I need to find the x pls help and show work

The sketch of graph of f(x) is downward-facing parabola. The value of K is 1/6. The probability that the actual tracking weight is greater than the prescribed weight is 2/9. The probability that the actual weight is within of the .25g prescribed weight is 1/2.  The probability that the actual weight differs from the prescribed weight by more than 0.5 g is approximately 0.3334.

To sketch the graph of f(x), we first note that the function is defined only on the interval [2, 4], and it is zero everywhere else. On this interval, the function is a downward-facing parabola centered at x = 3. We can plot the graph.

To find the value of k, we need to use the fact that the total area under the curve of f(x) must be equal to 1, since f(x) is a probability density function. Therefore, we can integrate f(x) over the interval [2, 4] and set the result equal to 1:

1 = ∫[2,4] k(1 - (x-3)^2) dx

 = k[x - (x-3)^3/3] evaluated from 2 to 4

 = k[(4 - (4-3)^3/3) - (2 - (2-3)^3/3)]

 = k(4 - 8/3 + 2 + 8/3)

 = k(6)

Thus, k = 1/6.

To find the probability that the actual tracking weight is greater than the prescribed weight of 3g, we need to integrate f(x) over the interval [3, 4]:

P(X > 3) = ∫[3,4] f(x) dx

         = ∫[3,4] 1/6(1 - (x-3)^2) dx

         = 1/6[x - (x-3)^3/3] evaluated from 3 to 4

         = 1/6[(4 - (4-3)^3/3) - (3 - (3-3)^3/3)]

         = 1/6(4 - 8/3)

         = 2/9

Therefore, the probability that the actual tracking weight is greater than the prescribed weight.

The given pdf is:

f(x) = k(1 - (x-3)^2)    2 <= x <= 4

      0                 otherwise

To find the value of k, we need to integrate the pdf over its support, which is from 2 to 4, and set the result equal to 1:

1 = ∫₂⁴ k(1 - (x-3)^2) dx

 = k ∫₂⁴ (1 - (x-3)^2) dx

 = k [x - (x-3)^3/3] ₂⁴

 = k [4 - (4-3)^3/3 - 2 + (2-3)^3/3]

 = k [8/3 - 2/3]

 = 2k

Therefore, k = 1/2.

To find the probability that the actual weight differs from the prescribed weight by more than 0.5 g, we need to calculate the probability of the event { |X - 3| > 0.5 }. This event represents the set of all values of X that are more than 0.5 g away from the prescribed weight of 3 g.

We can calculate this probability as follows:

P(|X - 3| > 0.5) = P(X < 2.5 or X > 3.5)

= P(X < 2.5) + P(X > 3.5) (by the addition rule of probability)

Now, using the given pdf of X, we can find these probabilities as:

P(X < 2.5) = 0 (since f(x) = 0 for x < 2.0)

P(X > 3.5) = ∫(3.5 to 4) f(x) dx

= ∫(3.5 to 4) k(1-(x-3)^2) dx (using the given pdf)

= k ∫(0.5 to 1) (1-t^2) dt (where t = x-3)

= k [t - (1/3)t^3] (evaluating the integral)

= k [(4-3.5) - (1/3)((1-0.5^3)]

= k [0.1667]

Therefore, the required probability is:

P(|X - 3| > 0.5) = P(X < 2.5 or X > 3.5) = P(X > 3.5) = k [0.1667]

We need to find the value of k to calculate the probability. The pdf of X must integrate to 1 over its entire domain, so we have:

1 = ∫(2 to 4) f(x) dx

= k ∫(2 to 4) (1-(x-3)^2) dx

= k ∫(-1 to 1) u (1-u^2) du (where u = x-3)

= k [u^2/2 - u^4/4] (evaluating the integral)

= k [(1/2) - (1/4)]

= k [0.5]

Thus, k = 2.

Substituting this value of k in the expression we derived earlier, we get:

P(|X - 3| > 0.5) = P(X < 2.5 or X > 3.5) = P(X > 3.5) = k [0.1667]

= 2 [0.1667]

= 0.3334

Therefore, the probability is more than 0.5 g is approximately 0.3334.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

_____The given question is incomplete, the complete question is given below:

The actual tracking weight of a stereo cartridge that is set to track at 3g

on a particular changer can be regarded as a continuous rv X

with pdf f(x) = k(1-(x-3)^2)   2less than equal to x less than equal to 4, f(x) = 0  otherwise

a. Sketch the graph of f(x)

.

b. Find the value of k.

.

c. What is the probability that the actual tracking weight is greater than the prescribed weight?

d. What is the probability that the actual weight is within

of the .25g prescribed weight?

e. What is the probability that the actual weight differs from the prescribed weight by more than .5g

?

As per given utility function, Tane will accept any job as long as the job comes with a certain payment of at least $40,000 (approx.).

Tane's utility function, \(U(W)=W^{0.5}\), indicates that he has a concave utility function, implying diminishing marginal utility of wealth. This means that Tane values each additional dollar of wealth less as his wealth increases.

Considering the job offer with a base salary of $30,000 and a potential $70,000 bonus with a 0.5 probability, we can calculate the expected value of this salary scheme. The expected value is calculated as the sum of each possible outcome multiplied by its respective probability:

Expected Value = (0.5 * $30,000) + (0.5 * $100,000) = $65,000

Since the expected value is less than $80,000 (approx.), which is the minimum certain payment Tane would accept, Tane would not accept the job offer with the probabilistic salary scheme.

However, Tane's utility function indicates that he values certainty in income. As long as the job comes with a certain payment of at least $40,000 (approx.), Tane would prefer to accept the job because the certain payment guarantees a minimum level of income, providing him with a higher level of certainty and potentially higher utility compared to the probabilistic salary scheme. Therefore, Tane will accept any job as long as the job comes with a certain payment of at least $40,000 (approx.).

Learn more about utility function here : https://brainly.com/question/31055643

#SPJ11

Answer:

it's law

Step-by-step explanation:

i think it is law of mathematics. isn't it?

The area of the given figure which has the shape of a trapezium would be = 58.5cm²

To calculate the area of the trapezium given above, the formula for area of a trapezium should be used and this is given below;

Area of a trapezium= 1/2(a+b)h

Where;

a= 12cm

b= 7.5cm

height= 6cm

Area of trapezium = 1/2(12+7.5) × 6

= 19.5×3 = 58.5cm²

Therefore, the area of the given shape above is calculated as 58.5cm²

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

Answer:

Assuming you want to know what fraction of the original amount you have.

a = allowance

(1/2)a = what have left after Monday

(1/2(1/2)a = what you have after Tuesday

(1/2)(1/2)(1/2)a = what you have after Wednesday.

Doing the multiplication.

(1/8)a = what you have left.

You have 1/8 of what you had at the start.

Hope this help u

Answer:

1/8 i think

Step-by-step explanation:

Answer:

(5,4) is the distance between when you count manually or subtract.

Answer:

(n-2) x 180 degrees where n is the number of sides

Step-by-step explanation:

From one vertex of the polygon you draw triangles inside the polygon.  Multiply the number of triangles by 180 since all triangles interior angles add up to 180 degrees.

example

Pentagon has 5 sides.  (5-2) x 180 = 540 degrees

This is the same as 180n-360

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

Explanation:

Draw any polygon you want. Let's say we draw a hexagon. Split the hexagon into 6 triangles. Check out the diagram below.

The goal is to find what the red angles sum to. Recall that any triangle always has its three angles add to 180 degrees. We have 6 triangles, so all of the angles (red+blue) add to 6*180 = 1080 degrees. However, we don't want to include the blue inner angles. So we'll subtract off 360 since the blue angles add up to this amount (they form a full rotation).

So we have 6*180 - 360 as the expression that represents the sum of the interior angles for this hexagon. The hexagon doesn't have to be a regular polygon.

We can generalize to any polygon and not just hexagons. Simply replace that "6" with n and we get n*180 - 360 which is the same as 180n-360 = 180(n-2)

Answer:

12

Step-by-step explanation:

Mark brainliest pls

To calculate Evan's AGI (Adjusted Gross Income) and taxable income if he files as a single taxpayer, we need to consider his income and deductible expenses.

Calculate Evan's total income:
  - Salary: $73,650
  - Part-time hourly pay: $700

  Total income = Salary + Part-time pay = $73,650 + $700 = $74,350

Deductible expenses:
  - Moving expenses: $1,200
  - Student loan interest: $2,890
  - Uniform cost: $1,490
  - Cash contribution: $1,345

  Total deductible expenses = $1,200 + $2,890 + $1,490 + $1,345 = $6,925

Calculate AGI:
  AGI = Total income - Total deductible expenses
  AGI = $74,350 - $6,925 = $67,425

Evan's taxable income is equal to his AGI since there were no other deductions mentioned in the question.

Therefore, Evan's AGI is $67,425, and his taxable income is also $67,425.

To know more about income , visit ;

https://brainly.in/question/15692103

#SPJ11

Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.

We have,

Income:

Salary: $73,650

Part-time work pay: $700

Total income: $73,650 + $700 = $74,350

Deductible Expenses:

Cost of moving possessions: $1,200

(This deduction applies if the move meets certain distance and time requirements. Since the move was 125 miles away, it meets the distance requirement.)

Interest paid on student loans: $2,890

Cost of purchasing a delivery uniform: $1,490

Cash contribution to State University deliveryman program: $1,345

Total deductible expenses:

$1,200 + $2,890 + $1,490 + $1,345

= $6,925

Now we can calculate Evan's AGI and taxable income:

AGI (Adjusted Gross Income)

= Total income - Deductible expenses

AGI = $74,350 - $6,925 = $67,425

Taxable Income = AGI - Standard Deduction

For a single filer in 2022, the standard deduction is $12,550.

Taxable Income = $67,425 - $12,550 = $54,875

Therefore,

Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ4

Answer: the value for a is 3 and the value for c is -5, a) 3 and -5.

The given function is f(x) = acos(k(x−d))+c, and the range of this function is specified as {y∣−5≤y≤1,y∈R}.

To find the values of a and c, we need to consider the range of the function. The range represents all the possible values that the function can take. In this case, the range is given as −5≤y≤1.

Let's analyze the given range. The range starts at -5 and ends at 1. Since a is positive, we know that the amplitude of the cosine function is positive. The amplitude is the absolute value of a, which represents the distance between the maximum and minimum values of the function.

Since the range goes from -5 to 1, the amplitude must be at least 6 (the absolute difference between -5 and 1). However, we need to consider that the cosine function oscillates between -1 and 1. Therefore, the amplitude should be half of the range, which is 3.

So, we have found the value for a: a = 3.

Now, let's find the value for c. The constant term c represents the vertical shift of the graph of the function. In this case, we are given that the range starts at -5, which means the graph is shifted downwards by 5 units compared to the standard cosine function.

Therefore, the value for c is -5.

In conclusion, if a is positive, the values for a and c are:
a) 3 and -5.

To learn more about function calculations:

https://brainly.com/question/31033930

#SPJ11

Answer:

D.30/34

Step-by-step explanation:

edge

Answer:

D. 30/34

Step-by-step explanation:

edge

Answer:

8 is the correct answer of this question

Answer:

8

Step-by-step explanation:

The y component of vector B can be found using the equation A×B = 82k. Since vector A = 135i, then the y component of vector B must be 82 / 135.

We know that A×B = |A||B|sinθn, where θ is the angle between A and B, and n is the unit vector perpendicular to both A and B (which points either in the positive or negative z direction).

In this problem, A = 135 i and A×B = 82 k, so we have:

|A||B|sinθn = 82 k

|A| = 135

|A×B| = 82

The magnitude of the cross-product is |A||B|sinθ, so we can solve for sinθ:

|A×B| = |A||B|sinθ

82 = 135|B|sinθ

sinθ = 82 / (135|B|)

Since we know that B is perpendicular to A, we can say that B has the form B = b j, where b is some scalar and j is the unit vector in the y direction. Then we have:

A•B = 0

135(0) + b y = 0

y = 0

But we also know that the cross-product of A and B points in the z direction, so the angle θ between A and B must be in the x-y plane (since A and B are both in the x-y plane). This means that sinθ = 1, so we have:

|A×B| = |A||B|sinθ

82 = 135|B|

|B| = 82 / 135

Therefore, the y component of vector B is:

y = b|j| = b = 0 + b j = (82 / 135) j

So the answer is y = 82 / 135.

Learn more about vector at https://brainly.com/question/30407078

#SPJ11

Answer:

9(5+8)

Step-by-step explanation:

Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

(1/4) ∫(16-π) 16-π (-cos(2t^2 - π)) / t + C This is the final result of the integral. To evaluate the integral ∫3 3t sin(2t^2 - π) dt, we can use integration techniques, specifically integration by substitution.

Let's denote u = 2t^2 - π. Then, differentiating both sides with respect to t gives du/dt = 4t.

Rearranging the equation, we have dt = du / (4t). Substituting this expression for dt in the integral, we get:

∫3 3t sin(2t^2 - π) dt = ∫3 sin(u) du / (4t)

Next, we need to substitute the limits of integration. When t = 3, u = 2(3)^2 - π = 16 - π, and when t = -3, u = 2(-3)^2 - π = 16 - π.

Now, the integral becomes:

∫(16-π) 16-π sin(u) du / (4t)

We can simplify this by factoring out the constant terms:

(1/4) ∫(16-π) 16-π sin(u) du / t

Now, we can integrate sin(u) with respect to u:

(1/4) ∫(16-π) 16-π (-cos(u)) / t + C

Finally, substituting u back in terms of t, we have:

(1/4) ∫(16-π) 16-π (-cos(2t^2 - π)) / t + C

This is the final result of the integral.

To learn more about  integral click here:

brainly.com/question/31862795

#SPJ11

Step-by-step explanation:

There are many different types of variations  as follows:

1) Direct variations in which the relationship between two different variables is direct.

2) Inverse variations in which the relationship between two different variables is opposite.

3) Joint variations in which the relationship between one variable varies directly with the product of two or more variables.

4) Combined variations in which one variable is directly proportion to second variable but inversely proportion with third variables.

option 'A', 'B', 'D' , 'E' are correct.

Given:

The linear equations are,

The objective is to solve by elimination method.

The equations can be rearranged as,

To solve the equation, multiply equation (1) b

, the result will give us the volume of the solid under the surface z = x^2 + y^2 and above the region x^2 + y^2 = 3x in the xy-plane.

To compute the volume of the solid under the surface z = x^2 + y^2 and above the region x^2 + y^2 = 3x in the xy-plane, we can use polar coordinates to simplify the integration.

In polar coordinates, we have x = rcosθ and y = rsinθ. Let's first determine the region of integration in terms of polar coordinates.

x^2 + y^2 = 3x can be rewritten as r^2 = 3rcosθ, which simplifies to r = 3cosθ.

To find the limits of integration for r, we need to determine the intersection points between the curve r = 3cosθ and the origin (r = 0). Setting r = 3cosθ to 0, we have:

3cosθ = 0

cosθ = 0

θ = π/2, 3π/2

Thus, the limits for θ will be from π/2 to 3π/2.

Now, we can express the volume as an integral in polar coordinates:

V = ∫∫R (x^2 + y^2) dA

where R represents the region of integration.

Converting the Cartesian coordinates (x, y) to polar coordinates (r, θ), we have:

V = ∫∫R r^2 r dr dθ

Substituting the expression for r = 3cosθ, we have:

V = ∫[π/2 to 3π/2] ∫[0 to 3cosθ] (r^2) r dr dθ

Simplifying the integral, we have:

V = ∫[π/2 to 3π/2] ∫[0 to 3cosθ] (r^3) dr dθ

Evaluating the inner integral:

∫[0 to 3cosθ] (r^3) dr = (1/4) (3cosθ)^4

                            = (27/4)cos^4θ

Substituting this back into the volume integral:

V = ∫[π/2 to 3π/2] (27/4)cos^4θ dθ

Evaluating the outer integral:

V = (27/4) ∫[π/2 to 3π/2] cos^4θ dθ

At this point, the integral can be evaluated using standard techniques or numerical methods.

Once the integral is evaluated, the result will give us the volume of the solid under the surface z = x^2 + y^2 and above the region x^2 + y^2 = 3x in the xy-plane.

To know more about Polar Coordinates related question visit:

https://brainly.com/question/31904915

#SPJ11

The solution to the logarithm equation is log5(2x-7) = 0 is x = 4.

What is logarithm ?

A logarithm is a mathematical function that represents the exponent to which a fixed number, called the base, must be raised to produce a given value. In other words, a logarithm is the inverse operation of exponentiation.

For example, if we have the equation \(10^3 = 1000\), the logarithm of 1000 with base 10 is 3, because \(10^3 = 1000\). Similarly, the logarithm of 8 with base 2 is 3, because \(2^3 = 8.\)

According to the question:

To solve for x in the equation:

log5(2x-7) = 0

We can use the definition of logarithms which states that log_b(x) = y is equivalent to \(b^y = x.\)

Applying this to the given equation, we get:

\(5^0 = 2x - 7\)

\(1 = 2x - 7\)

\(2x = 8\)

\(x = 4\)

Therefore, the solution to the equation is log5(2x-7) = 0 is x = 4.

To know more about logarithm visit:
https://brainly.com/question/30226560
#SPJ1

Answer: B

Step-by-step explanation:

To find the values of x, we first need to write the function into an equation. We can derive 2 equations from the problem.

Equation 1: y=2|x+6|-4

Equation 2: y=6

Now, we can substitute.

2|x+6|-4=6

Let's solve for x.

2|x+6|-4=6        [add both sides by 4]

2|x+6|=10          [divide both sides by 2]

|x+6|=5              [subtract both sides by 6]

x=-1

Now that we know x=-1 is one of the solutions, we can eliminate C and D.

We know that the absolute value makes the number inside positive always. Therefore, let's solve for x with -5 instead.

|x+6|=-5              [subtract both sides by 6]

x=-11

Therefore, we know that B is the correct answer.

You can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.

Determine the range of the data: 0.6 to 4.7.

Divide the range by the number of classes (5) to find the class width: (4.7 - 0.6) / 5 = 0.76.

Determine the lower limits of each class by starting at the minimum value (0.6) and adding the class width repeatedly: 0.6, 1.36, 2.12, 2.88, 3.64, 4.4.

Count the number of data values that fall into each class and record it in a table.

Draw a bar for each class using the lower limit of the class as the x-axis value and the height of the bar equal to the number of data values in the class.

After creating the histogram, you can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.

Learn more about histogram in brainly.com/question/30354484

#SPJ1

Answer:

22

Step-by-step explanation:

QS =2×11 = 22

__________

Answer:

120 seconds

Step-by-step explanation:

To find the number of seconds it takes for the two fish tanks to have the same amount of water, we need to set up an equation to represent the amount of water in each tank at a given time.

Let's call the number of seconds it takes for the two tanks to have the same amount of water "t." At time "t," the amount of water in the first tank will be 150 - 0.5t, and the amount of water in the second tank will be 120 + 0.25t. We want to find the value of "t" that makes these two quantities equal.

So, we set up the equation 150 - 0.5t = 120 + 0.25t and solve for "t":

150 - 0.5t = 120 + 0.25t

0.25t = 30

t = 30 / 0.25

t = 120 seconds

Therefore, it will take 120 seconds for the two fish tanks to have the same amount of water.

Answer:

after 40 seconds, the two tanks will have the same amount of water.

Step-by-step explanation:

Let x represent the number of seconds after which both tanks will have the same amount of water.

A fish tank has 150 gallons of water and is being drained at a rate of 1/2 gallons each second. It means that the number of gallons of water that would be in the tank after t seconds is 150 - 0.5t

A second fish tank has 120 gallons and it is being filled at a rate of 1/4 gallons each second. It means that the number of gallons of water that would be in the tank after t seconds is 120 + 0.25t

For the volume of both tanks to he the same, then

120 + 0.25t = 150 - 0.5t

0.25t + 0.5t = 150 - 120

0.75t = 30

t=40 seconds

Answer:

w = 17

Step-by-step explanation:

w / 4 = 68

w = 68 * 4

w = 272