Let {X}be a Markov chain with state space S= {0,1,2,3,4,5) where X, is the position of a particle on the X-axis after 7 steps. Consider that the particle may be at a any position 7, where r=0,1,...,5

Answer:

$33.60

Step-by-step explanation:

Yearly interest is $16.80

Answer:

what do you need help with?

Step-by-step explanation:

please tell me what do you need helpwith

To cause the particle to move to the right at 51 m/s, the net work done on it must be equal to the change in kinetic energy. The initial kinetic energy of the particle is (1/2)mv^2 = (1/2)(40 g)(25 m/s)^2 = 31,250 J. The final kinetic energy of the particle is (1/2)mv^2 = (1/2)(40 g)(51 m/s)^2 = 52,020 J. Therefore, the net work done on the particle is 52,020 J - 31,250 J = 20,770 J.

To solve this problem, we'll use the work-energy theorem, which states that the net work done on an object is equal to its change in kinetic energy:

W = ΔKE = KE_final - KE_initial

First, we need to calculate the initial and final kinetic energies (KE) of the particle:

KE_initial = (1/2) * m * v_initial^2
KE_final = (1/2) * m * v_final^2

Given that the particle has a mass (m) of 40 g (0.04 kg) and initial velocity (v_initial) of -25 m/s (negative because it's moving to the left), we can find KE_initial:

KE_initial = (1/2) * 0.04 kg * (-25 m/s)^2 = 12.5 J

Similarly, with a final velocity (v_final) of 51 m/s (positive because it's moving to the right):

KE_final = (1/2) * 0.04 kg * (51 m/s)^2 = 52.404 J

Now, calculate the net work (W):

W = ΔKE = KE_final - KE_initial = 52.404 J - 12.5 J = 39.904 J

Expressed to two significant figures, the net work done on the particle is:

W ≈ 40 J

Learn more about Equal:

brainly.com/question/29194324

#SPJ11

The final expression is: 7 [(1/4)x⁴ - 32x²] + 7 [(8/3)x³ - 512x] + C

The given expression is: 7 (x+8) (x² - 64) -dx

To integrate this expression, we can use the following steps:

Step 1: Multiply the terms inside the parentheses

Step 2: Distribute the 7, and then separate the expression into two separate integrals

Step 3: Integrate each of the two terms separately

Here is the complete solution:

7 (x+8) (x² - 64) -dx= 7 [(x³ - 64x) + (8x² - 512)] -dx

= 7 ∫ (x³ - 64x) dx + 7 ∫ (8x² - 512) dx

= 7 [(1/4)x⁴ - 32x²] + 7 [(8/3)x³ - 512x] + C where C is the constant of integration.

Hence, the final answer is: 7 [(1/4)x⁴ - 32x²] + 7 [(8/3)x³ - 512x] + C

Know more about expression here:

https://brainly.com/question/1859113

#SPJ11

Answer: If the ratio of 1:4 Cordial and water mixture is a total of 1 L, then you need a ration of 2:8 Cordial mixture two make 2 Liters mixture.

Explanation: In every 1 Cordial mixture, there is added 4 mixtures of water. (I suppose the 1:4 ratio is 1 L together). To make two Liters, we need twice as many proportions. That would mean we will need a ratio of 2:8 of cordial and water.

If I misunderstood the problem, please explain the 1:4 ratio. I need to know how many Liters is the 1:4 ratio. Is it 1/4 of a liter? 1:4 adding up to 1 Liter?

If we don't know how much Liters are in that ratio, we can't find how much Liters of mixture we need to add of both Cordial and Water to make a mixture of 2 Liters.

This is because y is a factor of 5y and it's also a factor of y^2 = y*y

It's the largest common factor between the two given expressions.

Hello.

The highest common factor of

\(\mathrm{5y} \:and\:y^{2}\)

is

\(y\)

y is the greatest common factor (G.C.F.) also called the Highest Common Factor (HCF)

Therefore, y is the highest common factor of 5y and y².

I hope it helps.

Have a nice day.

\(\boxed{imperturbability}\)

The function f(x) is given by f(x) = (1/14)h^14 + C, and the value of a is unknown without additional information about the specific value of x.

To determine the function f(x) and the value of a based on the given limit lim(h→0) [h^12 / h^(-1)], we can analyze the expression and simplify it.

First, let's simplify the expression inside the limit:

[h^12 / h^(-1)] = h^(12 - (-1)) = h^13.

Now, we can rewrite the given limit as:

lim(h→0) h^13.

Since this limit represents a derivative f′(a), we can determine the function f(x) and the value of a by integrating the expression h^13 with respect to h.

∫h^13 dh = (1/14)h^14 + C,

where C is the constant of integration.

Therefore, the function f(x) is:

f(x) = (1/14)h^14 + C.

To find the value of a, we need to substitute a specific value of x into the function f(x). However, the value of x is not provided in the given information. Without knowing the value of x, we cannot determine the specific value of a.

To learn more about value

https://brainly.com/question/28152321

#SPJ11

Answer:

1680

Step-by-step explanation:

Considering repeatition is not allowed.

We can  use permutation to reach to the required answer.

Consider four digits to be placed in four boxes. Now for the number to be odd, unit digit must be odd. Therefore, unit digit can only be filled by 1, 3, 5,7, or 9. That is 5 ways. Now, other three boxes can be filled with 8, 7 and 6 ways respectively.

Therefore, Total numbers = 5×8×7×6 = 1680

A critical value, z Subscript alphas is (c) z-score with an area of ?? to its left.

A critical value, denoted as z (Subscript α/2), is a point on the standard normal distribution curve, which is used in hypothesis testing. It helps to determine whether to accept or reject the null hypothesis. In this context, the critical value denotes the z-score with an area of ?? to its left, which represents the probability of observing a value more extreme than the critical value in the left tail of the distribution.

The critical value z Subscript α/2 signifies the z-score with an area of ?? to its left on the standard normal distribution curve, which is crucial for hypothesis testing.

To know more about probability, visit:

https://brainly.com/question/30034780

#SPJ11

Answer:

1. QR = HI

2. angle W and angle T

3. WB = UV

Step-by-step explanation:

It could me fill in the part of the proof, since I notice on all of them they only mark one or two of the congruencies on the shapes. I'm not really sure of 3's answer.

Hope this helped somewhat and good luck

As t increases the curve is changing according to the plot points given by the parametric equations.

The coordinates of the points that make up a geometric object, such as a curve or surface, are frequently expressed using parametric equations; in this case, the equations are collectively referred to as a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. It describes a collection of numbers that represent functions with one or more independent variables. The parameters used here are the independent variables. For the representation of the coordinates that make up geometric objects like curves and surfaces, parametric equations are used. Additionally, a curve that is not a function can be drawn using parametric equations.

The equations are

x=1-t²

y=2t-t²,-1≤t≤2

The sketch is in the diagram picture.

To know more about parametric equations, click here:

https://brainly.com/question/12718642

#SPJ4

The number of collections of 50 coins that can be chosen from this pile is: C(125, 25) = 177,100,565,136,000
This is a very large number, which shows that there are many possible collections of 50 coins that can be chosen from the pile.

If the pile contains only 25 quarters but at least 50 of each other kind of coin, then the total number of coins in the pile must be at least 50 + 50 + 50 = 150. Let's assume that there are 150 coins in the pile, including the 25 quarters.
To choose a collection of 50 coins from this pile, we need to exclude the 25 quarters and choose 25 coins from the remaining 125 coins. We can do this in C(125, 25) ways, which is the number of combinations of 25 items chosen from a set of 125 items.
Therefore, the number of collections of 50 coins that can be chosen from this pile is:
C(125, 25) = 177,100,565,136,000

Learn more about quarters here:

https://brainly.com/question/30873037

#SPJ11

There are 351 possible collections of 50 coins that can be chosen, considering the given conditions.

To find the number of collections of 50 coins that can be chosen, we will consider the given conditions:
The pile contains only 25 quarters.

There are at least 50 of each other kind of coin (pennies, nickels, and dimes).
Now, let's break this down step by step:
Determine the minimum number of coins from each kind required to make a collection of 50 coins.
- 25 quarters (as it's the maximum available)
- The remaining 25 coins must be a combination of pennies, nickels, and dimes.
Find the different combinations of pennies, nickels, and dimes that can be chosen to make a collection of 50 coins.
- We need 25 more coins, so we can divide them into three groups:
 a) Pennies (P)
 b) Nickels (N)
 c) Dimes (D)
Calculate the combinations for the remaining 25 coins.
- Using the formula for combinations with repetitions: C(n+r-1, r) = C(n-1, r-1)
 Where n is the number of types of coins (3) and r is the number of remaining coins (25)
- C(3+25-1, 25) = C(27, 25) = 27! / (25! * 2!) = 351.

For similar question on combination.

https://brainly.com/question/27242731

#SPJ11

Answer:

Step-by-step explanation:

Andrew likes to solve puzzles.

       It took him 4.5 minutes to complete one puzzle with 18 numbers.

       It took him 6 minutes and 24 seconds to complete a different puzzle with 32 numbers.

a     For each puzzle work out how many seconds it took Andrew to complete one number.

b     Use your answer to part a to decide which puzzle Andrew completed faster.

You need two formulas for this:

C = πd or C = 2πr ( d = 2r ) Where C is circumference and d is diameter, r is radius

A = πr² Where A is area, and r is radius

First you get the diameter and radius by substituting the value of pi and circumference. With that, you can calculate the Area of the circle with the second formula. square² the radius then multiply it to 3.14. Remember that radius is half of diameter.

Answer:

\(\boxed {\boxed {\sf a=132.665 \ cm^2}}\)

Step-by-step explanation:

1. Find the Radius

We are given the circumference of 40.82 centimeters. The formula for circumference is

\(c=\pi d\)

The diameter is twice the radius, so we can also write this formula as:

\(c= \pi 2r\)

Substitute 40.82 for the circumference and use 3.14 for pi.

\(40.82 \ cm= (3.14) 2r\)

\(40.82=6.28 r\)

6.82 and r are being multiplied. The inverse of multiplication is division. Divide both sides by 6.82

\(\frac{40.82 \ cm}{6.28}=\frac{6.28 r}{6.82}\)

\(6.5 \ cm=r\)

2. Calculate the Area

Now we can calculate the area using this formula:

\(a= \pi r^2\)

The radius is 6.5 centimeters and we are using 3.14 for pi.

\(a= 3.14(6.5 \ cm)^2\)

Solve the exponent.

\(a= 3.14 (42.45 \ cm^2)\)

Multiply.

\(a=132.665 \ cm^2\)

The area is 132.665 square centimeters.

The probability of z being less than 0.25 as 0.5987 based on population proportion.

To use the normal approximation, we first need to check if the conditions are met. For this, we need to check if np and n(1-p) are both greater than or equal to 10.

np = 98 x 0.56 = 54.88

n(1-p) = 98 x 0.44 = 43.12

Since both np and n(1-p) are greater than 10, we can use the normal approximation.

Next, we need to find the mean and standard deviation of the sampling distribution of proportion.

Mean = np = 54.88

Standard deviation = sqrt(np(1-p)) = sqrt(98 x 0.56 x 0.44) = 4.43

Now we can standardize the variable X and find the probability:

z = (X - mean) / standard deviation = (56 - 54.88) / 4.43 = 0.25

Using a standard normal table or calculator, we can find the probability of z being less than 0.25 as 0.5987.

Therefore, P(X < 56) = P(Z < 0.25) = 0.5987.

Note that we rounded the mean and standard deviation to two decimal places, but you should keep the full values in your calculations to minimize rounding errors.

Learn more about proportion here:

https://brainly.com/question/13031441

#SPJ11

Answer:

sin148 and cos58

Step-by-step explanation:

sin32=0.530

sin148=0.530

cos58=0.530

Hope it is helpful for you

please follow me

Answer:

Option 4.

\(\angle BCA =\angle B' C'A'\\\)

Step-by-step explanation:

By graphing these we see that these triangles are Similar which means that there corresponding angles measure is equal i-e  all angles are equal and hence option 4 is the answer

Answer:

The measure of angle ABC = The measure of angle A prime B prime C prime

Step-by-step explanation:

Answer:

x = 180-35 = 145

y = 35

Hope it helps

Answer:  the degree will go down 90 degrees

Step-by-step explanation: An obtuse triangle is one that has an angle greater than 90°. An acute triangle is defined as a triangle in which all of the angles are less than 90°.

The general solution of the differential equation is given as y = c₁e^(20t) + c₂e^(-20t).

The differential equation y'' - 400y = 0 can be transformed into an auxiliary equation by assuming that the solution is exponential.

The general solution to a differential equation of this form can be obtained by solving this auxiliary equation.

For a second-order differential equation, we usually obtain a quadratic equation.

Here's the working on how to find the general solution of the differential equation, y''-400y=0:

Step 1: Write the characteristic equation of the differential equation.

y′′-400y = 0 → r² - 400 = 0 → (r + 20) (r - 20) = 0

So, r₁ = -20 and r₂ = 20.

Step 2: The solution of the differential equation is given by

y = c₁e^(20t) + c₂e^(-20t), where c₁ and c₂ are arbitrary constants.

The general solution of the differential equation y''-400y=0 is given by y = c₁e^(20t) + c₂e^(-20t), where c₁ and c₂ are constants.

Know more about the general solution

https://brainly.com/question/30285644

#SPJ11

The value of x, to the nearest tenth, is approximately 4.96. The steps involved using the tangent ratio and solving for the unknown side in a right triangle.

In a triangle, the angle opposite to the side x as angle A, and the side opposite to the angle 33° as side B, and the largest side as side C. So we have:

Angle A = 90° - 33° = 57° (since the sum of angles in a triangle is 180°)

Side B = 8

Side C = 15

Side x = ?

Write the formula for the tangent ratio in terms of the sides of the triangle. For angle A, we have:

tangent(A) = opposite/adjacent

Substitute the known values into the formula and solve for the unknown side. Substituting the values we have, we get

tangent(33°) = x/8

Multiplying both sides by 8, we get:

x = 8 * tangent(33°)

Use a calculator to find the value of the tangent of 33 degrees. We get:

tangent(33°) ≈ 0.6494

Substitute the value of the tangent into the formula we obtained in step 3 and solve for x. We get

x ≈ 8 * 0.6494

x ≈ 5.1952

Round the answer to the nearest tenth, since the question asks for the value of x to the nearest tenth. We get

x ≈ 4.96

Therefore, the value of x, to the nearest tenth, is approximately 4.96.

To know more about Trigonometric Ratio:

https://brainly.com/question/31511603

#SPJ1

The variables on the horizontal and vertical axes of a scatter plot are always continuous.Corresponding: When two sets of data are plotted on a scatter plot, each data point in the two sets has a corresponding point in the other set.

When you plot two sets of data on a scatter plot, you should use different colors or symbols for the data points from each set.The horizontal axis represents one variable while the vertical axis represents the other. Each point on the graph represents one set of data that corresponds to both variables, with the x-value and y-value corresponding to the respective data points being plotted.Scatterplot versus: A scatter plot has two axes that correspond to two variables. In a scatter plot, we can determine how one variable changes as the other variable changes. The variables on the horizontal and vertical axes of a scatter plot are always continuous.Corresponding: When two sets of data are plotted on a scatter plot, each data point in the two sets has a corresponding point in the other set. When you plot two sets of data on a scatter plot, you should use different colors or symbols for the data points from each set.

learn more about  variables here;

https://brainly.com/question/14783330?

#SPJ11

!! for 2 and 3 these values are rounded

1) 693.5/18,250 = .038 x 100% = 3.8% commission

2) ~118.5%  --- divide tip/meal then x 100%

3) ~21.33%   divide sale price/over org., then subtract by 100%

Answer:

Paul=Steve

Step-by-step explanation:

Answer:

The expression that represents Paul’s height in inches is 3/4t - 16. The expression that represents Steve’s height in inches is 4/3t - 6. Paul and Steve are the same height, so the equation that represents this relationship is

3/2t - 16 = 4/3t - 6

( PLATO/EDMENTUM ANSWER)

The fast-food worker receives 3 hours of break time per day.

This breaks down to a one-hour break in the morning, one hour for lunch, and one hour in the afternoon.

Mathematically, this can be expressed as

Additionally, the worker works 8 hours per day, Monday through Friday. This can be expressed as 5 days x 8 hours = 40 hours per week. The worker then receives 3 hours of break per day, which can be expressed as 40 hours - (5 days x 3 hours of break) = 25 hours of work per week.

Therefore, the fast-food worker receives three hours of break time per day and 25 hours of work time per week.

Learn more about Work and Time:

https://brainly.com/question/14464103

#SPJ4

The minimum value of PQ is 2 units.

To find the minimum value of PQ, we need to determine the position of P that minimizes the distance between P and Q.

The line y = x + 2 represents the original line. To rotate this line 90 degrees clockwise about (0,0), we need to swap the x and y coordinates and negate the new x coordinates. The equation of the new line, L, becomes x = y + 2.

Since Q is given as (0,2), we can substitute these coordinates into the equation of line L:

x = y + 2

0 = 2 + 2

0 = 4

As the equation is not satisfied, the point (0,2) does not lie on line L.

However, we can still find the minimum value of PQ. The minimum value occurs when P is located on the line perpendicular to L and passing through Q. This perpendicular line has the equation x = -2.

Substituting this equation into the distance formula, we get:

PQ = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((-2 - 0)^2 + (y - 2)^2)

= sqrt(4 + (y - 2)^2)

= sqrt(4 + y^2 - 4y + 4)

= sqrt(y^2 - 4y + 8)

To find the minimum value of PQ, we can complete the square:

PQ = sqrt((y - 2)^2 + 4)

= sqrt(y^2 - 4y + 4 + 4)

= sqrt(y^2 - 4y + 8)

The minimum value of PQ occurs when the expression inside the square root is minimized. The vertex of the parabola y^2 - 4y + 8 is given by the x-coordinate x = -(-4) / (2*1) = 2. Therefore, the minimum value of PQ is obtained when y = 2.

Substituting y = 2 into the expression for PQ, we get:

PQ = sqrt(2^2 - 4*2 + 8)

= sqrt(4 - 8 + 8)

= sqrt(4)

= 2

For more such questions on  perpendicular line

https://brainly.com/question/1202004

#SPJ8

if the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, then 20,281 collections of 50 coins can be chosen.

what are quarters?

Given that:

25 quarters and only 40 dimes

No. of. Ways with at least 26 quarters and 41 dimes.

26 + 41 = 67 coins, but we have only 50 coins.

There are 0 ways to select at least 26 quarters and 41 dimes.

\(A_{1}\) = at least 26 quarters

\(A_{2}\) = at least 41 dimes

Using inclusion / exclusion rule for the two sets:

N(\(A_{1} U A_{2}\)) = N ( \(A_{1}\)) + N ( \(A_{2}\))- N (\(A_{1}\) ∩ \(A_{2\))

                = 2925 + 220 - 0

                = 3145

Therefore, no . of . ways with at most 25 quarters and at most 40 dimes are

= 23426 - 3145

= 20,281 ways

To learn more about exclusion rule check the given link

https://brainly.com/question/12239906

#SPJ4

Answer:

-2.5

Step-by-step explanation:

Using the sine rule, a/sinA = b/sinB.

So, sinB = bsinA/a

substituting sinA = -1, a = 10 and b = 4, we have

sinB = 10 × (-1)/4

= -10/4

= -5/2

= -2.5