What Are the factors of 24 and 32

We first graph the three points given.

The centre of the circle seems to be located at the point (3,-2) and therefore, the radius is 2.

Then the equation of the circle is

The graph of this equation exactly goes through these three points as shown in the figure below.

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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Therefore, Wn = (R1 + R2 +...+Rn) / (X1 + X1 +...+Xn), Wn -> E[R]/E[X] as n -> [infinity] by using the law of large numbers.

The formula Wn = (R1 + R2 +...+Rn) / (X1 + X1 +...+Xn) represents the average reward earned during the first n cycles in a renewal reward process. To show that Wn -> E[R]/E[X] as n -> [infinity], we need to use the law of large numbers. This law states that as the number of observations increases, the sample average will converge to the expected value of the variable being observed. In this case, as n -> [infinity], the sample average Wn will converge to the expected value of the ratio E[R]/E[X], which is the desired result.

Therefore, Wn = (R1 + R2 +...+Rn) / (X1 + X1 +...+Xn), Wn -> E[R]/E[X] as n -> [infinity] by using the law of large numbers.

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Main Answer: As n approaches infinity, Wn converges to E[R]/E[X].

Supporting Question and Answer:

How can we show that a sequence of random variables converges to a certain value?

To show that a sequence of random variables converges to a certain value, we can use mathematical techniques such as the law of large numbers or limit theorems.

Body of the Solution:To show that Wn converges to E[R]/E[X] as n approaches infinity, we need to demonstrate that the limit of Wn as n approaches infinity is equal to E[R]/E[X].

Let's break down the problem step by step:

First, let's define the random variables involved:

R1, R2, ... Rn:

Rewards obtained during each cycle (assumed to be independent and identically distributed random variables).

X1, X2, ... Xn:

Lengths of each cycle (also assumed to be independent and identically distributed random variables).

We are given that y1 and y2 are linearly independent solutions to the homogeneous differential equation, which means they are distinct solutions and not proportional to each other.

The average reward earned during the first n cycles, Wn, is defined as the sum of rewards R1, R2, ..., Rn divided by the sum of cycle lengths X1, X2, ..., Xn.

To show that Wn converges to E[R]/E[X] as n approaches infinity, we need to show that the limit of Wn as n approaches infinity is equal to E[R]/E[X].

We can start by expressing Wn in terms of the expected values of R and X:

Wn = (R1 + R2 + ... + Rn) / (X1 + X2 + ... + Xn) = (1/n) * (R1 + R2 + ... + Rn) / (1/n) * (X1 + X2 + ... + Xn)

Now, let's consider the numerator (R1 + R2 + ... + Rn) and denominator (X1 + X2 + ... + Xn) separately:

The numerator (R1 + R2 + ... + Rn) is the sum of n independent and identically distributed random variables with mean E[R].

The denominator (X1 + X2 + ... + Xn) is the sum of n independent and identically distributed random variables with mean E[X].

As n approaches infinity, by the law of large numbers, the sum of these random variables will converge to n times their respective means. Therefore, we can rewrite the numerator and denominator as:

(R1 + R2 + ... + Rn) approaches n * E[R]

(X1 + X2 + ... + Xn) approaches n * E[X]

Substituting these limits into our expression for Wn:

Wn = (1/n) * (R1 + R2 + ... + Rn) / (1/n) * (X1 + X2 + ... + Xn) = (1/n) * (n * E[R]) / (n * E[X]) = E[R] / E[X]

Thus, we have shown that as n approaches infinity, Wn converges to E[R]/E[X].

This demonstrates that the average reward earned during the first n cycles, Wn, approaches the ratio of the expected reward E[R] to the expected cycle length E[X] as the number of cycles increases.

Final Answer: Therefore,we prove that Wn -> E[R]/E[X] as n -> [infinity].

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To find the difference between 87 and 12 12, we need to convert 12 12 to an improper fraction.

12 12 = (12 x 2 + 12) / 2 = 36/2 + 12/2 = 48/2 = 24

Now we can subtract the fractions:

87 - 24/12 = 87 - 2 = 85

Therefore, the difference between 87 and 12 12 is 85.

the magnitude of the magnetic field at the point p which is equidistant from the wire is 170.833*10^-7

Given ,

Current = 4.10 I

Resistance = 4.80cm = 0.048m

Constant = 4π*10^-7 h/m

To determine magnetic field

B=μ*I / 2πR

= 4π*10^-7 * 4.10  /  2π * 0.048

=8.20*10^-7 / 0.048

= 170.833*10^-7

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Answer:

3.375

3\(\frac{375}{1000}\)

\(\frac{27}{8}\)

Step-by-step explanation:

The first answer divide 81 by 24 and you will get the decimal answer of 3.375.

0.375 is \(\frac{375}{1000}\)

\(\frac{81}{24}\)  Divide the top and the bottom by 3 to get \(\frac{27}{8}\)

The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

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Answer:

\(-\frac{4}{9}\)

Step-by-step explanation:

Slope = \(\frac{y_2-y_1}{x_2-x_1}\)

Let's say (5,-1) is \((x_2,y_2)\) and (-4,3) is \((x_1,y_1)\)

Let's substitute the slope formula.

\(\frac{-1-3}{5-(-4)} =\frac{-4}{5+4} =\frac{-4}{9}\)= \(-\frac{4}{9}\)

The slope is \(-\frac{4}{9}\)

Hope this helps :)

Have a great day!

The given scenario can be considered a binomial setting because it satisfies the four conditions for a binomial distribution:

1. The experiment consists of a fixed number of trials: The meeting involves 20 businessmen, so the number of trials is fixed at 20.

2. Each trial has two possible outcomes: A businessman either wears a tie too tight (success) or does not (failure).

3. The probability of success is constant: The given information does not provide the probability of a businessman wearing a tie too tight, so we assume that the probability remains the same for each businessman.

4. The trials are independent: The wearing of ties too tight by one businessman does not affect the probability for another businessman, so the trials can be considered independent.

b. To find the mean (μ) and standard deviation (σ) of X, we need to use the formulas for the binomial distribution. For a binomial distribution, the mean is calculated as μ = n * p, and the standard deviation is calculated as σ = √(n * p * (1 - p)), where n is the number of trials and p is the probability of success.

In this case, n = 20 (the number of businessmen) and the probability of success (p) is not given. Since the probability is not specified, we assume it to be 10% or 0.1 (as stated in the research). Therefore, the mean is μ = 20 * 0.1 = 2, and the standard deviation is σ = √(20 * 0.1 * 0.9) ≈ 1.34.

c. To find P(X = 2), we can use the binomial probability formula: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where (n choose k) represents the number of ways to choose k successes out of n trials.

Using n = 20, k = 2, and p = 0.1, we can calculate:

P(X = 2) = (20 choose 2) * 0.1^2 * (1 - 0.1)^(20 - 2).

d. To find P(X > 0), we need to calculate the probability of having at least one businessman with a tie too tight. This is the complement of the probability of having none of the businessmen with tight ties, which is equivalent to P(X = 0). Therefore, P(X > 0) = 1 - P(X = 0).

e. To find P(X = 0), we can use the binomial probability formula with k = 0:

P(X = 0) = (20 choose 0) * 0.1^0 * (1 - 0.1)^(20 - 0).

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Answer:

\(a_{n}\) = 6n - 4

Step-by-step explanation:

There is a common difference between consecutive terms in the sequence, that is

8 - 2 = 14 - 8 = 6

This indicates the sequence is arithmetic with n th term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 6 , thus

\(a_{n}\) = 2 + 6(n - 1) = 2 + 6n - 6 = 6n - 4

Thus the formula representing the sequence is

\(a_{n}\) = 6n - 4

The surface area of the regular pyramid is equal to 1209 m² to the nearest whole number. The first option is correct.

Area of a regular polygon = 1/2 × apothem × perimeter

Area of the hexagon = (1/2 × 8.5√3 × 102) m²

Area of the hexagon = 750.8440 m²

Area of one triangle face = (1/2 × 17 × 9) m²

Area of one triangle face = 76.5 m²

Area of six triangle face = (76.5 × 6) m²

Area of six triangle face = 459 m²

Surface area of the regular pyramid = 750.8440 m² + 459 m²

Surface area of the regular pyramid = 1209.8440 m²

Therefore, the surface area of the regular pyramid is equal to 1209 m² to the nearest whole number. The first option is correct.

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Probability of receiving a hand with exactly three suits \(= (4 * (13^3)) / 2,598,960\)

What is Combinatorics?

Combinatorics is a branch of mathematics that deals with counting, arranging, and organizing objects or elements. It involves the study of combinations, permutations, and other related concepts. Combinatorics is used to solve problems related to counting the number of possible outcomes or arrangements in various scenarios, such as selecting items from a set, arranging objects in a specific order, or forming groups with specific properties. It has applications in various fields, including probability, statistics, computer science, and optimization.

To calculate the probability of receiving a hand with exactly three suits when dealt 5 cards from a well-shuffled deck of cards, we can use combinatorial principles.

There are a total of 4 suits in a standard deck of cards: hearts, diamonds, clubs, and spades. We need to calculate the probability of having exactly three of these suits in a 5-card hand.

First, let's calculate the number of favorable outcomes, which is the number of ways to choose 3 out of 4 suits and then select one card from each of these suits.

Number of ways to choose 3 suits out of 4: C(4, 3) = 4

Number of ways to choose 1 card from each of the 3 suits\(: C(13, 1) * C(13, 1) * C(13, 1) = 13^3\)

Therefore, the number of favorable outcomes is \(4 * (13^3).\)

Next, let's calculate the number of possible outcomes, which is the total number of 5-card hands that can be dealt from the deck of 52 cards:

Number of possible outcomes: C(52, 5) = 52! / (5! * (52-5)!) = 2,598,960

Finally, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:

Probability of receiving a hand with exactly three suits =\((4 * (13^3)) / 2,598,960\)

This value can be simplified and expressed as a decimal or a percentage depending on the desired format.

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Therefore, Caleb paid approximately $14,067.90 for the shares.

Let's assume the amount Caleb paid for the shares is represented by the variable "x". According to the given information, his selling price was 130% of the amount he paid.

Selling price = 130% of the amount paid

$18,189.27 = 1.3 * x

To find the amount he paid for the shares, we can solve the equation for "x" by dividing both sides by 1.3:

x = $18,189.27 / 1.3

Calculating this, we find:

x ≈ $14,067.90

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Answer:

a). A = -2x² + 200x

b). Widths = 40 feet and 60 feet

Step-by-step explanation:

It is given that length of the fencing material = 200 feet

a). Peg wants to cover the vegetable garden from three sides with the given fencing material.

If length of the garden = l

and width of the garden = x

l + x + x = 200

l + 2x = 200

l = (200 - 2x) feet

Therefore, area of the garden = Length × width

A = \((200-2x)\times x\)

A = -2x² + 200x

b). Foe A = 4800 square feet,

4800 = -2x² + 200x

2x² - 200x + 4800 = 0

x² - 100x + 2400 = 0

x² - 60x - 40x + 2400 = 0

x(x - 60) - 40(x - 60) = 0

(x - 60)(x - 40) = 0

x = 40, 60 feet

Therefore, widths of Peg's garden will be 40 feet and 60 feet.

Answer:

0.02987 %

Step-by-step explanation:

2.987 / 100 = 0.02987 %

Explanation: The 4th one is the distributive property because it shows an     equal sign and the 5th one is the inverse property of addition because it uses more than addition.

Answer: 4th one is distributive property 5th one is inverse property of addition

P.S. I am sure 95% sure that I am correct.

Answer:

9

Step-by-step explanation:

no, I don't think so because 6/2=3 and in the bracket 1+2=3 and if we multiple them then the answer should be 9 (3×3=9)

The answer to your question is 9 !

The width of the parking lot is 78 m

We have been given the perimeter of a rectangular parking lot which is equal to 350 m.

We know the perimeter of a rectangular plot is 2 X (width of the plot ) + 2 X (length of the parking lot ).

And the length of the parking lot is given as 97 m.

2 X (width of the plot ) +2 X (length of the parking lot ) =350 m

2 X (width of plot ) + 2 X 97 =350

2 X (width of the plot ) =156 m

width of the plot = 78 m

Hence the width of the plot is 78 meters.

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The width of this rectangular parking lot is equal to 78 meters.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following:

P = 2(L + W)

350 = 2(97 + W)

175 = 97 + W

Width, W = 175 - 97

Width, W = 78 meters.

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The value of s for the given value is 24.05.

Given is an equation v² = u²+2gs, we need to find the value of s if v = 25, u = 12 and g = 10,

So,

25² = 12² + 2(10)s

625 = 144 + 20s

20s = 481

s = 24.05

Hence the value of s for the given value is 24.05.

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In a nonequivalent control group interrupted time series design, the independent variable is studied as a factor that influences the dependent variable, while accounting for potential confounding factors. The design involves two groups: the treatment group, which receives the intervention or manipulation of the independent variable, and the nonequivalent control group, which does not receive the intervention.

The control group serves as a comparison for assessing the impact of the independent variable on the treatment group. By comparing the outcomes of both groups over a series of time points before and after the intervention, researchers can analyze the effect of the independent variable while minimizing the influence of extraneous factors.

This design is particularly useful when random assignment of participants to the treatment and control groups is not feasible, as it helps to control for potential threats to internal validity. By using an interrupted time series approach, the researcher can better understand the patterns of change in the dependent variable and establish a causal relationship between the independent variable and the observed outcomes.

In summary, in a nonequivalent control group interrupted time series design, the independent variable is studied as a factor that affects the dependent variable, while using a control group to account for potential confounding factors and enhance the validity of the findings.

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Answer:

kinder

Step-by-step explanation:

1. 8

2. 2

The Vertex is at (3, 0)

The Axis of symmetry is; x = 3

The x-intercept is; x = 3

We are given the quadratic equation as;

y = -2(x - 3)²

Expanding this gives us;

y = -2(x² - 6x + 9)

y = -2x² + 12x - 18

x coordinate of vertex = -b/2a = -12/(2 * -2) = 3

y coordinate of vertex = f(3) = -2(3)² + 12(3) - 18 = 0

Vertex is at (3, 0)

Axis of symmetry is the x coordinate of vertex = -b/2a = -12/(2 * -2) = 3

x-intercepts is gotten by finding the roots which are; x = 3 and 3

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Answer:

A and E

Step-by-step explanation:

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\) ← distance formula

it is important that the x and y coordinates are placed correctly, that is not mixed together.

First version

let (x₁, y₁ ) = X (- 5,  4 ) and (x₂, y₂ ) = Y (7, 15 ) , then

XY = \(\sqrt{(7-(-5)^2+(15-4)^2}\) → A

or

Second version

let (x₁, y₁ ) = Y (7, 15 ) and (x₂, y₂ ) = X (- 5, 4 ) , then

XY = \(\sqrt{(-5-7)^2+(4-15)^2}\) → E

Haruka hiked about 14 kilometres in total.

According to the question

We don't know precisely how many kilometres Haruka travelled in the morning, but she hiked several kilometres in the morning and six kilometres in the afternoon. We may utilise the information provided—that her afternoon hike was 25% shorter than her morning trip—to solve the problem.

The unknown quantity (the number of kilometres hiked in the morning) may be represented as X in algebra. We may express the equation as follows if Haruka travelled 6 kilometres in the afternoon, which was 25% less than her morning hike:

6 = X - 0.25X

This equation can be simplified to:

6 = 0.75X

And finally, by solving for X, we get:

X = 8

In the morning, Haruka walked 8 kilometres. The distance travelled in the morning and afternoon are simply added together to provide the total number of kilometres hiked:

8 + 6 = 14 kilometers

Thus, during the course of the two excursions, Haruka covered a distance of 14 kilometres.

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Haruka hiked about 14 kilometres in total.

According to the question

We don't know precisely how many kilometres Haruka travelled in the morning, but she hiked several kilometres in the morning and six kilometres in the afternoon. We may utilise the information provided—that her afternoon hike was 25% shorter than her morning trip—to solve the problem.

The unknown quantity (the number of kilometres hiked in the morning) may be represented as X in algebra. We may express the equation as follows if Haruka travelled 6 kilometres in the afternoon, which was 25% less than her morning hike:

6 = X - 0.25X

This equation can be simplified to:

6 = 0.75X

And finally, by solving for X, we get:

X = 8

In the morning, Haruka walked 8 kilometres. The distance travelled in the morning and afternoon are simply added together to provide the total number of kilometres hiked:

8 + 6 = 14 kilometers

Thus, during the course of the two excursions, Haruka covered a distance of 14 kilometres.

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The value of a car that depreciates over time can be modeled by the function \(J(t)=27000(0.9)^{2t+2}\) has an equivalent form of \(J(t) = 21870(0.81)^t\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

The value of the car is given as:

\(J(t)=27000(0.9)^{2t+2}\)

The equation can be written as:

\(J(t)=27000(0.9)^{2t} (0.9)^2\\\\J(t) = 27000(0.81)^t(0.81)\\\\J(t) = 21870(0.81)^t\)

Hence, the value of a car that depreciates over time can be modeled by the function \(J(t)=27000(0.9)^{2t+2}\) has an equivalent form of \(J(t) = 21870(0.81)^t\).

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Answer:

12.75

Step-by-step explanation:

The first number, 51, is called the dividend.

The second number, 4 is called the divisor.

Answer:

can you tell me please

Step-by-step explanation:

nicest

Answer:

3.2 seconds

Step-by-step explanation: