2. Find the 20th percentile for the pdf f(x;0.5) - [0.5e-0.5x 10 x20 otherwise 3. Suppose that X is a continuous random variable with pdf f(x). Compute the fol- lowing probabilities. (a) P(X < 17(0.20

Answer:

\sqrt{7}i or -\sqrt{7}i

Step-by-step explanation:

square root both sides of the equation

since you can't sqrt a negative number, you substitute sqrt of -1 to i

Which gets the answer.

Answer:

12m

Step-by-step explanation:

To find:

The sketch of v, 2v and 1/2 v.

Solution:

Given the v = <3,2>.

(a)

The sketch of v is shown below:

(b)

The value of 2v can be obtained as follows:

The sketch of 2v is shown below:

(c)

The value of 1/2 v can be obtained as follows:

The sketch of 1/2 v is shown below:

The area of the sidewalk is 84.78 square meters if a circular flower bed is 23 m in diameter and has a 3 m wide circular sidewalk.

A circular flower bed is 23 m in diameter and has a circular sidewalk around it that is 3 m wide. The area of the sidewalk is square meters. The formula used: The area of the circle is given by:

πr²

Here, r = (d + 2w)/2, where d is the diameter and w is the width.

Substitute the values of d, w, and π in the above formula to get the area of the circular sidewalk.

Diameter of circular flower bed = 23 m

Width of circular sidewalk = 3 m

Radius of circular flower bed, r = (23+3)/2 = 13 m

Radius of circular sidewalk = (23+3+3)/2 = 14 m

Area of the circular sidewalk = π(14² - 13²) m²= π(14+13)(14-13) m²= 3.14(27) m²= 84.78 m²

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To determine the variance of a geometric random variable X with parameter p, we can use the conditional variance formula.

The formula for the variance of a geometric random variable is given by:

Var(X) = (1 - p) / (p^2)

Where p is the parameter of the geometric distribution, representing the probability of success on each trial.

This formula assumes that the random variable X represents the number of trials required until the first success in a sequence of independent Bernoulli trials, where each trial has a probability of success p.

By plugging in the value of p into the formula, you can calculate the variance of the geometric random variable X.

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The percent of the utterances in the sample need to be 1 word in length is 13.3%.

Your information is incomplete. Therefore, an overview will be given. Let's assume that the number if 1 word is 12 and the total number of words given is 90.

Therefore, the percentage will be:

= 1 word/Total words × 100

= 12/90 × 100.

= 13.3%

In conclusion, the percentage is 13.3%.

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Answer:

168 unlimited-ride passes.

Step-by-step explanation:

50x+20y=10680

x+y=282

Multiply.

20(x+y=282)

20x+20y=5640

Subtract.

50x-20x+20y-20y=10680-5640.

30x=5040

x=168

Hope this helps plz hit the crown :D

It's C, I took the test and got it right.

Answer:

g(4)=7

Step-by-step explanation:

1/2(4) = 2

2+5 = 7

g(4)=7

To delete something you no longer need, simply select the content and use the delete or backspace key on your keyboard.

If you want to delete something you no longer need, whether it's a file, document, or any other digital content, there are a few steps you can follow. First, locate the item you want to delete, whether it's in a file explorer, email inbox, or any other application. Select the item by clicking on it or highlighting it. Then, use the delete or backspace key on your keyboard, or look for a delete option within the application or menu.

It's important to note that when you delete something, it is typically moved to the recycle bin or trash folder, depending on your operating system or application settings. This acts as a safety net, allowing you to recover the deleted content in case you change your mind. If you're certain you want to permanently delete the item, you can empty the recycle bin or trash folder, which will permanently remove the content from your system.

Before deleting anything, it's always a good practice to double-check and ensure that you won't need the content in the future. Consider making backups or copies of important files, especially if they contain valuable or irreplaceable information. Additionally, be mindful of any potential consequences or dependencies associated with the content you're deleting, such as shared files or linked documents, to avoid unintended disruptions or loss of data.

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The quadratic equation that is satisfied here is given as x^2 + 5x - 176 = 0

Let's call the two integers x and y, where x is the smaller integer (N). Then, we have:

xy = 176

and

y = x + 5

We can substitute the second equation into the first equation to get:

x(x + 5) = 176

Expanding the left side, we get:

x^2 + 5x - 176 = 0

This is a quadratic equation that N satisfies.

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Answer:

u=1

v = 10

Step-by-step explanation:

For the triangles to be congruent

IG = PR

50 = u+49

50 - 49 = u

1 = u

GH = RQ

v+6 = 16

v = 16-6

v = 10

Answer:

2(209 + 467) - 9/10

Step-by-step explanation:

The end behavior of the function f(x) = -x^3(x + 9)^3(x + 5) indicates that as x approaches positive or negative infinity, the function approaches negative infinity.

To determine the end behavior of the function, we examine the behavior of the function as x becomes very large (approaching positive infinity) and as x becomes very small (approaching negative infinity).

As x approaches positive infinity, the dominant term in the function is -x^3. Since x is being raised to an odd power (3), the term -x^3 approaches negative infinity. The other factors, (x + 9)^3 and (x + 5), do not change the sign or the behavior of the function significantly. Therefore, as x approaches positive infinity, f(x) also approaches negative infinity.

Similarly, as x approaches negative infinity, the dominant term in the function is also -x^3. Again, since x is being raised to an odd power (3), the term -x^3 approaches negative infinity. The other factors, (x + 9)^3 and (x + 5), do not change the sign or the behavior of the function significantly. Therefore, as x approaches negative infinity, f(x) also approaches negative infinity.

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Therefore, the expression that equals 3B - 3C in standard form is -21x² - 6x + 24.

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated or simplified to obtain a single value or another expression. In algebra, expressions are often used to represent mathematical relationships or formulas, and can be manipulated using various algebraic techniques such as factoring, expanding, simplifying, and solving for unknown variables. Expressions are also used in calculus, probability theory, and many other branches of mathematics to describe mathematical models and relationships.

Here,

We can start by substituting the expressions for B and C into the expression for 3B - 3C and simplifying:

3B - 3C = 3(-3x - 7x²) - 3(-x² - 8 - x)

= -9x - 21x² + 3x² + 24 + 3x

= -21x² - 6x + 24

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Answer:

y = -3

Step-by-step explanation:

This is because horizontal lines have a slope of 0. And for horizontal lines, the equation of the line is y = b. So, b is the y-intercept and the y intercept is -3 so that is the equation of the line.

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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Answer:

I think it’s just option 1. Tell me if I was wrong.

Step-by-step explanation:

The dimension of the rectangle 18 feet by 13feet

A rectangle is a 2 dimensional shape having two sides.

Area of a rectangle = length * width

Given the following parameters

Length = x + 8

Width = x + 3

Area = 234ft^2

Substitute the given parameters into the formula

(x+8)(x+3) = 234
x² + 3x + 8x + 24 = 234

x² + 11x = 234 - 24
x² + 11x = 210

x² + 11x - 210 = 0

Factorize

x² + 21x - 10x - 210 = 0

x(x+21) - 10(x+21) = 0
x - 10 = 0
X = 10

Leength = x + 8

Length = 18 feet

Width = x + 3

Width = 3 + 10
Width = 13feet

Hence the dimension of the rectangle 18 feet by 13feet

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Answer:

2121 Items

Step-by-step explanation:

Multiply 303 by 7 To get the answer 2121.

Answer:

43 rows & 2 left over

Step-by-step explanation:

So first, we have to do long division for 303 by 7.

303 ÷ 7 = 43 R 2

So you have 43 rows and 2 left over.

Hope this helped! :)

(a)  The general solution is y = \(tan((1/3) x^3 + C)\). (b) This code will generate a direction field with blue arrows indicating the slope at different points and four integral curves corresponding to different values of the constant of integration C.

(a) To find the general solution to the differential equation \(y′ = x^2(1 + y^2),\)we can separate variables and integrate.

Separating variables:

\(dy / (1 + y^2) = x^2 dx\)

Integrating both sides:

\(∫(1 + y^2)^(-1) dy = ∫x^2 dx\)

Using the integral formula\(∫(1 + u^2)^(-1) du\) = arctan(u) + C, where C is the constant of integration, we have:

arctan(y) =\((1/3) x^3 + C\)

Taking the arctangent of both sides to eliminate the natural logarithm, we obtain the general solution:

y = tan((1/3) x^3 + C)

(b) Plotting a direction field and integral curves can be done using various software tools. One popular option is Python with the matplotlib library. Here's an example code snippet that generates the direction field and four integral curves for the given region:

```python

import numpy as np

import matplotlib.pyplot as plt

# Define the differential equation

def dy_dx(x, y):

   return x**2 * (1 + y**2)

# Define the region

x = np.linspace(-1, 1, 20)

y = np.linspace(-1, 1, 20)

# Create a grid of points in the region

X, Y = np.meshgrid(x, y)

# Calculate the slope at each point in the grid

U = 1

V = dy_dx(X, Y)

# Plot the direction field

plt.quiver(X, Y, U, V, color='b', alpha=0.5)

# Plot integral curves

C = [-2, -1, 0, 1, 2]  # Constants of integration

for c in C:

   Y_solution = np.tan((1/3) * X**3 + c)

   plt.plot(X, Y_solution, 'r')

# Set plot limits and labels

plt.xlim([-1, 1])

plt.ylim([-1, 1])

plt.xlabel('x')

plt.ylabel('y')

# Show the plot

plt.show()

```

This code will generate a direction field with blue arrows indicating the slope at different points and four integral curves (red curves) corresponding to different values of the constant of integration C. Adjust the values of the constants and the plot limits as desired to customize the plot to your needs.

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(a) Find the general solution to y′=x2(1+y2). (b) Using the software of Python generate a code to plot a direction field and 4 integral curves for the region −1≤x,y≤1.

The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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Answer:

Step-by-step explanation:

Corresponding angles are congruent

thus, 8x - 17 = 5x +19

Hope it helps!

Answer:

C. 8x-17 =5x+19

Step-by-step explanation:

Assuming line a and b are parallel then we know that the two given angles are corresponding angles. This means they are also equivalent. Therefore...

8x-17=5x+19

Answer:

y = - 1.25x + 9

Step-by-step explanation:

A(0,9)  B(4,9)   C(4,4)

AB² = (4-0)² + (9-9)² = 16

AC² = (4-0)² + (4-9)² = 41

BC² = (4-4)² + (4-9)² = 25

AC is hypotenuse with y interception of 9

slope = 5/4 = -1.25

equation: y = - 1.25x + 9

Answer:

see below

Step-by-step explanation:

Function 1

Find the slope

m = ( y2-y1)/ (x2-x1)

   = (-5 -3) /(3 - -1)

   = ( -5-3)/(3+1)

   = -8/4

   = -2

Function 2

Using the points (0,4) and (-1,0)

m = ( y2-y1)/ (x2-x1)

m = ( 0-4)/(-1-0)

   = -4/-1

    = 4

The function with the greater rate of change is function 2

#Function 1

Slope=

#Function 2

Slope

Function 2 has greater rate of change

The metric system of measurement is based on the number 10.

This system is also known as the International System of Units (SI) and is used in most countries around the world. In the metric system, various units of measurement are defined as multiples or fractions of a base unit, which is defined for each quantity being measured. For example, the base unit for length is the meter, and the base unit for mass is the kilogram. Prefixes such as kilo-, centi-, and milli- are used to indicate multiples or fractions of the base unit, based on factors of 10. For example, a kilometer is 1000 meters, a centimeter is 1/100 of a meter, and a milligram is 1/1000 of a gram. This makes the metric system easy to use and convert between units, as well as consistent and universally recognized.

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Answer:

x = 74 degrees

Hope that helps

Answer:

74

Step-by-step explanation:

2x+32=180

2x=148

x=74

Answer: 49^((1)/(2))=7

Step-by-step explanation:

We will investigate how to determine the y-intercept of an equation of a line.

A general equation of a line is given in a slope-intercept form as follows:

Where,

The slope of the line is already determined and expressed as follows:

To determine the y-intercept of an equation of a line we need a coordinate pair. We are given a table of values through which the line passes. We can use any of the coordinate pair. We will pick the first pair:

We will plug in the respective coordinate values in the given equation and solve for y-intercept ( c ) as follows:

Therefore, the value of the y-intercept when plugged in the general equation we have: