Can someone help me with this. Will make brainliest. Need answer and explanation/work. Thank you.

The probability of rolling a 7 with two dice is 1/6.

Probability is the measure of how likely something is to happen. It is expressed as a number between 0 and 1, where 0 indicates that something is impossible and 1 indicates that something is certain. Probability is used in a variety of ways, including to measure the chance of winning a game, the likelihood of an event occurring, or the probability of a certain outcome from a given set of data. Probability can also be used to make predictions about the future, as well as to analyze data and make decisions.

Therefore, the probability of Calamitous Clod rolling a 7 is also 1/6. This is because the probability of rolling a certain number on a die is the same regardless of the number of dice being used. Therefore, the probability of Calamitous Clod rolling a 7 is 1/6.

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We are asked to evaluate the limit of the given expression as x approaches infinity. Using analytic methods, we will simplify the expression and determine the limit value.

To evaluate the limit of the expression \\((\lim_{{x \to \infty}} \frac{{11x^3 - 4x}}{{5x^3 - 2}}\)\), we can focus on the highest power of x in the numerator and denominator. Dividing both the numerator and denominator by \(\(x^3\)\), we get:

\(\(\lim_{{x \to \infty}} \frac{{11 - \frac{4}{x^2}}}{{5 - \frac{2}{x^3}}}\)\)

As x approaches infinity, the terms \(\(\frac{4}{x^2}\) and \(\frac{2}{x^3}\) approach\) zero, since any constant divided by an infinitely large value becomes negligible.

Therefore, the limit becomes:

\(\(\frac{{11 - 0}}{{5 - 0}} = \frac{{11}}{{5}}\)\)

Hence, the limit of the given expression as x approaches infinity is\(\(\frac{{11}}{{5}}\)\).

Now let's move on to part (b), which asks about the implications of the result from part (a) on horizontal asymptotes. The result \(\(\frac{{11}}{{5}}\)\)indicates that there is a horizontal asymptote at y = \(\(\frac{{11}}{{5}}\)\). This means that as x approaches infinity or negative infinity, the function tends to approach the horizontal line y = \(\(\frac{{11}}{{5}}\)\). The presence of a horizontal asymptote can provide valuable information about the long-term behavior of the function and helps in understanding its overall shape and range of values.

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Answer: 48n + 120

Step-by-step explanation:

12(4n+10)

12(4n) + 12(10)

48n + 120

The error are;

1) The percentages do not sum to 100%

2)  Showing the pie chart on a slant violates the area principle.

A pie chart is used to show the relationship between variables. We can use the bar chart to categorize the relationship that exists between different variables. In this case, we are looking at the responses to a climate change survey.

We can see that there are the following errors in the chart;

1) The percentages do not sum to 100%

2)  Showing the pie chart on a slant violates the area principle.

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The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;

Part A:

Part B:

Part C:

Part A:

The correlation is the relationship between variables based on statistical data.

From the given table, the difference between consecutive terms of the x and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.

Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10

Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50

Therefore;

Part B:

Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the x and y-values is a linear function, which can be found as follows;

Slope of the equation, m = ∆y/∆x

Which gives;

m = 50/10 = 5

y - 2 = 5•(x - 0)

The function that best fits the data is therefore;

Part C:

The slope of the function is the coefficient of the variable x in the equation, y = m•x + c

The y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c

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Answer:

2 units.

Step-by-step explanation:

Because the line segment is simply translated, the length stays the same. It is perfectly identical to the original line segment.

Answer:

Our two selected points:

-3, 3

2, -4

-4 -(3)           7

_____ = - _____ = -7/5, D is your answer

2 - (-3)         5

An inscribed circle is tangent to

all 3 sides of the triangle it is inscribed in.

The correct option is the second option

Explanation

A circle is inscribed in the triangle if the triangle's three sides are all tangents to a circle. In this situation, the circle is called an inscribed circle, and its center is called the inner center, or incenter.

Since the triangle's three sides are all tangents to the inscribed circle, the distances from the circle's center to the three sides are all equal to the circle's radius

The method of sampling used in this scenario is convenience sampling.

Convenience sampling involves selecting individuals who are readily available and easily accessible to participate in the study.

In this case, the psychology students administered the survey to their friends, which suggests that the participants were chosen based on convenience and proximity rather than using a random or systematic sampling method.

Convenience sampling is commonly used in situations where it is more practical or feasible to select participants who are easily reachable, such as in classroom settings or personal networks.

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A linear-quadratic state estimator and a particle filter are both estimation techniques used in control systems, but they differ in their underlying principles and application domains.

A linear-quadratic state estimator, often referred to as a Kalman filter, is a widely used optimal estimation algorithm for linear systems with Gaussian noise. It assumes linearity in the system dynamics and measurements. The Kalman filter combines the predictions from a mathematical model (state equation) and the available measurements to estimate the current state of the system. It provides a closed-form solution and is computationally efficient. However, it relies on linear assumptions and Gaussian noise, which may limit its effectiveness in nonlinear or non-Gaussian scenarios.

On the other hand, a particle filter, also known as a sequential Monte Carlo method, is a non-linear and non-Gaussian state estimation technique. It employs a set of particles (samples) to represent the posterior distribution of the system state. The particles are propagated through the system dynamics and updated using measurement information. The particle filter provides an approximation of the posterior distribution, allowing it to handle non-linearities and non-Gaussian noise. However, it is computationally more demanding than the Kalman filter due to the need for particle resampling and propagation.

The choice between a linear-quadratic state estimator and a particle filter depends on the characteristics of the system and the nature of the noise. The Kalman filter is suitable for linear and Gaussian systems, while the particle filter is more versatile and can handle non-linearities and non-Gaussian noise. However, the particle filter's computational complexity may be a limiting factor in real-time applications.

In summary, a linear-quadratic state estimator (Kalman filter) is a computationally efficient estimation technique suitable for linear and Gaussian systems. A particle filter, on the other hand, provides more flexibility by accommodating non-linearities and non-Gaussian noise but requires more computational resources. The choice between these methods depends on the specific system characteristics and the desired accuracy-performance trade-off.

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Answer:

6(x+2)

Step-by-step explanation:

I hope this helps you out and if your feeling generous plz mark brainliest it helps me a lot thank you:)

The equation for the tangent line is y = -3x + 4 The value of dx²dy² at this point is 0 The given values of x, y, and t are:x = 2t⁴ + 10y = t⁸t = -1 We can find the value of y when t = -1 by substituting the value of t in the equation for y: y = (-1)⁸ = 1So, the point on the curve is (2(-1)⁴ + 10, (-1)⁸)

= (12, 1)We can find the derivative of x with respect to t as follows:dx/dt

= 8t³When t = -1, dx/dt = 8(-1)³

= -8

So the slope of the tangent line is -8.We can find the derivative of y with respect to x using the chain rule as follows:dy/dx = dy/dt ÷ dx/dtdy/dt

= 8t⁷dx/dt

= 8t³dy/dx

= 8t⁷ ÷ 8t³

= t⁴We can find the value of dy/dx when t

= -1 as follows:dy/dx

= (-1)⁴

= 1  So, the value of dy²/dx² at this point is:dy²/dx²

= d/dx (dy/dx)dy/dt = 8t⁷dx/dt

= 8t³dy²/dx²

= d/dt (dy/dx) ÷ dx/dtdy²/dx²

= 56t⁶ ÷ (-8)When t = -1, dy²/dx²

  = 56(-1)⁶ ÷ (-8) = 0  The equation for the tangent line is y

= mx + b, where m is the slope and b is the y-intercept. We have already found that the slope is -8 and the point on the curve is (12, 1).So, we can find b as follows:1

= -8(12) + b b = 97Therefore, the equation for the tangent line is

y = -8x + 97. We can simplify this equation as follows:

y = -3x + 4 (by dividing both sides by -8)

Thus, the equation for the tangent line is y = -3x + 4.The value of dx²dy² at this point is 0.

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When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

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The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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Answer:

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180 degrees

so

70 + 35 + x = 180 add like terms

105 + x = 180 subtract 105 from both sides

x = 75

Answer:

75  degrees

Step-by-step explanation

triangles add up to 180 degrees so, 70+35= 105 degrees, 180-105= 75 degrees

Answer:

125 sweets

Step-by-step explanation:

Let the total # of sweets the teacher bought be the variable, x.

We can set up this equation to find the # of sweets she bought:

40 · 3 + 5 = x

Because she gave 3 sweets each to her 40 students, we have to multiply these two numbers to get the # of sweets the teacher gave out.

120 + 5 = x

Then, since there's 5 extra sweets left, we can add it to the # of sweets the teacher gave out to get the total amount of sweets she bought.

125 = x

x = 125

125 sweets

Answer:

Total sweets = 125

Step-by-step explanation:

Number of sweets given to each student = 3

Number of sweets given to 40 students = 40*3 = 120

Number of sweets left with the teacher = 5

Total sweets = 120 + 5 = 125

Answer:

2.5

Step-by-step explanation

Pi R squared

radius is half diameter, so .9

Square the .9

Multiple that to 3.142

Answer:

Multiple of 3 from -3 to 15 are:-

3, 6, 9, 12 , 15

hope it is helpful to you ☺️

The probability that six families participated in a Halloween party is 0.16859

As per the given statement, "T3Yh of all families in Canada participated in a Halloween party."This implies that the probability of families participating in a Halloween party is 30%.

Now, if we select 14 families randomly, the probability of selecting 6 families from the selected 14 families is determined by the probability mass function as follows:

`P(x) = (14Cx) * 0.3^x * (1 - 0.3)^(14 - x)`

where P(x) represents the probability of selecting x families that participated in a Halloween party.

Here, x = 6

Thus, `P(6) = (14C6) * 0.3^6 * (1 - 0.3)^(14 - 6)``

P(6) = 0.16859`

Hence, the probability that six families participated in a Halloween party is 0.16859.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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The length of an edge of the cubical tank is approximately 9.41 cm.

To find the length of an edge of the cubical tank, we can use the given information.

We know that the water in the cubical tank was poured into an empty rectangular container until it was completely filled. Therefore, the volume of water in the rectangular container is equal to the volume of the cubical tank.

Let's assume that the length of an edge of the cubical tank is x cm. Since it is a cube, the volume of the cubical tank is x^3 cubic cm.

Now, let's calculate the volume of the rectangular container. We know that there were 788 cm of water left in the cubical tank. So, the volume of the rectangular container is 788 cubic cm.

Since the volume of the cubical tank is equal to the volume of the rectangular container, we have the equation: x^3 = 788.

To solve for x, we take the cube root of both sides of the equation: x = ∛788.

Calculating this, we find that x ≈ 9.41 cm.

Therefore, the length of an edge of the cubical tank is approximately 9.41 cm.

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Answer:

Your answer would be 7/20 or 0.35.

Answer:

the length of DE is 1/2*9 = 4.5

the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

The given partial differential equation is:

au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)

a) BCs (Boundary Conditions):

We have u(0, t) = 0 and u(π, t) = 0.

IC (Initial Condition):

We have u(x, 0) = x.

To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.

The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:

X(x) * T'(t) = 4 * X''(x) * T(t) / a

Dividing both sides by X(x) * T(t) gives:

T'(t) / T(t) = 4 * X''(x) / (a * X(x))

Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².

T'(t) / T(t) = -λ²

X''(x) / X(x) = -λ² * (a / 4)

Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.

Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.

Now, applying the boundary conditions:

1) u(0, t) = 0:

Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.

2) u(π, t) = 0:

Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.

Now, let's find the expression for u(x, t) using the initial condition:

u(x, 0) = X(x) * T(0) = x

Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:

C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x

This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.

Therefore, the solution for the initial value problem is:

u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)

where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.

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Answer:

30 m

Step-by-step explanation:

Picture the question as a triangle

The length of the string is the hypotenuse, 60 m

The angle from the ground is 30

The right angle C is from the height of the kite to the ground

The missing angle A 60 is located on the top of the kite

now find b, the height

The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

cos(A)=adj/hyp

cos(A)=b/c

b=c*cos(A)

b=60*cos(60)

b=30

The mode of a sample is the value that appears most often in the data set. It can be larger, smaller or equal to the mode of the population, depending on the sample size and the distribution of the population.

The mode of a sample is not necessarily equal to the mode of the population if the sample is truly random, as there is no guarantee that the most frequent value in the population will appear in the sample.

For example, let’s say the population has a mode of 10. If the sample size is 50, the probability of the sample having a mode of 10 is 0.2. The probability of the sample having a mode of 11 or larger is 0.4. The probability of the sample having a mode of 9 or smaller is also 0.4.

This means that the mode of the sample can be larger, smaller or equal to the mode of the population. It does not have to be equal to the mean of the population, as the mean is an average of all the values in the population and is not necessarily the most frequent value. Furthermore, the mode of the sample cannot be 500, as this is the size of the population, not a value that appears in the data set.

The mode of the sample can be larger, smaller or equal to the mode of the population, and cannot be equal to the mean of the population or equal to the size of the population.

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Answer: To calculate x in an equation, you can first look at the other numbers that aren't missing any values [say 2x + 60x = 248]. To find the value of x, bring the variable(s) to the left and bring all the remaining numbers to the right (I'm trying to explain this in a simple way)

Step-by-step explanation: math

Consequently, x = -6 and y = 0 provide the system of equations answer. The response gathering yields "(-6,0)" as the outcome.

She came back to compete in the meeting's final event, winning the knockout race. Their quick removal is the letdown. Take pride in your quick removal.

To solve this system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the equations. Here's how to do it:

To find: multiply the second solution by 4.

12x - 36y = -72

Eliminate x by combining the two equations:

5x + 4y + 12x - 36y = -30 - 72

Simplify and combine like terms:

17x - 32y = -102

Solve for x:

17x = 32y - 102

x = (32/17)y - 6

Substitute this expression for x into one of the original equations, and solve for y:

5x + 4y = -30

5[(32/17)y - 6] + 4y = -30

Simplify and solve for y:

(160/17)y - 30 = -30

(160/17)y = 0

y = 0

Substitute this value for y back into either of the original equations and solve for x:

3x - 9y = -18

3x - 9(0) = -18

3x = -18

x = -6

So the solution to the system of equations is x = -6 and y = 0. Therefore, the solution set is {(-6,0)}.

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Based on the given table, the profit-maximizing level of output for company Econislife is 4 units. At this quantity, the company's profit is $40.

To determine the profit-maximizing level of output, we need to analyze the relationship between total revenue (TR) and total costs (TC) for different quantities of output. The profit can be calculated as the difference between total revenue and total costs.

Looking at the table, we can see that as the quantity increases from 1 to 5, both total revenue and total costs increase. However, at a certain point, the increase in total costs outpaces the increase in total revenue, leading to a decrease in profit.

To find the profit-maximizing level of output, we compare the profits at different quantities.

Quantity 1: TR = $28, TC = $40, Profit = TR - TC = $28 - $40 = -$12

Quantity 2: TR = $56, TC = $45, Profit = TR - TC = $56 - $45 = $11

Quantity 3: TR = $84, TC = $55, Profit = TR - TC = $84 - $55 = $29

Quantity 4: TR = $112, TC = $72, Profit = TR - TC = $112 - $72 = $40

Quantity 5: TR = $140, TC = $120, Profit = TR - TC = $140 - $120 = $20

From the above calculations, it is evident that the profit is highest at Quantity 4. Therefore, the profit-maximizing level of output for company Econislife is 4 units. At this quantity, the company's profit is $40.

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