SHOW WORK FOR THE EQUATION ABOVE THE QUESTION PLEASE!! Show me how you got the answer.

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

(a) The probability that the student has a shoe size of 8 is 5/23.

(b) The probability that the student has a shoe size of 7 or smaller is 12/23.

To calculate the probabilities, we need to determine the number of students with the shoe sizes mentioned and divide it by the total number of students.

Given the table shows the shoe sizes of 23 students, we can find:

(a) The probability that the student has a shoe size of 8:

Looking at the table, we need to count the number of students with a shoe size of 8.

Let's assume there are 5 students with a shoe size of 8.

The probability would be:

P(shoe size 8) = Number of students with shoe size 8 / Total number of students = 5 / 23.

(b) The probability that the student has a shoe size of 7 or smaller:

We need to count the number of students with shoe sizes 7 or smaller. Let's assume there are 12 students with a shoe size of 7 or smaller.

The probability would be:

P(shoe size 7 or smaller) = Number of students with shoe size 7 or smaller / Total number of students = 12 / 23.

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Question: The table shows the shoe size of 23 students.

A student is picked at random.

there are 2 ansers

(a) Work out the probability that the student has a school size of 8.

(b) Work out the probability that the student has a school size of 7 or smaller.

The number of respondents needed in a poll to adequately represent a larger population depends on several factors, such as the size of the population, the level of confidence desired, and the margin of error tolerated.

The general rule of thumb is that a sample size of at least 400 respondents is needed to provide a representative sample for a population of 100,000 or less. However, for larger populations, a sample size of at least 1,000 respondents may be required.

It is also important to note that a larger sample size does not always guarantee more accurate results. Other factors such as the sampling method, the wording of the questions, and the response rate can also impact the accuracy of poll results. Therefore, it is essential to carefully design and conduct polls to ensure their results are adequately representative of the larger population.

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The given relation is a set of four ordered pairs {(1, -2), (-2, 0), (-1, 2), (1, 3)}. The first element of each pair represents the input or domain value, and the second element represents the output or range value.

The domain of the relation is the set of all first elements of the ordered pairs, which is {1, -2, -1}. Notice that there are two ordered pairs with input value 1 and one ordered pair with input value -2 and -1. Therefore, we can simplify the domain as {-2, -1, 1}.

The range of the relation is the set of all second elements of the ordered pairs, which is {-2, 0, 2, 3}.

To check whether the relation is a function or not, we need to ensure that each input value (i.e., element of the domain) is associated with a unique output value (i.e., element of the range). In other words, there should not be more than one ordered pair with the same first element.

In this case, the input value 1 is associated with two different output values (-2 and 3), which violates the definition of a function. Therefore, the relation is not a function.

To make it a function, we can either remove one of the ordered pairs with input value 1 or change one of the output values associated with input value 1.

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For a jar contains 5 red discs, 10 blue discs and m green discs,

a) The probability that the first disc selected is red is equals to

[tex]\frac{5}{15 + m}.[/tex]

b) The smallest value of m for which Var(X)< 0.6 is equals to 13.

We have a jar contains different colour discs. Number of red discs = 5

Number of green discs = m

Number of blue discs = 10

Total number of discs = 5 + 10 + m

= 15 + m

The process is performed four times, so, possible value n = 4. We have to determine the probability that the first disc selected is red.

a) Probability is defined as the ratio of favourable outcomes to the total possible outcomes. So, the probability that the first disc selected is red,[tex] P(red) = \frac{ 5}{(15 + m)}[/tex]

(b) The variance is calculated as

[tex]σ_{X²} = Var (X)[/tex]

[tex]= ∑_i (x_i − μ)² p(x_i) \\ [/tex]

= np(1 - p)

= [tex] 4(\frac{5}{15 + m})×(1- \frac{5}{15 + m}) < 0.6[/tex]

[tex] \frac{20( 10 - m)}{(15 + m)²} < 0.6[/tex]

=> 200 - 20m < 0.6( 15 + m)²

=> 200 - 20m < 9.0 + 0.6 m² + 18

=> 0.6m² + 20m - 200 + 27 > 0

=> 0.6m² + 20m - 173 > 0

=> m > 12.2075, so, m = 13

Hence, the smallest value of m for which Var(X)<0.6 is 13.

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The probability that the sample mean age is between 19 and 22 years is approximately 0.8186 or 81.86% (rounded to four decimal places).

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

We know that the sample mean age of 9 students follows a normal distribution with a mean of 21 years and a standard deviation of 3/sqrt(9) = 1 year (since the standard error of the mean is the standard deviation divided by the square root of the sample size).

To find the probability that the sample mean age is between 19 and 22 years, we first need to standardize the values using the standard normal distribution. We can do this by subtracting the mean and dividing by the standard error:

z1 = (19 - 21) / 1 = -2

z2 = (22 - 21) / 1 = 1

Now we need to find the probability that the sample mean falls between -2 and 1 standard deviations from the mean of the standard normal distribution. We can look this up in a standard normal distribution table or use a calculator:

P(-2 < Z < 1) = 0.8186

Therefore, the probability that the sample mean age is between 19 and 22 years is approximately 0.8186 or 81.86% (rounded to four decimal places).

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The inevitable difference between the mean of a sample and the mean of a population based on chance alone is known as sampling error.

Sampling error is a result of the random nature of sampling from a population, meaning that any given sample is unlikely to perfectly represent the entire population. This is where probability comes into play, as the likelihood of obtaining a certain sample is dependent on the probability of each member of the population being selected.

Therefore, in order to minimize sampling error, researchers often use random sampling techniques to ensure that each member of the population has an equal probability of being selected for the sample.

The inevitable difference between the mean of a sample and the mean of a population based on chance alone is a) sampling error. This occurs because a random sample may not perfectly represent the entire population, leading to slight variations in the mean.

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Answer:

Molly earned $55.44 in interest at the end of six years.

Step-by-step explanation:

To calculate the interest earned by Molly's savings account, we can use the formula:

Interest = Principal x Rate x Time

where:

Principal is the initial amount of money deposited ($220.00)

Rate is the annual interest rate (4.2% or 0.042 as a decimal)

Time is the number of years the money is invested (6 years)

Plugging in the values, we get:

Interest = $220.00 x 0.042 x 6

Interest = $55.44

Therefore, Molly earned $55.44 in interest at the end of six years.

Yes, it is true that if AB = BA and A is invertible, then [tex]A^{(-1)}B = BA^{(-1).[/tex]

To prove this, we can start with the equation AB = BA and multiply both sides by [tex]A^{(-1)[/tex] on the left. This gives:

[tex]A^{(-1)}AB = A^{(-1)BA[/tex]

Simplifying the left-hand side using the associative property of matrix multiplication and the fact that [tex]A^{(-1)}A = I[/tex] (the identity matrix), we get:

[tex]IB = A^{(-1)}BA[/tex]

Simplifying the left-hand side further, we get:

[tex]B = A^{(-1)}BA[/tex]

Now, we can multiply both sides of this equation by A on the right to obtain:

[tex]BA = AA^{(-1)BA[/tex]

Using the fact that [tex]AA^{(-1) }= A^{(-1)}A = I[/tex], we can simplify the right-hand side to get:

[tex]BA = A^{(-1)}B(AA^{(-1)})[/tex]

Once again using the fact that [tex]AA^{(-1)} = A^{(-1)}A = I[/tex], we get:

[tex]BA = A^{(-1)}B[/tex]

Therefore, we can show that if AB = BA and A is invertible, then [tex]A^{(-1)}B = BA^{(-1).[/tex]

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Answer:  Hence, the length of swimming pool is 52 m and its breadth if 25 m.  

Step-by-step explanation:

The perimeter of rectangular swimming pool is 154 m and its length is 2 meter more than twice its breadth.

The area of the base of Barbara's woodshed is 72 square feet.

To find the area of the base of Barbara's woodshed, we need to know the shape of the base. In this case, the base is in the shape of a rectangle. A rectangle is a four-sided figure with opposite sides parallel and equal in length.

To calculate the area of a rectangle, we need to multiply its length by its width. In this case, the length of the rectangle is 12 feet, and its width is 6 feet. So, the area of the base of the woodshed is:

Area = Length x Width

Area = 12 ft x 6 ft

Area = 72 square feet

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Complete Question:

Barbara built a woodshed. She made the base of the woodshed in the shape of the drawing. What is the area of the base of Barbara's woodshed? Include the unit. When the dimensions are given as 12 ft,6 ft, 11 ft and 7 ft.

The triangle with sides a=13 mm, b=84 mm, and c=85 mm is a(n) right triangle. This is because it satisfies the Pythagorean theorem (a² + b² = c²). In this case, 13² + 84² = 169 + 7056 = 7225, and 85² = 7225, so the theorem holds true.

A right triangle is a triangle with two perpendicular sides and one angle that is a right angle (i.e., a 90-degree angle). The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The hypotenuse, or side c in the illustration, is the side that is opposite the right angle. Legs are the sides that meet at the correct angle. Side a may be thought of as the side that is opposite angle A and next to angle B, whereas side b is the side that is next to angle A and next to angle B.

A right triangle is considered to be a Pythagorean triangle and its three sides are referred to as a Pythagorean triple if the lengths of all three of its sides are integers.

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The side lengths for this problem are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For segment d, we have that it is opposite to the angle of 60º, while 7 is the adjacent segment, hence:

tan(60º) = d/7

[tex]\sqrt{3} = \frac{d}{7}[/tex]

[tex]d = 7\sqrt{3}[/tex]

For segment b, it is opposite/adjacent (does not matter as sin(45º) = cos(45º)) to an angle of 45º, while the hypotenuse is of 5 units, hence:

sin(45º) = b/5

[tex]b = 5 \times \frac{\sqrt{2}}{2}[/tex]

[tex]b = \frac{5\sqrt{2}}{2}[/tex]

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The probability that high school A will lose some state funding is approximately 0.0287 or 2.87%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty.

We can use the normal distribution to approximate the probability that high school A will lose some state funding. Let X be the number of absent students on the selected school day. We know that X follows a normal distribution with mean µ = 120 and standard deviation σ = 10.5.

We need to find the probability that X is greater than 140. To do this, we standardize X by subtracting the mean and dividing by the standard deviation:

Z = (X - µ) / σ = (140 - 120) / 10.5 = 1.90

We can now use a standard normal distribution table or calculator to find the probability that a standard normal variable is greater than 1.90. The result is approximately 0.0287.

Therefore, the probability that high school A will lose some state funding is approximately 0.0287 or 2.87%.

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The area under the standard normal curve to the right of z = 0.69 is approximately 0.2451.

Using a standard normal table:

Locate the row for 0.6 in the left-hand column of the table and the column for 0.09 along the top row of the table.

The intersection of the row and column gives the area to the left of z = 0.69, which is 0.7549.

Subtract this area from 1 to find the area to the right of z = 0.69:

area to the right of z = 0.69 = 1 - 0.7549 = 0.2451

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One more time-consuming method to check for normality of a distribution that only works for large data sets is to use the Shapiro-Wilk test.

The Shapiro-Wilk test is a statistical test that checks whether a given sample of data comes from a normally distributed population. It works by calculating the test statistic W, which measures the deviation of the sample from a normal distribution. The test then compares the value of W to a critical value, which depends on the sample size and significance level.

While the Shapiro-Wilk test is a powerful tool for assessing normality, it is computationally intensive and may not be practical for smaller data sets. Moreover, it can be sensitive to sample size, so it may not provide reliable results for very small or very large samples.

In general, it is recommended to use multiple methods for checking normality, such as visual inspection of a histogram or Q-Q plot, in addition to formal statistical tests like the Shapiro-Wilk test.

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A parabola is a U-shaped curve that can be formed by intersecting a cone with a plane that is parallel to one of its sides.

To find an equation of a parabola given the vertex and focus, we can use the following formula:

For a parabola with vertex (h, k) and focus (h, k + p), the equation is:

(x - h)^2 = 4p(y - k)

where p is the distance from the vertex to the focus.

If the focus is at (h + p, k), then the equation is:

(y - k)^2 = 4p(x - h)

where p is the distance from the vertex to the focus.

what is distance?

In the context of a parabola, the distance is the distance between the vertex and the focus, which is also known as the focal length. It is a constant value that determines the shape and size of the parabola.

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The submarine depth after the dive is determined as 17 feet.

The current depth of the submarine is calculated as follows;

If the submarine is currently at a depth of -15 feet and then dives an additional 32 feet down, the new depth can be calculated by adding the two depths.

-15 feet + 32 feet = 17 feet

Therefore, the submarine is at a depth of 17 feet after the dive.

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A) A steer weighing 1000 pounds is 2.78 standard deviations below the mean.

B) A z-score of 1.85 is closer to the mean than a z-score of -2.78, we can conclude that a steer weighing 1000 pounds is more unusual than one weighing 1250 pounds.

A) To find how many standard deviations below the mean a steer weighing 1000 pounds is, we need to use the formula for standard score (or z-score):

z = (x - μ) / σ

where x is the weight of the steer, μ is the mean weight, and σ is the standard deviation. Substituting the values we have:

z = (1000 - 1150) / 54

z = -2.78

B) To determine which is more unusual, we need to compare the z-scores for a steer weighing 1000 pounds and one weighing 1250 pounds. Using the same formula as before:

For a steer weighing 1000 pounds:

z1 = (1000 - 1150) / 54

z1 = -2.78

For a steer weighing 1250 pounds:

z2 = (1250 - 1150) / 54

z2 = 1.85

A positive z-score means the weight is above the mean, while a negative z-score means the weight is below the mean. Therefore, a steer weighing 1250 pounds is 1.85 standard deviations above the mean, while a steer weighing 1000 pounds is 2.78 standard deviations below the mean.

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Step-by-step explanation:

sqrt (50)    does NOT = 2 sqrt (10)

sqrt(50) = sqrt (2 *25) = 5 sqrt 2   = approx 7.1

Step-by-step explanation:

A, Jaclyn is not correct cause she make a product of √50 to 2√25 but it must be √2×25 then the answer will be 5√2 so she make √2 out from radical by 2 but it must be √2 itself

B, Then when we work √50 to simplest form it is 5√2

and √2 is 1.414 so 5×1.414 = 7.07 approximate to 7.1

The algebraic expression for the number of hours Andrea spent studying this month is 2H - 14, where H represents the number of hours Jonah spent studying last month.

Let A represent the number of hours Andrea spent studying this month.

Since Andrea spent twice as many hours studying as Jonah this month, we can write

A = 2J

And since Jonah spent 7 fewer hours studying this month than last month, we can write

J = H - 7

Substituting J = H - 7 in the first equation, we get

A = 2(H - 7)

Simplifying this expression, we get

A = 2H - 14

Therefore, the algebraic expression for the number of hours Andrea spent studying this month is 2H - 14.

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If the price of corn feed is $4 and corn feed is on the horizontal axis, and the price of soybean feed is $5 and soybean feed lies on the vertical axis, then the expansion path is C =5S/2 (option a).

To find the expansion path, we need to find the optimal combination of inputs that will maximize pig production while keeping the cost of production at a minimum. This can be achieved by calculating the ratio of the prices of the two inputs, which is given by:

Price ratio = Price of soybean-based feed/Price of corn-based feed

Price ratio = 5/2

Now, we can use this price ratio to find the optimal combination of inputs that will minimize the cost of production while maximizing pig production. This can be done by solving for the quantity of soybean-based feed used in terms of the quantity of corn-based feed used:

S = (5/2)C

This equation represents the expansion path, which shows the optimal combination of inputs that will minimize the cost of production while maximizing pig production. We can prove this by substituting the value of S into the production function:

P = 8C + 25((5/4)C)

P = 8C + 31.25C

P = 39.25C

Hence the correct option is (a)

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The measure of the angle O is 81.77 degrees.

To find the measure of ∠O, we can use the Law of Cosines, which states that:

[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]

where c is the side opposite the angle we want to find (in this case, side o), a and b are the other two sides (in this case, sides m and n), and C is the angle opposite side c (in this case, ∠O).

Substituting the given values, we get:

[tex]o^2 = m^2 + n^2 - 2mn*cos(O)[/tex]

[tex]59^2 = 55^2 + 48^2 - 2(55)(48)*cos(O)\\3481 = 3025 + 2304 - 5280*cos(O)\\756 = 5280*cos(O)\\cos(O) = 756/5280\\O = cos^{-1}(756/5280)\\O = 81.77 degrees[/tex]

Therefore, the measure of ∠O to the nearest [tex]10^{th[/tex] of degree is approximately 81.77 degrees.

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It is a true statement that when rainfall increases, the water level in the lake goes up. The rainfall is the independent variable in the situation.

The answer is yes because independent variable is the one that is manipulated or changed in an experiment. The dependent variable is the one that is observed or measured.

In this situation, rainfall is independent variable because it is what is being manipulated or changed. The water level in the lake is the dependent variable because it is what is being observed or measured.

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Helps to increase the internal validity of the study, or the degree to which we can attribute changes in the dependent variable to the independent variable.

a) It is important to use caution when drawing causal conclusions from correlational studies.

b) To increase the internal validity of the study, or the degree to which we can attribute changes in the dependent variable to the independent variable.

a) People may easily accept the conclusion of the study because of a common misunderstanding of correlational studies. Correlation only shows a relationship between two variables but it doesn't necessarily mean that one variable causes the other. There could be other variables that influence both variables or there may be a third variable causing the relationship. In this case, there could be other factors that contribute to hyperactivity, such as excitement from the party or the presence of peers, that also influence the consumption of sugary snacks. Therefore, it is important to use caution when drawing causal conclusions from correlational studies.

b) Hypothesis: Consuming sugary snacks causes an increase in hyperactivity in children between the ages of 5 and 7 years.

Independent variable: Consumption of sugary snacks.

Dependent variable: Hyperactivity as measured by the number of times children leave their seats.

Random assignment can be achieved by randomly assigning children to one of two groups: a group that receives a sugary snack and a control group that receives a non-sugary snack. Random assignment is important for experiments because it helps to ensure that differences in the groups are due to chance rather than any pre-existing differences between the groups. This helps to increase the internal validity of the study, or the degree to which we can attribute changes in the dependent variable to the independent variable.

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The statements are always true regarding the diagram are m∠5 + m∠3 = m∠4, m∠3 + m∠4 + m∠5 = 180° and m∠2 + m∠3 + m∠5 = 180°. So, correct answers are A, B and E.

The given triangle and its exterior angles are shown in the diagram. We are also given the interior angles of the triangle, which are angles 2, 3, and 5, and their corresponding exterior angles, which are angles 1, 4, and 6. We need to determine which statements are always true regarding the diagram.

A) m∠5 + m∠3 = m∠4: This statement is true because angle 4 is the exterior angle at angle 3, and it is equal to the sum of angles 3 and 5. Therefore, m∠4 = m∠3 + m∠5, and we can substitute this into the given equation to obtain m∠5 + m∠3 = m∠3 + m∠5, which is always true.

B) m∠3 + m∠4 + m∠5 = 180°: This statement is also true because the sum of the exterior angles of a triangle is always 360°. Therefore, we have m∠1 + m∠4 + m∠6 = 360°. But m∠1 = m∠2, and m∠6 = m∠5, so we can substitute these in to obtain m∠2 + m∠3 + m∠5 = 360° - m∠4.

Since the sum of the interior angles of a triangle is 180°, we have m∠2 + m∠3 + m∠5 = 180° + m∠4, which can be rearranged to give the given equation.

C) m∠5 + m∠6 =180°: This statement is not always true. It depends on whether angle 6 is an exterior angle or not. If it is, then this statement is true because the sum of an exterior angle and its adjacent interior angle is always 180°. But if angle 6 is not an exterior angle, then this statement may not be true.

D) m∠2 + m∠3 = m∠6: This statement is not always true. It depends on whether angle 6 is an exterior angle or not. If it is, then this statement is true because angle 2 and angle 3 are adjacent interior angles to angle 6. But if angle 6 is not an exterior angle, then this statement may not be true.

E) m∠2 + m∠3 + m∠5 = 180°: This statement is true because the sum of the interior angles of a triangle is 180°, and angles 2, 3, and 5 are the interior angles of the triangle.

Therefore, the statements that are always true regarding the diagram are A), B), and E).

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Complete question is:

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.

A) m∠5 + m∠3 = m∠4

B) m∠3 + m∠4 + m∠5 = 180°

C) m∠5 + m∠6 =180°

D) m∠2 + m∠3 = m∠6

E) m∠2 + m∠3 + m∠5 = 180°

There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

There are 12 elements of the group     \(U_{13}\)   , namely all the positive integers less than 13, as these are relatively prime to 13. Now, if there are primitive roots, there are     \(\phi (\phi (n))\)    of them. So we must compute     \(\phi (12) = \phi (4\times 3) = \phi (4) \phi (3) = 2\times 2 = 4\)   . There are 4 incongruent primitive roots.

To find them, take the powers each element in turn:

1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1  (2 has order 12, it is a primitive root)

Of course, the higher powers of 2 cannot be.

Proceeding this way, we get next get that 6, 7, and 11 are also primitive roots.

For example, the powers of 6 give: 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1. We see 6 has order 12 and it is a primitive root. So 2, 6, 7, 11.

Therefore, There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

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An equation of the plane through the point (-1, -5, 1) and perpendicular to the vector (5, 4, 2) can be -4x + 5y - 2z = 11.

First, the normal vector of the plane must be determined. The vector perpendicular to the given vector (5, 4, 2) is (-4, 5, -2).

Now, the equation of the plane can be determined using the given point and the normal vector. The standard form of the equation of a plane is Ax + By + Cz = D.

We can use the point (-1, -5, 1) and the normal vector (-4, 5, -2) to calculate the values of A, B, C, and D in the equation. To do this, we can use the point-normal form of the equation of a plane.

The point-normal form is (x - x1) × nx + (y - y1) × ny + (z - z1) × nz = 0. We can plug in the point and normal vector values into this equation to calculate A, B, C, and D.

Therefore, the equation of the plane is -4x + 5y - 2z = 11.

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