Use the method variation of parameters find the general solution of the following differential equation given that y1=x and y2= x^3 are solutions of its corresponding homogenous equation.
X^2y''-3xy' +3y = 12x^4

The amount of chlorine in the pool at the start of any given week, we need to know the amount of chlorine in the pool at the start of the previous week.

Let Cn be the amount of chlorine in the pool at the start of the nth week.

We can start by finding the amount of chlorine in the pool at the start of the second week. Since 40% of the chlorine evaporates, we have:

C2 = 0.6(C1 + 16)

Now, we can use this formula to find the amount of chlorine in the pool at the start of the third week:

C3 = 0.6(C2 + 16)

We can continue this process to find a recursive rule for Cn:

Cn = 0.6(Cn-1 + 16)

where C1 = 34.

This formula tells us that to find the amount of chlorine in the pool at the start of any given week, we need to know the amount of chlorine in the pool at the start of the previous week. We can use this formula repeatedly to find the amount of chlorine in the pool at the start of any week.

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The correct option is (B) yes because all the elements of set R are in set A.

Given sets:

So,

Therefore, the correct option is (B) yes because all the elements of set R are in set A.

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The complete question is given below:
Consider the sets below. U = {x | x is a real number} A = {x | x is an odd integer} R = {x | x = 3, 7, 11, 27} Is R ⊂ A?

(A) yes, because all the elements of set A are in set R

(B) yes, because all the elements of set R are in set A

(C) no because each element in set A is not represented in set R

(D) no, because each element in set R is not represented in set A

Answer:

Probability that a student who passed the test did not  complete the homework = 0.07

Step-by-step explanation:

Given:

Total number of students = 28

Number of students who passed the test = 18

Number of students who completed  the assignment = 23

Number of students who passed the test and also completed the  assignment = 16

To find: probability that a student who passed the test did not  complete the homework

Solution:

Probability refers to chances of occurrence of some event.

Probability = number of favorable outcomes/total number of outcomes

Let A denotes the event that students passed the test and B denotes the event that students completed  the assignment

P(A only) = \(P(A)-P(A\cap B)\)

Here,

\(P(A)=\frac{18}{28}\,,\,P(A\cap B)=\frac{16}{28}\)

So,

\(P(A\,\,only)=\frac{18}{28}-\frac{16}{28}=\frac{2}{28}=\frac{1}{14}=0.07\)

Therefore,

probability that a student who passed the test did not  complete the homework = 0.07

Answer:

2/9

Step-by-step explanation:

The accurate diagram of the end of the roof will given a side length of 6.2 cm, 6.2 cm and 8 cm.

The accurate diagram of the end of the roof is determined by constructing the given angles of the triangle and the corresponding side lengths of the triangle.

Since the base angles of the triangle are equal, the two opposite side length of the triangle must be equal.

To construct the triangular diagram of the end of the roof we will follow the steps below;

Thus, the accurate diagram of the end of the roof will given a side length of 6.2 cm, 6.2 cm and 8 cm.

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Answer:

Never second guess yourself

Step-by-step explanation:

Answer: Any value of f that is less than 3 1/3 satisfies the inequality. The solutions to the inequality are all values of f that are less than 3 1/3.

Step-by-step explanation:

Here, from the figure we see that,

Line EI is parallel to HG.

And EH and GI act as the transversal lines for the given parallel pair.

So, we get

Therefore, we have two angles and one side equal in two triangles.

Henceproved that , they are congruent with the ASA (Angle Side Angle)rule.

The difference of the number of students with green eyes and blond hair and the number of students with gray eyes is 14.

The correct matches of the descriptions with the correct values:

1. The number of students with blue eyes and blond hair = 42

The given table shows the survey results of students' eye and hair colors. Blue eyes and blond hair are found in the intersection of the Blue row and the Blond column.

The value in that intersection is 42, which represents the number of students with blue eyes and blond hair.

2. The number of students with gray eyes and brown hair = 5

Gray eyes and brown hair are found in the intersection of the Gray row and the Brown column.

The value in that intersection is 5, which represents the number of students with gray eyes and brown hair.

3. The difference of the number of students with gray eyes and brown hair and the number of students with green eyes and black hair = 6

The number of students with gray eyes and brown hair is 5, and the number of students with green eyes and black hair is 11.

Subtracting these values, we get:

11 - 5 = 6

Therefore, the difference of the number of students with gray eyes and brown hair and the number of students with green eyes and black hair is 6.4.

The difference of the number of students with green eyes and blond hair and the number of students with gray eyes

= 14

The number of students with green eyes and blond hair is 21, and the number of students with gray eyes is 35. Subtracting these values, we get:

35 - 21 = 14

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we have shown that E[X] = 1/√(2π) * e^(-a^2/2) for the given random variable X.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To show that E[X] = 1/√(2π) * \(e^{(-a^2/2)}\), where X is defined as X = {Z if Z > a, 0 otherwise}, we need to calculate the expected value of X.

The expected value (E) of a random variable X is given by:

E[X] = ∫(x * f(x)) dx

where f(x) is the probability density function (PDF) of X.

For the given random variable X, we have two cases:

Case 1: X = Z if Z > a

Case 2: X = 0 otherwise

Let's calculate the expected value of X by considering both cases separately.

Case 1: X = Z if Z > a

In this case, the PDF of X is given by the PDF of the standard normal distribution, which is:

f(x) = 1/√(2π) * \(e^{(-x^2/2)}\)

Since X = Z if Z > a, we need to calculate the expected value of X when Z > a. This can be expressed as:

E[X] = ∫(x * f(x) | x > a) dx

= ∫(x * (1/√(2π) * \(e^{(-x^2/2)}\)) | x > a) dx

= ∫(x * (1/√(2π) * \(e^{(-x^2/2)}\)) | x = a to ∞) dx

= 1/√(2π) * ∫(x * \(e^{(-x^2/2)}\)| x = a to ∞)

Now, let's perform a u-substitution, where u = -x²/2. Then du = -x dx.

When x = a, u = -a²/2, and when x approaches ∞, u approaches -∞.

Therefore, the integral becomes:

E[X] = 1/√(2π) * ∫(\(e^u\) du | u = -a²/2 to -∞)

= 1/√(2π) * [\(e^u\)| u = -a²/2 to -∞]

= 1/√(2π) * (\(e^{(-\infty)} - e^{(-a^2/2)}\))

Since \(e^{(-\infty)}\) approaches 0, we have:

E[X] = 1/√(2π) * (0 - \(e^{(-a^2/2)}\))

= 1/√(2π) * (-\(e^{(-a^2/2)}\))

= -1/√(2π) * \(e^{(-a^2/2)}\)

Now, we consider Case 2: X = 0 otherwise. In this case, the PDF of X is simply 0, as X is always 0 when Z ≤ a.

Therefore, the expected value of X for Case 2 is 0.

To calculate the overall expected value, we need to consider the probabilities of each case. In Case 1, X takes the value of Z with probability P(Z > a), and in Case 2, X takes the value of 0 with probability P(Z ≤ a).

Since Z is a standard normal random variable, P(Z ≤ a) = Φ(a), where Φ denotes the cumulative distribution function (CDF) of the standard normal distribution.

Therefore, the expected value of X can be calculated as:

E[X] = P(Z > a) * E[X | X = Z] + P(Z ≤ a) * E[X |

X = 0]

= (1 - Φ(a)) * (-1/√(2π) * \(e^{(-a^2/2)}\)) + Φ(a) * 0

= -1/√(2π) * \(e^{(-a^2/2)}\) + 0

= -1/√(2π) *\(e^{(-a^2/2)}\)

= 1/√(2π) * \(e^{(-a^2/2)}\)

Hence, we have shown that E[X] = 1/√(2π) * \(e^{(-a^2/2)}\) for the given random variable X.

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Answer:

-5n-6n< 8-8n-n

-11n < -9n + 8

-2n < 8

n > -4

Answer:

n>-4

Step-by-step explanation:

Let's solve your inequality step-by-step.

−5n−6n<8−8n−n

Step 1: Simplify both sides of the inequality.

−11n<−9n+8

Step 2: Add 9n to both sides.

−11n+9n<−9n+8+9n

−2n<8

Step 3: Divide both sides by -2.

−2n

−2

<

8

−2

n>−4

Answer:

n>−4

The impact of critic reviews and star ratings on one's strategies would depend on the individual and their approach to the game.

Some players may be heavily influenced by reviews and ratings, using them to adjust their strategies in order to please the critics and achieve higher scores.

Others may choose to ignore them altogether and focus on their own personal goals or strategies. Still, others may use the feedback as a tool for improvement, taking the criticism constructively and using it to make changes in their approach to the game.

Ultimately, it is up to the individual player to decide how much weight they place on reviews and ratings and how they choose to use them in their gameplay.

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The value of x in the given equation i.e \(\frac{16x+12}{2}=100\) is 11.825

Given that equation  \(\frac{16x+12}{2}=100\)  and asked to evaluate the value of x in the given equation

⇒ \(\frac{16x+12}{2}=100\)(given equation)

To solve the given equation, need to use the various mathematical  operations i.e division and subtraction)

⇒8x+6=100 ( using the operation division)

⇒8x=100-6 (using the operation subtraction)

⇒8x=94

⇒x=\(\frac{94}{8}\)(using the operation division)

⇒x=11.825

By using the mathematical  operations i.e division and subtraction the value of x came as 11.825

⇒Therefore, The value of x in the given equation i.e \(\frac{16x+12}{2}=100\) is 11.825

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Answer using slope formula:

\(\frac{y2-y1}{x2-x1}\)

We can find the slope.

Substitute:

\(\frac{5-2}{2-1}\)

Subtract:

\(\frac{3}{1}\)

\(\frac{3}{1}= 3\)

Our slope is 3.

Now we will use Point Slope formula:

\(y-y1=m(x-x1)\)

To find our equation.

I will use the first ordered pair, (1,2).

Substitute:

\(y-2=3(x-1)\)

Your answer is C. (y − 2) = 3(x − 1).

Hope this helped! :)

The final two equations which represent the given situation are:

2x - y = -6 and 3x - y = -5.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a linear equation of two variables.

Suppose,

The larger number is 'y' and the smaller number is 'x'.

First relation,

'y' is equal to twice the sum of a smaller number (x) and 3. So we represent this as:

y = 2(x+3)

y = 2x + 6

2x - y = -6                     ............(1)

Second relation,

The larger number (y) is equal to 5 more than 3 times the smaller number (x). So we represent this as:

y = 5 + 3x

3x - y = -5                     .............(2)

Hence, the final two equations which represent the given situation are:

2x - y = -6 and 3x - y = -5.

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Answer: 30 centimeters

Step-by-step explanation:

    We will subtract and then convert units.

2.8 meters less 2.5 meters = 2.8 meters - 2.5 meters = 0.3 meters

0.3 meters * 100 = 30 centimeters

If this problem is not asking for 2.8 meters minus 2.5 meters - and is stating something else - please comment so I can fix my answer.

Answer:

55miles per hour

Step-by-step explanation:

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

5.820640033

10.52810879

23.05597586

Step-by-step explanation:

For the first one use law of sine

\(\frac{x}{\sin(48)}=\frac{6}{\sin(50)}\\x=5.820640033\)

2.)

Solve for angle ABD

98

Next use law of cosine

x²=8²+5.820640033²-2*8*5.820640033*cos(98)

x=10.52810879

now just find the area

.5*8*5.820640033*sin(98)= 23.05597586

20−6√3

Step by step Explanation:

√12+4√25−√108−1/4 √192

2√3+4×5-√108-2√3

2√3+20-√108-2√3

20−6√3

Answer:

the 90th percentile is 9.

The 90th percentile of the distribution is 9.

The 90th percentile of the distribution in the table is 9.

To find the 90th percentile, we need to look at the values of X and their corresponding cumulative percentages (C%). The 90th percentile is the value of X at which 90% of the data falls below.

Looking at the table, we can see that the value of X at the 90th percentile is 9, as it corresponds to a cumulative percentage of 100%. This means that 90% of the data falls below the value of 9.

Therefore, the 90th percentile of the distribution is 9.

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The summation notation calculator is a instrument is frequently referred to as a sigma notation calculator since it makes it simple to calculate the sum of a set of integers, also known as Sigma.

The consecutive addition of a group of numbers is known as a summation. One of the four fundamental arithmetic operations, along with subtraction, multiplication, and division, is addition. For a few numbers, particularly integers, it is easy to do, but with fractions and real numbers, it can be more difficult. This is where our summation calculator might be useful. The numbers can be manually entered or copied and pasted, separated by any non-numerical sign, with the exception of the minus and dot. There are shortcuts for computing the sums of particular sequences.

The lower and upper bounds, a mathematical formula to be used to compute each member of the sum series, and lastly the name of the variable to be used in the sigma expression must all be entered in the "Sigma notation" mode.

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We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:

The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:

Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:

Where (from tables):

Finally, the interval at 98% confidence level is:

Answer:

i dont know i just needed points

Step-by-step explanation:

^^

No, we cannot draw a triangle with sides 3 cm, 3.5 cm, and 6.5 cm.

Let's understand the concept behind this:

Apply the triangle's length-of-sides property, which stipulates that the total of any two sides should be more than the value of the third side. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side.

We must determine whether the supplied side lengths constitute a triangle. We now understand that the triangle's third side should be greater than the sum of any two of its sides. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side. So, we'll try every combination and see if it meets the criteria.

Let’s assume AB = 3 cm, BC = 3.5 cm and AC = 6.5 cm.

AB + AC = 3 + 6.5 cm = 9.5 cm > 3.5 cm = BC.

AC + BC = 6.5 + 3.5 = 10 cm > 3 cm = AB.

AB + BC = 3 + 3.5 cm  = 6.5 cm = AC.

However, in this case, the length of the third side is equal to the total lengths of the other two sides, which renders the triangle's condition incorrect.

Therefore, there does not exist any triangle with sides of 3 cm, 3.5 cm, and 6.5 cm.

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Answer:

\(A= 50\)

\(B = 90^\circ\)

\(C = 50^\circ\)

\(D = 40\)

Step-by-step explanation:

Given

See attachment for gemstone

Required

Determine A, B, C and D

The diagonals of a rhombus meet at \(90\ degrees.\)

So:

\(B = 90^\circ\)

Divide the rhombus into two triangles (upper and lower).

Considering the lower triangle.

Since the two sides are equal (4mm), then the triangle is isosceles.

The base angle of an isosceles triangle \(are\ equal.\)

So:

\(C = 50^\circ\)

Split the lower triangle into two, you get two right-angled triangles.

From one of these triangles, we have:

\(C + D + 90 = 180\)

\(D = 180 - 90 - C\)

\(D = 180 - 90 - 50\)

\(D = 40\)

Lastly, A and C are corresponding angles.

So:

\(A = C\)

\(A= 50\)

The obtained t-value is approximately (b) 3.46.

The obtained t-value can be calculated using the formula:

t = ΣD / (sD / √(n))

where ΣD is the sum of the differences between paired observations, sD is the standard deviation of the differences, and n is the sample size.

Given ΣD = 24, n = 8, and s₂D = 6, we can find sD by taking the square root of s₂D:

sD = √(s₂D) = √(6) ≈ 2.45

Substituting the given values, we get:

t = ΣD / (sD / √(n)) = 24 / (2.45 / √(8)) ≈ 3.46

Therefore, the obtained t-value is approximately (b) 3.46.

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Domain is basically all of x values.

Range is basically all of y values.

That means if you want to find the domain, you can check from the coordinate-x and if you want to find the range, you can check from the coordinate-y.  

As you can see in the graph, there are the colored and non-colored dot. Both present the inequality symbol. If it's a colored circle/dot then it's either ≤ or ≥ but if it is non-colored dot then it's either > or <

From the graph, we can say that the minimum value is at -4 when x = -5

and there is no maximum value considering the x = 1 then y = 7 isn't counted due to being uncolored dot.

As mentioned, Domain is the set of all x values. We check the coordinate-x plane and notice that it begins from x = -5 to x = 1. That means it is -5≤x<1

Remember that the x = 1 one is uncolored so it's either > or < but it is < because 1 has more value than -5. Now we know the domain.

About range, we check coordinate-y plane. It starts from -4 to 7. Therefore, the range is -4≤y<7.

Therefore, Domain is -5≤x<1 and Range is -4≤y<7