write the parametric equations x = 4 e^t , \quad y = 2 e^{-t} as a function of x in cartesian form. y = equation editorequation editor with x\gt 0.

The value of x in the chord of the circle using the chord-chord power theorem is 8.

Chord - chord power theorem simply state that "If two chords of a circle intersect, then the product of the measures of the parts of one chord is equal or the same as the product of the measures of the parts of the other chord".

From the diagram:

The first chord has consist of 2 segments:

Segment 1 = 10

Segment 2 = 4

The second chord also consist of 2 sgements:

Segment 1 = 5

Segment 2 = x

Now, usig the Chord-chord power theorem:

10 × 4 = 5 × x

Solve for x:

40 = 5x

5x = 40

Divide both sides by 5

5x/5 = 40/5

x = 40/5

x = 8.

Therefore, the value of x is 8.

Learn more about the Chord-chord power theorem here: https://brainly.com/question/15298662

#SPJ1

In a spring-mass system, the restoring force of the spring and the damping force play a crucial role in governing the motion of the mass. However, in an aging system, these forces may weaken exponentially over time, leading to changes in the dynamics of the system.

Consider the initial value problem of an aging spring-mass system, where the equation of motion of the mass is governed by weakened restoring and damping forces. The solution to this problem involves finding the displacement of the mass over time.

One approach to solving this problem is to use the theory of differential equations. We can use the equation of motion and apply the necessary mathematical tools to find the solution. Alternatively, we can use numerical methods such as Euler's method or the Runge-Kutta method to obtain approximate solutions.

As the restoring and damping forces weaken over time, the system's motion becomes less oscillatory and more damped. The amplitude of the oscillations decreases, and the frequency of the oscillations also decreases. The system eventually approaches an equilibrium state where the mass comes to rest.

In conclusion, an aging spring-mass system with weakened restoring and damping forces is an interesting problem in the field of physics and engineering. Understanding the dynamics of such systems can be useful in predicting the behavior of real-world systems that degrade over time.

Learn more about  spring-mass system here:

https://brainly.com/question/31593319

#SPJ11

The height of the given cone is 6.75 cm.

Given that, the volume of a cone is 324π cm² and the length of the diameter is 24 cm.

Here, radius of the cone = 24/2 = 12

We know that, the volume of the cone is 1/3 πr²h.

Now, 1/3 πr²h = 1/3 π×12²h

324π = 1/3 π×12²×h

324 = 1/3 ×144×h

324 = 48h

h=324/48

h=6.75 cm

Therefore, the height of the given cone is 6.75 cm.

To learn more about the volume of a cone visit:

https://brainly.com/question/1984638.

#SPJ1

This equation holds true for any value of x, which means that f(x) = ∑(n=0)(∞) xn/n! is indeed a solution of the differential equation f′(x) = f(x).

To show that the function f(x) = ∑(n=0)(∞) xn/n! is a solution of the differential equation f′(x) = f(x), we need to demonstrate that f′(x) = f(x) holds true for this function.

Let's first compute the derivative of f(x) using the power series representation:

f(x) = ∑(n=0)(∞) xn/n!

f'(x) = ∑(n=1)(∞) nxn-1/n!

Now we can substitute f(x) and f'(x) into the differential equation:

f′(x) = f(x)

∑(n=1)(∞) nxn-1/n! = ∑(n=0)(∞) xn/n!

We can rewrite the left-hand side of this equation by shifting the index of summation by 1:

∑(n=1)(∞) nxn-1/n! = ∑(n=0)(∞) (n+1)xn/n!

We can also factor out an x from each term in the series:

∑(n=0)(∞) (n+1)xn/n! = x∑(n=0)(∞) xn/n!

Now we can see that the right-hand side of this equation is just f(x) multiplied by x, so we can substitute f(x) = ∑(n=0)(∞) xn/n! to get:

x ∑(n=0)(∞) xn/n! = ∑(n=0)(∞) xn/n!

for such more question on differential equation

https://brainly.com/question/25731911

#SPJ11

To show that the function f(x) = ∑(n=0 to infinity) xn/n! is a solution to the differential equation f′(x) = f(x), we need to show that f′(x) = f(x).

First, we find the derivative of f(x):

f′(x) = d/dx [ ∑(n=0 to infinity) xn/n! ]

= ∑(n=1 to infinity) xn-1/n! · d/dx (x)

= ∑(n=1 to infinity) xn-1/n!

Now, we need to show that f′(x) = f(x):

f′(x) = f(x)

∑(n=1 to infinity) xn-1/n! = ∑(n=0 to infinity) xn/n!

To do this, we can write out the first few terms of each series:

f′(x) = ∑(n=1 to infinity) xn-1/n! = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...

f(x) = ∑(n=0 to infinity) xn/n! = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...

Notice that the only difference between the two series is the first term. In the f′(x) series, the first term is x^0/0! = 1, while in the f(x) series, the first term is also x^0/0! = 1. Therefore, the two series are identical, and we have shown that f′(x) = f(x).

Therefore, f(x) = ∑(n=0 to infinity) xn/n! is indeed a solution to the differential equation f′(x) = f(x).

Learn more about function here : brainly.com/question/12431044

#SPJ11

The maximize his score the student should answer 5 computation problems and 5 word problems in a maximum score of 80.

Let number of computation problems answered as C and the number of word problems answered as W.

Given the time constraint of 35 minutes, we can set up the following equation:

2C + 5W ≤ 35

Since the student may answer no more than 10 problems, we have another constraint:

C + W ≤ 10

The student wants to maximize their score, which is calculated as:

Score = 6C + 10W

First, let's solve the system of inequalities to determine the feasible region:

2C + 5W ≤ 35

C + W ≤ 10

We find that when C = 5 and W = 5, both constraints are satisfied, and the score is:

Score = 6C + 10W

= 6(5) + 10(5)

= 30 + 50

= 80

Therefore, to maximize his score the student should answer 5 computation problems and 5 word problems in a maximum score of 80.

Learn more about Inequalities here:

https://brainly.com/question/20383699

#SPJ1

Answer:

4 according to the numbers you provided integer x the = 4

Step-by-step explanation:

The first partial derivatives of the function f(x, y) = x^4 - 6xy^5 are ∂f/∂x = 4x^3 - 6y^5 and ∂f/∂y = -30xy^4.

The first partial derivatives of the function f(x, y) = x^4 - 6xy^5 with respect to x and y can be found as follows.

The partial derivative with respect to x (denoted as ∂f/∂x) can be obtained by treating y as a constant and differentiating the function with respect to x. In this case, the derivative of x^4 with respect to x is 4x^3. The derivative of -6xy^5 with respect to x is -6y^5, as the constant -6y^5 does not depend on x. Therefore, the first partial derivative of f(x, y) with respect to x is ∂f/∂x = 4x^3 - 6y^5.

Similarly, the partial derivative with respect to y (denoted as ∂f/∂y) can be found by treating x as a constant and differentiating the function with respect to y. The derivative of -6xy^5 with respect to y is -30xy^4, as the constant -6x does not depend on y. Thus, the first partial derivative of f(x, y) with respect to y is ∂f/∂y = -30xy^4.

In summary, the first partial derivatives of the function f(x, y) = x^4 - 6xy^5 are ∂f/∂x = 4x^3 - 6y^5 and ∂f/∂y = -30xy^4. These derivatives represent the rates at which the function changes with respect to each variable individually.

Learn more about partial derivatives here:

https://brainly.com/question/28750217

#SPJ11

The negative binomial, geometric, and Poisson distributions do not have a specified maximum value of X.

In the negative binomial distribution, X represents the number of trials needed to achieve a fixed number of successes. The number of trials can vary indefinitely, so there is no maximum value for X.

Similarly, in the geometric distribution, X represents the number of trials needed to achieve the first success. Since the number of trials can continue indefinitely until the first success occurs, there is no predetermined maximum value for X.

The Poisson distribution models the number of events occurring in a fixed interval of time or space. The number of events can be arbitrarily large, and thus there is no specific maximum value for X.

On the other hand, the binomial and hypergeometric distributions have a fixed number of trials or population size, respectively, which defines the maximum value of X. In these distributions, X represents the number of successes within the specified constraints.

Therefore, the negative binomial, geometric, and Poisson distributions do not have a specified maximum value of X, making them distinct from the binomial and hypergeometric distributions.

learn more about "binomial":- https://brainly.com/question/24756209

#SPJ11

The function t(x, y) = (x, 2xy, y) is not a linear transformation from R2 to R3.

To determine if t(x, y) = (x, 2xy, y) is a linear transformation, we need to check if it satisfies the two properties of linearity: preservation of vector addition and scalar multiplication.

For preservation of vector addition, we need t(u + v) = t(u) + t(v) to hold for all vectors u and v in R2.

However, if we consider two arbitrary vectors u = (x1, y1) and v = (x2, y2),

we have t(u + v) = t(x1 + x2, y1 + y2) = (x1 + x2, 2(x1 + x2)(y1 + y2), y1 + y2),

while t(u) + t(v) = (x1, 2x1y1, y1) + (x2, 2x2y2, y2) = (x1 + x2, 2x1y1 + 2x2y2,

y1 + y2). Since 2(x1 + x2)(y1 + y2) is not equal to 2x1y1 + 2x2y2 in general, preservation of vector addition does not hold.

Similarly, for scalar multiplication, we need t(cu) = c * t(u) to hold for all vectors u in R2 and scalar c.

However, if we consider an arbitrary scalar c and vector u = (x, y),

we have t(cu) = t(cx, cy) = (cx, 2(cx)(cy), cy),

while c * t(u) = c(x, 2xy, y) = (cx, 2cxy, cy).

Since 2(cx)(cy) is not equal to 2cxy in general, preservation of scalar multiplication does not hold.

Therefore, t(x, y) = (x, 2xy, y) does not satisfy the properties of linearity and is not a linear transformation from R2 to R3.

Learn more about linear transformation here: brainly.com/question/13595405

#SPJ11

Option A is correct, 57.17% is the probability that he hits the target at least four out of next six attempts.

Let's calculate the probability of hitting the target exactly four times out of six attempts:

P(4 hits) = C(6, 4) × (0.65)⁴ ×  (1 - 0.65)⁶⁻⁴

The probability of hitting the target exactly five times out of six attempts:

P(5 hits) = C(6, 5) × (0.65)⁵ × (1 - 0.65)⁶⁻⁵

Now calculate the probability of hitting the target all six times:

P(6 hits) = (0.65)⁶

Now, we can find the probability that Tom hits the target at least four times by summing up the individual probabilities:

P(at least 4 hits) = P(4 hits) + P(5 hits) + P(6 hits)

P(at least 4 hits) = C(6, 4) × (0.65)⁴ ×  (1 - 0.65)⁶⁻⁴ + C(6, 5) × (0.65)⁵ × (1 - 0.65)⁶⁻⁵ +  (0.65)⁶

=57.17%

Hence,  57.17% is the probability that he hits the target at least four out of next six attempts.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

The expectation of the random variable X(t) at time t is E[X(t)] = π/2 if 0 ≤ t ≤ 1/2, and E[X(t)] = 2t if 1/2 < t ≤ 1.

The expectation of the random variable X(t) depends on the value of t.

At time intervals 0 ≤ t ≤ 1/2, the expectation is E[X(t)] = π/2. For time intervals 1/2 < t ≤ 1, the expectation is E[X(t)] = 2t.

To calculate the expectation, we need to consider the definition of X(t) in the fair coin experiment. If a head shows, X(t) is given by sin(πt), and if a tail shows, X(t) is given by 2t.

For 0 ≤ t ≤ 1/2, there will always be a head, so X(t) = sin(πt). Taking the expectation of sin(πt) over the interval [0, 1/2] yields E[X(t)] = π/2.

For 1/2 < t ≤ 1, there will always be a tail, so X(t) = 2t. Taking the expectation of 2t over the interval (1/2, 1] yields E[X(t)] = 2t.

To sketch the cumulative distribution function (CDF) F(X,t) at specific values of t, such as t = 0.25, t = 0.5, and t = 1, we need to integrate the probability density function (PDF) of X(t) from negative infinity up to X.

For t = 0.25, the CDF F(X,0.25) can be graphed by integrating the PDF of X(0.25) from negative infinity up to X.

Similarly, for t = 0.5, the CDF F(X,0.5) can be graphed by integrating the PDF of X(0.5) from negative infinity up to X.

Finally, for t = 1, the CDF F(X,1) can be graphed by integrating the PDF of X(1) from negative infinity up to X.

Learn more about variable

brainly.com/question/15078630

#SPJ11

There are a total of 8 distinct congruence classes modulo x^3 - x + 1 in Z2[x].

To determine the number of distinct congruence classes modulo x^3 - x + 1 in Z2[x], we will first understand the terms and then find the classes.

In Z2[x], the coefficients of the polynomial are in Z2, meaning they are either 0 or 1.

The modulo is x^3 - x + 1, which implies that we are considering polynomials whose degree is less than 3.

Now, let's list all distinct congruence classes modulo x^3 - x + 1 in Z2[x]:

1. Constant Polynomials:
  - 0 (degree 0)
  - 1 (degree 0)

2. Linear Polynomials:
  - x (degree 1)
  - x + 1 (degree 1)

3. Quadratic Polynomials:
  - x^2 (degree 2)
  - x^2 + 1 (degree 2)
  - x^2 + x (degree 2)
  - x^2 + x + 1 (degree 2)

There are a total of 8 distinct congruence classes modulo x^3 - x + 1 in Z2[x].

Know more about congruence here:

https://brainly.com/question/2938476

#SPJ11

$167,925 is the total value of the plumber's liabilities

To find the total value of the plumber's liabilities

we need to add up the amounts of the mortgage, credit card balance, and kitchen renovation loan.

Total liabilities = Mortgage + Credit card balance + Kitchen renovation loan

Total liabilities = $149,367 + $6,283 + $12,275

Total liabilities = $167,925

so the total value of the plumber's liabilities is $167,925.

To learn more on Liabilities click:

https://brainly.com/question/15006644

#SPJ1

The rate of f(x) is -47, the rate of g(x) is  -84, we can see that the rate of g(x) is twice the rate of f(x).

For a function f(x), the average rate of change on an interval (a, b) is:

R = [ f(b) - f()]/(b - a)

Here the interval is [-4, -2]

And the functions are:

f(x) = 7x²

g(x) = 14x²

Then the rates are:

f(-4) = 7*(-4)² = 112

f(-2) = 7*(-2)² = 28

Then the rate is:

R = (28 - 112)/(-2 + 4) = -47

g(-4) = 14*(-4)² = 224

g(-2) = 14*(-2)² = 56

the rate is:

R' = (56 - 224)/(-2 + 4) = -84

These are the rates, and we can see that the rate of g(x) is twice the rate of f(x).

Learn more about rates of change at:

https://brainly.com/question/8728504

#SPJ1

Answer:

x = 3

Step-by-step explanation:

2(x+4) + 2 = 5x + 1

2x + 8 + 2 = 5x + 1

2x + 10 = 5x + 1

-3x + 10 = 1

-3x = -9

x = 3

To solve for x, we need to simplify the equation and isolate the variable. Let's proceed with the given equation:

2(x + 4) + 2 = 5x + 1

First, distribute the 2 to the terms inside the parentheses:

2x + 8 + 2 = 5x + 1

Combine like terms on the left side:

2x + 10 = 5x + 1

Next, let's move all terms containing x to one side of the equation and the constant terms to the other side. We can do this by subtracting 2x from both sides:

2x - 2x + 10 = 5x - 2x + 1

Simplifying further:

10 = 3x + 1

To isolate the x term, subtract 1 from both sides:

10 - 1 = 3x + 1 - 1

9 = 3x

Finally, divide both sides of the equation by 3 to solve for x:

9/3 = 3x/3

3 = ×

Therefore, the solution to the equation is x = 3.

The amount of glitter that is needed to cover the prism completely is 87.6 kg.

In Mathematics, the surface area of a triangular prism can be calculated by using this mathematical expression:

Total surface area of triangular prism = (Perimeter of the base × Length of the prism) + (2 × Base area)

Total surface area of triangular prism = (S₁ + S₂ + S₃)L + bh

where:

By substituting the given side lengths into the formula for the surface area of a triangular prism, we have the following;

Total surface area of triangular prism = (13 × 25) + (1/2 × 21 × 10 × 2) + (16 × 25) + (21 × 25)

Total surface area of triangular prism = 325 + 210 + 400 + 525

Total surface area of triangular prism = 1,460 m².

For the amount of glitter that is needed, we have:

Amount of glitter = (60 × 1,460)/1000

Amount of glitter = 87.6 kg.

Read more on triangular prism here: brainly.com/question/21173224

#SPJ1

Answer: 1086.396 inches squared

Step-by-step explanation:

Hi there,

The area formula for an octagon is:

[tex]A=2s^{2} (1+\sqrt{2} )[/tex]

With "A" representing area and "S" representing side length.

You are given the side length, so just plug that in for "S" and input it into your calculator. It should look something like this:

[tex]A=2(15)^{2} (1+\sqrt{2} )\\[/tex]

A= 1086.396 inches squared.

I hope this helps.

Good luck :)

As the value of R-squared (R2) gets higher, the line will be a better fit for the data (Option A).

R-squared (R2) is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data.

Option B is incorrect: The value of R2 can range from negative infinity to positive infinity, although it is commonly reported between 0 and 1. Negative R2 values occur when the regression model performs worse than a horizontal line, and values above 1 are not possible.

Option C is incorrect: R2 values above 1.0 are not possible as R2 represents the proportion of variance explained, which cannot exceed 100%.

Option D is incorrect: A value of 1.0 for R2 indicates that the regression model explains all the variance in the dependent variable, meaning there is no deviation of the data from the line. It does not indicate maximum deviation.

Learn more about R-squared here:

https://brainly.com/question/27511381

#SPJ11

The Cartesian coordinates for give polar coordinates are (-3.00, 5.20), (-0.77, 3.07) and  (-5, 0), respectively. and plot is given.

The calculations for finding the Cartesian coordinates of each point given its polar coordinates.

6, 4/3

Plot the point (6, 4/3) in the polar coordinate system. This means starting at the origin, moving outwards 6 units, and rotating counterclockwise by an angle of 4/3 radians (or 240 degrees).

To find the Cartesian coordinates (x, y), we can use the formulas x = r cos(θ) and y = r sin(θ), where r is the distance from the origin to the point, and theta is the angle the line from the origin to the point makes with the positive x-axis.

Using the given polar coordinates, we have r = 6 and theta = 4/3 * π radians (or 240 degrees in degrees mode on a calculator).

Plugging these values into the formulas gives

x = 6 cos(4/3 * π) ≈ -3.00

y = 6 sin(4/3 * π) ≈ 5.20

Therefore, the Cartesian coordinates of the point (6, 4/3) are approximately (-3.00, 5.20).

-4, 3/4

Plot the point (-4, 3/4) in the polar coordinate system. This means starting at the origin, moving left 4 units, and rotating counterclockwise by an angle of 3/4 radians (or 135 degrees).

Using the formulas x = r cos(θ) and y = r sin(θ), we have:

x = -4 cos(3/4 * π) ≈ -0.77

y = 4 sin(3/4 * π) ≈ 3.07

Therefore, the Cartesian coordinates of the point (-4, 3/4) are approximately (-0.77, 3.07).

-5, -3

Plot the point (-5, -3) in the polar coordinate system. This means starting at the origin, moving left 5 units, and rotating clockwise by an angle of pi (or 180 degrees).

Using the formulas x = r cos(θ) and y = r sin(θ), we have:

x = -5 cos(π) = -5

y = -3 sin(π) = 0

Therefore, the Cartesian coordinates of the point (-5, -3) are (-5, 0). Note that this is on the x-axis, since the point lies in the second quadrant of the polar coordinate system. points are plotted on graph.

To know more about Cartesian coordinates:

https://brainly.com/question/15215968

#SPJ4

The value of the integral is 8π/11.

To evaluate the integral [tex]\int_2^0\int_8y^2 \sqrt{(y/(11x^2))} x dy dx[/tex] using polar coordinates, we first need to express the integrand in terms of polar coordinates.

Converting the Cartesian coordinates (x, y) to polar coordinates (r, θ), we have:

x = r cos(θ)

y = r sin(θ)

Also, we have:

[tex]\sqrt{(y/(11x^2))[/tex]

= [tex]\sqrt {(r sin(\theta)/(11r^2 cos^2(\theta)))[/tex]

= [tex]\sqrt{(sin(\theta)/(11r cos(\theta)))[/tex]

So, the integral becomes:

[tex]\int_2^0 \int_8-y^2 \sqrt(y/(11x^2)) x dy dx[/tex]

= [tex]\int_0^{(\pi/2)} \int_0^{(8 sin(\theta))} \sqrt(sin(\theta)/(11r cos(\theta))) r dr d\theta[/tex]

Integrating with respect to r first, we have:

[tex]\int_0^{(\pi/2)} \int_0^{(8 sin(\theta))} \sqrt(sin(\theta)/(11r cos(\theta))) r dr d\theta[/tex]

= [tex]\int_0^{(\pi/2)} [1/2 \sqrt(sin(\theta)/11 cos(\theta)) r^2][/tex]evaluated from r = 0 to r = 8 sin(θ) dθ

= [tex]\int_0^{(\pi/2)} 1/2 \sqrt(sin(\theta)/11 cos(\theta)) (8 sin(\theta))^2 d\theta[/tex]

= [tex]\int_0^{(\pi/2)} 32/11 sin^2(\theta) d\theta[/tex]

Using the identity sin²(θ) = (1 - cos(2θ))/2, we can rewrite this as:

[tex]\int_0^{(\pi/2)} 32/11 (1/2 - 1/2 cos(2\theta)) d\theta[/tex]

= [16/11 θ - 8/11 sin(2θ)] evaluated from θ = 0 to θ = π/2

= 8π/11

For similar questions on integral

https://brainly.com/question/22008756

#SPJ11

Answer:

----------------------

Find the amount of work in man*days and then divide the result by 20:

Hence the same work will be completed by 225 men.

The trig model or equation that represents the data is T = 65 + 10sin(2pi/12(m-1))

T is the temperature in degrees Fahrenheit, m is the month (1 = January, 2 = February, etc.)

This model was arrived at by using the following steps:

The amplitude of the sine curve is 10 degrees Fahrenheit, which represents the difference between the highest and lowest temperatures in the year. The period of the sine curve is 12 months, which represents the time it takes for the temperature to complete one cycle.

The equation of the sine curve can be used to predict the temperature for any month of the year. For example, the temperature in Atlanta in March is predicted to be 75 degrees Fahrenheit. Hence the trig model or equation that represents the data is T = 65 + 10sin(2pi/12(m-1))

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

The probability of spinning yellow, tossing heads, and selecting the number 2 is approximately 0.083325 or 8.33%.

To find the probability of spinning yellow, tossing heads, and selecting the number 2, we need to calculate the individual probabilities of each event and then multiply them together.

Given:

Spinner with three equal size sections (red, green, yellow)

Coin toss with two outcomes (heads, tails)

Two cards labeled with 1 and 2

Firstly calculate the probability of spinning yellow:

Since the spinner has three equal size sections, the probability of spinning yellow is 1/3 or 0.3333.

Secondly calculate the probability of tossing heads:

Since the coin has two possible outcomes, the probability of tossing heads is 1/2 or 0.5.

Thirdly calculate the probability of selecting the number 2:

Since there are two cards labeled with 1 and 2, the probability of selecting the number 2 is 1/2 or 0.5.

Lastly multiply the probabilities together:

To find the probability of all three events occurring, we multiply the individual probabilities:

Probability = (Probability of spinning yellow) * (Probability of tossing heads) * (Probability of selecting the number 2)

Probability = 0.3333 * 0.5 * 0.5

Probability = 0.083325

Therefore, the probability of spinning yellow, tossing heads, and selecting the number 2 is approximately 0.083325 or 8.33%.

To study more about Probability:

https://brainly.com/question/13604758

https://brainly.com/question/24756209

The polynomial that represents the volume of the room in standard form is x³ + 20x² + 10x + 144 cubic units.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (side lengths) into the formula for the volume of this rectangular room, we have the following;

Volume of rectangular room = (x + 6) × (x + 12) ×  (x + 2)

Volume of rectangular room = x³ + 20x² + 10x + 144 cubic units.

Read more on volume of prism here: brainly.com/question/21012007

#SPJ1

The sum of angles in any triangle is 180 degrees.

We are given that;

The line AB parallel to CD

Now,

angle ACD = angle A (alternate interior angles) angle BCD = angle C (corresponding angles) angle ACD + angle BCD + angle B = 180 (sum of angles in a straight line)

Substituting angle A for angle ACD and angle C for angle BCD, we get:

x + z + y = 180

which is equivalent to:

x + y + z = 180

Therefore, by the angles the answer will be 180 degrees.

Learn more about angles here:

https://brainly.com/question/27458498

#SPJ1

(a) The log returns of Apple Inc and Johnson & Johnson do not follow a normal distribution.

(b) The tails of the log returns of both stocks are compared with a t-distribution with 4 degrees of freedom.

(a) To determine if the log returns of Apple Inc and Johnson & Johnson follow a normal distribution, we can perform a normality test, such as the Shapiro-Wilk test, Anderson-Darling test, or Kolmogorov-Smirnov test, on the log return data. If the p-value from the test is less than the chosen significance level (e.g., 0.05), we reject the null hypothesis of normality.

(b) To compare the tails of the log returns with a t-distribution, we can fit a t-distribution with 4 degrees of freedom to the data and compare the probability density functions (PDFs) of the t-distribution and the empirical distribution of the log returns.

This can be visually assessed by plotting the PDFs or quantitatively analyzed using statistical measures such as the Kullback-Leibler divergence or the Kolmogorov-Smirnov test.

(c) To compare the distributions of the log returns during the 2008 financial crisis and two years after the crisis, we can create side-by-side boxplots, histograms, and QQ-plots. The boxplots will show the distribution's central tendency, spread, and skewness.

The histograms will provide a visual representation of the frequency distribution, and the QQ-plots will compare the quantiles of the log returns with the theoretical quantiles of a normal distribution.

(d) To determine the appropriate degree of freedom for modeling the log returns of Apple Inc two years after the financial crisis, we can fit various t-distributions with different degrees of freedom to the data and compare their goodness-of-fit using statistical measures like Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC).

The best fitting t-distribution will have the lowest AIC or BIC value. A QQ-plot and a histogram with the overlayed density of the best fitting t-distribution can be used to visually assess the goodness-of-fit.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ11

The solutions to the quadratic equation [tex]2x^2 - 11x + 12 = 0[/tex] are x = 3/2 and x = 4..

To solve the inequality [tex]2x^2 - 11x + 12 = 0[/tex] by factorizing, we have to find the roots of the quadratic equation and determine the values of x for which the inequality holds true.

The factorization of the quadratic equation 2x² - 11x + 12 = 0 is:

(2x - 3)(x - 4) = 0.

Setting each factor equal to zero gives us two equations:

2x - 3 = 0 and x - 4 = 0.

Solving, we get:

From 1, 2x = 3

x = 3/2

From 2, x = 4.

Therefore, the roots of the quadratic equation are x = 3/2 and x = 4.

Read more about factorization

brainly.com/question/10718512

#SPJ1

Answer:

90$

Step-by-step explanation:

1. Find out what the question is asking

2. So now we have to find how much 18% of 500$ is

3. In conclusion, 18% commission of 500$ is 90$

Answer:

  19,683

Step-by-step explanation:

You want the 10th term of a geometric sequence with first term 1 and a common ratio of 3.

The n-th term of a geometric sequence with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

For a1=1 and r=3, the 10th term is ...

  a10 = 1·3^(10-1) = 3^9 = 19,683

Karl would put 19,683 pennies in the jar on the 10th day.

__

Additional comment

On the 24th day, Karl would be putting into the jar the last of the 288 billion pennies in circulation.

The volume of added pennies on the 10th day is more than 7 liters, bringing the total that day to more than 10 liters. That's a pretty big jar.

The function y=(x-2)²-1 has vertex (2, -1), focus (2, -3/4) and axis of symmetry is x=2.

1) y=-x²+4x+3

From the given graph,

Direction: Opens Down

Vertex: (2,7)

Focus: (2,27/4)

Axis of Symmetry: x=2

Directrix: y=29/4

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (2+√7,0),(2−√7,0)

y-intercept(s): (0,3)

Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

Range: (−∞,7],{y|y≤7}

3) y=(x-2)²-1

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (2,−1)

Focus: (2,−3/4)

Axis of Symmetry: x=2

Directrix: y=−5/4

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (3,0),(1,0)

y-intercept(s): (0,3)

Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

Range: [−1,∞),{y|y≥−1}

Therefore, the function y=(x-2)²-1 has vertex (2, -1), focus (2, -3/4) and axis of symmetry is x=2.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ1

After observing both the graphs the required fields are described below.

In the given graph of the equation,

y = -x² + 4x + 3

From the graph of the this curve

We can see that,

X - intercept of this graph is at (-0.646 , 0) and (4.646, 0)

Y - intercept of this graph is at (0, 3)

Vertex of this graph is at (2, 7)

Domain is whole real line,

Range is (-∞, 7]

Axis of symmetry is x axis.

Increasing in the interval : (-∞, 2]

Decreasing in the interval : [7, ∞)

In the given graph of the equation,

y = (x-2)² - 1

From the graph of the this curve

We can see that,

X - intercept of this graph is at (1 , 0) and (3, 0)

Y - intercept of this graph is at (0, 3)

Vertex of this graph is at (2, -1)

Domain is real number,

Range is [-1, ∞)

Axis of symmetry is x axis.

Increasing in the interval : (-∞, 1]U[3,∞)

Decreasing in the interval : (1, 3)

To learn more about graph of function visit:

https://brainly.com/question/12934295

#SPJ1