(a) {(-1)^n/n}, where n is a natural number. The terms alternate in sign but their absolute values converge to 0, making the sequence Cauchy, but not monotone.
(b) {2n}, where n is a natural number. The terms are always increasing but the difference between consecutive terms remains constant (2), so it's not a Cauchy sequence.
(c) {(-1)^n}, where n is a natural number. The terms alternate between -1 and 1, making the sequence bounded, but the difference between consecutive terms is 2, so it's not a Cauchy sequence.
(a) An example of a sequence of real numbers that is Cauchy but not monotone is:
1, 1/2, 2/3, 1/4, 3/5, 1/6, 4/7, 2/8, 5/9, 3/10, 6/11, 4/12, ...
This sequence is Cauchy because, for any two positive integers m and n, the terms a_m and a_n eventually get arbitrarily close to each other as m and n get larger. However, the sequence is not monotone because it oscillates between increasing and decreasing terms.
(b) An example of a sequence of real numbers that is monotone but not Cauchy is:
1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, ...
This sequence is monotone decreasing because each term is smaller than the previous one. However, it is not Cauchy because the difference between any two terms eventually becomes arbitrarily large as the terms get further down the sequence.
(c) An example of a sequence of real numbers that is bounded but not Cauchy is:
1, 1/2, 2/3, 1/4, 4/5, 1/6, 6/7, 1/8, 8/9, 1/10, 10/11, 1/12, ...
This sequence is bounded because all of its terms are between 0 and 1. However, it is not Cauchy because the terms oscillate between small and large values and do not eventually get arbitrarily close to each other.
Learn more about Sequence:
brainly.com/question/30262438
#SPJ11
the picture below shows the shape of a design painted on the side of a building. The design was formed by combining triangles and rectangles.
What is the area of the wall covered by the design?
Therefore , the solution of the given problem of surface area comes out to be 212 square feet of the wall are therefore covered by the design.
What exactly does an area mean?The total size of the object can be determined by calculating how much room would be required to completely cover its exterior. When choosing a similar product with a cylindrical form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.
Here,
We must first determine the area of each individual form before adding them together to determine the portion of the wall that the design covers.
Taking a look at the rectangle first, we can observe that it has the following area:
=> 120 square feet= 10 feet x 12 feet.
=> 40 square feet = (1/2)(10 ft)(8 ft).
Consequently, the two triangles' combined area is:
=> 80 square feet = 2 x 40 square feet.
=> (12 square feet) = (1/2)(6 ft)(4 ft).
The total area of all the shapes is as follows:
=> 212 square feet= 120 square feet, 80 square feet, and 12 square feet.
=> 212 square feet of the wall are therefore covered by the design.
To know more about surface area visit:
https://brainly.com/question/2835293
#SPJ1
Answer: the answer is 261 ^2 ft!
Step-by-step explanation:
Suppose we assume that X1, X2, . . . , Xn is a random sample from a「(1, θ) distribution a) Show that the random variable (2/θ) ∑n i =1 Xi has a X^2- distribution with 2n degrees of freedom. (b) Using the random variable in part (a) as a pivot random variable, find a (1-α) 100% confidence interval for θ.
The sum of random variables (2/θ) ∑n i =1 Xi has a X^2- distribution with 2n degrees of freedom. Using this as a pivot random variable, a (1-α) 100% confidence interval for θ is [(2(n-1)S^2)/χ^2(1-α/2,2n), (2(n-1)S^2)/χ^2(α/2,2n)]..
To show that (2/θ) ∑n i =1 Xi has a X^2-distribution with 2n degrees of freedom, we can use the following steps
Calculate the sample mean X = (1/n) ∑n i =1 Xi.
Calculate the sample variance S^2 = (1/n) ∑n i =1 (Xi - X)^2.
Calculate the test statistic T = (2/θ) ∑n i =1 Xi.
Substitute X and S^2 into T to get T = (2/θ) nX = (2/θ) (n-1)S^2.
We know that (n-1)S^2/θ has a X^2-distribution with n-1 degrees of freedom. Therefore, (2(n-1)S^2)/(θ^2) has a X^2-distribution with 2(n-1) degrees of freedom.
Substituting (2/θ) nX = (2/θ) (n-1)S^2 into this expression, we get
T = (2/θ) nX = (2/θ) (n-1)S^2 = (2(n-1)S^2)/(θ^2)
Hence, T has a X^2-distribution with 2n degrees of freedom.
Using the random variable from part (a) as a pivot random variable, we can construct a (1-α) 100% confidence interval for θ as follows:
(2(n-1)S^2)/χ^2(α/2,2n) ≤ θ ≤ (2(n-1)S^2)/χ^2(1-α/2,2n
Here, χ^2(α/2,2n) and χ^2(1-α/2,2n) are the α/2 and 1-α/2 percentiles of the X^2-distribution with 2n degrees of freedom, respectively.
Thus, a (1-α) 100% confidence interval for θ is [(2(n-1)S^2)/χ^2(1-α/2,2n), (2(n-1)S^2)/χ^2(α/2,2n)].
To know more about random variable:
https://brainly.com/question/17238189
#SPJ4
A wind turbine in West Texas with a 50-meter diameter has damage on the tip of one of
its 3 blades. Workers are on a platform that is 2 meters below the tip of the damaged
blade at its lowest point. In maintenance mode, the turbine is set to complete one full
rotation every ten minutes to allow computes to analyze the effect of the damage and help
workers identify any adjustments that need to be made after repairs. Generate a
trigonometric function using cosine that models the height above the platform (h) of the
damage on the tip of the turbine blade as a function of time (t). y = acos(b(x - c)) + d
Answer:
Step-by-step explanation:
The trigonometric function using cosine that models the height above the platform (h) of the damage on the tip of the turbine blade as a function of time (t) can be represented by:
h = acos[(2/50) (πt - π/2)] + 2
where:
a = amplitude = 1
b = period = 2π/B = 2π/(50/2) = π/25
c = phase shift = π/2
d = vertical shift = 2
So the final function is:
h = acos[(2/50) (πt - π/2)] + 2
Richard and Stephen win some money and share it in the ratio 2:1. Richard gets £12 more than Stephen. How much did Stephen get?
Answer:
if richie boi got 12 and the ratio is 2:1 that steven got 6
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIEST!!!
1. The graph of the equation lines |y| -3 ≥ 0 is b
2. the equation of the line that passes through points (-3, -4) and (2, 5) is 9x - 5y + 7 = 0. Option D
3. The equation of a line that passes through points (2, 2) and (2, -3) is
x - 2 = 0 . Option C
How to identify the graph of the equation lines |y| -3 ≥ 0To identify the graph of the inequality |y| - 3 ≥ 0, we can first rewrite the inequality as two separate inequalities:
y - 3 ≥ 0 and -y - 3 ≥ 0
Now, solve each inequality for y:
y ≥ 3 and y ≤ -3
The graph of the inequality |y| - 3 ≥ 0 consists of two horizontal lines y = 3 and y = -3, with the shaded region including the lines and extending to positive infinity above y = 3 and to negative infinity below y = -3.
The above answers are in response to the questions below as seen in the image.
2. A line passed though two points (-3, -4) and (2, 5). The equation of the line is?
a. 7x + 9y + 57 = 0 b. 5x + 5y - 35 = 0
c. 9x - 5y - 43 = 0 d. 9x - 5y +7 = 0
3. The equation of a line that passed through (2,2) and (2, -3) is .......?
a. x - 2 = 0 b. 2x - 3y = 0
c. x - 2 = 0 d. x + 3 + 0
Find more exercises on equation of a line;
https://brainly.com/question/2564656
#SPJ1
Let f(x) = x2 – 5x. Round all answers to 2 decimal places. = a. Find the slope of the secant line joining (1, f(1) and (7, f(7)). Slope of secant line ____
The slope of the secant line joining (1, f(1)) and (7, f(7)) is 3.
To find the slope of the secant line joining (1, f(1)) and (7, f(7)), we'll use the formula:
Slope = (f(7) - f(1)) / (7 - 1)
First, let's find the values of f(1) and f(7) using the given function
f(x) = x^2 - 5x:
f(1) = (1)^2 - 5(1) = 1 - 5 = -4
f(7) = (7)^2 - 5(7) = 49 - 35 = 14
Now, substitute these values into the slope formula:
Slope = (14 - (-4)) / (7 - 1) = (14 + 4) / 6 = 18 / 6 = 3
So, the slope of the secant line joining (1, f(1)) and (7, f(7)) is 3.
To learn more about secant lines visit : https://brainly.com/question/30162649
#SPJ11
Why does sample size need to be accounted for in the t-distribution? Choose the correct answer below O A. The accuracy of the t-distribution depends on the sample size. O B. The t-distribution should not be used for large sample sizes. O C. The t-distribution becomes less skewed as the sample size increases. O D. The t-distribution should not be used for small sample sizes. O E. The t-distribution changes for different sample sizes. Click to select your answer.
The reason for accounting for sample size in the t-distribution is to account for the variability of smaller samples.
What is the reason for accounting for sample size in the t-distribution?
The t-distribution is a probability distribution used to test hypotheses and estimate confidence intervals for small sample sizes.
It is based on the sample mean and standard deviation, which can have greater variability than the population mean and standard deviation.
As the sample size increases, the sample mean and standard deviation become more accurate estimates of the population mean and standard deviation, and the t-distribution becomes less skewed and more similar to the standard normal distribution.
This is because the standard error of the mean decreases with increasing sample size, resulting in more precise estimates and narrower confidence intervals.
Therefore, it is important to account for sample size in the t-distribution to obtain accurate statistical inference and avoid misleading conclusions.
Learn more about t-distribution
brainly.com/question/13576312
#SPJ11
find f. f ''() = sin() cos(), f(0) = 4, f '(0) = 1 f() = incorrect: your answer is incorrect.
The solution function is f(θ) = -sin(θ) - cos(θ) + 5.
Now, let's move on to the problem at hand. We are given the second derivative of a function, which is equal to sin(θ) + cos(θ). In order to find the function itself, we need to integrate the second derivative. Integrating is the opposite of differentiating and allows us to find the original function given its derivative.
We start by integrating the second derivative with respect to θ. Since the integral of sin(θ) is -cos(θ), and the integral of cos(θ) is sin(θ), we have:
f '(θ) = -cos(θ) + sin(θ) + C1,
where C1 is the constant of integration. We don't know the value of C1 yet, so we'll have to use the initial condition f '(0) = 2 to solve for it. Plugging in θ = 0 and f '(0) = 2, we get:
2 = -cos(0) + sin(0) + C1
2 = 1 + C1
C1 = 1
Now we know the value of C1, and we can use it to find f(θ). We integrate f '(θ) with respect to θ:
f(θ) = -sin(θ) - cos(θ) + C2,
where C2 is the constant of integration. We can find the value of C2 using the initial condition f(0) = 4. Plugging in θ = 0 and f(0) = 4, we get:
4 = -sin(0) - cos(0) + C2
4 = -1 + C2
C2 = 5
To know more about function here
https://brainly.com/question/28193995
#SPJ4
Complete Question:
Find f.
f ''(θ) =sin(θ) + cos(θ)
f(0) = 4
f '(0) = 2
find an equation for the tangent plane to the surface z 1 = x y 3 cos ( z ) z 1=xy3cos(z) at the point ( 1 , 1 , 0 ) (1,1,0) .
Equation for the tangent plane to the surface z 1 = x y 3 cos ( z ) z 1=xy3cos(z) at the point ( 1 , 1 , 0 ) (1,1,0) is :
z = x + 3y - 4
To find the equation for the tangent plane to the surface z1 = xy^3cos(z) at the point (1, 1, 0), follow these steps:
1. First, find the partial derivatives of the given function with respect to x and y. The given function is z1 = xy^3cos(z).
2. Find ∂z1/∂x by differentiating with respect to x:
∂z1/∂x = y^3cos(z)
3. Find ∂z1/∂y by differentiating with respect to y:
∂z1/∂y = 3xy^2cos(z)
4. Now, evaluate the partial derivatives at the given point (1, 1, 0):
∂z1/∂x(1, 1, 0) = 1^3cos(0) = 1
∂z1/∂y(1, 1, 0) = 3*1^1*1^2*cos(0) = 3
5. Finally, write the equation for the tangent plane using the obtained values and the given point (1, 1, 0). The general equation for a tangent plane is:
z - z0 = ∂z1/∂x(x - x0) + ∂z1/∂y(y - y0)
Substitute the values to get the equation for the tangent plane:
z - 0 = 1*(x - 1) + 3*(y - 1)
Your answer: z = x + 3y - 4
Learn more about : Equation of a Plane - https://brainly.com/question/31417315
#SPJ11
Brandy has a garden in the shape of a right triangle. The length of the legs are 48 yards and 14 yards. What is the length of the hypotenuse?
A. 50 yards
B. 69 yards
C. 34 yards
D. 62 yards
The length of the hypotenuse of Brandy's garden is 50 yards.
What is the length of the hypotenuse?To find the length of the hypotenuse of a right triangle when given the lengths of the legs, we can use the Pythagorean theorem
In this case, Brandy's garden has legs of length 48 yards and 14 yards. Let's label these legs as a and b, where a = 48 and b = 14.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2
where c is the length of the hypotenuse.
Substituting the values of a and b, we get:
c^2 = 48^2 + 14^2
Simplifying the right side of the equation, we get:
c^2 = 2304 + 196
c^2 = 2500
Taking the square root of both sides, we get:
c = 50
Therefore, the length of the hypotenuse of Brandy's garden is 50 yards.
Read more about right triangles at
https://brainly.com/question/2437195
#SPJ1
use the result of part (a) to find the direction in which the function f(x, y) = x^3 y − x^2y^3 decreases fastest at the point (4, −2).
The direction in which the function f(x, y) = x³y - x²y³ decreases fastest at the point (4, -2) is along the vector ⟨96, 64⟩.
To find the direction in which the function f(x, y) = x³y - x²y³ decreases fastest at the point (4, -2), we need to compute the gradient of the function and then find the negative of the gradient at the given point.
Compute the partial derivatives of the function f(x, y) with respect to x and y.
∂f/∂x = 3x²y - 2xy³
∂f/∂y = x³ - 3x²y²
Evaluate the partial derivatives at the point (4, -2).
∂f/∂x(4, -2) = 3(4)²(-2) - 2(4)(-2)³ = -32
∂f/∂y(4, -2) = (4)³ - 3(4)²(-2)² = -128
Compute the negative of the gradient at the point (4, -2).
The gradient is the vector formed by the partial derivatives: ∇f = ⟨∂f/∂x, ∂f/∂y⟩
At the point (4, -2), ∇f = ⟨-32, -128⟩
The negative of the gradient is -∇f = ⟨32, 128⟩.
This is the required vector.
Learn more about vector:
https://brainly.com/question/3184914
#SPJ11
Fill in the ANOVA table. Source of Variation Sum of Squares Degrees of Freedom Mean Squares F-Test Statistic Treatment 353 4 Error 4116 21 Total Complete the ANOVA table by filling in the missing values. Source of Variation Sum of Squares Degrees of Freedom Mean Squares F-Test Statistic Treatment 353 4 nothing nothing Error 4116 21 nothing Total nothing nothing (Type an integer or decimal rounded to three decimal places as needed.)
Source of Variation Sum of Squares Degrees of Freedom Mean Squares F-Test Statistic Treatment 353 4 88.25 4.146 Error 4116 21 196.57 and Total 4469 25.
To complete the ANOVA table, we need to calculate the Mean Squares for Treatment and Error, the Total Sum of Squares, and the F-Test Statistic. Here are the calculations:
1. Mean Squares for Treatment = (Sum of Squares for Treatment) / (Degrees of Freedom for Treatment) = 353 / 4 = 88.25
2. Mean Squares for Error = (Sum of Squares for Error) / (Degrees of Freedom for Error) = 4116 / 21 = 195.52
3. Total Sum of Squares = Sum of Squares for Treatment + Sum of Squares for Error = 353 + 4116 = 4469
4. Total Degrees of Freedom = Degrees of Freedom for Treatment + Degrees of Freedom for Error = 4 + 21 = 25
5. F-Test Statistic = (Mean Squares for Treatment) / (Mean Squares for Error) = 88.25 / 195.52 = 0.451
The completed ANOVA table:
Source of Variation | Sum of Squares | Degrees of Freedom | Mean Squares | F-Test Statistic
Treatment | 353 | 4 | 88.25 | 0.451
Error | 4116 | 21 | 195.52 |
Total | 4469 | 25 | |
Learn more about Degrees:
brainly.com/question/364572
#SPJ11
The portion of a student’s ballpoint pen that contains the ink is a cylinder with a diameter of 0. 400 cm and a height of 11. 5 cm. If the ink lasts 7 weeks, what is the volume of ink that the student uses each week?
The volume of ink used by the student each week is 4.12cm³.
The ballpoint is cylinder in shape. The equation for volume of a cylinder is 2πrh. Where,π is equal to 3.14,r is the radius of the cylinder, h is the height of the cylinder.
Let's find out the volume of the ballpen.
Volume of the ballpen=2πrh
=2×3.14×0.4×11.5
=28.88 cm³
The ink lasted for 7 weeks. The volume of ink that the student uses each week will be total volume divided by 7.
The ink used by the student each week is 28.88÷7.That is 4.12cm³.
Learn more about volume:
https://brainly.com/question/28058531
#SPJ4
The volume of the ink that a student uses is 0.63
The ballpoint pen is of the cylinder shape. The volume of is given by the formula:
[tex]V = \pi r^{2}h[/tex]
Here V is volume of the cylinder
r is radius
r= d/2
r=0.400/2
r=0.200
h is the height of the cylinder
[tex]V=\pi *0.200^{2} * 5[/tex]
[tex]V=0.62832[/tex] cubic units
which is approximately taken as 0.63
The volume of the object is the mass or the space consumed. The volume of the cubic units can be calculated by using the formula V= length* width* height.
The volume is represented by the symbol V. When the object is a hollow cylinder then the formula is:
[tex]V=\pi (R^{2}-r^2)h[/tex] cubic units
There are different types of cylinder this includes solid cylinder, circular cylinder and hollow cylinder. Therefore a cylinder is shape that consists of three dimension and the base of the is circle. The cylinder has height and radius and the line segments from the center of the height of the cylinder. The cylinder are curve in shape and also has a tube shape.
The radius of the cylinder is found by the half of the diameter and the volume of the cylinder is by multiplying the the value of with the radius and height of the cylinder.
To read more about volume of cylinder follow the link below:
https://brainly.com/question/12165015
https://brainly.com/question/16134180
#SPJ4
3 cm 3.5 cm 7 cm find the area
Answer:
[tex]73.5cm^{2}[/tex]
Step-by-step explanation:
describe and sketch the surface of 4x^2 + y^2 =4
The surface described by the equation 4x² + y² = 4 is an ellipse with a center at (0, 0), a major axis length of 4, and a minor axis length of 2.
1. First, let's rewrite the equation in the standard form of an ellipse: (x² / (4/4)) + (y² / (4/1)) = 1, which simplifies to (x² / 1) + (y² / 4) = 1.
2. Now we can identify the major and minor axes:
- The major axis is along the y-axis since 4 is greater than 1. Its length is 2 × √4 = 4.
- The minor axis is along the x-axis with a length of 2 × √1 = 2.
3. Next, we find the center of the ellipse. In this case, it's at the origin (0, 0).
4. Finally, let's sketch the ellipse:
- Draw the x and y-axes.
- Mark the center at (0, 0).
- Plot the points along the major axis at (0, ±2).
- Plot the points along the minor axis at (±1, 0).
- Connect the points to form an ellipse, making sure the curve is wider along the y-axis and narrower along the x-axis.
You can learn more about ellipses at: brainly.com/question/14281133
#SPJ11
write the system x′=e3tx−9ty 8sin(t)x′=e3tx−9ty 8sin(t), y′=8tan(t)y 8x−3cos(t)y′=8tan(t)y 8x−3cos(t) in the form ddt[xy]=p(t)[xy] f⃗ (t).
To write the system in the form ddt[xy]=p(t)[xy] f⃗ (t), we need to express the derivatives x′ and y′ in terms of xy. We can do this by multiplying the first equation by 8sin(t) and the second equation by 8x - 3cos(t):
8sin(t)x′ = 8sin(t)e^(3t)x - 72sin(t)ty
(8x - 3cos(t))y′ = 8tan(t)(8x - 3cos(t))y
Now we can add these two equations and simplify:
8sin(t)x′ + (8x - 3cos(t))y′ = 8sin(t)e^(3t)x - 72sin(t)ty + 8tan(t)(8x - 3cos(t))y
ddt[xy] = (8sin(t)e^(3t) - 72sin(t)t + 8tan(t)(8x - 3cos(t)))xy
So the system in the desired form is ddt[xy] = (8sin(t)e^(3t) - 72sin(t)t + 8tan(t)(8x - 3cos(t)))xy f⃗ (t).
To learn more about Trigonometry & Derivatives : https://brainly.com/question/15552289
#SPJ11
Pls help plssss, I will give 5 starsss
The polynomial x^2 - 3x - 18 can be factored as (x + 6)(x - 3). This can be determined by using the quadratic formula, setting it equal to zero and solving for x. The two solutions are then used to divide the original equation into factors of x plus or minus those values. In this case, the factors would be x + 6 and x - 3.
That is the second answer choice in your screen.
Brainliest?
(c) Recall that the equation of an ellipse in the 2-dimensional plane is c(x1 −a) 2 +d(x2 −b) 2 −1 = 0. Show that an SVM using the polynomial kernel of degree 2, K(u, v) = (1 + u · v) 2 , is equivalent to a linear SVM in the feature space (1, x1, x2, x2 1 , x2 2 , x1x2) and hence that SVMs with this kernel can separate any elliptic region from the rest of the plane. The (axis-aligned) ellipse equation expands into six terms
0 = cx2
1 + dx2
2 − 2acx1 − 2bdx2 + (a
2
c + b
2
d − 1)
corresponding to weights w = (2ac, 2bd, c, d, 0) and intercept a
2 + b
2 − r
2
. This shows that an
elliptical boundary is linear in this feature space, allowing linear separability.
In fact, the four features x1, x2, x2
1
, x2
2
suffice for any axis-aligned ellipse.
SVMs with a polynomial kernel of degree 2 can separate any elliptic region from the rest of the plane because the elliptical boundary becomes linear in the given feature space, allowing for linear separability.
1. Recall the equation of an ellipse in a 2-dimensional plane: c(x1-a)^2 + d(x2-b)^2 - 1 = 0.
2. The polynomial kernel of degree 2 for SVM is given by equation K(u, v) = (1 + u·v)^2.
3. Consider the feature space (1, x1, x2, x1^2, x2^2, x1x2). In this space, the kernel equation becomes linear, as it has six terms corresponding to weights w = (2ac, 2bd, c, d, 0) and an intercept (a^2 + b^2 - r^2).
4. Since the boundary of the ellipse is linear in this feature space, it allows for linear separability.
5. In fact, the four features x1, x2, x1^2, x2^2 suffice for any axis-aligned ellipse.
As a result, any elliptic region can be isolated from the rest of the plane by SVMs with polynomial kernels of degree 2, as the elliptical boundary becomes linear in the feature space and permits linear separability.
Learn more about "ellipse": https://brainly.com/question/16904744
#SPJ11
2x-3y+6=0 and 4x-5y+2=0
The answer of the given question based on the equations are, the solution to the system of equations is (x,y) = (12,10).
What is Equation?An equation is mathematical statement that shows that the two expressions are equal. An equation contains an equals sign (=) and consists of two expressions, referred to as the left-hand side (LHS) and the right-hand side (RHS), which are separated by the equals sign. The expressions on either side of the equals sign can include variables, constants, and mathematical operations like addition, subtraction, multiplication, and division.
Multiply the first equation by 2 and the second equation by -1 to eliminate the x term.
4x - 6y + 12 = 0
-4x + 5y - 2 = 0
Add two equations to eliminate x term.
-y + 10 = 0
y = 10
Substitute value of y back into one of original equations and solve for the x.
2x - 3y + 6 = 0 (using the first equation)
2x - 3(10) + 6 = 0
2x - 24 = 0
x = 12
Therefore, the solution to the system of equations is (x,y) = (12,10).
To know more about Expression visit:
https://brainly.com/question/1859113
#SPJ1
A) Sketch a histogram for X ~ B (5, 0. 5)
b) Sketch a histogram for X ~ B (10, 0. 5)
c) Sketch a histogram for X ~ B (20, 0. 5)
d) Sketch a histogram for X ~ B (100, 0. 5)
From the R language code probability histogram for binomial distributions, X ~ B (5, 0. 5), X ~ B (10, 0. 5), X ~ B (20, 0. 5) and X ~ B (100, 0. 5) are present in above figure 1, 2, 3 and 4 respectively.
A random variable is numeric value of the outcome from probability experiment so, it's value is determined by chance. A probability histogram is a histogram where the horizontal axis corresponds to the value of the variable and the vertical axis represents the probability of the value of the variable. Now, we sketch the histogram for different binomial Probability distribution.
a) X ~ B (5, 0. 5), here X --> random variable, n = 5, probability of sucess, p= 0.5
Using the R language code,
success <--0:n
plot(success, dbinom(success, size= n, prob= p),type='h')
success <--0: 5
plot(success, dbinom(success, size= 5, prob= 0.5),type='h')
The above figure 1 represents required histogram.
b) X ~ B (10, 0. 5), here X --> random variable
n = 10, probability of sucess, p = 0.5
Using the R language code,
success <--0: 5
plot(success, dbinom(success, size= 10, prob= 0.5),type='h')
The above figure 2 represents required histogram.
c) X ~ B (20, 0. 5), here X --> random variable
n = 20, probability of sucess, p = 0.5
Using the R language code,
success <--0: 5
plot(success, dbinom(success, size= 20, prob= 0.5),type='h')
The above figure 3 represents required histogram.
d) X ~ B (10, 0. 5), here X --> random variable
n = 10, probability of sucess, p = 0.5
Using the R language code,
success <--0: 100
plot(success, dbinom(success, size= 100, prob= 0.5),type='h')
Hence, the above figure 4 represents required histogram.
For more information about probability histogram, visit:
https://brainly.com/question/29562593
#SPJ4
Consider a test of H0: µ = 9. For the following case, give the rejection region for the test in terms of the z-statistic: Ha: µ > 9, ΅ = 0.01
A) z > 1.28
B) |z| > 2.575
C) z > 2.33
D) |z| > 2.33
The answer is: C) z > 2.33
For the given hypothesis test with Ha: µ > 9 and a significance level (α) of 0.01, the rejection region in terms of the z-statistic can be determined by finding the critical z-value.
This is because, for a one-tailed test with α = 0.01, the critical z-value corresponds to the value at which there is a 1% probability in the tail to the right. Using a standard normal distribution table, we find that the critical z-value is 2.33.
If the calculated z-statistic is greater than 2.33, we reject the null hypothesis H0: µ = 9.
The answer is: C) z > 2.33
To learn more about null hypothesis visit:
brainly.com/question/28920252
#SPJ11
Which is the graph of the function f(x) = -√√x
7
4
4
4.
O
6
4
2₂-
O
26.
tot
50
4
0+
The graph of the function -sqrt(x) is in the first option
What is graph of radical functionThe graph of a radical function is a curve that represents the output values of the function as they vary with the input values. A radical function is a function that contains a radical or root symbol such as √x, ³√x, or ⁴√x.
The general form of a radical function is f(x) = √(ax + b) + c, where a, b, and c are constants.
The graph of this function will have a domain of all non-negative values of x (since you cannot take the square root of a negative number) and a range of all non-negative values of y.
When the range is negative like in the question we have the graphs as in option one and attached
Learn more about radical function at
https://brainly.com/question/23033957
#SPJ1
Find the Value of each expression. a. 12 + (-10) b. (-5) - 6 c. (-42) + 17 d. 35 - (-8) e. (-4 1/2) + 3
Answer: A. 2,
B. -11,
C. -25
D. 43
e. -3/2
Step-by-step explanation:
Is this picture a
A) Rotation
B) Slide translation
C) Dilation
D) Reflection
The sοlutiοn οf the given prοblem οf cοοrdinates cοmes οut tο be οptiοn D reflectiοn.
What did a cοοrdinate plane actually mean?When used in assοciatiοn with particular οther algebraic elements οn this place, such as Euclidean space, a parameter can precisely determine pοsitiοn using a number οf features οr cοοrdinates. One can use cοοrdinates, which appear as cοllectiοns οf numbers when flying in reflected space, tο lοcate οbjects οr lοcatiοns. The y and x measurements can be used tο find an οbject οver twο surfaces.
Here,
Accοrding tο the phοtοgraph,
the figure lοοks tο have undergοne reflectiοn οr tο have flipped οver a vertical line οf reflectiοn.
This change is οften referred tο as "flipping" οr "mirrοring."
Therefοre , the sοlutiοn οf the given prοblem οf cοοrdinates cοmes οut tο be οptiοn D reflectiοn.
To know more about coordinates visit:
brainly.com/question/27749090
#SPJ1
prove that the function f(x,y)=4arctan(xy) is differentiable at (1,1). then find the linearization l(1,1)
The linearization of f at (1,1) is l(x,y) = π/2 + 2(x-1) + 2(y-1).
To prove that the function f(x,y) = 4arctan(xy) is differentiable at (1,1), we need to show that the partial derivatives of f with respect to x and y exist and are continuous at (1,1).
First, let's find the partial derivatives of f:
∂f/∂x = 4y / (1 + (xy)^2)
∂f/∂y = 4x / (1 + (xy)^2)
At (1,1), we have xy = 1, so
∂f/∂x (1,1) = 4/2 = 2
∂f/∂y (1,1) = 4/2 = 2
Since these partial derivatives are constant, they are clearly continuous at (1,1), so f is differentiable at (1,1).
To find the linearization l(1,1) of f at (1,1), we use the formula:
l(x,y) = f(1,1) + ∂f/∂x (1,1) (x-1) + ∂f/∂y (1,1) (y-1)
Substituting in the values we found earlier:
l(x,y) = 4arctan(1) + 2(x-1) + 2(y-1)
l(x,y) = π/2 + 2(x-1) + 2(y-1)
So the linearization of f at (1,1) is l(x,y) = π/2 + 2(x-1) + 2(y-1).
To know more about linearization visit:
https://brainly.com/question/20286983
#SPJ11
23.LetVi={x∈R|−1/i ≤ x ≤ 1/i} =[−1/i,1/i] for all positive integers i.
a. ∪ i=I 4 VI = b. ∩ i=I 4 VI = c. Are V1, V2, V3 mutually disjoint? Explain
d. ∪ i=I n vi = e. ∩ i=I [infinity] n VI = f. ∪ i=I n vi = g. ∩ i=I [infinity] vi =
Integers-An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign (−1, −2, −3, etc.).[1] The negative numbers are the additive inverses of the corresponding positive numbers.[2] In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold
a. The union of all V i for i = 1 to 4 is equal to [-1/4, 1/4]. This is because V i is defined as the interval [-1/i, 1/i], so when we take the union of all four, we get the interval that goes from the smallest value of -1/4 to the largest value of 1/4.
b. The intersection of all V i for i = 1 to 4 is equal to the empty set, or {}. This is because there is no value that exists in all four intervals at the same time. As the size of the intervals becomes smaller, the chances of having a common value decrease until they reach 0.
c. Yes, V1, V2, and V3 are mutually disjoint. This is because the interval for V i becomes smaller as i increases, so V1 only includes values that are not in V2 or V3, V2 only includes values that are not in V1 or V3, and V3 only includes values that are not in V1 or V2.
d. The union of all V i for i = 1 to n is equal to [-1/n, 1/n]. This is the same as the union for i = 1 to 4, but with n instead of 4.
e. The intersection of all V i for i = 1 to infinity is equal to {0}. This is because as i approaches infinity, the intervals get smaller and smaller, until they only include the value of 0.
f. The union of all V i for i = 1 to n is equal to [-1/n, 1/n], which is the same as part d.
g. The intersection of all V i for i = 1 to infinity is equal to the empty set, or {}. This is because there is no value that exists in all the intervals as the intervals become smaller and smaller.
Hi there! I'm happy to help you with this question. Here are the answers to the parts you've asked about:
a. ∪ i=I 4 VI = ⋃{V1, V2, V3, V4} = [-1,1]
b. ∩ i=I 4 VI = ⋂{V1, V2, V3, V4} = [0,0] or {0}
c. V1, V2, V3 are not mutually disjoint because their intersection is not empty. They all have the integer 0 in common.
d. ∪ i=I n VI = ⋃{V1, V2, V3, ..., Vn} = [-1, 1], since the intervals become smaller as 'i' increases, but they always include the range of [-1, 1].
e. ∩ i=I ∞ VI = ⋂{V1, V2, V3, ...} = [0,0] or {0}, as all the intervals converge to 0.
f. The symbol "n" seems to be a typo, so I'll assume it's meant to be "∞". In that case, ∪ i=I ∞ VI = ⋃{V1, V2, V3, ...} = [-1, 1].
g. ∩ i=I ∞ VI = ⋂{V1, V2, V3, ...} = [0,0] or {0}, as all the intervals converge to 0.
To know more about Integers visit: brainly.com/question/14232618
#SPJ11
The maximum proportion of available volume that can be filled by hard spheres in diamond is0.520.340.320.68
The maximum proportion of available volume that can be filled by hard spheres in diamond is 0.34.
This is known as the packing fraction or the fraction of the available space in a crystal that is occupied by the atoms or molecules that make up the crystal. In the case of diamond, the atoms are carbon, which are arranged in a tetrahedral lattice.
The packing fraction is determined by the size and shape of the atoms or molecules and the way they are arranged in the crystal lattice. In the case of diamond, the carbon atoms are relatively large and the tetrahedral arrangement leaves some space between them.
The maximum possible packing fraction for a crystal made up of hard spheres is 0.74, which corresponds to a face-centered cubic lattice. However, the actual packing fraction for diamond is lower due to the size and shape of the carbon atoms and the tetrahedral arrangement.
To learn more about volume visit;
brainly.com/question/1578538
#SPJ11
many of a bank's customers use its atms to transact business after normal banking hours. during the early evening hours customers arrive at a certain atm location at a rate of one every 7.2 minutes. on average 11.9 customers per hour can be served by the atm. what is the expected number of customers waiting for the atm?
The expected number of customers waiting for the ATM is approximately 0.78.
We can utilize the M/M/1 lining model to take care of this issue. Here, appearances follow a Poisson distribution and administration time follows a remarkable conveyance. The appearance rate is given as 1 client each 7.2 minutes or 60/7.2 clients each hour. This is equivalent to 8.33 clients each hour. The help rate is given as 11.9 clients each hour. Utilizing Little's regulation, the normal number of clients in the line (Lq) is equivalent to the appearance rate (λ) squared split by the contrast between the help rate (μ) and the appearance rate (λ):[tex]Lq = λ^2/(μ(μ-λ))[/tex]Subbing the qualities, we get: Lq = [tex](8.33^2)/(11.9(11.9 - 8.33))[/tex] Lq ≈ 0.78 Consequently, the normal number of clients hanging tight for the ATM is roughly 0.78.
To learn more about Poisson distribution, refer:
https://brainly.com/question/23917661
#SPJ4
mr. riggs is building a triangular sandbox using three boards. he already has two boards that measure 9 feet and 12 feet. he is trying to figure out which lengths are possible for the length of the third board of his sandbox. his neighbor tells him any length will work. mr. riggs disagrees. which lengths below will work for the length of the third board of his triangular sandbox?
Based on the mentioned informations and values provided, it can be said that any length between 3 feet and 21 feet (exclusive) will work for the length of the third board of Mr. Riggs' triangular sandbox.
For a triangle to be formed, the length of the third board must be greater than the difference between the other two lengths and less than their sum. Let's call the length of the third board "x". Then the linear inequation, which can be formed is :
9 + 12 > x > 12 - 9
21 > x > 3
Therefore, any length between 3 feet and 21 feet (exclusive) will work for the length of the third board of Mr. Riggs' triangular sandbox.
Learn more about linear inequation :
https://brainly.com/question/17040954
#SPJ4
what are all possible ways of writing $\frac{1}{64}$ as an integer raised to an integer power?
To write $\frac{1}{64}$ as an integer raised to an integer power, we need to find integers $a$ and $b$ such that $\frac{1}{64}=a^b$.
We can start by expressing $64$ as a power of $2$: $64=2^6$. Then, we can rewrite $\frac{1}{64}$ as $\frac{1}{2^6}$. This means we need to find integers $a$ and $b$ such that $a^b=\frac{1}{2^6}$. Since $a$ must be an integer, we can rewrite $\frac{1}{2^6}$ as $\left(\frac{1}{2}\right)^6$. This means $a=\frac{1}{2}$ and $b=6$. Therefore, one possible way of writing $\frac{1}{64}$ as an integer raised to an integer power is $\left(\frac{1}{2}\right)^6$.
Another possible way is to write $\frac{1}{64}$ as $(-1)^2\cdot\left(\frac{1}{8}\right)^2$. This is because $(-1)^2=1$ and $\frac{1}{8}=\left(\frac{1}{2}\right)^3$. So, we have $1\cdot\left(\frac{1}{2}\right)^6=(-1)^2\cdot\left(\frac{1}{8}\right)^2$. Overall, the possible ways of writing $\frac{1}{64}$ as an integer raised to an integer power are: - $\left(\frac{1}{2}\right)^6$- $(-1)^2\cdot\left(\frac{1}{8}\right)^2$.
To know more about integers click here
brainly.com/question/10930045
#SPJ11
