what is the y-intercept of the line of best fit?
first awnser gets brainlyist​

The solution to this equation \(y" - 5y' + 4y = e^(3x)\) which is a non homogeneous differentia equation is  \(y(x) = c1 e^(4x) - (1/4) c1 e^(3x) + c2 e^(x) + (1/6) e^(4x)\), where c1, c2 are the arbitrary constants of  the integration.

The given equation is a non homogeneous second-order differential equation and to solve it using the method of variation of parameters, we must first find the the general solution of the corresponding homogeneous equation \(y" - 5y' + 4y = 0.\)

we have;

\(r^2 - 5r + 4 = 0\)

By factorization, it become;

(r - 4)(r - 1) = 0

With the roots as r = 4 and r = 1, The general solution of the homogeneous equation is given as;

\(y_h(x) = c1 e^(4x) + c2 e^(x)\)

Form of non homogenous equation is given as;

\(y_p(x) = u1(x) e^(4x) + u2(x) e^(x)\)

where u1(x) and u2(x) are functions to be determined.

First derivative of  y_p(x) '

\(y_p'(x) = u1'(x) e^(4x) + 4u1(x) e^(4x) + u2'(x) e^(x) + u2(x) e^(x)\)

Second derivative of  y_p(x) '

\(y_p''(x) = u1''(x) e^(4x) + 8u1'(x) e^(4x) + 16u1(x) e^(4x) + u2''(x) e^(x) + 2u2'(x) e^(x) + u2(x) e^(x)\)

When this y_p(x), y_p'(x), and y_p''(x) is inputed into the nonhomogeneous equation, we have

\(u1''(x) e^(4x) + 8u1'(x) e^(4x) + 16u1(x) e^(4x) + u2''(x) e^(x) + 2u2'(x) e^(x) + u2(x) e^(x) - 5[u1'(x) e^(4x) + 4u1(x) e^(4x) + u2'(x) e^(x) + u2(x) e^(x)] + 4[u1(x) e^(4x) + u2(x) e^(x)] \\= e^(3x)u1''(x) e^(4x) + 4u1'(x) e^(4x) + u2''(x) e^(x) + 2u2'(x) e^(x) = e^(3x)\)

\(u1''(x) + 4u1'(x) = 0\\u2''(x) + 2u2'(x) = e^(3x)\)

The solutions of the above equations are ;

\(u1'(x) = c1 e^(-4x)\\u2'(x) = (1/2) e^(3x)\)

Integrating u1'(x) with respect to x,

\(u1(x) = (-1/4) c1 e^(-4x) + c2\\u2(x) = (1/6) e^(3x) + c3\)

N.B: c1,c2,c3 are arbitrary constants of integration.

The solution of the nonhomogeneous equation is given as;

\(y_p(x) = (-1/4) c1 e^(-x) e^(4x) + (1/6) e^(3x) e^(x)\\y_p(x) = (-1/4) c1 e^(3x) + (1/6) e^(4x)\\y(x) = y_h(x) + y_p(x)\)

By substituting \(y_h(x)\)and \(y_p(x)\) into the above equation, we have

\(y(x) = c1 e^(4x) + c2 e^(x) - (1/4) c1 e^(3x) + (1/6) e^(4x)\\y(x) = c1 e^(4x) - (1/4) c1 e^(3x) + c2 e^(x) + (1/6) e^(4x)\)

Thus, the general solution of the non homogeneous equation \(y" - 5y' + 4y = e^(3x) is y(x) = c1 e^(4x) - (1/4) c1 e^(3x) + c2 e^(x) + (1/6) e^(4x)\), where c1, c2 are arbitrary constants of integration.

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C is the most accurate one i guess

According to the question The fuel efficiency of 9.1 km/L is approximately equivalent to 1.49252 miles per gallon (mpg).

To convert kilometers per liter (km/L) to miles per gallon (mpg), we can use the following conversion factors:

\(\[ 1 \text{ kilometer} = 0.621371 \text{ miles} \]\)

\(\[ 1 \text{ liter} = 0.264172 \text{ gallons} \]\)

First, we convert the fuel efficiency from km/L to km/gallon:

\(\[ 9.1 \text{ km/L} \times 0.264172 \text{ gallons/L} = 2.402032 \text{ gallons/km} \]\)

Next, we convert the distance unit from kilometers to miles:

\(\[ 2.402032 \text{ gallons/km} \times 0.621371 \text{ miles/km} = 1.49252 \text{ miles/gallon} \]\)

Therefore, the fuel efficiency of 9.1 km/L is approximately equivalent to 1.49252 miles per gallon (mpg).

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The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.

Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.

For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.

For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.

For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.

Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.

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Answer:

(630 ÷ 7) ÷ (2 ⋅ 9) ⋅ 25 = 125

Step-by-step explanation:

630 ÷ 7 ÷ 2 ⋅ 9 ⋅ 25 = 125

(630 ÷ 7) ÷ (2 ⋅ 9) ⋅ 25 = 125

         90 ÷ 18 ⋅ 25 = 125

           5 ⋅ 25 = 125

               125 = 125

All of the statements are True when the expressions are evaluated using appropriate illustrations.

STATEMENT: 1

Real numbers have both rational and irrational values and can thus be manipulated using arithmetic operators like addition.

As a result, the statement is correct.

STATEMENT: 2

Real numbers can be expressed or raised to the power of another number in a variety of ways, including being squared.

STATEMENT: 3

All positive integers have a squared value that is greater than or equal to the value.

STATEMENT: 4

A sum's absolute value is always less than or equal to the sum of two numbers' absolute values.

Therefore, all of the statements are True when the expressions are evaluated using appropriate illustrations.

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The complete question is given below:
Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements are true or false.

a. There are real numbers u and v with the property that u+v b. There is a real number x such that x2 c. For all positive integers n,n2≥n.

d. For all real numbers a and b,|a+b|≤|a|+|b|

Step-by-step explanation:

since there is no graph it's a bit hard to answer this question, but I'll try. I can help solve the equation that represents the ratio of the two numbers:

(x + 1/2)/y = 1/3

This can be simplified to:

x + 1/2 = y/3

To graph this equation, you would need to plot points that satisfy the equation. One way to do this is to choose a value for y and solve for x. For example, if y = 6, then:

x + 1/2 = 6/3

x + 1/2 = 2

x = 2 - 1/2

x = 3/2

So one point on the graph would be (3/2, 6). You can choose different values for y and solve for x to get more points to plot on the graph. Once you have several points, you can connect them with a line to show the relationship between x and y.

(Like I said, it was a bit hard to answer this question, so I'm not 100℅ sure this is the correct answer, but if it is then I hoped it helped.)

I hope this helps you .

Keep learning

Answer:

The area of a circle.

Step-by-step explanation:

Can I get brainiest please

Answer:

The correct option is;

\(\ \underset{JS}{\rightarrow} \right |\)

Step-by-step explanation:

The given diagram consists of a a starting point, J having a direction passing through the point S and the line has one arrowhead on the right pointing to infinity, which is the symbol for a ray, JS

The denotation of a ray is made by the name of the ray having an overhead arrow as follows;

ray \(\ \underset{JS}{\rightarrow} \right |\)

Option B is correct that is \(\overrightarrow{JS}\).

It has magnitude, direction, and follows the law of vector addition.

As the direction is given from J to S. our JS vector becomes \(\overrightarrow{JS}\).

Thus, option B is correct that is \(\overrightarrow{JS}\).

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We have proved the statement that S≅W by 3 properties reflexive property, symmetric property, and transitive property.

Given that,

Let R be the relation defined on A as follows, and let A be the set of all statement forms in the three variables p, q, and r. S R T⇔ S and T have the same truth table for all S and T in A. substantiate the equivalence of R.

We have to demonstrate that it satisfies each of the properties you choose.

We know that,

By reflexive property,

S ≅ S  means that S has the same truth table as S.

T≅ T denotes that T and T have the same truth table.

By symmetric property,

S ≅T denotes that S and T share the same truth table.

At that time, T and S share the same truth table.

So, T ≅ S

By transitive property,

S≅T and T≅V and V≅W

S shares a truth table with S. Truth table between T and T W's truth table is the same for V and V.

S, T, V, and W all have the same truth table as a result.

S specifically has the same truth table as W.

Then S≅T≅V≅W ---> S≅W

Therefore, We have proved the statement that S≅W by 3 properties reflexive property, symmetric property, and transitive property.

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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Answer:

y= 2/3x -1

Step-by-step explanation:

Ok so basically we want to put it in the form y=mx+b where m is 2/3 and passes through the point (9,5). So sub in the x and y of the point in brackets into the equation. 5= 2/3(9) + b and solve for b so b = -1. Therefore the equation is y=2/3x -1

The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).

The difference of two expressions is determined by subtracting one from the other.

Find the difference of each of the expressions given to determine which will give us 5.

-3 - (-8)

= -3 + 8

= 5

-2 - 3 = -5 [this is not the same as 5]

1 - (-4)

= 1 + 4

= 5

7 - (-2)

= 7 + 2

= 9

-3 - (-8) and 1 - (-4) will give us a difference of 5.

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Answer:

0.616m

Step-by-step explanation:

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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The maximum purchase price per unit of the component that Ms. Alexander should negotiate with her supplier is $19.00, which is equal to the variable cost per unit to manufacture the part in-house.

In this scenario, Ms. Alexander needs to determine the maximum price per unit that she should be willing to pay the supplier for the component. She conducted a cost analysis and found that manufacturing the part in-house would require $450,000 in capital equipment and have a variable cost of $19.00 per unit.

Since there is no fixed cost associated with purchasing the component from the supplier, the maximum purchase price per unit should not exceed the variable cost per unit of manufacturing in-house. This ensures that the company does not incur additional costs by outsourcing the component.

Therefore, Ms. Alexander should negotiate a price with the supplier that is equal to or lower than the variable cost per unit, which is $19.00. By doing so, the company can avoid the initial capital investment and ongoing variable costs associated with in-house production, making it more cost-effective to purchase the component from the supplier.

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The midpoint of AB is M(4,1), If the coordinates of A are (2,8), then the coordinates of B are (6,-6).

The midpoint formula states that the midpoint of a line segment in a coordinate plane is given by the average of the x-coordinates and the average of the y-coordinates.

The midpoint of AB is M(4,1) and the coordinates of A are (2,8).

Therefore, we can write the following equation: x-coordinate of the midpoint = (x-coordinate of A + x-coordinate of B) / 2y-coordinate of the midpoint = (y-coordinate of A + y-coordinate of B) / 2

Substituting the given values into the above equation, we get:4 = (2 + x-coordinate of B) / 2 1 = (8 + y-coordinate of B) / 2

Simplifying the equations above, we get: x-coordinate of B = 6 y-coordinate of B = -6

Therefore, the coordinates of B are (6,-6).

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The correct option is B.

The symbolic statement (p ∨ q) ∧ ~r represents "The chair is broken or it is time to sleep, and I do not study".

The statement (p ∨ q) ∧ ~r can be broken down as follows:

p ∨ q represents "The chair is broken or it is time to sleep".~r represents "I do not study".

The ∧ symbol represents "and".Therefore, the entire statement can be written as "The chair is broken or it is time to sleep, and I do not study"."It is time to sleep or the chair is broken and I do not study".

Hence the correct option is B.

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Answer:

\(1/32\)

Step-by-step explanation:

To understand this question you would first of all need to know about negative exponents and multiply fraction by integers.

Example I would like to find out \(2^{-2}\),

You would first normally solve this question by squaring, which would result in 4 then divide it by 1. Like this: \(1/2^{2}\)

Which would be 0.25 or 1/4

Lets apply this knowledge to the following question:

1. \(2^{-3} / 2^{2}\)

2. \(\frac{1}{8} / 4\)

3. \(1/32\)

Answer:

50 years

Step-by-step explanation:

Assuming it doesn't compound, 5,000*3 = 15,000.

5,000 * 6% = 5,000 * 0.06 = 300.

15,000 / 300 = 50 years.

Answer:  (4y-9z)( 16y^2 + 36yz + 81z^2 )

=======================================================

Explanation:

We'll use the difference of cubes factoring rule

a^3 - b^3 = (a-b)(a^2+ab+b^2)

In this case,

So,

a^3 - b^3 = (a-b)(a^2+ab+b^2)

64y^3 - 729z^3 = (4y-9z)( (4y)^2 + (4y)(9z) + (9z)^2 )

64y^3 - 729z^3 = (4y-9z)( 16y^2 + 36yz + 81z^2 )

The total time required taken by the bell to ring 20 times is equal to 180 seconds, or 3 minutes.

If it takes the bell 90 seconds to ring 10 times, we can calculate the average time it takes for each ring,

Average time per ring

= Total time / Number of rings

= 90 seconds / 10 rings

= 9 seconds per ring

To find out how long it will take the bell to ring 20 times,

we can multiply the average time per ring by the number of rings,

Time to ring 20 times

= Average time per ring × Number of rings

= 9 seconds per ring × 20 rings

= 180 seconds

Therefore, it will take the bell 180 seconds, or 3 minutes, to ring 20 times.

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Answer:

Step-by-step explanation:

Centroid of a triangles is a point of intersection of it's medians.

Centroid divides the medians in the ratio of 2 : 1.

By this property of the centroid,

SH : HM = 2 : 1

Since, SM = 24,

SH = \((\frac{2}{2+1})(SM)\)

     = \(\frac{2}{3}\times 24\)

SH = 16

HM = SM - SH

      = 24 - 16

HM = 8

TH : DH = 2 : 1

Since, DH = \((\frac{1}{2+1})(TD)\) = 4

          \(\frac{1}{3}(TD) = 4\)

          TD = 12

Therefore, TH = TD - DH

                         = 12 - 4

                  TH = 8

Since, EH = \((\frac{1}{2+1})(ER)\) = 6

           \(\frac{1}{3}(ER)=6\)

           ER = 18

Therefore, HR = ER - EH

                        = 18 - 6

                  HR = 12

a + 12a = 330

Add like terms

13a = 330

a = 25.38

25.38 * 12 = 304.56

Round up -> 305

305 children attend

Answer:

-2.5 is greater

Step-by-step explanation:

it's greater because it's closer to the whole # 1

Answer:

-2.5

Step-by-step explanation:

When you have negatives , the lowest number would always be the greatest

The probability that a high school junior will take less than 135 minutes to complete the SAT exam is 0.5745.

To determine the probability, the standard normal distribution table or calculator is utilized.

The standard normal distribution table, also known as the z-score table, is used to find the probability of a certain z-score or a range of z-scores.

The SAT exam's time is normally distributed, with a mean of 150 minutes and a standard deviation of 25 minutes.The formula for z-score is as follows:

z=(x-μ)/σ

Where x is the time to complete the SAT exam, μ is the mean of the time to complete the SAT exam, and σ is the standard deviation of the time to complete the SAT exam.

To calculate the z-score, the time of 135 minutes is substituted for x, the mean μ of 150 minutes is substituted for μ, and the standard deviation σ of 25 minutes is substituted for σ.The computation is as follows:

z=(135-150)/25= -0.60

Using the standard normal distribution table, the probability of getting a z-score of -0.60 is 0.2743.

To obtain the probability that a high school junior will complete the SAT exam in less than 135 minutes, the area under the standard normal curve to the left of z = -0.60 must be computed. Because the normal curve is symmetrical, the region to the right of z = -0.60 is equal to 1 - 0.2743 = 0.7257.

Finally, to obtain the region to the left of z = -0.60, 0.7257 must be subtracted from 1:1 - 0.7257 = 0.2743

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Answer:

118ft

Step-by-step explanation:

dont ask how i got it i just got the answer from my teacher but they didnt show me the work. ur welcome

Using the binomial distribution, there is a 0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

For this problem, the values of the parameters are:

p = 0.5, n = 13

The probability that at most eleven of the thirteen babies are girls is:

\(P(X \leq 11) = 1 - P(X > 11)\)

In which

P(X > 11) = P(X = 12) + P(X = 13)

Then:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 12) = C_{13,12}.(0.5)^{12}.(0.5)^{1} = 0.0016\)

\(P(X = 13) = C_{13,13}.(0.5)^{13}.(0.5)^{0} = 0.0001\)

So:

P(X > 11) = P(X = 12) + P(X = 13) = 0.0016 + 0.0001 = 0.0017

\(P(X \leq 11) = 1 - P(X > 11) = 1 - 0.0017 = 0.9983\)

0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.

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