please solve Q4
Question 4. Find the derivative of f(x) = 2x e3x Question 5. Find f(x)

If all of the discretionary expenses are eliminated, there would be $569.56 per month available to put towards savings.

What is meant by expenses?

Expenses refer to the costs or expenditures incurred in the course of doing business or any other activity. They are typically measured in monetary terms and can include items such as supplies, rent, wages, and other operating costs.

What is meant by savings?

Savings refer to the amount of money that is not spent or used for consumption after accounting for expenses. It can be calculated by subtracting total expenses from total income and is often used as a measure of financial stability or success.

According to the given information

First, let's calculate the total income for one week of work:

Hourly pay: $12.75/hr

Weekly hours worked: 45 hr/wk

Regular pay = Hourly pay x Weekly hours worked = $12.75 x 45 = $573.75

Now, let's calculate the deductions:

FICA: 6.65% of $573.75 = $38.17

Federal tax withholding: 9.75% of $573.75 = $55.91

State tax withholding: 6.5% of $573.75 = $37.28

Total deductions = $38.17 + $55.91 + $37.28 = $131.36

So the total realized income for one week of work is:

Realized income = Regular pay - Total deductions = $573.75 - $131.36 = $442.39

Since a month is assumed to be 4 weeks, the total realized income for one month is:

Total realized income = Realized income x 4 = $442.39 x 4 = $1769.56

Assuming fixed expenses of $1200 per month, the discretionary expenses are:

Discretionary expenses = Total realized income - Fixed expenses = $1769.56 - $1200 = $569.56

Next, let's calculate the total income for the next month, assuming you work 22 hours of overtime and are paid 1.5 times your regular rate for only the overtime pay:

Overtime pay rate: $12.75 x 1.5 = $19.13/hr

Overtime hours: 22 hr

Regular hours: 45 hr

Regular pay = $12.75 x 45 = $573.75

Overtime pay = $19.13 x 22 = $420.86

Total income = Regular pay + Overtime pay = $573.75 + $420.86 = $994.61

Now, let's calculate the deductions for the next month:

FICA: 6.65% of $994.61 = $66.11

Federal tax withholding: 9.75% of $994.61 = $97.03

State tax withholding: 6.5% of $994.61 = $64.65

Total deductions = $66.11 + $97.03 + $64.65 = $227.79

So the total realized income for the next month is:

Realized income = Total income - Total deductions = $994.61 - $227.79 = $766.82

Assuming the same fixed expenses of $1200 per month, the discretionary expenses are:

Discretionary expenses = Total realized income - Fixed expenses = $766.82 - $1200 = -$433.18

Since the discretionary expenses are negative, it means there is not enough money to cover them. In this case, it would be necessary to cut down on discretionary expenses or find ways to increase income.

Finally, let's assume that the discretionary expenses are eliminated. The total realized income would be:

Total realized income = Realized income - Discretionary expenses = $1769.56 - $569.56 = $1200

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Answer:

12 = 2 × 2 × 3

48 = 3 × 2 × 2 × 2 × 2

60 = 3 × 2 × 5 × 2

Thus HCF = 2 × 2× 3 = 12

Answer: the answer is 12 hope it helps

Step-by-step explanation:

x > 6

Hi there !

1/2 x + ²⁾3 < ²⁾2x - ²⁾6

x + 6 < 4x - 12

6 + 12 < 4x - x

18 < 3x

3x > 18

x > 18/3

x > 6

Good luck !

Answer:

\(\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}\)

Step-by-step explanation:

Given

\(p = 60\%\)

\(n = 4\)

Required

The distribution of x

The above is an illustration of binomial theorem where:

\(P(x) = ^nC_x * p^x *(1 - p)^{n-x}\)

This gives:

\(P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}\)

Express percentage as decimal

\(P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}\)

\(P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}\)

When x = 0, we have:

\(P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}\)

\(P(x=0) = 1 * 1 *(0.40)^4\)

\(P(x=0) = 0.0256\)

When x = 1

\(P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}\)

\(P(x=1) = 4 * (0.60) *(0.40)^3\)

\(P(x=1) = 0.1536\)

When x = 2

\(P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}\)

\(P(x=2) = 6 * (0.60)^2 *(0.40)^2\)

\(P(x=2) = 0.3456\)

When x = 3

\(P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}\)

\(P(x=3) = 4 * (0.60)^3 *(0.40)\)

\(P(x=3) = 0.3456\)

When x = 4

\(P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}\)

\(P(x=4) = 1 * (0.60)^4 *(0.40)^0\)

\(P(x=4) = 0.1296\)

So, the probability distribution is:

\(\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}\)

1. This task would likely be framed as a supervised learning problem

2. This task would also be framed as a supervised learning problem.

3. This task would typically be framed as an unsupervised learning problem.

4. This task would likely be framed as a regression problem since the goal is to estimate the repair time,

5. This task can be considered as an unsupervised learning problem.

Deciding whether to issue a loan to an applicant based on demographic and financial data (with reference to a database of similar data on prior customers):

This task would likely be framed as a supervised learning problem. The goal is to predict whether to approve or reject a loan application based on the given data. Hence, it can be considered a classification problem.

In an online bookstore, making recommendations to customers concerning additional items to buy based on the buying patterns in prior transactions:

This task would also be framed as a supervised learning problem. The goal is to recommend additional items to customers based on their buying patterns. It can be approached as a recommendation system using collaborative filtering techniques, which involve predicting customer preferences. This can be considered a classification problem.

Identifying segments of similar customers:

This task would typically be framed as an unsupervised learning problem. The objective is to identify groups or clusters of similar customers based on their attributes or behaviors. Unsupervised learning algorithms such as clustering can be used to accomplish this task.

Estimating the repair time required for an aircraft based on a trouble ticket:

This task would likely be framed as a regression problem since the goal is to estimate the repair time, which is a continuous variable. Supervised learning techniques such as regression algorithms can be employed to predict the repair time based on the provided input features.

Automated sorting of mail by zip code scanning:

This task can be considered as an unsupervised learning problem. The aim is to sort mail based on zip codes, which involves grouping similar items together. Unsupervised learning algorithms like clustering can be utilized to identify patterns and group the mail accordingly.

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We are given that there are 112 sixth graders .

In order to estimate the 47% let us first find the following :

10 % of 112 is about 11.2 , we get this by saying

10 /100 x 112 = 0.1 * 112 = 11.2.

so, if 10 % is 11.2 ; then

20 % is 11.2 x 2 = 22.4

30 % is 11.2 x 3 = 33.6

40 % is 11.2 x4 = 44.8

50 % is 11.2 x 5 = 56

Now lets make an estimation :

since we have 40 % = 44.8 and 50 % = 56 ,

47 % is much more closer to 50 % than it is to 40 %

Therefore, 47 % will be around 56 sixth graders .

Answer:

\(\huge\boxed{x=-1;\ y=-1.5}\)

Step-by-step explanation:

\(\left\{\begin{array}{ccc}-2x+y=3.5\\-2y=3x&\text{divide both sides by (-2)}\end{array}\right\\\left\{\begin{array}{ccc}-2x+y=3.5&(1)\\y=-1.5x&(2)\end{array}\right\\\\\\\text{Substitute (2) to 1):}\\-2x+(-1.5x)=3.5\\-2x-1.5x=3.5\qquad\text{combine like terms}\\-3.5x=3.5\qquad\text{divide both sides by (-3.5)}\\\dfrac{-3.5x}{-3.5}=\dfrac{3.5}{-3.5}\\\boxed{x=-1}\\\\\text{Substitute it to (2):}\\y=1.5(-1)\\\boxed{y=-1.5}\)

Answer:

0.76

or

-0.76

hope this helps

The solution to the system is (3, 17)

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

y 3x 8y 5x 2

Express properly

So, we have

y = 3x + 8

y = 5x + 2

Subtract the equations

So, we have

2x - 6 = 0

Evaluate the like terms

2x = 6

So, we have

x = 3

Substitute x = 3 in y = 3x + 8

y = 3 x 3 + 8

Evaluate

y = 17

Hence, the solution is x = 3 and y - 17

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Answer:

y = 3(x-1) + 3

This is because the 1 equals h in this equation and 3 equals k, which will give you the point (1,3)

Answer: B

Explanation: The range is a set or a range of y-values of a function. In the graph, the y-value points are -7, -4, 1, 3, and 7. So, the answer is B.

:)

Answer:

the g (7) - value

Step-by-step explanation:

sana maka tulong

The solution to the differential equation y' + 3y = f(t), y(0) = α using Laplace transforms is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).

We use the Laplace transform on both sides of the problem in order to solve the given differential equation. Let Y(s) and F(s) represent the Laplace transforms of y(t) and f(t), respectively. Taking the Laplace transform of both sides of the equation, we have:

sY(s) - y(0) + 3Y(s) = F(s)

Substituting y(0) = α, we get,

sY(s) - α + 3Y(s) = F(s)

Rearranging the equation and solving for Y(s), we have,

Y(s) = (F(s) + α)/(s + 3)

Now, we need to find the inverse Laplace transform of Y(s) to obtain y(t). Using the properties of Laplace transforms, we know that the inverse Laplace transform of Y(s) is y(t) = L⁻¹{Y(s)}. Applying the inverse Laplace transform, we find,

y(t) = αe⁻³ᵗ + L⁻¹{F(s)/(s+3)}

The term αe⁻³ᵗ corresponds to the initial condition y(0) = α. The remaining term L⁻¹{F(s)/(s+3)} represents the inverse Laplace transform of F(s)/(s+3), which depends on the specific function f(t) and its Laplace transform.

Therefore, the solution to the differential equation is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).

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The solution for x in the triangles is 9

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

The triangles

From the figure, we have the following ratio

3x - 6 : 15 = 77 : 55

Express as fraction

This gives

(3x - 6)/15 = 77/55

So, we have

(x - 2)/5 = 7/5

Multiply

x - 2 = 7

Add 2 to both sides

x = 9

Hence, the value of x is 9

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The equation of the new function g(x) is g(x) = 2 - |x+2|

Transformation is. way of changing the position of an object on an xy-plane.

Given the parent function  f(x) = |x+3|.

If the function is translated 2 units down and 1 unit right, then the resulting function will be |x+3 - 1| - 2 which is equivalent to  |x+2| - 2

The reflection of the resulting function across the x-axis is given as:

g(x) = -(|x+2|-2)

g(x) = 2 - |x+2|

Hence the new function g(x) if the parent function undergo the transformation is g(x) = 2 - |x+2|

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The mean of the sampling distribution of sample means for a sample of size 150 is approximately 81, and the standard deviation is approximately 2.0.

In order to compute the mean and standard deviation of the sampling distribution, we can use the properties of the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample means will be approximately normally distributed, regardless of the shape of the population distribution. The mean of the sampling distribution will be equal to the mean of the population, which in this case is 81.

The standard deviation of the sampling distribution, also known as the standard error, can be calculated by dividing the standard deviation of the population by the square root of the sample size. In this case, the standard deviation of the population is 25, and the sample size is 150. Therefore, the standard deviation of the sampling distribution is 25 / √150, which is approximately 2.0.

This means that if Mary takes multiple random samples of size 150 from the population of similar businesses and calculates the mean startup costs for each sample, the distribution of those sample means will have a mean of 81 and a standard deviation of 2.0. By comparing the mean of her sample to the mean of the sampling distribution, Mary can assess how her online startup costs compare to the known population mean.

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Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer: 59049 or 4.64

Step-by-step explanation: 59049 is the answer to 3^sqrt(100), but I wasn't totally sure if you meant ^3sqrt(100) or not so I solved both.

3^sqrt(100) = 59048

^3sqrt(100) = 4.64158

Based on the given confidence interval, there is evidence to support the claim that the true average echo duration of lightning flashes is 0.8 seconds.

To determine if the evidence supports the claim that the true average echo duration of lightning flashes is 0.8 seconds, we need to check if the value 0.8 falls within the confidence interval.

The 95% two-sided confidence interval for the true average echo duration is (0.743, 0.877). Since the value 0.8 falls within this interval, it means that the true average echo duration of lightning flashes of 0.8 seconds is within the range of values that is supported by the data.

Therefore, based on the given confidence interval, there is evidence to support the claim that the true average echo duration of lightning flashes is 0.8 seconds.

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Based on the given statements, the correct statement is: Some wolves eat sheep, and all sheep eat grass. Dead grass is always brown, while living grass can be green or yellow.

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Based on the logical statements given, none of the statements can be confirmed as correct from the information available.

A logical statement is a statement that can be assigned a truth value, either true or false. Logical statements are used in logic and mathematics to represent information and to make inferences.

In the given question, based of the statements given, we can evaluate the following options to determine which one is correct:

1. All wolves eat sheep.

2. All grass is green.

3. All sheep are brown when dead.

Let's analyze each statement:

1. All wolves eat sheep.

  Based on the given information, there is no explicit statement indicating that all wolves eat sheep. It only mentions that "some wolves eat sheep." Therefore, statement 1 is not necessarily correct.

2. All grass is green.

  The given information states that "some grass is green, some grass is yellow," which means that not all grass is green. Therefore, statement 2 is not correct.

3. All sheep are brown when dead.

  The given information does not provide any direct statement about the color of sheep when they are dead. It only mentions that "all dead grass is brown." Therefore, statement 3 is not supported by the given information.

Based on the analysis, none of the given statements can be confirmed as correct based solely on the provided information.

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Answer:

4pi/15=θ  - i think

Step-by-step explanation:

S = r*θ

r=9

s=12pi/5

12pi/5=9*θ

12pi/45=θ

4pi/15=θ

in a class of 12 boys and 9 girls, the teacher selects three students at random to write problems on the board then the probability that all the students selected are boys is 0.165

given that a class consists of 12 boys and 9 girls. The teacher picks three students to present their work to the rest of the class  and says that the three students are being selected at random

Here selecting any 3 students from the group of total 21 students is combination because order does not matter.

Total no of ways of selecting any 3 from total 21 = 21C3 = 1330

No of ways of selecting only 3 boys = No of ways of selecting random 3 boys from total 12 boys

= 12C3 =220

the probability be that all three students

selected are boys=220/1330 = 0.165

Hence , the probability that all the students selected are boys is 0.165

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Answer:

To three decimal places, The process capability index is 0.167

Step-by-step explanation:

We have to find the process capability index,

Upper specification = 16.5 ounces,

Lowe specification = 15.5 ounces

Mean = 16.0 ounces

Standard Deviation = S = 1 ounce

process capability index = (upper specification - lower specification)/6S

process capability index = (16.5 - 15.5)/6(1)

= 1/6

Process capability index = 1/6 = 0.16666667

To 3 decimal places, we get,

Process capability index = 0.167

Answer:

(x-3) (x+1)

Step-by-step explanation:

Factor

x^2 − 2x + 3

What two numbers multiply to 3 and add to -2

3 and -1

(x-3) (x+1)

Let's find a set of parametric equations for the rectangular equation y = 5(x - 1)² given that t = 1 at (3, 20).To do this, we'll assume that x and y are both functions of t. Therefore, let's substitute x = x(t) and y = y(t) in the given rectangular equation.

We need to find the values of a, b, and c such that this expression matches with y = 5(x - 1)², and also satisfies the condition that t = 1 at (3, 20). Let's equate both expressions\(y = 5(a²t⁴ + 2abt³ + (a²b² + 2ac - 2a)t² + (abc - ab - a)t + ac² - 2bc + 1)y = 5(x - 1)²y = 5[(at² + bt + c) - 1]²y = 5(at² + 2bt + (b² - 2b + 1))y = 5at² + 10bt + 5(b² - 2b + 1)-----(2)\)Comparing the coefficients of t² and t in equations (1) and (2), we get:a²b² + 2ac - 2a = b² - 2b + 1abc - ab - a = 10bDividing both sides of the second equation by a, we get:b²c - bc - 10 = 0

Multiplying the first equation by 4a, we get:\(4a³b² + 8a²c - 8a² = 4b²a² - 8ba² + 4a²a²b² + 8a³c - 8a³\)Multiplying the second equation by 2a, we get:2abc - 2ab - 2a = 20b Substituting b from this equation in the first equation, we get:4a³b² + 8a²c - 8a² = 4a²a²b² - 16ba² + 8a³c - 8a³4a²b² + 8ac - 8a = a²b² - 4b + 2a³c - 2a³Dividing both sides by 4a, we get:a²b²/4 + 2ac/a - 2 = a²a²b²/4 - ba + a³c - a³/2

Now, let's substitute a = 1, since t = 1 when x = 3. Therefore, we have:b²/4 + 2c - 2 = b²/4 - b + c - 1/2b = 9 - 2cSubstituting this value of b in equation (1), we get:3 = a + (9 - 2c) + c3 = a + 10 - c So, a - c = -7Substituting a = 1 in equation (2), we get:

y = 5t² + 20t - 15Therefore, the set of parametric equations for the rectangular equation y = 5(x - 1)² if t = 1 at (3, 20) is:

x = t² + 2t + 1y = 5t² + 20t - 15

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The income minus expenses is $4,000, so we spend less than we earn.

Income is anything that we obtain or get, usually from wages, gifts, or allowances.

Expenses are anything that we spend to get something that we want such as spend on food, housing, savings, transportation, utilities, or any personal expenses.

For example, we can compute income and expenses below

So the total income is $16,000 and the total expense is $12,000. Then the income - expense is $4,000. So we spend less than we earn.

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The answer is (B). There are 14 possible heights for the tower in the shape of a rectangular prism by using the sum of an arithmetic series.

To find the possible heights, we need to add up the heights of each of the four blocks, which are 6, 6, 3, and 3. Then we can use the formula for the sum of an arithmetic series to find the number of possible heights:

S = (n/2)(a1 + an)

where S is the sum of the heights, n is the number of terms (in this case, n = 4), a1 is the first term (6), and an is the last term (3).

Plugging in the values, we get:

S = (4/2)(6 + 3)

S = 18

This means that the tower can have a height ranging from 6 (one block) to 18 (four blocks stacked on top of each other), inclusive. However, we need to subtract the heights that are impossible to obtain, which are 7, 9, 16, and 17. These heights can only be obtained if two of the blocks are placed on their longest sides, which would cause the tower to be unstable. Therefore, the number of possible heights is 18 - 4 = 14.

Therefore, the answer is (B) 14.

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Value of ∫90f(x)dx is 2/3. By property 1 of integration ∫f(x)dx  = ∫f(t)dt Because f(x) is a continuous function ,so we can apply property 1.

A function f(x) is said to be a continuous function in calculus at a point x = a if the curve of the function does NOT break at the point x = a. The mathematical definition of the continuity of a function is as follows. A function f(x) is continuous at a point x = a if

f(a) exists;

limₓ → ₐ f(x) exists;

[i.e., limₓ → ₐ₋ f(x) = limₓ → ₐ₊ f(x)] and

Both of the above values are equal. i.e., limₓ → ₐ f(x) = f(a).

Is this definition really giving the meaning that the function shouldn't have a break at x = a? Let's see. "limₓ → ₐ f(x) exists" means, the function should approach the same value both from the left side and right side of the value x = a and "limₓ → ₐ f(x) = f(a)" means the limit of the function at x = a is same as f(a). These two conditions together will make the function to be continuous at that point.

A function is said to be continuous over an interval if it is continuous at each and every point on the interval. i.e., over that interval, the graph of the function shouldn't break or jump.

∫90f(x)dx = 4

Therefore,   ∫f(x)dx = 4/90  

Let,    X² = t

By differentiate both side ,

We get,

2xdx = dt

so, 30/2 ∫f(t)dt

from property 1 : ∫f(x)dx = ∫f(t)dt    

15∫f(t)dt = (4/90) × 15 = 2/3

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Answer:

53

Step-by-step explanation:

90 - 37 = 53

Answer:

38.33

Step-by-step explanation:

Given: Total amount = 120, Amount used = 74

To find: percent that was not spent

Solution: Firstly, find how much is 74 out of 120. To find the percentage of a number when it is in decimal form, you just need to multiply the decimal number by 100. For this case, to convert 74 to a percentage, 74 x 100 = ...61.67%

Then, 100% - 61.67 = 38.33