!) + (x³/3!) + ...

The Taylor series for sin(x) is:

sin(x) = x - (x³/3!) + (x⁵/5!) - ...

Multiplying these two series, we get:

f(x) = [tex]e^x[/tex] sin(x) = (1 + x + (x²/2!) + (x³/3!) + ...) × (x - (x³/3!) + (x⁵/5!) - ...)

Expanding this out and collecting the terms with x³, we get:

f(x) = x - (x³/3!) + (7x³/5!) + ...

Therefore, the coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x) is -1/6 + 7/120 = 1/15.

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Check the picture below.

so if we just get the volume of the whole box, and the volume of the balls, if we subtract the volume of the balls from that of the whole box, what's leftover is the part we didn't subtract, namely the empty space.

[tex]\stackrel{ \textit{\LARGE volumes} }{\stackrel{ whole~box }{(3.5)(3.5)(12.1)}~~ - ~~\stackrel{\textit{three balls} }{3\cdot \cfrac{4\pi (1.65)^3}{3}}} \\\\\\ 148.225~~ - ~~17.9685\pi ~~ \approx ~~ \text{\LARGE 91.8}~cm^3[/tex]

It is possible for one set of data to have a scatterplot that appears linear while the other does not, even if both groups started with the same number of dice and followed the same removal procedure.

This is because the way the dice were removed could have been different between the two groups, leading to different patterns of results. Additionally, other factors such as the order in which the dice were removed or the number of trials conducted could also affect the resulting scatterplot.

Ultimately, the scatterplot is a visual representation of the relationship between the variables being measured, and it can take on many different forms depending on the specific data and conditions being analyzed.

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Answer:

Step-by-step explanation:

To determine if there is a positive linear association between the hours worked and the daily wages of waiters in a restaurant, you can create a scatter plot of the data and look for a pattern.

Once you have the data, you can use a statistical software or a spreadsheet program to create a scatter plot. You can then visually inspect the scatter plot to see if there is a clear pattern of a positive linear association between the two variables.

If there is a positive linear association, the data points on the scatter plot will form a roughly straight line that slopes upwards from left to right. The closer the data points are to the line, the stronger the association.

So, the data table that indicates a positive linear association between the hours worked and the daily wages of waiters in a restaurant is the one where the scatter plot shows a clear upward trend.

Option e. "The number of trials is not fixed" would be the correct answer.

The assumption of the Binomial distribution that is NOT included in the options provided is that the number of trials must be fixed in advance. This means that the Binomial distribution applies only to situations where there is a fixed number of independent trials, each with the same probability of success, and the interest is in the number of successes that occur in these trials. Therefore, option e. "The number of trials is not fixed" would be the correct answer.

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The Surface Area of the regular hexagonal prism is 92.784 square unit.

We have,

a = 2 unit

h= 6 unit

So, surface area of Prism

= 6 ah + 3√3 a²

= 6(2)(6) + 3√3 (2)²

= 72 + 12√3

= 92.784 square unit.

Thus, the Surface Area is 92.784 square unit.

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The perimeter and area of the given polygon are:

Perimeter = 22.325 units

Area = 25 square units

Using Pythagoras theorem, we can find the length of the sides of the polygon as:

a = √(1² + 3²)

a = √10

b = √(3² + 3²)

b = 2√9

c = √(3² + 3²)

c = 2√9

d = √(1² + 3²)

d = √10

e = 4

Thus:

Perimeter = 2√10 + 4√9 + 4

Perimeter = 22.325 units

Area = 2(¹/₂ * 1 * 3) + 2(¹/₂ * 3 * 3) + (4 * 3)

= 25 square units

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The average rate of change of f(x) = x with respect to x over the interval a = 1 is 1.

To determine the average rate of change of f(x) = x with respect to x over the interval a, we'll use the formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

In this case, the interval a is 1, so let's choose an interval b. We can use any value for b, but let's choose b = 2 for simplicity.

Step 1: Find f(a) and f(b)
f(x) = x, so:
f(1) = 1
f(2) = 2

Step 2: Plug the values into the formula
Average Rate of Change = (f(2) - f(1)) / (2 - 1)
Average Rate of Change = (2 - 1) / (2 - 1)

Step 3: Calculate the result
Average Rate of Change = (1) / (1)

The average rate of change of f(x) = x with respect to x over the interval a = 1 is 1.

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The equation which can be used to determine the total amount, t, Frankie will have spent after m months on his cell phone plan is t = 30 + 45m.

Given that,

Frankie has a new cell phone plan.

He will pay a one-time activation fee of 30$, and 45$ each month.

One time activation fee = $30

Amount each month = $45

Amount for m months = 45m

Total amount for the plan = 30 + 45m

If t represents the total amount for the cell phone activation plan, the required equation can be written as,

t = 30 + 45m

Hence the required equation for the cell phone plan is t = 30 + 45m.

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Phil's life expectancy is 56.3 years.

Based on the provided data, the life expectancy for Phil, a 21-year-old male, is 56.3 years. Therefore, the correct answer is 56.3 years.

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This change in shipping costs may or may not affect the company.

We need additional information to determine the exact effect.

Option B is the correct answer.

We have,

While the reduction in shipping costs from Plant 3 to the North region is significant, we need more information about the company's current shipping plan, routes, and costs associated with other plants to determine if this change will impact their overall shipping strategy.

Thus,

This change in shipping costs may or may not affect the company.

We need additional information to determine the exact effect.

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The density of the ball in the air is given as follows:

d = 4 x 10^5 ounces/ft³.

The density is calculated as the division of the mass by the volume of an object, as follows:

d = m/v.

The ball in this problem is spherical with a diameter of 0.05 feet = radius of 0.025 feet, hence the volume is given as follows:

V = 4 x 3.1416 x 0.025³/3

V = 6.545 x 10^-5 ft³.

The ball in the air is inflated, hence the mass is given as follows:

m = 22.93 ounces.

Thus the density of the ball is given as follows:

d = 22.93/(6.545 x 10^-5)

d = 4 x 10^5 ounces/ft³.

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There is no solution to this problem. None of the answer choices (A, B, C, D) are correct.

Let's start by representing the original two-digit number as 10x + y, where x represents the tens digit and y represents the ones digit.

When we reverse the digits, we get the number 10y + x. According to the problem, this number is 9 less than three times the original number:

10y + x = 3(10x + y) - 9

Simplifying this equation, we get:

10y + x = 30x + 3y - 9

7y - 29x = -9

We also know that the difference between these two numbers is 45:

(10x + y) - (10y + x) = 45

9x - 9y = 45

x - y = 5

Now we have two equations with two variables, which we can solve using substitution or elimination. I'll use elimination:

7y - 29x = -9
-7y + 7x = 35 (multiplying the second equation by -7)

Adding these two equations, we get:

-22x = 26

x = -13/11

This doesn't make sense, since x should be a digit between 1 and 9.

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Result:

1. Based on the properties, the most precise name for figure is A. parallelogram

2. From the properties, the most precise name for the figure is B. rhombus.

We can determine the precise name of the figure calculating the slopes of AB, BC, CD, and DA using the slope formula and/or the distance formula:

1. Using the slope formula:

AB = (0 - (-6))/(2 - (-5)) = 2

BC = (9 - 0)/(11 - 2) = 9/9 = 1

CD = (3 - 9)/(4 - 11) = -6/-7 = 6/7

DA = (-6 - (-5))/( -5 -(-5)) = 0

Calculate the lengths of the sides using distance formula:

AB = [tex]\sqrt((2 - (-5))^2 + (0 - (-6))^2)[/tex] = [tex]\sqrt(7^2 + 6^2)[/tex] = [tex]\sqrt{85}[/tex]

f BC = [tex]\sqrt((11 - 2)^2 + (9 - 0)^2)[/tex] = [tex]\sqrt(9^2 + 9^2)[/tex] = 9√2)

CD = [tex]\sqrt((4 - 11)^2 + (3 - 9)^2)[/tex] = sqrt[tex]\sqrt(7^2 + 6^2)[/tex] = √85

DA = [tex]\sqrt((-5 - 4)^2 + (-6 - (-9))^2)[/tex] = [tex]\sqrt(9^2 + 3^2)[/tex] = 3√10

The slopes of AB and CD are equal (2 and 6/7, respectively), and the slopes of BC and DA are equal (1 and 0, respectively).

Therefore, opposite sides are parallel that is a parallelogram.

2. First, we can calculate the slopes of AB, BC, CD, and DA using the slope formula:

AB = (1 - (-4))/(-7 - (-9)) = 5/2

BC = (5 - 1)/(1 - (-7)) = 4/4 = 1

CD = (0 - 5)/(-1 - 1) = -5/-2 = 5/2

DA = (-4 - 0)/(-9 - (-1)) = 4/8 = 1/2

Next, using the distance formula, we calculate the lengths of the sides:

AB = [tex]\sqrt((-7 - (-9))^2 + (1 - (-4))^2)[/tex] = [tex]\sqrt(2^2 + 5^2)[/tex] = [tex]\sqrt29[/tex]

BC = [tex]\sqrt{(1 - (-7))^2 + (5 - 1)^2}[/tex] = [tex]\sqrt(8^2 + 4^2)[/tex] = 4[tex]\sqrt17[/tex]

CD = [tex]\sqrt((-1 - 1)^2 + (0 - 5)^2)[/tex] = [tex]\sqrt(2^2 + 5^2)[/tex] = [tex]\sqrt29[/tex]

DA = [tex]\sqrt((-9 - (-1))^2 + (-4 - 0)^2)[/tex] = [tex]\sqrt(8^2 + 4^2)[/tex] = [tex]\sqrt80[/tex])

The slopes of AB and CD are equal (5/2 and 5/2, respectively), and the slopes of BC and DA are equal (1 and 1/2, respectively). meaning the opposite sides are parallel.

AB and CD have the same length ([tex]\sqrt(29)[/tex]), and BC and DA have the same (4[tex]\sqrt(17}[/tex]), which means it's a rhombus.

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Answer:

1/870 ≈ 0.0011494 or about 0.115% (rounded to 6 decimal places)

Step-by-step explanation:

The first digit can be any of the numbers between 10 and 40, except for those that end in 6 (since the last digit of all three numbers is 6). This leaves us with 30 numbers to choose from for the first digit. Similarly, the second digit can be any of the numbers between 10 and 40, except for those that end in 6 and the one chosen for the first digit. This leaves us with 29 numbers to choose from for the second digit.

For the third digit, we have only one option since we know it ends in 6.

So the total number of possible combinations is:

30 * 29 * 1 = 870

Out of these, only one combination is the correct one. Therefore, the probability of guessing the combination correctly on the first try is:

1/870 ≈ 0.0011494 or about 0.115% (rounded to 6 decimal places)

Answer:

[tex]\textsf{y=\frac{1}{3}x+3}[/tex][tex]y = \frac{1}{3} x+3[/tex]

Step-by-step explanation

[tex]\textsf{*slope intercept form: y = mx +b}[/tex]

---------------------------------------------

[tex]\textsf{x - 3y = -9}[/tex]

Subtract x from both sides:

[tex]\textsf{-3y = -x - 9}[/tex]

Divide both sides by -3:

-3y/-3 = -x/-3 - 9/-3

[tex]\textsf{y = 1/3x +3}[/tex]

[tex]-jurii[/tex]

When a=0.02 and n=24, [tex]X_{left}^{2}[/tex] = 9.260 and [tex]X_{right}^{2}[/tex]= 41.638. In order to calculate [tex]X_{left}^{2}[/tex] and [tex]X_{right}^{2}[/tex] when a=0.02 and n=24, we need to use the chi-squared distribution table. This table provides us with the critical values for a given level of significance (alpha) and degrees of freedom (df).

To answer your question, when a=0.02 and n=24, we will find the [tex]X_{left}^{2}[/tex] and [tex]X_{right}^{2}[/tex] values using the Chi-square distribution table.

Step 1: Determine the degrees of freedom. In this case, the degrees of freedom (df) are equal to n-1, so df = 24 - 1 = 23.

Step 2: Determine the significance level (alpha) and divide it by 2. Since a = 0.02, the significance level is [tex]\frac{\alpha}{2} =0.01[/tex] for each tail (left and right) of the distribution.

Step 3: Use the Chi-square distribution table to find the critical values. Look for the values corresponding to the degrees of freedom (23) and significance level (0.01) in each tail.

According to the Chi-square distribution table:
[tex]X_{left}^{2}[/tex]= 9.260
[tex]X_{right}^{2}[/tex]= 41.638

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Answer:

Please mark me the brainliest

Bank Balance  | Amount Owed

---------------------|-------------

-$150               | $150

-$325              | $325

-$275              | $275

To find the amount owed, we simply take the absolute value of each bank balance. The player who owes the greatest amount is the one with the largest absolute value bank balance. In this case, that would be Malcolm, who owes $325.

Step-by-step explanation:

The surface area of the figure is 132 square units.

Option D is the correct answer.

We have,

The figure has two types of shapes.

- 3 rectangles

- 2 triangles

Now,

Area of the 3 rectangles.

= 5 x 10 + 4 x 10 + 3 x 10

= 50 + 40 + 30

= 120 square units

Area of 2 triangles.

= 1/2 x 4 x 3 + 1/2 x 4 x 3

= 1/2 x 12 + 1/2 x 12

= 6 + 6

= 12 square units

Now,

Total surface area.

= 120 + 12

= 132 square units.

Thus,

The surface area of the figure is 132 square units.

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Answer: -15

Step-by-step explanation:

x+y=10

y=-x+10

2x+3(-x+10)=45

2x-3x+30=45

-x=15

x=-15

Answer:

A P-value < 0.01

Step-by-step explanation: