The joint density f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere, the variables X and Y are uncorrelated but not independent.
The problem requires the determination of whether the random variables X and Y are independent and uncorrelated. For that, the expectation of the product of X and Y is needed. Evaluating E(XY). For the two variables X and Y, their joint density is given as:
f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere
To evaluate the expectation of XY, multiply the variables X and Y as follows: E(XY) = ∫∫xy f(x,y) dy dx.
We evaluate the above equation over the range of the variables.
Since the domain of the density function is given by -y < x < y and 0 < y < 1, E(XY) = ∫∫xy f(x,y) dy dx = ∫0¹ ∫-[tex]y^{y}[/tex] xy dy dx
The above equation can be simplified as:
E(XY) = ∫0¹ (1/3)*y³ dy = 1/12
Hence the covariance between X and Y is given by: Cov (X, Y) = E(XY) - E(X)E(Y) = E(XY) = 1/12.
The variance of X is calculated as follows: E(X) = ∫∫xf(x, y) dy dx
For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere.
Thus, E(X) = ∫∫x f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex] x dy dx= 0.
Hence, Var(X) = E(X²) - [E(X)]² = E(X²) - 0² = E(X²).
The variance of X² is calculated as follows:
E(X²) = ∫∫x² f(x, y) dy dx. For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere.
Thus, E(X²) = ∫∫x² f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex] x² dy dx= 1/3
Hence, Var(X) = E(X²) - [E(X)] ² = 1/3 - 0 = 1/3
The variance of Y² is calculated as follows: E(Y²) = ∫∫y² f(x, y) dy dx
For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere. Thus, E(Y²) = ∫∫y² f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex]y² dy dx= 1/3
Hence Var(Y) = E(Y²) - [E(Y)]² = 1/3 - [E(Y)]²
The covariance between X and Y is given by: Cov (X, Y) = E(XY) - E(X)E(Y) = 1/12 - 0 = 1/12.
We can evaluate the correlation between X and Y as: Corr (X, Y) = Cov (X, Y) / √Var (X) Var(Y)= (1/12) / [(1/3) * (1/3)] = 1/4
Thus, the variables X and Y are uncorrelated but not independent.
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Solve using elimination. 9x − 9y = –18 10x − 9y = –13
Answer:
y = 5, y = 7
Step-by-step explanation:
PLS HELP PLS IM BEGGING
Answer:
b: 118
c: 62
Step-by-step explanation:
Angle B is a vertical angle from the given angle, so they are congruent.
Angle C is supplementary (2 angles that add up to 180 degrees) from the given angle, so we can subtract 118 from 180 to give us 62, which is angle c.
Hope this helps! :)
Answer: b=118 c=62
Step-by-step explanation: All angles add up to 360 degrees. We know one angle equals 118. We can also tell that angle b is identical to angle 118 because they are complementary angles. Now we add 118+118 which equals 236. Subtract 360 from 236. That gives us 124. Divide 124 by two since their are two angles. That gives us 62. c=62 and b=118
Use the given conditions to write an equation for the line. Passing through (-8,6) and parallel to the line whose equation is 8x - 3y -4 = 0 The equation of the line is (Simplify your answer. Type an equation using X and y as the variables.
The equation of the line that passes through (-8, 6) and parallel to the line whose equation is 8x - 3y -4 = 0, is 3y - 8x + 46 = 0
How do i determine the equation of the line?First, we shall obtain the slope of the line. Details below:
8x - 3y -4 = 0
Rearrange the equation with y as the subject, we have
8x - 4 = 3y
y = 8x/3 - 4/3
Thus,
Slope (m₁) = 8/3
Recall,
Slope of parallel lines are equal.
Thus,
The slope of line, is given as:
m₂ = m₁ = 8/3
Now, we shall obtain the equation of line. Details below
Coordinate = (-8, 6) x coordinate 1 (x₁) = -8y coordinate 1 (y₁) = 6Slope of line (m₂) = 8/3Equation of line =?y - y₁ = m₂(x - x₁)
y - 6 = 8/3(x - (-8))
y - 6 = 8/3(x + 8)
Multiply through by 3
3(y - 6) = 8(x + 8)
Clear bracket
3y - 18 = 8x - 64
Rearrange
3y - 8x - 18 + 64 = 0
3y - 8x + 46 = 0
Thus, the equation of line is 3y - 8x + 46 = 0
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What is the answer to 3x+2(x-1)
I have a statistic that is normally distributed with a very large sample size. I add a single subject that is way above the median to the sample. What is likely to happen?
Adding a single subject that is way above the median to a sample with a very large sample size is likely to have a minimal impact on the overall distribution and statistics of the sample.
When the sample size is very large and the distribution of the statistic is approximately normal, the Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution, regardless of the underlying population distribution. This means that the sample mean is less sensitive to individual extreme values.
If a single subject is added to the sample that is way above the median, it will have a relatively small effect on the overall sample mean. This is because the impact of a single extreme value diminishes as the sample size increases.
When adding a single subject that is way above the median to a sample with a very large sample size, the effect on the overall distribution and statistics of the sample is expected to be minimal. The large sample size ensures that the sample mean remains robust and less influenced by individual extreme values. Therefore, the addition of a single subject with a very high value is unlikely to significantly alter the characteristics of the sample distribution or the calculated statistics such as the mean or standard deviation.
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Jennifer painted a tabletop that is shaped like a circle. the circumference of the tabletop is 6π. Which measurement is closest to the area of the tabletop in square feet?
28.26 sq. Ft is the area of the table top
Brianna is going to the amusement park, where she has to pay a set price of
admission and another price for tickets to go on each of the rides. Brianna made the
linear graph below to indicate the money she might spend in total. What does the
y-intercept in the graph represent?
Im pretty sure the answer is A but if not then it is C
This is bcuz B doesn’t make sense because the graph doesn’t say anything close to 100 rides and D doesn’t make sense either.
Hope this helped.
Can I get help with number 20
Answer:
-5/4
Step-by-step explanation:
2
M2|L23
Division Diver Duo
5,626 ÷ 62
How many times can 62 go into 562
The result of 5,626 divided by 62 is approximately 90 with a remainder of 48.
To calculate the division of 5,626 by 62, you can use long division. Here are the steps:
90
______________
62 | 5,626
- 4,96
-----
1,66
1,55
----
110
62
----
48
Therefore, the result of 5,626 divided by 62 is approximately 90 with a remainder of 48.
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using a different method, for every question, solve the following functions 1. f(x) = x+ex 3 2. f(x) = X - C03 X € = 0.0001 2 3. f(x) = x - x + sinx-1 2 Find √29 by Newton-Raphson method
The following functions 1. f(x) = x+ex 3 2. f(x) = X - C03 X € = 0.0001 2 3. f(x) = x - x + sinx-1 2 By using Newton-Raphson method √29 is 4.5826.
Solve f(x) = x + e^x = 0:
Unfortunately, this equation cannot be solved analytically. We can use numerical methods such as the Newton-Raphson method to find an approximate solution. However, in this case, we will move on to the next function.
Solve f(x) = x^3 - 0.0001 = 0:
To solve this equation, we can rearrange it as follows:
x^3 = 0.0001
Taking the cube root of both sides, we get:
x = ∛0.0001
Using a calculator, we find that ∛0.0001 ≈ 0.04641588834.
Therefore, the solution to the equation f(x) = x^3 - 0.0001 = 0 is approximately x ≈ 0.0464.
Solve f(x) = x - x^2 + sin(x) - 1 = 0:
This equation also cannot be solved analytically. We can use numerical methods such as the Newton-Raphson method or graphing methods to find an approximate solution. Let's use the Newton-Raphson method.
Applying the Newton-Raphson method, we start with an initial guess, let's say x0 = 1:
Iteratively, we update x using the formula:
x_n+1 = x_n - f(x_n) / f'(x_n)
The derivative of f(x) is:
f'(x) = 1 - 2x + cos(x)
Using the initial guess:
x1 = x0 - f(x0) / f'(x0)
= 1 - (1 - 1^2 + sin(1) - 1) / (1 - 2(1) + cos(1))
≈ 1.2227
We repeat the process with x1 as the new guess:
x2 = x1 - f(x1) / f'(x1)
≈ 1.2196
Continuing this iterative process, we find:
x3 ≈ 1.2196
x4 ≈ 1.2196
The solution to the equation f(x) = x - x^2 + sin(x) - 1 = 0 is approximately x ≈ 1.2196.
Now, let's move on to finding √29 using the Newton-Raphson method.
To find √29 using the Newton-Raphson method, we need to solve the equation f(x) = x^2 - 29 = 0.
Using the Newton-Raphson method, we start with an initial guess, let's say x0 = 5:
Iteratively, we update x using the formula:
x_n+1 = x_n - f(x_n) / f'(x_n)
The derivative of f(x) is:
f'(x) = 2x
Using the initial guess:
x1 = x0 - f(x0) / f'(x0)
= 5 - (5^2 - 29) / (2 * 5)
= 5 - (25 - 29) / 10
= 5 - 4 / 10
= 5 - 0.4
= 4.6
We repeat the process with x1 as the new guess:
x2 = x1 - f(x1) / f'(x1)
= 4.6 - (4.6^2 - 29) / (2 * 4.6)
≈ 4.5826
Continuing this iterative process, we find:
x3 ≈ 4.5826
x4 ≈ 4.5826
The solution to the equation f(x) = x^2 - 29 = 0, which gives √29, is approximately x ≈ 4.5826.
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asfjpasjfaafdad adsafdshfd
4020
you're supposed to multiply the length value by 1760
:P
I NEED. HELP ASAP please!!!
Answer: It is a polynomial, and the degree is 4.
Step-by-step explanation: The degree is basically the biggest number exponent
Step-by-step explanation:
x xndndjjdjdjdowiekeie
Question 98 Unleaded gas is $2.80 per gallon. Which equation best represents y, the total cost at x pounds of plum?
Answer:
y = $2.80x
Step-by-step explanation:
Based in the information given :
Cost per gallon = $2.80
Number of gallons = x
The total cost, y which is the total cost of x gallons of gas will be :
Cost per gallon * number of gallons
$2.80 * x
Hence,
y = $2.80x
Which of the following points lies on the line 2x+3y=5?
Help me please thanks
Answer:
64 square cm
Step-by-step explanation:
(I pulled this out of the comments in case someone else needs this answer. Easier to see as an answer than as comments in the app)
Area 2 is easier, so we’ll start with that one. Area of a rectangle is length x width.
8 x 6 = 48 square cm
Area 1 is a triangle, so the formula is 1/2(base)(height). The height of the triangle is 8, because it’s the same as the base of the rectangle. The base of the triangle is 4, because we can subtract the 6 from the rectangle from the total side length of 10. Does that make sense?
So 1/2 (4)(8)= 1/2(32) = 16 square cm
Then we add 16 + 48 = 64 square cm
On average, the number of text messages students send is within 100 messages of the average, which is 500 text messages per day. The mean absolute deviation in this situation is
The mean absolute deviation in the given situation, where the average number of text messages students send is within 100 messages of the mean of 500 messages per day, can be calculated.
Mean absolute deviation (MAD) measures the average distance between each data point and the mean of the data set.
In this case, the average number of text messages sent by students is 500 messages per day.
Since the average is within 100 messages of the mean, we can assume a range of 400 to 600 messages.
To calculate the MAD, we need to determine the deviation of each data point from the mean. In this case, the deviations can range from -100 to 100 messages.
Since the data points are evenly distributed around the mean, the sum of these deviations will be zero.
However, to calculate the absolute deviation, we take the absolute values of the deviations.
Considering the range of -100 to 100 messages, the absolute deviations for each data point would be 100, 99, 98, ..., 2, 1, 0, 1, 2, ..., 98, 99, 100.
The average absolute deviation would be the sum of these absolute deviations divided by the total number of data points, which is 201 (from -100 to 100 inclusive).
Therefore, the mean absolute deviation in this situation is the average of these absolute deviations, which can be calculated as (100 + 99 + 98 + ... + 2 + 1 + 0 + 1 + 2 + ... + 98 + 99 + 100) / 201.
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I need to know how much metal is needed to make the can
Answer:
we don't have any wasted metal and everything goes perfectly. In the real world, waste is inevitable.
A triangle has a 90° angle. What type of triangle is it?
Acute triangle
Right triangle
Equilateral triangle
Isosceles triangle
A triangle with a 90° angle is called a right triangle.
Option B is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
Acute triangle:
The angle is less than 90 degrees.
Right triangle:
The angle is 90 degrees.
Equilateral triangle:
All sides of the triangle are equal.
Isosceles triangle:
Two sides of the triangle are equal.
Thus,
A triangle with a 90° angle is called a right triangle.
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Use the consumption function C = C₁ + bY and the income function Y=C+ S. to derive expressions for the MPC, APC, MPS. and APS. 7 marks 5. Given the consumption functions C= 50+ 0.5Y, Deduce expressions for the marginal propensity to save and the average propensity to save. Show that the MPS>APS. Confirm this statement by evaluating APS and MPS at Y = 20. 6 marks 6. Find the derivatives of the following functions. AC = + QI(Q) 3 marks Page 2 y=(√2+1)(√2-3) 3 marks 7. Determine the intervals along which each of the following curves is increasing or decreasing (consider the positive half of the plane, z>0) 5 marks (a) AC=Q²-20Q+120 (b) TR=50Q-Q²
In the given problem, we start by deriving expressions for the marginal propensity to consume (MPC), average propensity to consume (APC), marginal propensity to save (MPS), and average propensity to save (APS) using the consumption function and income function.
Deriving expressions for MPC, APC, MPS, and APS:
Using the consumption function C = C₁ + bY and the income function Y = C + S, we can derive the following expressions:
MPC (Marginal Propensity to Consume) = ΔC / ΔY
APC (Average Propensity to Consume) = C / Y
MPS (Marginal Propensity to Save) = ΔS / ΔY
APS (Average Propensity to Save) = S / Y
Deducing expressions for MPS and APS:
Given the consumption function C = 50 + 0.5Y, we can deduce the expressions for MPS and APS as follows:
MPS = ΔS / ΔY = Δ(Y - C) / ΔY = 1 - MPC
APC = C / Y = (50 + 0.5Y) / Y
APS = S / Y = (Y - C) / Y = 1 - APC
Confirming MPS > APS:
To confirm that MPS is greater than APS, we evaluate them at Y = 20:
MPS = 1 - MPC = 1 - 0.5 = 0.5
APC = C / Y = (50 + 0.5 * 20) / 20 = 52.5 / 20 = 2.625
APS = 1 - APC = 1 - 2.625 = -1.625
Since APS is negative and MPS is positive, it is evident that MPS > APS.
Derivatives of the given functions:
a) AC = Q² - 20Q + 120
The derivative of AC with respect to Q is: d(AC)/dQ = 2Q - 20
b) TR = 50Q - Q²
The derivative of TR with respect to Q is: d(TR)/dQ = 50 - 2Q
Determining intervals of increase or decrease:
a) AC = Q² - 20Q + 120
The quadratic function AC has a positive coefficient for the quadratic term (Q²), indicating a U-shaped curve. It opens upward, which means it is increasing for Q values less than the vertex of the parabola (Q = 10) and decreasing for Q values greater than the vertex.
b) TR = 50Q - Q²
The quadratic function TR has a negative coefficient for the quadratic term (Q²), indicating a downward-opening parabola. It is decreasing for all values of Q.
In summary, we derived expressions for MPC, APC, MPS, and APS using the consumption function and income function. We confirmed that MPS > APS by evaluating them at a given income level.
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A particle is moving with acceleration a(t) = 12 t + 4. its position at time t =0 is s(0) = 8 and its velocity at time t =0 is v(0) = 9. What is its position at time t = 15?
The position function becomes s(t) = 2t³ + 2t² + 9t + 8. Finally, we substitute t = 15 into the position function to obtain the particle's position at time t = 15:s(15) = 2(15)³ + 2(15)² + 9(15) + 8 = 3378. The particle's position at time t = 15 is 3378 units.
Given, the acceleration of the particle is a(t) = 12t + 4 and the particle's position and velocity at t = 0 are s(0) = 8 and v(0) = 9 respectively. To find the particle's position at time t = 15, we need to integrate the acceleration function and use the initial conditions to determine the constants of integration as follows: Integrating the acceleration function yields the velocity function:v(t) = ∫a(t) dt = ∫(12t + 4) dt = 6t² + 4t + C where C is the constant of integration. Using the initial condition that v(0) = 9, we have:9 = 6(0)² + 4(0) + C => C = 9.
Therefore, the velocity function becomes: v(t) = 6t² + 4t + 9 Now, we integrate the velocity function to obtain the position function as follows: s(t) = ∫v(t) dt = ∫(6t² + 4t + 9) dt = 2t³ + 2t² + 9t + D where D is the constant of integration. Using the initial condition that s(0) = 8, we have:8 = 2(0)³ + 2(0)² + 9(0) + D => D = 8Therefore, the position function becomes: s(t) = 2t³ + 2t² + 9t + 8Finally, we substitute t = 15 into the position function to obtain the particle's position at time t = 15:s(15) = 2(15)³ + 2(15)² + 9(15) + 8 = 3378. Therefore, the particle's position at time t = 15 is 3378 units.
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To find the x-intercept, we let y = 0 and solve for x and to find y-intercept, we let x=0 and solve for y. Figure out the x-intercept and y-intercept in given equation of the line. 6x + 2y = 12
Answer:
X-intercept: (2, 0) Y-intercept: (0, 6)Step-by-step explanation:
X-intercept means y-coordinate of 0:
6x +2×0 = 12
6x = 12
x = 2 ← x-coordinate
Y-intercept means x-coordinate of 0:
6×0 + 2y = 12
2y = 12
y = 6 ← y-coordinate
p is a plane in r3. its equation is: x 4y − 3z = 0. this plane is the nullspace of what matrix a ? find the basis for the nullspace of a. find the basis for the line p⊥ that is perpendicular to p.
The vector [1, 1, 1]ᵀ as it is symmetrical to the ordinary vector. Thus, "[1, 1, 1]T" serves as the foundation for the line p.
We can rewrite the plane's equation as a matrix equation to find the matrix A whose nullspace matches the given plane. The plane's equation is as follows:
x - 4y + 3z = 0
We can revise it in lattice structure as:
Where [A] is a 1x3 matrix and [x, y, z]T is a column vector, [A] = [0]. The rows of the matrix [A] will serve as the equation's coefficients for x, y, and z due to the equation's homogeneity and linearity.
As a result, matrix A is:
[A] = [1, -4, 3] We must solve the equation A * x = 0, where x is a column vector, in order to determine the nullspace's basis. For this situation, we really want to address:
We can represent it as a system of equations: [1, -4, 3,] [x, y, z]T = [0].
x - 4y + 3z = 0
To track down the reason for the nullspace, we settle the arrangement of conditions and express the arrangement concerning boundaries. Let's figure out the system:
x = 4y - 3z
Picking y = t (a boundary), we can revamp the arrangement as:
The nullspace of matrix A is spanned by the vector [4, 1, 1]T, so "[4, 1, 1]T" serves as the foundation for the nullspace of A. Since x = 4t, y = t, and z = t,
Presently, to find the reason for the line p⊥ that is opposite to p, we know that any vector in p⊥ is symmetrical to any vector in p. Hence, the reason for p⊥ can be found by finding a vector that is symmetrical to the ordinary vector of p (which is [1, - 4, 3]ᵀ).
We can pick the vector [1, 1, 1]ᵀ as it is symmetrical to the ordinary vector. Thus, "[1, 1, 1]T" serves as the foundation for the line p.
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qüîz 10-2 Gina wilson answers please
Answer:
I don't know how to do it the subject
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(2) dac 4+2 with n = 12 SO T12 = ___ M12 = ___ S12 =___. Report answers accurate to 4 places. Remember not to round too early in your calculations.
Using the Trapezoidal Rule with n = 12, the approximation is T12 = -15.6667. Using the Midpoint Rule with n = 12, the approximation is M12 = -92. Using Simpson's Rule with n = 12, the approximation is S12 = -155.7778. So T12 =-15.6667, M12 =-92, S12 = -155.7778.
To approximate the integral using numerical methods, we'll use the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with n = 12.
Using the Trapezoidal Rule, the approximation is given by:
T12 = h/2 * [f(a) + 2(f(x1) + f(x2) + ... + f(x11)) + f(b)]
where h = (b - a)/n and xi represents the equally spaced points between a and b.
Using the Midpoint Rule, the approximation is given by:
M12 = h * [f(x1/2) + f(x3/2) + ... + f(x23/2)]
where xi/2 represents the midpoints between xi-1 and xi.
Using Simpson's Rule, the approximation is given by:
S12 = h/3 * [f(a) + 4(f(x1) + f(x3) + ... + f(x11)) + 2(f(x2) + f(x4) + ... + f(x10)) + f(b)]
Now, let's calculate the approximations:
For T12:
h = (2 - 4)/12 = -1/3
T12 = (-1/3)/2 * [4 + 2(4 + 2 + ... + 4) + 2]
T12 = -1/6 * [4 + 2(4*11) + 2]
T12 = -1/6 * [4 + 88 + 2]
T12 = -1/6 * 94
T12 = -15.6667
For M12:
h = (2 - 4)/12 = -1/3
M12 = (-1/3) * [4 + 4*3 + 4*5 + ... + 4*23]
M12 = -1/3 * [4 + 12 + 20 + ... + 44]
M12 = -1/3 * [4 + 12 + 20 + ... + 44]
M12 = -1/3 * 276
M12 = -92
For S12:
h = (2 - 4)/12 = -1/3
S12 = (-1/3)/3 * [4 + 4*4 + 2(4 + 4*3 + 4*5 + ... + 4*11) + 2(4 + 4*2 + 4*4 + ... + 4*10) + 2]
S12 = (-1/9) * [4 + 16 + 2(4 + 12 + 20 + ... + 44) + 2(4 + 8 + 16 + ... + 40) + 2]
S12 = (-1/9) * [4 + 16 + 2(276) + 2(220) + 2]
S12 = (-1/9) * 1402
S12 = -155.7778
Therefore, the approximations are:
T12 = -15.6667
M12 = -92
S12 = -155.7778
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The height of a cylindrical vase is 11 inches as shown below. The base of the cylinder has a diameter of 4½ inches. Which measurement is closest to the volume of the cylinder in cubic inches? * 34 points 1,710.6 cubic inches 155.51 cubic inches 699.79 cubic inches 174.95 cubic inches
Answer:
174.95
Step-by-step explanation:
Volume=πr^2h
3.142 * (4.5÷2)^2 *11
=174.95
Este año en la escuela de inglés, el numero de usuarios de intagram ha alcanzado la cifra de 2604 alumnos, lo que supone un aumento del 24% respecto del año pasado. ¿ cuantos usuarios habia el año pasado?
Answer:
the number of users in the last year is 2,100
Step-by-step explanation:
The computation of the number of users in the last year is shown below:
Given that
The users are 2604 that are increased to 24% as compared with the last year
So, the users in the last year is
= 2604 ×100 ÷ 124
= 2,100
Hence, the number of users in the last year is 2,100
Answer:
688
Step-by-step explanation:
ithink
g(x) = 2x^3 when g(3) ????
Answer:18
Step-by-step explanation:3^3 times 2
The first term in an arithmetic sequence is 5. The fourth term in the sequence is −4. The tenth term
is −22.
Which function can be used to find the nth term of the arithmetic sequence?
Answer:
aₙ = -3n + 8Step-by-step explanation:
The nth term of an arithmetic sequence: aₙ = a₁ + d(n - 1)
{d = common difference}
a₁ = 5
a₄ = 5 + d(4 - 1)
-4 = 5 + 3d
-4 - 5 = 3d
3d = -9
d = -3
Therefore;
aₙ = 5 + (-3)(n - 1)
aₙ = -3n + 8
Check: a₁₀ = 5 + (-3)(10 - 1) = 5 - 27 = - 22
The nth term of the sequence is Tn = 8 - 3n
How to determine the function of the nth term?The given parameters are:
a = 5, first term
T4 = -4 --- the 4th term
T10 = -22 --- the 10th term
The nth term of an arithmetic sequence is:
Tn = a + (n - 1) * d
So, we have:
T4 = a + (4 - 1) * d
Substitute known values
-4 = 5 +(4 -1) * d
This gives
-4 = 5 + 3d
Subtract 5 from both sides
3d = -9
Divide by 3
d = -3
Recall that:
Tn = a + (n - 1) * d
So, we have:
Tn = 5 + (n - 1) * -3
Expand
Tn = 5 + 3 - 3n
Solve
Tn = 8 - 3n
Hence, the nth term of the sequence is Tn = 8 - 3n
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determine the type i error if the null hypothesis, h0, is: carmin believes that her chemistry exam will only cover material from chapters four and five.
a. Carmin believes that her chemistry exam will only cover material from chapters four and five when, in fact, it will cover material only from chapters four and five. b. Carmin believes that her chemistry exam will not cover material only from chapters four and five when, in fact, it will only cover material from chapters four and five. c. Carmin believes that her chemistry exam will only cover material from chapters four and five when, in fact, it will not cover material only from chapters four and five. d. Carmin believes that her chemistry exam will not cover material only from chapters four and five when, in fact, it will not cover material only from chapters four and five.
The type I error occurs when the null hypothesis is rejected, but in reality, the null hypothesis is true. In this case, the null hypothesis is "Carmin believes that her chemistry exam will only cover material from chapters four and five." The correct statement that corresponds to the type I error is option C: "Carmin believes that her chemistry exam will only cover material from chapters four and five when, in fact, it will not cover material only from chapters four and five."
A type I error is a false positive result, where the null hypothesis is incorrectly rejected even though it is true. In this scenario, if carmin believes that her chemistry exam will only cover material from chapters four and five, but in reality, the exam includes additional material beyond chapters four and five, it would be a type I error. Option C describes this situation, where Carmin believes the exam will cover only chapters four and five, but it actually includes material from other chapters.
Options A, B, and D do not correspond to a type I error because they either describe the correct belief or a different scenario where the null hypothesis is true.Therefore, option C represents the type I error in this context.
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Andy and Hershel folded the same- size square papers. Candy shaded 2 4 and Hershel shaded 1 2. Are the fractions equivalent? Explain.
Answer:
Yes, the fraction are equivalent
Step-by-step explanation:
Fraction shaded by candy = 2/4
Fraction shaded by Hershel = 1/2
If candy's fraction of 2/4 is reduced to it's lowest term ;
2 /4 = 1 /2 ; we also obtain the same fraction obtained by Hershel.
Hence, 2/4 is equivalent to 1/2