The time it takes for a statistics professor to mark his midterm test is normally distributed with a mean of 4.8 minutes and a standard deviation of 1.3 minutes. There are 60 students in the professor’s class. What is the probability that he needs more than 5 hours to mark all the midterm tests? (The 60 midterm tests of the students in this year’s class can be considered a random sample of the many thousands of midterm tests the professor has marked and will mark.)

The mean, also known as the average, is calculated by adding up all the values in a dataset and dividing by the total number of values in the dataset. The correct answer is b. mean.

The mean, also known as the average, is calculated by adding up all the values in a dataset and dividing by the total number of values in the dataset. It is the sum of all the values divided by the count of values in the dataset. The mean is a measure of central tendency and is commonly used to represent the "typical" or "average" value in a dataset.

Therefore, the mean is calculated by adding up all the values in a dataset and dividing by the total number of values in the dataset.

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False.

A scatter plot can help distinguish between a curvilinear and a linear relationship by visually displaying the data points, whereas the correlation coefficient primarily measures the strength and direction of a linear relationship between two variables, but does not account for curvilinear relationships.

On the other hand, the correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1, with values closer to -1 indicating a strong negative linear relationship, values closer to +1 indicating a strong positive linear relationship, and values close to 0 indicating little or no linear relationship.

However, the correlation coefficient does not account for curvilinear relationships, which means that even if the correlation coefficient is close to 0, there could still be a curvilinear relationship between the two variables.

Therefore, while a scatter plot can help distinguish between a curvilinear and a linear relationship by visually displaying the data points, the correlation coefficient primarily measures the strength and direction of a linear relationship between two variables, but does not account for curvilinear relationships.

It is important to use both tools in conjunction to fully understand the relationship between two variables.

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The average velocity of an object dropped off a building between 2 seconds and 3 seconds is less than the average velocity of the object between 2 seconds and 3.5 seconds.

This is because the velocity of a freely falling object due to gravity increases at a constant rate of 9.8 m/s² (assuming negligible air resistance). Therefore, the object's velocity at 3.5 seconds will be greater than its velocity at 3 seconds, resulting in a higher average velocity over the longer time interval.

In other words, the object falls faster as time passes, which means that its instantaneous velocity increases over time. Therefore, the average velocity over a longer time interval will be higher than the average velocity over a shorter time interval, assuming the object continues to fall freely with no additional forces acting upon it.

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The sign of a z-score tells us whether the data point is above or below the mean.

A positive z-score indicates that the data point is above the mean, while a negative z-score indicates that the data point is below the mean. The further away the z-score is from zero, the more extreme the data point is relative to the mean.
A z-score is a numerical value that represents how far a data point is from the mean in terms of standard deviations. The sign of a z-score, either positive (+) or negative (-), indicates the direction of the deviation from the mean.

A positive z-score (+) indicates that the data point is above the mean, or it is higher than the average value in the distribution. On the other hand, a negative z-score (-) indicates that the data point is below the mean, or it is lower than the average value in the distribution.

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Answer:

pootis

Step-by-step explanation:

this is pootis, he is very lovable.

The statement that is true about the triangles is: "The triangles must be similar." When two triangles have two pairs of corresponding congruent angles, they are called similar triangles. The corresponding sides of similar triangles are proportional to each other, but their lengths may differ. However, since two angles in each triangle are congruent, the third angle must also be congruent. Therefore, the triangles have the same shape, but possibly different sizes.

~~~Harsha~~~

The maximum possible volume of the box is 4.5 cubic meters and this is achieved by having a square bottom of the box with a  side length of 3 cm and a height of 1/2 cm.

Volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube,  cuboid,  cone,  cylinder or  sphere. Different shapes have different volume. The formula for volume is: volume = length x width x height.

 Let the side of the base of the square  be x cm. Then the area of ​​the base would be x² square cm.

 The material needed to make the box would be the sum of the areas of the bottom and  four sides. Since the bottom of the box is square  and the sides are perpendicular to the base, the area of ​​each side is x times the height.

 So the total  area of ​​the box would be:

x² + 4 (x times height)

We know that the total  area is 16 square cm, so we can write:

x² + 4 (x times the height) = 16

We want to maximize the volume of the box. The volume of a square box  is obtained as follows:

V = x² times height

We can solve the first height equation with x:

height = (16 - x²)/(4x)

Substituting this height expression  into the volume formula, we get:

V = x² times (16 - x²)/(4x)

Simplifying this expression, we get:

V = (4x³ -[tex]x^4[/tex])/16

We want to find the maximum value of V. To do this, we take the derivative of V with respect to x and set it  to zero:

dV/dx = (12x² - 4x³)/16 = 0

This gives us two solutions: x = 0 and x = 3.

 Since x represents the side of the square root, it must be positive. Therefore we choose x = 3.

 Substituting this value into the height expression, we get:

height = (16 - 3²)/(4 times 3) = 1/2

So the maximum volume of the box is:

V = 3² times 1/2 = 4.5 cubic meters

Therefore, the maximum possible volume of the box is 4.5 cubic meters and this is achieved by having a square bottom of the box with a  side length of 3 cm and a height of 1/2 cm.

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For fx=ln(x^4x): f(x) = ln(x^4x) = 5ln(x), f'(x) = 5/x, f''(x) = -5/x^2. For fx=2e^-x^2: f(x) = 2e^-x^2, f'(x) = -4xe^-x^2, f''(x) = (8x^2 - 4)e^-x^2. Using chain rule and product rule, we can find the solutions.

To find the second derivative f''(x) for the given functions, we'll first find the first derivative f'(x) and then derive it again.

For the first function, f(x) = ln(x^4/x):
1. Simplify: f(x) = ln(x^3)
2. Find f'(x) using the chain rule: f'(x) = (1/x^3) * 3x^2 = 3/x
3. Find f''(x): f''(x) = -3/x^2

For the second function, f(x) = 2e^(-x^2):
1. Find f'(x) using the chain rule: f'(x) = 2(-2x)e^(-x^2) = -4xe^(-x^2)
2. Find f''(x) using the product rule: f''(x) = -4e^(-x^2) - 4x(-2x)e^(-x^2) = -4e^(-x^2) + 8x^2e^(-x^2)

So, the second derivatives are f''(x) = -3/x^2 for the first function and f''(x) = -4e^(-x^2) + 8x^2e^(-x^2) for the second function.

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Using Kepler's Third Law, we can find the distance of the exo-planet from its star. The formula is P^2 = a^3, where P is the orbital period in years and a is the average distance from the planet to the star in astronomical units (AU).

the average distance of Le Grosse Homme from its star is approximately 2 AU, which is answer choice b).

To determine the distance of the exo-planet Le Grosse Homme to the star, we will use Kepler's Third Law, which states that the square of the orbital period (P) of a planet is proportional to the cube of the semi-major axis (a) of its orbit. The formula is given as:

P² = a³

In this case, the orbital period P is 2.8284 years. We can now solve for the semi-major axis (a), which represents the distance from the planet to the star in astronomical units (AU).

Step 1: Square the orbital period
(2.8284)² = 7.99968336

Step 2: Find the cube root of the squared orbital period to get the distance (a)
a = ∛(7.99968336) ≈ 2.0 AU

So, the distance of the exo-planet Le Grosse Homme to the star is approximately 2.0 AU. The correct answer is option (b) ~2.0 AU.

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The probability of a randomly selected ball bearing having a diameter greater than 5.85 millimeters is 0.325.

The probability of a randomly selected ball bearing having a diameter greater than 5.85 millimeters can be found using the following formula for a uniform distribution:

P(X > x) = (max - x) / (max - min)

where X is the random variable (diameter of the ball bearings), x is the specific value we are interested in (5.85 millimeters), max is the maximum value of the distribution (6.5 millimeters), and min is the minimum value of the distribution (4.5 millimeters).

Plugging in the values, we get:

P(X > 5.85) = (6.5 - 5.85) / (6.5 - 4.5)

= 0.65 / 2

= 0.325

Therefore, the probability of a randomly selected ball bearing having a diameter greater than 5.85 millimeters is 0.325.

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Since the line includes the point (–6, –9) and has a slope of –1/5, its equation in point-slope form is y + 9 = -1/5(x + 9).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-6, -9) and a slope of -1/5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-9) = -1/5(x - (-6))  

y + 9 = -1/5(x + 9).

In conclusion, we can logically deduce that the required equation is given by

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Answer:

The length and breadth giving the lowest perimeter is 6 and 10.

Step-by-step explanation:

Area= Length* Breadth
Therefore, we divide 60 into pairs of 2 factors.
(30,2), (20,3), (12,5), (60,1), (15,4), (10,6).
These are the possible values of length and breadth which can give us the area 60.

Perimeter=2*(Length+Breadth)
Now, to minimise perimeter, we take the pair with the lowest sum.

The pair comes out to be 6 and 10 with the sum of 16.

The distribution is positively skewed with 50% of the boys consuming the median number of drinks or less.

Researchers were interested in the patterns of alcohol consumption for teenage boys and recorded the number of alcoholic drinks consumed over the previous week. They analyzed the data using SPSS and found that the distribution of the number of drinks consumed was skewed. A histogram would normally be included with this description to illustrate the distribution.

The distribution of the number of alcoholic drinks consumed in the past week in a select group of teenage boys is displayed in Figure 1. The distribution is skewed, with 50% of the boys consuming 2 drinks or less. Typically, the boys consumed between 1 and 5 drinks in the past week, with half of the values falling in this range. The standard deviation of the number of alcoholic drinks consumed was 2.0, based on a sample size of 20.

The distribution of the number of alcoholic drinks consumed in the past week among a sample of teenage boys is displayed in Figure 1. The distribution is positively skewed with 50% of the boys consuming the median number of drinks or less. Typically, the boys consumed between the first quartile (Q1) and third quartile (Q3) drinks in the past week, with half of the values falling within this interquartile range.

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The volume of the solid obtained by rotating the region bounded by y = -16x and y = x^2/16 about the y-axis using slicing is  262144π/3 cubic units.

To find the volume of the solid obtained by rotating the region bounded by y = â16x and y = x²/16 about the y-axis, we can use the method of slicing.

Consider a vertical slice of thickness Δy at a distance y from the y-axis. The slice can be approximated by a washer with inner radius x1 and outer radius x2, where x1 and x2 are the x-coordinates of the points where the line y = â16x intersects the parabola y = x²/16. Thus:

x1 = -ây/16, x2 = ây/16

The area of the washer is given by

A = π(x2² - x1²) = π(ây/16)² - (-ây/16)² = π(2ây/16)²

The volume of the solid is obtained by integrating the area of the washers over the range of y

V = [tex]\int\limits^0_{256}[/tex] π(2ây/16)² dy

V = π/64[tex]\int\limits^0_{256}[/tex] y² dy

V = π/64 [y³/3]0 to 256

V = π/64 (256³/3)

V = 262144π/3

Therefore, the volume of the solid is V = 262144π/3 cubic units.

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The value of C is calculated to be -6.

If F(x) = x + 9x + C and F(1) = 4, we can use the given information to solve for C by using Green's theorem;

F(1) = 1 + 9(1) + C = 4

Simplifying, we get:

C = 4 - 1 - 9 = -6

Therefore, the value of C is -6.

If F(x) = x + 9x + C and F(1) = 4, we can still use the given information to solve for C:

F(1) = 1 + 9(1) + C = 4

Simplifying, we get:

C = 4 - 1 - 9 = -6

Now, we can use the value of C to simplify the expression for F(x):

F(x) = x + 9x - 6x^2

Simplifying further, we get:

F(x) = -6x^2 + 10x

Therefore, FC(x) = x² FC = -6x² + 10x² = 4x².

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The series of transformations that correctly maps parallelogram ABCD to parallelogram QRST is Reflect parallelogram ABCD across the x-axis and dilate the result by a scale factor of two centered at the orgigin

A quadrilateral of parallel opposite sides with equal lengths is the two-dimensional geometric shape widely known as a "parallelogram". As such, this four-sided figure has characteristic equal-measured opposites regarding their angles.

Though differing in size and form, parallelograms always possess these notable attributes. Meanwhile, sub-types have emerged from said category, which includes squares, rhombuses, and rectangles – each having additional outstanding qualities to define its uniqueness.

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a.) What fraction of the buildings are bigger than 150 meters high is 0.0038.

b.) The median height and the 95th percentile of the height distribution is 135.675 meters.

c.) In a random sample of 25 buildings, the approximate probability that fewer than 10 buildings exceed the median height is 0.1587. 

a) To discover the division of buildings that are taller than 150 meters, ready to utilize the standard normal distribution table or a calculator. To begin with, we have to standardize the esteem of 150 meters utilizing the equation:

z = (x - μ) / σ

where x = 150, μ = 110, and σ = 15

z = (150 - 110) / 15 = 2.67

Employing a standard typical dispersion table, we discover that the range to the correct of 2.67 is around 0.0038. This implies that as it were 0.38% of the buildings are taller than 150 meters.

b) The middle tallness of the building can be found utilizing the equation:

middle = μ = 110 meters

To discover the 95th percentile of the stature dispersion, we are able to utilize the standard ordinary dispersion table or a calculator. We ought to discover the z-score that compares to the 95th percentile, which is 1.645. Utilizing the equation for standardizing esteem, we get:

1.645 = (x - 110) / 15

Tackling for x, we get:

x = 135.675

Subsequently, the 95th percentile of the tallness dispersion is roughly 135.675 meters.

c) The number of buildings that surpass the middle tallness in a test of 25 buildings takes after binomial dissemination with parameters n = 25 and p = 0.5, since the likelihood of a building being taller or shorter than the middle is rise to 0.5.

We can utilize the ordinary guess to the binomial dissemination to inexact the probability that less than 10 buildings surpass the middle tallness. The cruel of the binomial conveyance is

μ = np = 25 x 0.5 = 12.5,

and the standard deviation is

σ = √(np(1-p)) = √(25 x 0.5 x 0.5) = 2.5.

To utilize the ordinary estimation, we ought to standardize the esteem of 10 utilizing the formula:

z = (x - μ) / σ

z = (10 - 12.5) / 2.5 = -1

Employing a standard typical conveyance table or a calculator, we discover that the region to the cleared out of -1 is roughly 0.1587.

Hence, the surmised likelihood that less than 10 buildings exceed the middle tallness is 0.1587. 

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There is a 2.97% probability that more than 2 parts in the sample of 10 will require rework.

The number of parts requiring rework in a sample of 10 follows a binomial distribution with n=10 and p=0.03. We want to find the probability that X exceeds 2, or P(X > 2).

Using the binomial probability formula, we can calculate the probability of X taking any value from 0 to 2 as follows:

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

=[tex](10 choose 0)(0.03)^0(0.97)^10 + (10 choose 1)(0.03)^1(0.97)^9 + (10 choose 2)(0.03)^2(0.97)^8[/tex]

≈ 0.9703

Therefore, the probability that X exceeds 2 can be found as:

P(X > 2) = 1 - P(X ≤ 2)

≈ 1 - 0.9703

≈ 0.0297

So, there is a 2.97% probability that more than 2 parts in the sample of 10 will require rework.

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Rosalia must invest approximately $6,738.65 today to have $10,000 in the high-interest savings account after 5 years.

The formula for the future value (FV) of an investment with continuous compounding is:

FV = [tex]Pe^{rt}[/tex]

where:

P = the principal (initial investment)

e = the mathematical constant e (approximately 2.71828)

r = the annual nominal interest rate

t = the time period (in years)

In this case, we want to solve for P. We know that FV = $10,000, r = SX per year, and t = 5 years. Substituting these values into the formula, we get:

$10,000 = P[tex]e^{5SX}[/tex]

Dividing both sides by [tex]e^{5SX}[/tex] , we get:

P = $10,000/[tex]e^{5SX}[/tex]

Rounding this to two decimal places, we get:

P ≈ $6,738.65

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As Schmuller emphasizes (p106-110), and as noted in class, R's sd function (sd(x) -- in the Basic R package), assumes n-1 in the denominator. The n-1 term would be used if the distribution of scores represented a sample of values on the variable.

This is because in a sample, there is inherent variability due to chance, and using n-1 instead of n in the denominator of the formula for standard deviation accounts for this variability. Therefore, the correct answer is c. a sample of values on the variable. As Schmuller emphasizes (p106-110), the R's sd function (sd(x) -- in the Basic R package) uses n-1 in the denominator. The n-1 term is applied when the distribution of scores represents:
c. a sample of values on the variable. This is because using n-1, known as Bessel's correction, provides an unbiased estimate of the population variance when working with a sample rather than the entire population.

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(a) The conditions for testing the hypothesis are:

1. Random sample 2. Normality:

(b) The box plot also shows that there are no outliers and the data is evenly spread, supporting the normality assumption. Therefore, the conditions for testing the hypothesis are satisfied.

1. Random sample: The sample of 10 orders is stated to be randomly selected, so this condition is met.
2. Normality: The manager must verify that the wait time is normally distributed. The normal probability plot shows that the data points are roughly linear, indicating that the data is normally distributed. Therefore, this condition is met.
3. Independence: The sample does not contain any others, so this condition is met.

(b) The box plot also shows that there are no outliers and the data is evenly spread, supporting the normality assumption. Therefore, the conditions for testing the hypothesis are satisfied.

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The function  sin x + cos y = 2y does not have critical points and there are there are no relative maxima or minima.

To find the critical points, we need to find the values of x and y such that the partial derivatives are equal to zero:

∂/∂x(sin x + cos y) = cos x = 0

∂/∂y(sin x + cos y) = -sin y = 2

From the first equation, we get cos x = 0, which means x = π/2 + nπ, where n is an integer.

From the second equation, we get -sin y = 2, which has no real solutions. Therefore, there are no critical points.

Since there are no critical points, there are no relative maxima or minima.

Hence, the function  sin x + cos y = 2y does not have critical points and there are there are no relative maxima or minima.

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As sample size decreases, the degrees of freedom decrease.

This affects both the group and error degrees of freedom. Specifically:

The group degrees of freedom (df between) decrease as the number of groups decreases. This is because there are fewer groups to estimate the population means from, resulting in fewer degrees of freedom for group differences.

The error degrees of freedom (df within) decrease as the sample size within each group decreases. This is because there is less information available to estimate the variation within each group, resulting in fewer degrees of freedom for residual variation.

The total degrees of freedom (df total) also decrease as the number of observations decreases, since the total degrees of freedom is equal to the number of observations minus 1.

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Since A and B are independent events, P(A | B) is equal to P(A), which is 0 since P(A) is given as 0.

The conditional probability P(A | B) represents the probability of event A occurring given that event B has already occurred. However, if the events A and B are independent, the occurrence of one event has no effect on the probability of the other event occurring.

Thus, knowing that event B has occurred does not provide any additional information about the probability of event A occurring.

In this case, the probability of event A is 0, regardless of whether event B has occurred or not, since there is no overlap between the two events.

Therefore, the conditional probability P(A | B) is also 0, which means that event B does not provide any information about the occurrence of event A in this scenario.

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The best integration technique to use for the given integral ∫2x(x^2+1)^5 dx is D) The substitution rule.

This is because you can substitute u = x^2 + 1, making the integral easier to solve. The other rules mentioned are differentiation rules, not integration techniques.

The substitution rule, also known as u-substitution, is a fundamental technique in integration that involves replacing a function inside the integral with a new variable, making it easier to solve. This is the reason why it is also known as the "inside-out" method.

In the given integral, we have the term (x^2+1)^5, which is a composite function. By letting u = x^2+1, we can simplify the integrand and express the integral in terms of u as follows:

∫2x(x^2+1)^5 dx = ∫(x^2+1)^5 d(x^2+1) [Substitute u = x^2+1]

= (1/2) ∫u^5 du [Integrate with respect to u]

= (1/12) u^6 + C [Replace u with x^2+1 and add the constant of integration]

Therefore, the solution to the integral is:

∫2x(x^2+1)^5 dx = (1/12) (x^2+1)^6 + C

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Percentage and angles.

To obtain the solution of the wave equation, we need to use the given initial conditions and apply them to the general solution of the wave equation. The wave equation is: ∂²y/∂x² = 1/v² * ∂²y/∂t² where v is the velocity of the wave.

The general solution to this equation is:

y(x,t) = f(x + vt) + g(x - vt)

where f and g are arbitrary functions that depend on the initial conditions.

Using the given initial conditions, we can determine the values of f and g. When x = 1, we have:

y(1,t) = f(1 + vt) + g(1 - vt) = P cos(pr)

Similarly, when x = 0, we have:

y(0,t) = f(vt) + g(-vt) = 0

To solve for f and g, we can use the method of separation of variables. Let:

f(1 + vt) = F(vt) and g(1 - vt) = G(-vt)

Substituting these expressions into the first initial condition, we have:

F(vt) + G(-vt) = P cos(pr)

Differentiating both sides with respect to t, we get:

v[F'(vt) - G'(-vt)] = -P pr sin(pr)

Dividing both sides by v and substituting v = √(T/ρ), where T is the tension and ρ is the mass density, we get:

[F'(vt) - G'(-vt)] = -P pr sin(pr) / √(Tρ)

Integrating both sides with respect to t, we get:

F(vt) - G(-vt) = -P cos(pr) / √(Tρ)

Using the second initial condition, we have:

F(0) + G(0) = 0

Substituting F(vt) = f(1 + vt) and G(-vt) = g(1 - vt), we get:

f(1) + g(1) = 0

Solving these two equations for f and g, we get:

f(x) = (P/2) cos(pr - 2πx/λ)

g(x) = -(P/2) cos(pr + 2πx/λ)

where λ = v/f is the wavelength.

Therefore, the solution to the wave equation is:

y(x,t) = (P/2) cos(pr - 2π(x - vt)/λ) - (P/2) cos(pr + 2π(x + vt)/λ)

which satisfies the initial conditions y(1,t) = P cos(pr) and y(0,t) = 0.

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This information could help healthcare providers tailor their treatment plans and interventions for patients diagnosed with that disease at the hospital.

As an AI language model, I don't have an intended future career. However, I can provide an example from the nursing profession. Let's say a nurse wants to do a hypothesis test to determine if the population mean age of patients diagnosed with a specific disease at a hospital is significantly different from the national population mean age for that disease. The target population for this hypothesis test would be all patients diagnosed with that disease at the hospital. The nurse could collect a sample of patient data from the hospital and use statistical analysis to determine if the hospital's population mean age for the disease is significantly different from the national population means age. This information could help healthcare providers tailor their treatment plans and interventions for patients diagnosed with that disease at the hospital.

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To find the curvature of the curve r(t), first compute its first and second derivatives, then use the curvature formula: κ(t) = (18t) / (9 + 9t^4)^(3/2), where r(t) = (3t + 9)i - 9j + (6 - 3/2t^2)k.

To find the curvature of the curve r(t), we need to compute the first and second derivatives of r(t), and then use the curvature formula. Given r(t) = (3t + 9)i - 9j + (6 - 3/2t^2)k:

First, find the first derivative r'(t):
r'(t) = (3)i - (3t^2)k

Next, find the second derivative r''(t):
r''(t) = (-6t)k

Now, we use the curvature formula:
κ(t) = |r'(t) × r''(t)| / |r'(t)|^3

Compute the cross product r'(t) × r''(t):
(3)i × (-6t)k = -18tj

Compute the magnitudes |r'(t) × r''(t)| and |r'(t)|^3:
|r'(t) × r''(t)| = |-18t| = 18t
|r'(t)| = √(3^2 + 0^2 + (-3t^2)^2) = √(9 + 9t^4)
|r'(t)|^3 = (9 + 9t^4)^(3/2)

Finally, find the curvature κ(t):
κ(t) = (18t) / (9 + 9t^4)^(3/2)

This is the curvature of the curve r(t) at any point t.

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Answer:

5

Step-by-step explanation:

becaus the x is more diferent like 4×15 is a representation of the algebar so is 5

The equation of the plane is -x - 20y + 4z + 1 = 0

The plane that contains the line r = (-4,-3,3) + f(4,1,0) and is parallel to the vector u = (0,1,5) must also be perpendicular to the vector u.

Let's find the normal vector of the plane first.

The direction vector of the line is d = (4,1,0).

Since the plane is parallel to u, its normal vector must be perpendicular to u.

Therefore, the normal vector of the plane is the cross product of d and u:

n = d × u = (4,1,0) × (0,1,5) = (-1,-20,4)

We can use the point-normal form of the equation of a plane:

n · (r - p) = 0

We can choose any point on the line as the point on the plane, so let's choose (-4,-3,3):

(-1,-20,4) · (r - (-4,-3,3)) = 0

Expanding the dot product, we get:

-x - 20y + 4z + 1 = 0

Hence,  the equation of the plane is -x - 20y + 4z + 1 = 0

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