letpbethetransitionprobabilitymatrixofamarkovchain.arguethatifforsome positive integer r, pr has all positive entries, then so does pn , for all integers n ???? r .

Using Standard deviation, approximately, 95% of the area under the normal curve falls between 2 standard deviations.

The area under a normal curve represents the total probability of an event occurring for a normally distributed random variable.

A normal distribution is a bell-shaped curve that describes a continuous probability distribution of a variable, where most values cluster around the mean, and the curve tapers off symmetrically on both sides.

The total area under the normal curve is equal to 1 or 100%, which means that the probability of all possible outcomes adds up to 1 or 100%.

The Empirical Rule states that:

Hence,

Approximately, 95% of the area under the normal curve falls between 2 standard deviations.

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The pack of four is a better value.

All you need to do to get the price per tin is divide the price by the amount in the pack.

2.72/4=0.68

6.39/9=0.71

Step-by-step explanation:

2×-5=-8 and 2×-5/8=-1.25

Answer:

x = 10.5

Step-by-step explanation:

I'll assume this is the equation: (2x-5)/8 = 2

(2x-5)/8 = 2

(2x-5) = 16   [Multiply both sides by 8]

2x = 21        [Add 5 to both sides]

x = (21/2)    [Divide both sides by 2]

or x = 10.5

The solution to the algebraic equation is x = 1. The last option is correct.

The solution to a linear algebraic equation can be achieved by finding the like terms and equating them to the constant variable.

From the given information:

8 - 2x = -8x + 14

-2x + 8x = 14 - 8

6x = 6

x = 1

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The measure of <3 is 20 degree.

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.

Given:

A Rhombus is a parallelogram with four equal sides and two sets of angle Equal.

As, m <1 = 160 degree then opposite angle <3 is 160.

Then, m<1 + m <3 = 180

160 + m<3 = 180

m <3 = 20

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\(\sf\purple{The\:value\:of\:x\:is\:3.638.}\) ✅

Step-by-step explanation:-

\(25x + 22x + 9 = 180 \\ ⇢ 47x = 180 - 9 \\ ⇢ 47x = 171 \\ ⇢ x = \frac{171}{47} \\ ⇢ x = 3.638\)

To verify:-

\(25 \times 3.638 + 22 \times 3.638 + 9 = 180 \\ ⇢ 90.95 + 80.036 + 9 = 180 \\ ⇢ 180 = 180 \\ ⇢ L.H.S.=R. H. S\)

Hence verified. ✔

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}\)

By multiplying the first equation by 2 and the second equation by -3, Alvin seeks to determine the number of solutions in his system of equations using the linear combination 9x + 4y.

Alvin's approach of multiplying the first equation by 2 and the second equation by -3 is aimed at manipulating the system of equations to reveal the number of solutions. By performing these operations, Alvin obtains the linear combination 9x + 4y. The coefficients 9 and 4 in this linear combination represent the constants by which the variables x and y are multiplied. The resulting expression, 9x + 4y, allows Alvin to analyze the coefficients and infer the number of solutions. Different combinations of coefficients could indicate different numbers of solutions, such as one unique solution, infinitely many solutions, or no solution at all.

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As x and 68° are alternate interior angles, so, x = 68°.

We are given a set of parallel lines and a transversal.

We can see that:

The type of angle pairs is alternate interior angles.

( as it forms an inverted F-shape)

Now, these angles are 68° and x°.

So, we know that, the alternate interior angles are equal to each other.

So, we get that:

x = 68°

Therefore, as x and 68° are alternate interior angles, so, x = 68°.

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ANSWER:

STEP-BY-STEP EXPLANATION:

Answer:

Step-by-step explanation:

Twice a number is 2n

Sum of 8 and twice a number is

Correct choice is B.

Answer:

me name mort am swag

Step-by-step explanation: me my mom. she say help the noob. am no help you. doodoo pants.

Answer:

Step-by-step explanation:

You keep the same slope since it's supposed to be parallel. But first you need to write it in slope intercept form. So the y can't have a number in front of it, so you must divided everything after the equal sign by the 3. So the equation becomes y=2/3x−1. Now you plug in the points to find a parallel equation using point slope form y−(4)=(23)(x−(−3)). Then you solve that and you get y=2/3x+6.

#1

We need height first

Use Pythagorean theorem

\(\\ \sf\longmapsto H^2=14^2-(10/2)^2\)

\(\\ \sf\longmapsto H^2=196-25\)

\(\\ \sf\longmapsto H^2=171\)

\(\\ \sf\longmapsto H\approx 13\)

Now

Area

\(\\ \sf\longmapsto \dfrac{1}{2}bh\)

\(\\ \sf\longmapsto \dfrac{1}{2}(5)(13)[)tex]

\(\\ \sf\longmapsto \dfrac{65}{2}\)

\(\\ \sf\longmapsto 32.5cm^2\)

#2

Area of SQR=300/2=150in^2

Now

\(\\ \sf\longmapsto \dfrac{1}{2}bh=150\)

\(\\ \sf\longmapsto \dfrac{1}{2}b(15)=150\)

\(\\ \sf\longmapsto \dfrac{b}{2}=10\)

\(\\ \sf\longmapsto b=20in\)

Using Pythagorean theorem

\(\\ \sf\longmapsto x^2=15^2+20^2\)

\(\\ \sf\longmapsto x^2=225+400\)

\(\\ \sf\longmapsto x^2=625\)

\(\\ \sf\longmapsto x=25in\)

The graph of y=3x^4-16x^3+24x^2+48 is concave down for x values greater than or equal to 0.

The graph of y=3x^4-16x^3+24x^2+48 is an example of a polynomial function. To determine the concavity of a polynomial function, we must first identify the intervals where the function is increasing and decreasing. In this case, the function is increasing for all x values greater than or equal to 0.

Next, we must find the second derivative and determine the intervals where the second derivative is negative. If the second derivative is negative, then the graph is concave down. For this polynomial, the second derivative is y'' = -48x + 48, which is negative for all x values greater than or equal to 0. This means that the graph of y=3x^4-16x^3+24x^2+48 is concave down for all x values greater than or equal to 0.

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The Thévenin equivalent circuit consists of the Voc and Rt, with Voc as the open-circuit voltage and Rt as the equivalent resistance seen by the load resistor when it is disconnected.

To determine the Thévenin equivalent circuit using Mesh Analysis, you follow these steps:Identify the load resistor (RL) and remove it from the circuit.Assign mesh currents (I1, I2, etc.) to the remaining meshes in the circuit.

The number of mesh currents will depend on the complexity of the circuit.Apply Kirchhoff's voltage law (KVL) to each mesh, writing an equation for each mesh current.

Solve the resulting system of equations to obtain the values of the mesh currents.Use Ohm's Law to find the voltage across the load resistor (VRL) in terms of the mesh currents.The open-circuit voltage (Voc) is equal to VRL since there is no load connected.

Determine the equivalent resistance (Rt) by calculating the ratio of Voc to the current flowing through the load resistor (IL).The Thévenin equivalent circuit consists of the Voc and Rt.

with Voc as the open-circuit voltage and Rt as the equivalent resistance seen by the load resistor when it is disconnected. This simplified representation allows for easier analysis of the original circuit when connected to various loads.

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Answer:

let KL be the string PL be perpendicular distance between them. and KL be height of kite flying.

in right angled triangle

relationship between perpendicular and hypotenuse is given by sin angle

sin 31°=p/h

h=65/sin31

KP=126.2m

the length of string is 126.2m

Answer:

127.45 m

Step-by-step explanation:

Given :-

To Find :-

Solution :-

Here we need to find out the length of the string here if we imagine a right angle triangle in which the height of the kite will be the perpendicular of the triangle and the length of the string will be the hypotenuse of triangle .

And the angle between the the string and the ground will be 31°.

Here we can use ratio of sine as ,

> sin∅ = p/h

> sin 31° = 65m/ h

> h = 65m/sin 31°

> h = 65m/0.51

> h = 127 .45 m

Answer: A)  -4.6

b) 4.6 spaces left from the original spot

c) the totaal distance travled was 18.2 cm

Step-by-step explanation:

for a you add the amounts together, if you go left that's negative so you use subtraction

for b you count the amount you have from zero

for c you add all the numbers together and forget the signs

the series converges within the interval -2 < x < 2.

the radius of convergence, r, is 2.

To find the radius of convergence, r, of the series ∑((\(-1)^n * n^4 * x^n/2^n\)) from n = 1 to infinity, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms in a series is L as n approaches infinity, then the series converges if L < 1 and diverges if L > 1.

Let's apply the ratio test to the given series:

lim (n→∞) |\(((-1)^{(n+1)} * (n+1)^4 * x^{(n+1)}/2^(n+1)) / ((-1)^n * n^4 * x^n/2^n)\)|

= lim (n→∞) |\(((-1)^{(n+1)} * (n+1)^4 * x^{(n+1)} * 2^n) / ((-1)^n * n^4 * x^n * 2^{(n+1)})|\)

= lim (n→∞) |\(((n+1)^4 * x * 2^n) / (n^4 * 2^{(n+1)})|\)

= lim (n→∞) |(\(n+1)^4 * x / (n^4 * 2)|\)

= |x/2| * lim (n→∞)\(|(n+1)^4 / n^4|\)

Now, let's simplify the limit term:

lim (n→∞) \(|(n+1)^4 / n^4|\)

= lim (n→∞)\(|(1 + 1/n)^4|\)

= \((1 + 0)^4\)

= 1

Therefore, the limit of the ratio is 1. According to the ratio test, if the limit is equal to 1, the test is inconclusive. In such cases, we need to examine the boundary cases separately.

At the boundary cases, the series can converge or diverge. So we check for convergence when |x/2| = 1.

When x/2 = 1, x = 2, and when x/2 = -1, x = -2.

Now, we need to consider the interval between x = -2 and x = 2 to determine the radius of convergence.

Since the ratio test was inconclusive and we have convergence at x = 2 and x = -2, we need to check the behavior at these points.

For x = 2, the series becomes ∑\(((-1)^n * n^4 * 2^n/2^n\)) = ∑(\((-1)^n * n^4\)), which is an alternating series. By the Alternating Series Test, this series converges.

For x = -2, the series becomes ∑(\((-1)^n * n^4 * (-2)^n/2^n\)) = ∑\(((-1)^n * n^4 * (-1)^n)\), which is also an alternating series. Again, by the Alternating Series Test, this series converges.

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To compute the amortization schedule for the first 3 months of the mortgage, we need to determine the monthly interest and principal payments.

First, we calculate the monthly interest rate by dividing the annual interest rate of 6% by 12, resulting in 0.005. To find the interest payment for each month, we multiply the remaining mortgage balance by the monthly interest rate. In the first month, the interest payment would be $210,900 multiplied by 0.005, which equals $1054.50.

Next, we subtract the interest payment from the monthly payment to obtain the principal payment. For the first month, the principal payment would be $1780 minus $1054.50, resulting in $725.50. To calculate the remaining mortgage balance, we subtract the principal payment from the previous balance. For the first month, the remaining balance would be $210,900 minus $725.50, which equals $210,174.50.

We repeat these calculations for the second and third months, using the updated mortgage balance as the starting point. The interest and principal payments change each month based on the decreasing mortgage balance. Overall, the amortization schedule for the first 3 months of the mortgage would include the monthly payment amounts, interest payments, principal payments, and the remaining mortgage balance after each month's payment.

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The volume of the prism is determined as  103.0 unit³.

The volume of the triangular prism is calculated by applying the following formula as shown below;

V = ¹/₂bhl

where;

The base of the prism is calculated as follows;

tan 25 = 4/b

b = 4/tan (25)

b = 8.58 units

The volume of the prism is calculated as follows;

V = ¹/₂ x 8.58 x 6 x 4

V = 103.0 unit³

,

Thus, the volume of the prism is a function of its base, height and length.

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Answer: In fraction form, the answer is \(26\frac{17}{45}\).

Step-by-step explanation: We are given \(6\frac{3}{4} +19\frac{6}{7}\) and have to find what the sum of the two numbers are. Before we can starting however, the first step is to make the denominators the same to do this, find the least common multiple of 7 and 4, and make that the denominator. Multiply the numerator as well to make the fraction the same. The least common multiple of 4 and 7 is 28. That gives us the problem \(6\frac{21}{28}+19\frac{24}{28}\). (Sorry I don't think I explained that well.)

The next step is to add the numerators of the fractions together. 21 +24 = 45, and the denominator stays the same. Also add the whole numbers together to make one mixed number. This gives us \(25\frac{45}{28}\).

The finals step is to get rid of the improper fraction next to 25. To do this, subtract 28 from 42, and get 17. Add 1 to the 25, and you get \(26\frac{17}{28}\).

\(6\frac{3}{4} +19\frac{6}{7}\)

\(6\frac{3(7)}{4(7)}+19\frac{6(4)}{7(4)}\)

\(6\frac{21}{28} +19\frac{24}{28}\)

\((6+19)+(\frac{21}{28} +\frac{24}{28})\)

\(25+\frac{45}{28}\)

\(25(+1)\frac{45(-28)}{28}\)

\(26\frac{17}{28}\)

Hope this helps! Have a great day!

The probability that a movie is either a superhero movie or produced by Marvel can be found using the addition rule of probability. The addition rule states that the probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection.

P(A U B) = P(A) + P(B) - P(A ∩ B) Here, A is the event that the movie is a superhero movie, and B is the event that the movie is produced by Marvel. So, the probability of the union of these two events is P(A U B).Now, given that about 30% of movies are superhero movies, and 9% of recent movies are produced by Marvel, and about 2% of recent superhero movies are from Marvel, we can find the probabilities as follows: P(A) = 0.30 (given)

P(B) = 0.09 (given)

P(A ∩ B) = 0.02 (given)

Now, substituting these values in the formula for the addition rule, we get:P(A U B) = P(A) + P(B) - P(A ∩ B)

= 0.30 + 0.09 - 0.02

= 0.37

The probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection.

P(A U B) = P(A) + P(B) - P(A ∩ B)

Here, A is the event that the movie is a superhero movie, and B is the event that the movie is produced by Marvel. P(A) = 0.30 (given)

P(B) = 0.09 (given)

P(A ∩ B) = 0.02 (given)

Now, substituting these values in the formula for the addition rule, we get:P(A U B) = P(A) + P(B) - P(A ∩ B)

= 0.30 + 0.09 - 0.02

= 0.37

Therefore, the probability that a movie is either a superhero movie or produced by Marvel is 0.37.

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The correct answer is (4x^3 - 8x^2 )

Solve by using Foil's Method

Multiply (x - 3)(4x^2)

Begin, by multiplying together, the first terms of binomial

= x * 4x^2 = 4x^3

Now, multiply the last term of binomial.

= -3 * 4x^2 = -12x^2

Sum up the partial products starting from the first to last product from the first to last product and collect it:

=(4x^3 - 8x^2 )

Now, Let us know

What is Foil's Method ?

FOIL a mathematical series of steps used to multiply two binomials.

By definition we have the meaning of FOIL is given by:

F: First

O: Outer

I: Inner

L: Last

Binomial is simply an expression that consist of two variables or terms separated by either the addition sign (+) or subtraction (-).

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In the triangle ABC, i) ABC = 52.12° ii) BCA = 31.08° and iii) AB = 8.11cm.

Based on the provided information, ∠ BAC = 96.8°; AC = 12.4cm, and BC = 15.6cm

i) According to the law of sine,

Sin ∠A/a = Sin ∠B/b = Sin ∠C/c where a is the length opposite to ∠A, and so forth.

Hence, based on the information, ∠ABC = ∠B

Sin ∠B/AC = Sin ∠A/BC

Sin ∠B/12.4 = Sin 96.8/15.5

Sin ∠B = (Sin 96.8/15.5)*12.4

∠B = Sin^-1((Sin 96.8/15.5)*12.4)

∠B = 52.12°

ii) As the sum of interior angles of a triangle is 180°. ∠As BCA = ∠C

∠A + ∠B + ∠C = 180

96.8 + 52.12 + ∠C = 180

∠C = 31.08

iii) According to the law of cosine,

c^2 = a^2 + b^2 – 2ab cos C where C is the angle opposite to c.

BC^2 = AB^2 + AC^2 – 2(AB)(AC)cos98.6

15.6^2 = AB^2 + 12.4^2 – 2(AB)(12.4)cos98.6

Solving for AB,

AB = 8.11cm

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Answer:

All of them would be under $65

Answer:

D

Step-by-step explanation: