Q1 Find the general solution of second order differential equation 4 – 2 – 2y = 2x sinh by using method of undetermined coefficients. (10 marks)

Answer:

7 + 2i is the simplified form

Step-by-step explanation:

Answer:

slop is 0.5 and intercept of y is -3

Answer:

½ is the slope,-3 is the intercept

Step-by-step explanation:

now to find the slope and intercept

we use the equation,

y=mx + c

where m is the slope

and c is the y intercept

so we compare 4y=2x-12 to the equation

but we first have to make y the subject of the equation in the question – 4y is already the subject –

y=2x-12/4

y=2x/4 -3

comparing...

we see that m is 2/4=½ c= -3

She decreased her candy intake by 15%

There are 60,466,176 possible passwords for a system that acknowledges both digits and letters of the alphabet (and does not differentiate between uppercase and lowercase letters) and requires a 5-character password with no repeated characters.

For the purpose of computing the total number of possible passwords, it is necessary to take into account the number of options available for each character position. Within the constraints of the system, there are 10 different options for each number (0-9) and 26 different options for each letter (A-Z).

There are a total of 36 options available to us when it comes to the first character position (26 letters and 10 numerals). We are left with 35 options for the second place because we are unable to recycle any of the characters (36 options, minus the one that has already been used). In a similar fashion, we have 34 options for the third position, 33 options for the fourth position, and 32 options for the fifth position.

To calculate the total number of possible passwords, we multiply the number of choices for each position together: 36 * 35 * 34 * 33 * 32 = 60,466,176. Given the parameters of this system, there are consequently sixty-four million, four hundred sixty-six thousand, one hundred seventy-seven different passwords that might be used.

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Answer: 92.5

So to find median all we have to do is rearange it from low - high and get the middle number

71  81  89  92  93  94  94  99

So take this and you know the middle is right in between 92 and 93

71  81  89  92      |      93  94  94  99

All you have to do then is take the mean of 92 and 93 (so do [92+93]/2)

Answer is 92.5

Answer:

soln,

3/5+7/8+3/10

3×8/5×8+7×5/8×5+3×4/10×4

24/40+35/40+12/40

24+35+12/40

71/40

Answer:

X= 4. Y = 3.

Step-by-step explanation:

If you have a graphing calculator, put the first equation into Y1. And second equation into Y2. Then, find the intersection of the two equations. That's how you find your answer.

1.02 1.05 1.08 1.00 1.00 1.06 1.08 1.01 1.04 1.07 1,00 kg: To test the hypothesis, at 5% significance, that the mean weight for the whole batch is over 1.00 kg, we can perform a one-sample t-test. The null hypothesis (H0) assumes that the mean weight is 1.00 kg, while the alternative hypothesis (H1) assumes that the mean weight is greater than 1.00 kg. By calculating the sample mean, sample standard deviation, and the test statistic, we can compare it with the critical value to determine if there is sufficient evidence to support the alternative hypothesis.

7.4: To test the hypothesis, at 1% significance, that the mean lifetime of electric light bulbs has not changed, we can use a one-sample t-test. The null hypothesis (H0) assumes that the mean lifetime is 1500 hours, while the alternative hypothesis (H1) assumes that the mean lifetime is different from 1500 hours. By calculating the sample mean, known standard deviation, and the test statistic, we can compare it with the critical value to determine if there is enough evidence to reject the null hypothesis.

7.5: To test the hypothesis, at 5% significance, that the drug gives more hours of sleep on average than the control for all patients in the hospital, we can perform a one-sample t-test. The null hypothesis (H0) assumes that there is no difference in the mean hours of sleep between the drug and the control, while the alternative hypothesis (H1) assumes that the drug provides more hours of sleep on average. By calculating the sample mean, sample standard deviation, and the test statistic, we can compare it with the critical value to determine if there is sufficient evidence to support the alternative hypothesis.

7.6: To test the hypothesis, at 1% significance, that the coin is biased, we can use a binomial test. The null hypothesis (H0) assumes that the coin is unbiased (probability of heads = 0.5), while the alternative hypothesis (H1) assumes that the coin is biased. By calculating the number of heads observed, the expected number of heads under the null hypothesis, and the test statistic, we can compare it with the critical value to determine if there is enough evidence to reject the null hypothesis and conclude that the coin is indeed biased.

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Answer:

There is a 8.11% of any randomly selected athlete to test positive.

Step-by-step explanation:

To make it easier, let's assume there are 100 athletes

5/100 have it

3/95 do not have it, but will test positive

1% of the 5 athletes who are using PEDs = 0.05%

This means that 4.95/100 will test positive

3/95 = 3.16%

(rounded, if you need a more precise answer, it's 3.1578947368421053)

3.16% + 4.95% = 8.11%

The work required to pump the water out of the spout is 200000.64 J.

Given, Length of the tank = 8 m

Density of water = 1000 kg/m3

The work required to pump the water out of the spout can be calculated as follows:

Step 1: Consider a layer of water 'dx' thick at a height of 'x' meter above the bottom of the tank.

The volume of this layer is given by,V = Area × height= (8 × x) × dx= 8x dx

The mass of this layer is given by,m = density × volume= 1000 × 8x dx= 8000x dx

The force required to lift this layer of water is given by, F = mg= 8000x dx × 9.8= 78400x dx

Step 2: To find the work done, we need to multiply the force by the distance moved.

The distance moved by this layer of water is given by d, where d = (8 - x).

Therefore, the work done in moving this layer of water is given by, dW = F × d= 78400x dx × (8 - x)= 627200x dx - 78400x² dx

Step 3: The total work done in pumping out all the water is given by the integral of dW from x = 0 to x = 8.

That is,W = ∫dW = ∫₀⁸ (627200x dx - 78400x² dx)= [313600x² - 261333.33x³]₀⁸= 200000.64 J

Therefore, the work required to pump the water out of the spout is 200000.64 J.

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The cross product of vector c and d is equal to (-4,9,13).

The cross product of two vectors a and b in three-dimensional space is a vector that is perpendicular to both a and b and thus normal to the plane containing them. Here, we have to find the cross product of two given vectors. The given vectors are:a = (3, -3, -2) and b = (3, -1, -2)  So, a x b = (4,0,6).The second one is given as: c = (1, -2,-2) and d=(-5,3,-1).

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.

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There will be approximately 320 bacteria in 10 hours.

To determine the number of bacteria in 10 hours, we need to calculate the number of doubling cycles that occur within that time period.

Since the bacteria population doubles every 2 hours, in 10 hours, there will be 10/2 = 5 doubling cycles.

Starting with approximately 5 bacteria, each doubling cycle will result in the population doubling. Therefore, the number of bacteria after 5 doubling cycles can be calculated as follows

5 bacteria * (2^5) = 5 * 32 = 160

Hence, there will be approximately 160 bacteria after 5 doubling cycles or after 10 hours.

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Answer:

909.09

Step-by-step explanation:

400 divided by 44% is about 909.09.

The total area of the regions between the curves is 1/3 square units

The total cost for making the first 10 units is 7.79

From the question, we have the following parameters that can be used in our computation:

y = √x and y = x²

With the use of graphs, the curves intersect at

x = 0 and x = 1

So, the area of the regions between the curves is

Area = ∫x² - √x

Integrate

[tex]Area = \frac{x^3}{3} - \frac{2x^\frac32}{3}[/tex]

Recall that x = 0 and x = 1

So, we have

[tex]Area = (\frac{0^3}{3} - \frac{2 * 0^\frac32}{3}) - (\frac{1^3}{3} - \frac{2 * 1^\frac32}{3} )[/tex]

Evaluate

Area =  0 + 1/3

Evaluate

Area =  1/3

Hence, the total area of the regions between the curves is 1/3 square units

Given that

MC(x) = √(x + 30)

Integrate to calculate the cost function

So, we have

[tex]C(x) = \frac{2}{3}(x + 30)^\frac23[/tex]

For the first 10, x = 10

So, we have

[tex]C(10) = \frac{2}{3}(10 + 30)^\frac23[/tex]

Evaluate

C(10) = 7.79

Hence, the total cost for making the first 10 units is 7.79

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Answer:

1/16

Step-by-step explanation:

Picture is attached. The quickest way is to simplify BEFORE plugging in x = 1/2

Methods to rid a model of multicollinearity include:  Include determination,Collection of data,Variable change,Regression ridge

Multicollinearity in a model can be addressed in a number of ways, including:

Include determination: Eliminating at least one connected factors can assist with mitigating multicollinearity. Stepwise regression or LASSO regression can be used to select the most important features by analyzing the correlation matrix.

Collection of data: By introducing variation in the predictors, more diverse and independent data can help reduce multicollinearity. Expanding test size can likewise help in relieving multicollinearity impacts.

Variable change: Multicollinearity can be reduced by transforming variables using centering, standardization, or power or logarithmic transformations. These changes change the scale or type of the factors, making them less associated.

Regression ridge: By adding a penalty term to the least squares estimation, ridge regression reduces the impact of multicollinearity and reduces the coefficients. This regularization method balances out the appraisals and works on model execution.

PCA, or Principal Component Analysis,: PCA can be used to generate uncorrelated linear combinations of the starting variables. These new factors, known as head parts, can be utilized as indicators in the model, successfully lessening multicollinearity.

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Answer:

Parallel: y = -2x + 2 (Or any value that isn't 4), Perpendicular: 1/2x + (Anything),

Neither: y = 4x - 7 (Or any random equation that does not have the same, or opposite reciprocal slope)

Step-by-step explanation:

Answer:

the yield is 7.68%

Step-by-step explanation:

The calculation of the yield is given  below:

we know that

Yield is

= Annual dividend ÷ Price per share

= $4.15 ÷ $54

= 7.68%

Here we divide the annual dividend by the price per share in order to determine the yield  

hence, the yield is 7.68%  

And, the same would be considered

Answer:

B -- (5 smoothings)(price of 1 smoothie) + tip = $23

Step-by-step explanation:

5 smoothies(price of 1 smoothie)+tip=23

Answer:

2 3 5 7

Step-by-step explanation:

The basis for Ker(T) is {}, and the basis for Im(T) is {1}.

Since, The kernel of T, denoted Ker(T), is the set of all elements in P₂ that are mapped to zero in R by T.

In other words, Ker(T) is the set of all polynomials in P₂ such that

T(p(x)) = p(1) = 0.

Hence, To find the kernel, we need to solve the equation p(1) = 0.

Since, The only polynomial that satisfies this condition is p(x) = 0.

Therefore, Ker(T) = {0}.

Now, the image of T.

The image of T is the set of all elements in R that are mapped to by some element in P₂ under T.

In other words, Im(T) is the set of all possible values of p(1) for all polynomials p(x) in P₂.

Some example: - If p(x) = 1 + 2x + x², then p(1) = 1 + 2 + 1 = 4.

So, we can see that Im(T) is the set of all real numbers.

Hence, the basis for the kernel and image of T.

Since Ker(T) = {0}, the basis for the kernel is the empty set, denoted by {}.

Since Im(T) is the set of all real numbers, any non-zero real number can be expressed as a scalar multiple of any other non-zero real number.

Therefore, the basis for Ker(T) is {}, and the basis for Im(T) is {1}.

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Null hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. Alternative hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.

The median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605.

The median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.As per the given question, Central Airlines claims that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. But, this claim is being challenged by the Association of Travel Agents, who believes that the median price is less than $605. Hence, we need to test whether the median price is less than $605 or not.Hence,Null hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. Alternative hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.

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Answer:

y=3x

Step-by-step explanation:

73.1 A(C2) is a quadrilateral with vertices (0, 0), (1, 0), (1, 2), and (0, 2).

73.2 The area of A(C2) is 2.

73.3 The determinant of A is 0

To draw C2 and A(C2),  to understand the transformation A and to the unit square.

Given the information:

A:

| 1 0 |

| 2 0 |

A maps the vector [1, 0] to [2, 0], and it maps the vector [0, 1] to [1, 1]. This provides us with the information to draw C2 and A(C2).

73.1 Draw C2 and A(C2):

C2 represents the unit square with vertices (0, 0), (1, 0), (1, 1), and (0, 1).

To draw A(C2), the transformation A to each vertex of C2 and connect the transformed vertices to form the image of C2 under A.

Applying A to the vertices of C2:

A(0, 0) = (1 × 0, 2 × 0) = (0, 0)

A(1, 0) = (1 × 1, 2 × 0) = (1, 0)

A(1, 1) = (1 × 1, 2 × 1) = (1, 2)

A(0, 1) = (1 × 0, 2 × 1) = (0, 2)

Connecting the transformed vertices, we get the image of C2 under A:

73.2 Compute the area of A(C2):

To compute the area of A(C2),  divide it into two triangles and calculate their areas separately.

Triangle 1: (0, 0), (1, 0), (1, 2)

Base of Triangle 1 = 1 - 0 = 1

Height of Triangle 1 = 2 - 0 = 2

Area of Triangle 1 = (1/2) × Base × Height = (1/2) × 1× 2 = 1

Triangle 2: (0, 0), (0, 2), (1, 2)

Base of Triangle 2 = 1 - 0 = 1

Height of Triangle 2 = 2 - 0 = 2

Area of Triangle 2 = (1/2) × Base × Height = (1/2) × 1 × 2 = 1

Total Area of A(C2) = Area of Triangle 1 + Area of Triangle 2 = 1 + 1 = 2

73.3 Compute det(A):

To compute the determinant of A (denoted as det(A)), use the formula for a 2x2 matrix.

A:

| 1 0 |

| 2 0 |

det(A) = (1 ×0) - (0 × 2) = 0 - 0 = 0

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Answer:

Y = 10 I believe

Step-by-step explanation:

To solve this we need to find what number, times 6, equals 18 - it's fairly easy to find the answer is three.

So what, minus seven, equals 3?

Answer:

Depends on the state you’re from

Step-by-step explanation:

Answer:

Yes you can! Grades from middle school don't matter when you get to high school. But try to get those grades up!

Answer:

7 books

Step-by-step explanation:

i cant write it in an equaction but basically 25 - 2 = 23

then 3 x 7 = 21 so he can only buy 7 books and he'll have 2 dollars left

Answer:

There are 30 days according to the Georgian calender of the month of april.

Step-by-step explanation:

Answer:

sorry

Step-by-step explanation:

Answer:

3 inches

Step-by-step explanation:

got it right on edg