Q4 Find the general solution of the second order differential equation y" – 54 +6 = 42 sec z. (10 marks)

Answer:5.83

Step-by-step explanation:

Answer:

True the product of a number and its reciprocal is equal to one.

Step-by-step explanation:

let the number be X

Now the reciprocal will be 1/X

And when we multiply them

X ×1 /X = 1

(a) A1 and A2 are not mutually exclusive because the probability of their intersection, P(A1∩A2), is not equal to zero.

(b) To compute P(A1∩B) and P(A2∩B), we can use the formula:

P(A∩B) = P(A) * P(B|A)

For A1∩B:

P(A1∩B) = P(A1) * P(B|A1)

        = 0.30 * 0.05

        = 0.015

For A2∩B:

P(A2∩B) = P(A2) * P(B|A2)

        = 0.70 * 0.20

        = 0.140

Therefore, P(A1∩B) = 0.015 and P(A2∩B) = 0.140.

(c) To compute P(B), we can use the law of total probability:

P(B) = P(B|A1) * P(A1) + P(B|A2) * P(A2)

Given that P(B|A1) = 0.05, P(A1) = 0.30, P(B|A2) = 0.20, and P(A2) = 0.70, we can substitute these values into the equation:

P(B) = 0.05 * 0.30 + 0.20 * 0.70

    = 0.015 + 0.140

    = 0.155

Therefore, P(B) = 0.155.

(d) Applying Bayes' theorem, we can compute P(A1|B) and P(A2|B):

P(A1|B) = (P(B|A1) * P(A1)) / P(B)

       = (0.05 * 0.30) / 0.155

       ≈ 0.097

P(A2|B) = (P(B|A2) * P(A2)) / P(B)

       = (0.20 * 0.70) / 0.155

       ≈ 0.903

Therefore, P(A1|B) ≈ 0.097 and P(A2|B) ≈ 0.903.

To explain the results in more detail, let's summarize the information in a table:

| Event | Prior Probability (P) | Conditional Probability (P(B|A)) |

| A1       | 0.30                         | 0.05                           |

| A2      | 0.70                         | 0.20                           |

We know that A1 and A2 are not mutually exclusive because P(A1∩A2) = 0. The table also shows the conditional probabilities of event B given A1 and A2.

To compute P(A1∩B) and P(A2∩B), we use the formula P(A∩B) = P(A) * P(B|A). Plugging in the values from the table, we find P(A1∩B) = 0.015 and P(A2∩B) = 0.140.

Next, we compute P(B) using the law of total probability, which considers the probabilities of B given A1 and A2, as well as the prior probabilities of A1 and A2. In this case, P(B) is found to be 0.155.

Finally, applying Bayes' theorem, we can determine the posterior probabilities of A1 and A2 given

B. Using the formula P(A|B) = (P(B|A) * P(A)) / P(B), we calculate P(A1|B) ≈ 0.097 and P(A2|B) ≈ 0.903.

These results demonstrate how conditional probabilities and Bayes' theorem can be used to update prior probabilities based on new information, in this case, the occurrence of event B.

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Answer:

question 1 isn't formatted properly, for question 2, k=-2

Step-by-step explanation:

5k-8+2=-16

5k-6=-16

5k=-10

k=-2

Answer:

7 + 5 = 12

Step-by-step explanation:

7 steps plus 5 steps equals 12 steps

Answer:

the desired equation is y = – 4x + 3

Step-by-step explanation:

Parallel lines have the same slope and thus similar equations.   Thus, the equation of a line parallel to the given line has the form y = – 4x  + C.  We need only find C.

The new line goes through (2, -5), and so we substitute 2 for x and -5 for y to obtain

-5 = – 4(2) + C.  Then -5 + 8 = C, or C = 3.

Then the desired equation is y = – 4x + 3

To find the three points that divide the line segment joining (x1,y1) and (x2,y2) into four equal parts, we can use the midpoint method three times.

First, let's find the midpoint between (x1,y1) and (x2,y2) using the midpoint formula:
midpoint1 = ((x1 + x2) / 2, (y1 + y2) / 2)

Next, we will find the midpoint between (x1,y1) and midpoint1:
midpoint2 = ((x1 + midpoint1[0]) / 2, (y1 + midpoint1[1]) / 2)

Lastly, we will find the midpoint between midpoint1 and (x2,y2):
midpoint3 = ((midpoint1[0] + x2) / 2, (midpoint1[1] + y2) / 2)

These three midpoints, midpoint1, midpoint2, and midpoint3, divide the line segment into four equal parts.

For example, if we have the points (2,4) and (10,8), the steps would be as follows:
1. Find the midpoint between (2,4) and (10,8):
  midpoint1 = ((2 + 10) / 2, (4 + 8) / 2)
            = (6, 6)
2. Find the midpoint between (2,4) and (6,6):
  midpoint2 = ((2 + 6) / 2, (4 + 6) / 2)
            = (4, 5)
3. Find the midpoint between (6,6) and (10,8):
  midpoint3 = ((6 + 10) / 2, (6 + 8) / 2)
            = (8, 7)

So, the three points that divide the line segment into four equal parts are (6, 6), (4, 5), and (8, 7).

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Answer:

$72,000

Step-by-step explanation:

Since, a jewelry store bought 8 beautiful diamond necklaces and each cost $9,000 that means;

1 = $9,000

2 = $18,000

3 = $27,000

4 = $36,000

5 = $45,000

6 = $54,000

7 = $63,000

8  = $72,000

or to summarize;

9,000 x 8 = $72,000

As a result, the jewelry store spend $72,000 on the necklaces.

RevyBreeze

The probability that a salesperson selected at random has above-average sales ability and has excellent potential for advancement is 0.27.

Probability simply means the likelihood that an event will occur.

In this case, the data for the 500 sampled salespeople are summarized in the table.

The probability that the person has above-average sales ability and has excellent potential for advancement will be:

= Number of people that above-average sales ability and has excellent potential for advancement / Total number of people

= 135 / 500

= 0.27

The probability is 0.27.

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Answer:

Step-by-step explanation:

√80 = √(2⁴ × 5) = √2⁴ × √5 = 4√5

5 × 8√80 = 160√5

Hayley will travel from Telford Central to Shrewsbury in 0 hours and 21 minutes if she takes the quickest route.

Based on the timetable provided, the fastest option for Hayley to get from Telford Central to Shrewsbury is by taking the 0915 train from Wellington to Shrewsbury, which arrives at 0920. Therefore, the total time it will take her is 21 minutes (from 0805 departure of Wellington to 0920 arrival in Shrewsbury).

To convert 21 minutes to hours and minutes, divide 21 by 60 to get the decimal value of 0.35 hours. Then convert the decimal value to minutes by multiplying it by 60, which gives:

0.35 hours × 60 = 21 minutes

So, it will take Hayley 0 hours and 21 minutes to get from Telford Central to Shrewsbury taking the fastest option.

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Answer:

70.132,70

Step-by-step explanation:

68.090,00

+ 2.042,70

_________

70.132,70

Answer:

The rigid transformation, which does not change the shape or size of the preimage. The non-rigid transformation, which will change the size but not the shape of the preimage.

Step-by-step explanation:

Answer:

A tranformation is rigid if it preserves the shape and size of the object. If the object changes its shape, or if the object changes its size under the transformation, then the transformation is not rigid

Step-by-step explanation:

The probability that exactly three out of two hundred randomly chosen individuals will have the disease is approximately 0.1668 or 16.68%.

To solve this problem, we need to use the binomial distribution formula. The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant.

In this case, the probability of success is 1.2%, which is equivalent to 0.012. The number of trials is 200, and we want to know the probability of exactly three successes.

The formula for the probability of exactly k successes in n trials is:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

where "n choose k" represents the number of ways to choose k items from a set of n items, and p is the probability of success.

Using this formula and plugging in the values we have, we get:

P(3) = (200 choose 3) * 0.012^3 * (1-0.012)^(200-3)

P(3) = (200! / (3! * 197!)) * 0.012^3 * 0.988^197

P(3) = 0.1668

Therefore, the probability that exactly three out of two hundred randomly chosen individuals will have the disease is approximately 0.1668 or 16.68%. This means that if we were to repeat this experiment many times, we would expect to see about 16.68% of the time that exactly three people out of two hundred have the disease.

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The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

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Complete Question:-

False. To obtain a representative sample, it is not necessary to sample a large fraction of the population.

The representativeness of a sample depends on its ability to accurately reflect the characteristics and variability of the population it is drawn from. The size of the sample required for representativeness is determined by the level of precision desired and the inherent variability within the population.

Sampling a large fraction of the population, also known as a census, is one way to achieve representativeness, but it is often impractical, time-consuming, and costly. Instead, researchers often use statistical techniques to select a smaller subset of the population that can still provide accurate estimates.

The key factor in obtaining a representative sample is the use of random sampling techniques, such as simple random sampling or stratified sampling, which ensure that every individual in the population has an equal chance of being included in the sample. By using appropriate sampling methods and considering the variability within the population, it is possible to obtain a representative sample without sampling a large fraction of the population.

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The correct statement(s) regarding error control is b. error correction is used to correct data errors. Error control is the process of detecting errors in data that is transmitted from one system to another, and then correcting the errors to ensure that the data is accurate.

It is important for ensuring that data is transmitted accurately, especially in situations where data loss could have serious consequences.

Here are the explanations to the statements: a. error detection is used to detect data errors, but not to correct them- False. Error detection refers to the process of detecting errors in data, but not correcting them.

b. error correction is used to correct data errors- True. Error correction is used to detect and correct errors in data.

c. error control methods only give us a probability that bit errors can be either detected and/or corrected- False.

Error control methods can both detect and correct errors in data with a high degree of accuracy.d. all statements are correct- False. Only statement b is correct.

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The percentage of value-added time in a trip to the emergency room is 15.83%.

Given the following data:

Time taken by triage nurse before assessment = 14 minutes

Average time taken for assessment by triage nurse = 5 minutes

Time taken before examination room = 79 minutes

Time taken in the examination room for vitals and notes by nurse = 11 minutes

Time taken before the doctor sees the patient = 22 minutes

Average time taken by the doctor for treatment = 17 minutes

Time taken for the nurse to come to discuss post-treatment instructions = 6 minutes

Time taken to review the instructions with the patient = 4 minutes

Let us first calculate the total time taken,

Total Time = Time before examination room + time in examination room + time after treatment + time taken by the triage nurse

Total Time = 79 + 11 + 22 + 17 + 6 + 4

                  = 139 minutes

Now, let us calculate the total time spent on assessment and treatment.

This will include the time taken by the triage nurse and the doctor.

Total Time Spent on Assessment and Treatment = Time taken by triage nurse + time taken by the doctor

Total Time Spent on Assessment and Treatment = 5 + 17

                                                                                  = 22 minutes

Now, we can calculate the percentage of value-added time as follows,

Percentage of Value-Added Time = Total Time Spent on Assessment and Treatment / Total Time * 100

Percentage of Value-Added Time = 22 / 139 * 100

Percentage of Value-Added Time = 15.83%

Therefore, the percentage of value-added time in a trip to the emergency room is 15.83%.

Rounding off this value to 2 decimal places, we get the final answer as 15.83%.

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Answer:

x=5

Step-by-step explanation:

Answer:

no

no

Step-by-step explanation:

20 beats heard by 4 second using fork

Answer:

Equivalent

Step-by-step explanation:

Decide whether the given rates (not estes) are equal.  Do do this, divide the number of beats by the number of seconds, in each case, separately:

30/20 beats/second = 1.5 beats/second

90/60 beats/second= 1.5 beats/second

These two rates are equivalent.

Answer:

B is the closet to pi hsiebfjwjgsbe9fbe

The angle between the lines with slopes -1 and 0 is 45 degrees (or π/4 radians).

To find the angle between two lines given their slopes, we can use the formula:

θ = atan(|(m1 - m2) / (1 + m1 * m2)|)

where m1 and m2 are the slopes of the two lines.

In this case, we have two lines with slopes -1 and 0.

Let's calculate the angle:

θ = atan(|(-1 - 0) / (1 + (-1) * 0)|)

= atan(|-1 / 1|)

= atan(1)

The arctangent of 1 is 45 degrees (or π/4 radians).

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Answer:

D. 5/1

Step-by-step explanation:

10/2 = 5

5/1 = 5

I hope this helps :)

The number of weeks when the tanks have same water is 64 weeks.

The equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation for the first tank will be 256 - 3g.

The equation for the second tank will be 385 - 5g.

The equation will be:

256 - 3g = 385 - 5g

Collect like terms

5g - 3g = 384 - 256

2g = 128

g = 128/2

g = 64

It'll take 64 weeks.

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Answer:

1/4 or 0.25

Step-by-step explanation:

Let W be the inverse of AB. Then WAB = I and (WA)B = l. Therefore, matrix B is invertible by part (j) of the IMT by letting C = WA.

We have A and B are two n × n matrices and AB is invertible. We have to prove that B is invertible by showing a valid reason given by one of the four options:

Option (a) False:

The first option is not valid proof. since W is the inverse of A B would imply WAB = I, as multiplying a matrix by its inverse will produce the identity matrix of the corresponding order. Here stated that WAB = B, which is invalid.

Option (b) False:

It is true that AB invertible implies \($(A B)^{\top}$\) is invertible but this does not imply B is invertible (not a valid statement).

Option (c) False:

A B is invertible does not mean \($A=B^{-1}$\). Since \($A=B^{-1}$\) implies AB = I, but AB need not be only the identity matrix. So these statements are invalid.

Option (d) True:

W being inverse of AB, this gives WAB = I

(WA) B = I since matrix multiplication is associative.

WA is the inverse of B, as multiplying WA by B produces the identity matrix I. Hence, this is valid proof to show that B is invertible.

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