suppose that a pair of dice is tossed. one die has 8 sides, the other has 9 sides. what is the expected value of the sum of the two dice?

The correct value of convolution of x(t) = u(t-1) with h(t) = \(e^(-t)u(t) is y(t) = -e^(-t) + 1.\)

To evaluate the convolution of x(t) = u(t-1) with h(t) = e^(-t)u(t), we can use the formula for convolution:

y(t) = ∫[0 to t] x(t - τ) * h(τ) dτ

Let's substitute the given functions:

x(t - τ) = u(t - τ - 1)

h(τ) = e^(-τ)u(τ)

Now we can compute the convolution:

y(t) = ∫[0 to t] u(t - τ - 1) * e^(-τ)u(τ) dτ

Since u(t - τ - 1) and u(τ) are both step functions, their product will be non-zero only when both functions are non-zero. Therefore, we can rewrite the integral as:

y(t) = ∫[0 to t] e^(-τ) dτ

Integrating this expression gives us:

y(t) = -e^(-t) + 1

So, the convolution of x(t) = u(t-1) with h(t) = \(e^(-t)u(t) is y(t) = -e^(-t) + 1.\)

Learn more about integrals here:

https://brainly.com/question/30094386

#SPJ11

Answer:

y + 9 ≤ -30

Step-by-step explanation:

The State of Nature is a term used in political philosophy to describe a hypothetical or empirical condition of humanity in which government does not exist.

The State of Nature is a philosophical theory about what life would be like if humans had no government, laws, or society. The State of Nature refers to a theoretical situation in which mankind exists without government or laws.

The concept is often used in political philosophy as a way to examine what life would be like without the restrictions of government or social norms.It describes the hypothetical condition of humanity when government or political institutions do not exist.

It's a term that was utilized by philosopher Thomas Hobbes to describe a primitive society where humans live without laws or regulations. According to Hobbes, the State of Nature is a "war of all against all," where life is "solitary, poor, nasty, brutish, and short."

Thus, in political philosophy, the State of Nature is utilized to demonstrate the necessity of government and civil society in regulating human behavior, preventing anarchy and chaos, and establishing justice and order.

Learn more about The State of Nature https://brainly.com/question/12254552

#SPJ11

The extent to which the researcher can refer that findings with a sample from which it was drawn is referred to as generalizability.

Generalizability refers to the ability to extrapolate study findings from a sample to the entire population. It also refers to the capacity to apply findings from one study to a similar environment in a different investigation.

Generalizability and transferability are two research traits that are related. When considering generalizability in research, there are two features or dimensions to consider: generalizability as it relates to the specific population on which the research is conducted, and generalizability on a global scale.

Such studies will be easier to generalize if the researcher uses adequate sampling approaches, sample sizes, and exact processes.

In general, a study has strong generalizability when the findings apply to a wide range of persons or situations. The study has weak generalizability if the results can only be applied to a subset of the population or in a very specific circumstance.

Learn more about sample here:

https://brainly.com/question/28382921

#SPJ4

Answer: if it was me i would say around 300

Step-by-step explanation: there is 5 among all right so... tbh i just guessed

The missing transformation types of the graph in the question are;

1) 90° clockwise rotation

2) 90° counterclockwise rotation

Transformation is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.

Translation is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.

Reflection is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.

Rotation is a method of transformation that involves  turning a given figure at an angle about a reference point.

Dilation is a method of transformation whereby the length of the sides of the figure is either increased or decreased.

Thus the answers to the question are listed as follows:

1)  A 90° clockwise rotation about the origin and then a translation left 6 units maps Shape l onto Shape II

2) A 90° counterclockwise rotation of shape II about the origin, followed by a reflection across the y-axis, and then a translation right 4 units and up 6 units confirms congruence between shape II and shape I.

Read more about Graph Transformation at; https://brainly.com/question/4289712

#SPJ1

Answer:

The 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.05, 0.112).

Step-by-step explanation:

Before building the confidence interval, the central limit theorem and subtraction of normal variables is explained.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Northern half:

1062 out of 2000, so:

\(p_N = \frac{1062}{2000} = 0.531\)

\(s_N = \sqrt{\frac{0.531*0.469}{2000}} = 0.0112\)

Southern half:

900 out of 2000, so:

\(p_S = \frac{900}{2000} = 0.45\)

\(s_S = \sqrt{\frac{0.45*0.55}{2000}} = 0.0111\)

Distribution of the difference:

\(p = p_N - p_S = 0.531 - 0.45 = 0.081\)

\(s = \sqrt{s_N^2 + s_S^2} = \sqrt{0.0112^2 + 0.0111^2} = 0.0158\)

Confidence interval:

The confidence interval is:

\(p \pm zs\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower bound of the interval is:

\(p - zs = 0.081 - 1.96*0.0158 = 0.05\)

The upper bound of the interval is:

\(p + zs = 0.081 + 1.96*0.0158 = 0.112\)

The 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.05, 0.112).

Step-by-step explanation:

3 more than twice n = 3+2n

3 more than twice n is atmost 50,

=> 3+2n <= 50 {(3+2n) is less than or equal to 50}

Answer:

3 + 2n ≤ 50

Step-by-step explanation:

"at most 50" means 50 or less.

Hope this helps.

Answer:

If you have an angle given in the form of degrees (°), minutes ('), and seconds ("), you can convert it to decimal degrees using the following formula: decimal degrees = Degrees + minutes/60 + seconds/3600.

For example, if you have an angle of 45° 34’ 53", you can convert it to decimal degrees as follows: 45 + 34/60 + 53/3600 = 45.581389 degrees

Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.

To know more about equation,

https://brainly.com/question/649785

#SPJ4

Answer:

(8 - 12 )

Step-by-step explanation:

Given

\(\frac{1}{4}\) x - \(\frac{1}{2}\) y = 8

\(\frac{1}{2}\) x + \(\frac{3}{4}\) y = - 5

Multiply both equations through by 4 to clear the fractions

x - 2y = 32 → (1)

2x + 3y = - 20 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate the x- term

- 2x + 4y = - 64 → (3)

Add (2) and (3) term by term to eliminate x

0 + 7y = - 84

7y = - 84 ( divide both sides by 7 )

y = - 12

Substitute y = - 12 into either of the 2 equations and solve for x

Substituting into (1)

x - 2(- 12) = 32

x + 24 = 32 ( subtract 24 from both sides )

x = 8

solution is (8, - 12 )

Answer:D:(8,-12)

Step-by-step explanation:took a test:D

answer:

x • y = 1

explanation:

\(\left(7^x\right)^y\:=\:7\)

\(\left(7^x\right)^y=7\)

\(xy=1\)

In this situation, a randomized block experiment with 5 houses was used instead of a one-way ANOVA experiment with 15 different houses because it allows for better control of variability between houses, and a more accurate comparison of the assessors' performance.

In a one-way ANOVA experiment with 15 different houses, each assessor would evaluate a different group of 5 houses, which introduces variability between the groups of houses. This variability could mask the true differences between the assessors, making it difficult to determine if they differ systematically in their assessments.

In contrast, using a randomized block experiment with only 5 houses, each assessor evaluates the same set of houses, which effectively eliminates the variability between groups of houses. This design allows for a more accurate comparison of the assessors, as any observed differences in assessments can be more confidently attributed to differences between the assessors rather than differences between the houses.

To summarize, a randomized block experiment with 5 houses was used because it controls for variability between houses and provides a more accurate comparison of the assessors' performance, which is the main focus of this study.

Learn more about ANOVA here:

https://brainly.com/question/23638404

#SPJ11

The area of the triangle with the given vertices is 11 square units.

Using calculus to find the area A of the triangle with the given vertices (0, 0), (4, 5), and (2, 8), we can apply the determinant method. This method involves creating a matrix using the coordinates of the vertices and then calculating the determinant of that matrix.
First, set up the matrix:
| 1  0  0 |
| 1  4  5 |
| 1  2  8 |
Next, find the determinant of this matrix:
| 1  0  0 |   | 4  5 |   | 2  8 |
| 1  4  5 | = | 2  8 | = | 2  3 |
Det = 1(4*8 - 5*2) - 0 + 0 = 32 - 10 = 22
Now, the area of the triangle A can be found by taking the absolute value of half the determinant:
Area = |(1/2) * Det| = |(1/2) * 22| = 11
The area of the triangle with the given vertices is 11 square units.

To know more about Calculus visit:
https://brainly.com/question/31801938
#SPJ11

A prime number doesn't have sequence so, it cannot be model with sequence.

Prime numbers are number that can only be divided by itself and 1.

E.g 2,3,5,7,11,13,17,19,23,29 etc.

So, note that this sequence doesn't have a pattern, it is neither Geometry Progression nor Arithmetic Progression.

Now, let take look at the model given

If n is prime, then 2n-1 is prime

Let take 5 for

n=5 is a prime number

2n-1=2(5)-1=10-1=9

9 is not a prime number so the model doesn't work

A prime number doesn't have sequence so, it cannot be model with sequence.

learn more about of sequence here

https://brainly.com/question/14852173

#SPJ4

Answer:

\(\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]\)

Step-by-step explanation:

The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9

\(\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]\)

To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.

\(A^{-1}\) = (1 / determinant of A) x Adjoint of A

the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2

Adjoint of A = \(\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]\)

\(A^{-1}\)= \(\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]\) = \(\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]\)

The approximate length of a side of the rhombus is 10.67 cm.

A rhombus is a quadrilateral with all sides of equal length.

The diagonals of a rhombus bisect each other at right angles.

Let's label the length of one diagonal as d1 and the other diagonal as d2.

In the given rugby-shaped figure, the length of d1 is 14 cm, and the length of d2 is 12 cm.

Since the diagonals of a rhombus bisect each other at right angles, we can divide the figure into four right-angled triangles.

Using the Pythagorean theorem, we can find the length of the sides of these triangles.

In one of the triangles, the hypotenuse is d1/2 (half of the diagonal) and one of the legs is x (the length of a side of the rhombus).

Applying the Pythagorean theorem, we have \((x/2)^2 + (x/2)^2 = (d1/2)^2\).

Simplifying the equation, we get \(x^{2/4} + x^{2/4} = 14^{2/4\).

Combining like terms, we have \(2x^{2/4} = 14^{2/4\).

Further simplifying, we get \(x^2 = (14^{2/4)\) * 4/2.

\(x^2 = 14^2\).

Taking the square root of both sides, we have x = √(\(14^2\)).

Evaluating the square root, we find x ≈ 10.67 cm.

Therefore, the approximate length of a side of the rhombus is 10.67 cm.

For more such questions on rhombus, click on:

https://brainly.com/question/88523

#SPJ8

In the original recipe, for every 1 1/2 cups of yogurt, Paul uses 1/2 cup of strawberries.

If Paul increases the recipe to include 2 cups of yogurt, we can find the corresponding amount of strawberries by setting up a proportion.

Let's set up the proportion:

(1 1/2 cups of yogurt) / (1/2 cup of strawberries) = (2 cups of yogurt) / (x cups of strawberries)

To solve for x, we can cross-multiply:

(1 1/2) * (x) = (2) * (1/2)

(3/2) * (x) = 1

Multiplying both sides by the reciprocal of 3/2 (which is 2/3):

(2/3) * (3/2) * (x) = (2/3) * (1)

x = 2/3

Therefore, Paul will need 2/3 cup of strawberries when he increases the recipe to include 2 cups of yogurt.

Answer:

m = 1

c = 4

Step-by-step explanation:

First let's review what a slope-intercept form is.

Slope-intercept form is a specific form of linear equations. It always has y on one side and all the other terms on the other. Its structure is:

\(y = mx + c\),

where m is the slope and c is the y-intercept.

You can easily read slope (m) and intercept (c) in your equation.

\(y = mx + c\\y = x + 4\)

You can see that m in front of x is 1, because x = 1x. Multiplying with 1 perserves the number.

So:

\(m = 1\\c = 4\)

Answer:

C 82 degrees

Step-by-step explanation:

Since triangle, ABC is congruent to EFG which means that the measurement for A is the same measurement for C.

Answer:

y = x

Step-by-step explanation:

So what we're going to want to do here is use the slope formula and the general equation y = mx + b.

Let's start.

The slope formula is y2-y1/x2-x1. So, put our points in here. 4-0/4-0. Slope: 1.

Okay, we have that. Now, a line that passes through the origin (0,0) is not going to have a y-intercept because it hits the y-axis at 0. So, that cancels out the b.

With our slope 1, the answer is just y = x. Very simple equation.

Hope this helped!

Infinite solutions

Try to solve this equation:

5x+4=5x+4

Move all the variables to the left:

5x-5x+4=4

Do you see what I see?

4=4

We end up with a true statement. 4 does indeed equal 4. Hope this helps!

~Just a joyful teen

\(-GraceRosalia\)

Therefore, the slope of the line passing through the origin which forms an angle of \(4\pi /7\) with the positive x-axis is 0.

To find the slope of the line passing through the origin which forms an angle of \(4\pi /7\)with the positive x-axis, we need to use trigonometry. The slope of a line is defined as the ratio of the change in y-coordinates to the change in x-coordinates, or rise over run.

Since the line passes through the origin, its y-intercept is zero. This means that we only need to find the x-intercept to determine the slope. We can use the angle formed by the line with the positive x-axis to find the x-intercept.

Let's call the angle formed by the line with the positive x-axis θ. Since the line passes through the origin, we can also say that it passes through the point (0,0). Using trigonometry, we can find the x-coordinate of the point where the line intersects the x-axis:

θ = \(4\pi /7\)

cos θ = a/h = x/1

x = cos θ

In this case, θ = \(4\pi /7\) so:
\(x = 2cos(4\pi /7)\)

Now we can calculate the slope:

slope = rise/run = y-coordinate/x-coordinate = y/x

Since the line passes through the origin, the y-coordinate at the x-intercept is also zero. This means that the slope is simply:

slope = 0/x = \(0/cos(4\pi /7)\)= 0

Learn more about slope here:

https://brainly.com/question/29184253

#SPJ11

1 gallon = 4 quarts

10 gallons = 40 quarts

30 gallons = 120 quarts

3 gallons = 12 quarts

33 gallons = 132 quarts

Answer: A. 132 quarts

Hope this helps!

Answer:

No hablo espanol.

puedes escribir en ingles

Step-by-step explanation:

Answer: 12

Step-by-step explanation: 3*4/1 = 12/1 =12

Based on the given input and output values, we can conclude that the relationship is not linear.

No, the relationship between the given input values (1, 2, 3, 4) and output values (46, 39, 32, 25) is not a linear function. In a linear function, the relationship between the input and output values can be described by a straight line. However, if we plot the given points on a graph, we can observe that they do not form a straight line. Instead, they form a pattern that is not linear.

A linear function can be represented by the equation y = mx + b, where "m" is the slope of the line and "b" is the y-intercept. In this case, there is no constant slope that can be applied to the input values to obtain the corresponding output values. The difference between the consecutive output values is not constant, indicating a non-linear relationship.

For such more questions on linear

https://brainly.com/question/2030026

#SPJ8

The parachutist started the free fall at a height of 68.12 meters above the ground.(b) The height at which the fall begins is 68.12 meters. The units of height are meters.

Given parameters: Initial velocity (u) = 0 m/s

           Final velocity (v) = 2.8 m/s

           Initial height (h) = ?

           Final height (s) = 65 m

Acceleration (a) = 2.4 m/s²Time taken (t) = ?

The formula for calculating the time taken in a free fall with an initial velocity is given by;

                                   v = u + at

Wherev = final velocityu = initial velocity

                       a = accelerationt = time taken

Rearranging the formula to get the time taken;

                       => t = (v - u) / a=> t = (2.8 - 0) / 2.4=> t = 1.17 seconds

(a) The parachutist is in the air for 1.17 seconds.

Since the parachutist starts from rest at a height (h) above the ground, her final velocity can be calculated using the formula;

                                 v² = u² + 2asWherev = final velocityu = initial velocitya = acceleration due to gravitys = height fallen

Rearranging the formula to get the initial height (h)

                                          ;=> h = s - u² / 2a

                                            => h = 65 - 0² / 2(2.4)

                                            => h = 68.12 meters (approx)

Therefore, the parachutist started the free fall at a height of 68.12 meters above the ground.(b) The height at which the fall begins is 68.12 meters. The units of height are meters.

Therefore, the answer in (a) is 1.17 seconds (s), while the answer in (b) is 68.12 meters (m).

Learn more about Acceleration .

brainly.com/question/12550364

#SPJ11