Can someone pls help me out with this equation of math.
I’ll mark you brainlist if you show your answer step by steps

Step-by-step explanation:

the intersection angles between a line and 2 parallel lines are the same for each parallel line (otherwise they would not be parallel).

and the intersection angles on one side of a line are the same as in the other side - just left-right mirrored.

so,

angle 2 = angle 4 = angle 6 = angle 8 = 60°

The average value of the function f(x) = -4x⁽⁻²⁾over the interval [-5, -2] is -1/4.

To find the average value, we need to compute the definite integral of the function over the given interval and divide it by the length of the interval.

To calculate the definite integral, we can integrate the function f(x) with respect to x. The integral of -4x⁽⁻²⁾ is -4 * (-1/x) = 4/x.

To evaluate the definite integral over the interval [-5, -2], we subtract the value of the integral at the lower limit (-2) from the value of the integral at the upper limit (-5). In this case, the definite integral is 4/(-2) - 4/(-5) = -10/2 + 2/5 = -5 + 2/5 = -23/5.

The length of the interval [-5, -2] is (-2) - (-5) = 3. Finally, we divide the value of the definite integral (-23/5) by the length of the interval (3) to find the average value: (-23/5) / 3 = -23/15 = -1/4.

Therefore, the average value of f(x) = -4x⁽⁻²⁾ over the interval [-5, -2] is -1/4.

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A data set that consists of observations on a variable or several variables over time is called a time-series data set.

It is used to study the behavior of a variable over time, and it has a natural ordering of observations. It is widely used in econometrics, finance, and other fields that require the analysis of time-dependent data.Time-series data can be either a continuous data set or a ., depending on the frequency of the observations. Continuous data sets have observations at each moment in time, whereas discrete data sets have observations at specific points in time such as daily, weekly, monthly, quarterly, or yearly.

The analysis of time-series data involves several techniques, such as trend analysis, seasonal analysis, and cyclical analysis. These techniques are used to identify patterns and trends in the data. Time-series data is an essential tool in the study of economic, financial, and social phenomena, and it provides valuable information for decision-making

Time-series data sets are a set of data that contains observations of one or more variables over time. Such data sets are crucial in the fields of finance, economics, and various other areas of research that depend on the analysis of time-dependent data.

There are two types of time-series data: continuous and discrete. The former records observations at every moment in time, while the latter has data at specific points in time, such as daily, weekly, or monthly. Trend, seasonal, and cyclical analyses are all examples of methods used to analyze time-series data.

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Answer:

The average monthly payment would be most affected by Mark's observation of one significantly lower payment. The reason is that the average is calculated by summing all the payments and dividing by the total number of payments, so any extreme values (such as the significantly lower payment) can have a substantial impact on the average value.

Step-by-step explanation:

Answer:

AB = 2

Step-by-step explanation:

Using the secant- secant theorem, that is

PA × PB = PD × PC , substitute values

10(10 + AB) = 8(8 + 7)

100 + 10AB = 8 × 15 = 120 ( subtract 100 from both sides )

10AB = 20 ( divide both sides by 10 )

AB = 2

we can estimate that the proportion of defectives being produced by the machine is around 0.316.

What is proportion?

A comparison between the size, number, or amount of one thing or group with that of another. In our class, there are three boys for everyone lady.

If the random sample of size 2 yields 2 defects, that means both items in the sample were defective. Let p be the proportion of defectives being produced by the machine.

The probability of selecting a defective item on the first draw is p, and the probability of selecting a defective item on the second draw is also p (assuming sampling without replacement).

Since both items were defective, the probability of this happening is p * p = p².

So,

p² = (number of samples with 2 defects) / (total number of samples)

We don't know the values of these numbers, but we can use them to estimate p. For example, if we had a total of 100 samples and 10 of them had 2 defects, then:

p² = 10/100 = 0.1

p ≈ √(0.1) ≈ 0.316

Hence, we can estimate that the proportion of defectives being produced by the machine is around 0.316.

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Answer:

B. 1/4

Step-by-step explanation:

-4-(-2)/-3-5=

-4+2/-3-5=

-2/-8=

1/4

The given relation is not an equivalence relation.

To show that a relation is an equivalence relation, it must satisfy three properties: reflexive, symmetric, and transitive.

Reflexive property: Every element should be related to itself. In this relation, we have (0, 0), (1, 1), and (6, 6), so the reflexive property holds.

Symmetric property: If (a, b) belongs to R, then (b, a) must also belong to R. Here, we have (0, 1), (1, 0), (1, 6), and (6, 1), which satisfy the symmetric property.

Transitive property: If (a, b) and (b, c) belong to R, then (a, c) must also belong to R. In this relation, we have (0, 1) and (1, 6), which implies (0, 6) should belong to R for the transitive property to hold. However, (0, 6) is not part of the relation R, so the transitive property is violated.

Therefore, the given relation is not an equivalence relation.

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Here are a few reasons why researchers exercise caution when interpreting statistical significance: Avoiding Type I and Type II errors, Generalizability, Replicability, Methodological limitations.

Researchers are careful about drawing conclusions regarding statistical significance because statistical significance is a measure of the likelihood that the observed results are not due to random chance. When conducting research, researchers aim to make inferences and draw conclusions based on evidence that is reliable and valid.

Here are a few reasons why researchers exercise caution when interpreting statistical significance: Avoiding Type I and Type II errors, Generalizability, Replicability, Methodological limitations.

Avoiding Type I and Type II errors: When testing hypotheses, there is always a possibility of making errors. Type I error occurs when a researcher mistakenly rejects a true null hypothesis (false positive), and Type II error occurs when a researcher fails to reject a false null hypothesis (false negative). By being cautious, researchers strive to minimize these errors and ensure that their conclusions are accurate.

Generalizability: Researchers often want to generalize their findings from a sample to a larger population. Statistical significance provides an indication of how likely the findings can be applied to the broader population. Drawing conclusions without considering statistical significance may lead to misleading or unreliable generalizations.

Replicability: Scientific research should be replicable, meaning that other researchers should be able to obtain similar results when conducting the same study. Statistical significance helps assess whether the observed effects are consistent and reproducible across different studies. Without proper consideration of statistical significance, it becomes difficult to determine if the results can be replicated reliably.

Methodological limitations: Research studies can have various limitations such as small sample sizes, confounding factors, measurement errors, or biases. By carefully assessing statistical significance, researchers can better understand the limitations of their study and make more informed conclusions.

In summary, researchers are cautious about drawing conclusions regarding statistical significance to ensure the validity, reliability, generalizability, and replicability of their findings. By exercising care in interpreting statistical significance, researchers aim to make robust and trustworthy conclusions based on the available evidence.

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The measure of the interior angle adjacent to the sixth exterior angle of the heaxagon is 118°.

Interior angles are those that lie inside a polygon.

To calculate an interior angle of a hexagon, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Recall that, the sum of an interior and exterior angle is 180°

Where:

Substitute the value of a into equation 2

Hence, the value of the interior angle is 118°.

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Answer:

9/40

Step-by-step explanation:

3/5 - 3/8

24/40 - 15/40

= 9/40

( I hope this was helpful) >;D

The limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

To use the ratio test, we take the limit of the absolute value of the ratio of the (k+1)th term to the kth term:

lim as k approaches infinity of |(6(k+1)^4)/(6k^4)|

Simplifying this expression, we get:

lim as k approaches infinity of |(k+1)^4/k^4|

Using L'Hopital's rule, we can evaluate this limit:

lim as k approaches infinity of |4(k+1)^3/4k^3|

lim as k approaches infinity of |(k+1)/k|^3

Since the limit is less than 1, by the ratio test, the series converges absolutely.

Alternatively, we can use the root test, which involves taking the kth root of the absolute value of the kth term:

lim as k approaches infinity of |(6k^4 k)^(1/k)|

Simplifying this expression, we get:

lim as k approaches infinity of |6^(1/k) * k^(4+1/k)|

The exponent 4+1/k approaches 4 as k approaches infinity, so we can ignore the 1/k term. Taking the limit of just the k^(4) term, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k)

Using the fact that lim as k approaches infinity of 6^(1/k) = 1 and lim as k approaches infinity of k^(4/k) = 1, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k) = 1

Since the limit is less than 1, by the root test, the series converges absolutely.
To determine if the given series converges absolutely or diverges, we can use the Ratio Test. The series is given as:

Σ(6k^4 * k) for k = 1 to ∞

First, let's simplify the series:

Σ(6k^5) for k = 1 to ∞

For the Ratio Test, we need to compute the limit as k goes to infinity of the ratio of consecutive terms:

lim (k → ∞) (|a_(k+1)| / |a_k|)

For our series, a_k = 6(k+1)^5 and a_(k+1) = 6k^5. So we have:

lim (k → ∞) (|6(k+1)^5| / |6k^5|)

We can simplify by canceling the common factor of 6:

lim (k → ∞) ((k+1)^5 / k^5)

Now, let's take the limit:

lim (k → ∞) (1 + 1/k)^5 / 1 = 1^5 / 1 = 1

For the Ratio Test, if the limit is less than 1, the series converges absolutely; if it is equal to 1, the test is inconclusive; if it is greater than 1, the series diverges.

In this case, the limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

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Considering the curve x³y + y³ = sin y - x, the final i is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

Implicit differentiation is a technique used to differentiate equations that are not explicitly expressed in terms of one variable. It is particularly useful when you have an equation that defines a relationship between two or more variables, and you want to find the derivatives of those variables with respect to each other.

To find dy/dx for the curve x³y + y³ = sin y - x², the implicit differentiation will be used which involves differentiating both sides of the equation with respect to x.

It is expressed as follows;

\(\frac{d}{dx} x^3y + \frac{d}{dx} y^3 = \frac{d}{dx} sin(y) - \frac{d}{dx} x^2\)

Then we'll differentiate each term:

For the first term, x^3y, we'll use the product rule

\(\frac{d}{dx} x^3y = 3x^2y + x^3 \frac{dy}{dx}\)

For the second term, y^3, we'll also use the chain rule

\(\frac{d}{dx} y^3 = 3y^2 \frac{dy}{dx}\)

For the third term, sin(y), we'll again use the chain rule

\(\frac{d}{dx} sin(y) = cos(y) \frac{dy}{dx}\)

For the fourth term, x², we'll use the power rule

\(\frac{d}{dx} x^2 = 2x\)

Substituting these expressions back into the original equation, we get:

3x²y + x³(dy/dx) + 3y²(dy/dx) = cos(y)(dy/dx) - 2x

Simplifying the equation:3x²y + x³(dy/dx) + 3y²(dy/dx) - cos(y)(dy/dx) = -2x

Dividing both sides by 3y² - cos(y), we get:(x³ - cos(y))(dy/dx) = -2x / (3y² - cos(y))

Hence, the final answer is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

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a) X is geometrically distributed if sophie have constant probability of 0.2

b) Probability that such she doesn't catch the ball on the first toss and catch on the second toss is P(X=2) is 0.16 .

c) The value of  P(X > 4) = 0.4536.

a) X is geometrically distributed since we're waiting for Sophie's first successful catch.

Geometric distribution is defined as the time required until the first success in a sequence of independent Bernoulli trials with constant probability p. Since Sophie has a constant probability of 0.2 of catching a ball, X is geometrically distributed. So the answer is geometric.

b) The probability that it will take exactly two tosses for Sophie to catch a ball is the probability that she does not catch the ball on the first toss and catches the ball on the second toss. P(X = 2) = (0.8) (0.2) = 0.16

c) Probability that more than 4 tosses will be required P(X > 4) = 1 - [P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)] = 1 - [(0.2) + (0.16) + (0.128) + (0.1024)] = 1 - 0.5464 = 0.4536. The probability that more than 4 tosses will be required is 0.4536.

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Answer:

360

Step-by-step explanation:

Answer: HJ and JH

Step-by-step explanation:

Basically just name the letters in both ways that you can. the symbol would be a line above them since this is a side or line.

so like: (look at the picture)

hope this helps! :)

HJ and JH is the two representation of the given line segment.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

A line segment can be represented in two ways one is either one end to another and the second is opposite to the other.

The denotation of a line segment let's say AB is representing the length of the line segment.

And length can never change by measuring either one end or another.

So HJ and JH are two ways to represent the line segment.

Hence "HJ and JH is the two representation of the given line segment".

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Choose a length of rope that is greater than the distance between the fence post and the house, taking into account the safety margin.

To ensure the goat cannot reach the house, you need to consider the distance between the fence post and the house. The length of the rope should be greater than the distance between these two points.

To determine the distance between the fence post and the house, you can use the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the diagonal of the rectangle is the hypotenuse, and the sides are the length and width of the rectangle.

Once you have the distance between the fence post and the house, you can add a safety margin to ensure the goat cannot reach the house.

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Answer:

6 meters

Step-by-step explanation:

the perimeter is all of the sides added up so to find the added width you subtract the added length which is 30 so 42-30 is 12 so the added width is 12. To find one width you divide 12 by 2 so one width of the rectangle would be 6 meters

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

2/20

Step-by-step explanation:

if you add all of the marbles you will get 20 marbles in total.

Answer:

xxxxxxxx

111111

Step-by-step explanation:

Sorry & I really sorry

Answer:

Dont know how to explain

Step-by-step explanation:

Answer:

9 scoops

Step-by-step explanation:

3 scoops = 45g

3/45 scoops = 1g

3/45*135 scoops = 135g = 9 scoops

Answer:

wHOLE number

Step-by-step explanation:

IT is a whole number

The following bit vector represents a disk where blocks 1,5,8,11,14 are free, and the rest is allocated is False.

What is Bit-Vector?

Bits are stored in a bit array, which is a type of array data structure. An easy set data structure can be implemented using it. Bit-level parallelism in hardware can be quickly used by a bit array to perform operations.

When files are generated, the system allots space for them by keeping track of the free disk blocks. Additionally, free space management becomes essential in order to utilise the space freed up by deleting the files.

The system keeps track of the disk blocks that are not assigned to any files or directories in a list called free space. Implementing the free space list primarily entails:

A bitmap or bit vector is a sequence or group of bits, where each bit stands for a disk block. The bit has two possible values: 0 and 1: 0 means the block is allocated, and 1 means the block is free.

A bitmap of 16 bits can be used to represent the given instance of disk blocks on the disk in Figure 1 (where green blocks are allocated) as 0000111000000110.

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Answer:

2.5 goes in 10 4 times

5x4 = 20

colleen can make 20 bracelets in 10h

Answer:

1.18x=y

Step-by-step explanation:

x= amount of pounds of kidney beans

y= the cost

the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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the distance from the plane to the radar station is increasing at a rate of approximately 30.84 kilometers per minute.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, A plane flying with a constant speed of 25 km/min passes over a ground radar station at an altitude of 12 km and climbs at an angle of 30 degrees.

We can use the law of cosines to find d:

d² = 12² + (h + 12)² - 2(12)(h + 12)cos(θ)

Since the plane is climbing at an angle of 30 degrees, we can use trigonometry to find h:

sin(30) = h / (25 km/min * 2 min)

h = 25 km/min

Now we can substitute this value of h into the equation for d and simplify:

d² = 12² + (25 + 12)² - 2(12)(25 + 12)cos(θ)

d² = 12² + 37² - 2(12)(37)cos(θ)

d² = 144 + 1369 - 888cos(θ)

d² = 1513 - 888cos(θ)

To find the rate at which d is changing, we can take the derivative of both sides of this equation with respect to time:

2dd/dt = -888(d(cos(θ))/dt)

Since the plane is flying with a constant speed of 25 km/min, we can use trigonometry to find d(cos(θ))/dt:

cos(θ) = 12/d

d(cos(θ))/dt = -(12/d²)(dd/dt)

d(cos(θ))/dt = -(12/d²)(25 km/min)

Now we can substitute these values into the equation for the rate of change of d:

2dd/dt = -888(-(12/d²)(25 km/min))

2dd/dt = (888*12)/(d²)(25 km/min)

dd/dt = (5328)/(d²) km/min

Finally, we can substitute the value we found for d into this equation to get the rate at which d is changing 2 minutes later:

d = sqrt(1513 - 888cos(θ))

θ = 30 degrees

dd/dt = (5328)/(d²) km/min

dd/dt = (5328)/(1513 - 888cos(30)) km/min

dd/dt ≈ 30.84 km/min

Therefore, the distance from the plane to the radar station is increasing at a rate of approximately 30.84 kilometers per minute.

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Answer:

10

Step-by-step explanation:

10 goes into 30, 70, and 20.