what is the inverse of f(x)? show the work
f(x)+3x+5

Answer: 6+4+2+2+2+766

Step-by-step explanation:

655*565(77)

The requreid solution to the trigonometric problem is,
1. a = 4 and b = 2√2
2. x = 2√2 and y = 2√2
3. y = 3√2/2 and x = 3

1.

In the figure we have,
perpendicular = 2√2
base = b
hypotenuse = a

Using trigonometric ratios,

sin45 = 2√2/a
1/√2 = 2√2/a
a = 2 × 2
a = 4

Now,
tan45 = 2√2/b
1 = 2√2 / b
b = 2√2

Similarly,
2. x = 2√2 and y = 2√2
3. y = 3√2/2 and x = 3

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The probability that the customer will default. is 0.2337.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

P(missing one month payment | not default) = 0.21

P(missing one month payment | default) = 1

P(missing one month payment) = P(missing one month payment | default) * P(default) + P(missing one month payment | not default) * P(not default)

= 1 * 0.03 + 0.21 * 0.97

= 0.2337

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Answer:what

Step-by-step explanation:what does this mean

The volume of the region is approximately 333.3.

The volume of the region bounded by the two equations z = x2 y2 and z = 20 − x2 − 2y2 can be calculated by setting up a triple integral and integrating it with respect to x, y, and z. To do this, we must first find the limits of integration.

For the x variable, the two equations both contain x2 so the limits of integration would be -√20 and √20. For the y variable, the equations contain y2 so the limits of integration would be -√10 and √10.

Finally, for the z variable, the limits of integration would be 0 and 20. Using these limits we can now write our triple integral, ∫∫∫(20 - x2 - 2y2)dx dy dz, and integrate it to find the volume of the region.

After integrating, we find that the volume is approximately 333.3.

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Answer:

x = 67/5

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Equality Properties

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

5x + 7 = 91 - 17

Step 2: Solve for x

a) The extended free body diagram for the ladder is illustrated below.

b) The equations for the horizontal and vertical forces on the ladder is \(t = r \times F_{friction} + r \times W_{worker} - (L - r) \times W_{ladder}\)

c) The equation for the sum of the torques on the ladder is\(h = (L - r) - [(\mu L)/2(1 - \mu)] x [W_{\text{ladder} + W_{\text{worker}}]/W_{\text{ladder}}\)

In the aftermath of an ice storm, assessing damage to power poles is essential for power companies. However, climbing up an icy power pole can be dangerous. Therefore, a ladder is used to climb up to the top of the pole. But, what happens when the ladder slips? In this scenario, we will explore the physics behind the ladder's stability while the worker is climbing up the icy pole.

To begin with, we need to draw the extended free-body diagram for the ladder. This diagram will help us understand the forces acting on the ladder. We can assume that the worker is standing at a height of h on the ladder.

Now, we can write the equations for the horizontal and vertical forces acting on the ladder. The horizontal force can be given as:

\(F_{horizontal} = F_{friction}\)

where \(F_{friction}\)is the frictional force acting on the ladder. The vertical force can be given as:

\(F_{vertical} = N - W_{ladder} - W_{worker}\)

where N is the normal force, \(W_{ladder}\) is the weight of the ladder, and \(W_{worker}\) is the weight of the worker.

We also need to write the equation for the sum of the torques acting on the ladder. This can be given as:

\(t = r \times F_{friction} + r \times W_{worker} - (L - r) \times W_{ladder}\)

where r is the distance of the worker from the bottom of the ladder, L is the length of the ladder, and x denotes the cross product.

To find the height up the ladder where the worker can go without slipping, we need to set the frictional force equal to the maximum value of the frictional force, which is given by:

\(F_{friction-max} = \mu N\)

where μ is the coefficient of friction between the ladder and the ground. Substituting this value in the equation for \(F_{horizontal}\), we get:

\(F_{friction-max} = \mu N = F_{horizontal}\)

Substituting the value of \(F_{friction-max}\) in the equation for \(F_{vertical}\)we get:

\(N - W_{ladder} - W_{worker} = \mu N\)

Simplifying this equation, we get:

\(N = (W_{ladder} + W_{worker})/(1 - \mu)\)

Now, substituting the value of N in the equation for τ, we get:

\(t = r \times \mu N + r x W_{worker} - (L - r) x W_{ladder}\)

Simplifying this equation, we get:

\(h = (L - r) - [(\mu L)/2(1 - \mu)] x [W_{\text{ladder} + W_{\text{worker}}]/W_{\text{ladder}}\)

where h is the height up the ladder where the worker can go without slipping.

Therefore, using the above equations, we can determine the height up the ladder where the worker can go without slipping. It is important to note that the coefficient of friction plays a crucial role in determining the stability of the ladder.

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Answer:

ygjjjyc

Step-by-step explanation:

trzerxcgvjyu

Answer:

  20%

Step-by-step explanation:

You want to find what percent of 400,000 is 80,000.

The given relation can be expressed as ...

  what% × 400,000 = 80,000

Using the equivalence of % and /100, this can be written ...

  what/100 × 400,000 = 80,000

Simplifying, this is ...

  what × 4,000 = 80,000

Dividing by the coefficient of the variable gives ...

  what = 80,000/4,000 = 80/4 = 20

Then your answer is ...

  what% = 20%

The missing number is 20%.

__

Additional comment

Effectively, you're expressing the fraction 80,000/400,000 as a percentage:

  80,000/400,000 × 100% = 20%

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Direct labor efficiency variance = $6,100 F.

Given that

Standard labor-hours per unit of output     8.5 hours

Standard labor rate                                     $12.30 per hour

Standard labor hours allowed                          6,800 hours (800 units *                                         8.5 hours allowed)

The following data pertain to operations concerning the product for the last month:

Actual hours worked  6,300 hours

Actual total labor cost  $74,970

Actual output                  800 units

We can determine the labor efficiency variance using the following equation:

1. Direct labor efficiency variance = (Standard hours allowed - Actual labor hours) * Standard rate

2. Direct labor efficiency variance = (6,800 hours - 6,300 hours) * $12.20

3. Direct labor efficiency variance = $6,100 F

The variance is favorable as the actual labor hours used are less than the standard hours allowed.

Hence the answer is Direct labor efficiency variance = $6,100 F.

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Answer:

708480

Step-by-step explanation:

You follow the order of BEDMAS. There are brackets in this equation, meaning we have to focus on what is inside the brackets first. The next step is Exponents. So you multiply 2.05 by 10^5.

This would give you 205000.

You then multiply this number by the number on the outside of the brackets which is 3.456.

This would give you 708480. (You can get these answers by using a calculator).

Don't forgot to follow the order of BEDMAS or whatever law of operations you were taught (BIDMAS/BIMDAS etc)

The attached image shows the triangle with coordinates A(1,4), B(1,7) and C(3,5) and reflected over the line y = 2x + 1.

Reflection refers to the transformation of a geometric shape by flipping it across a line called the line of reflection.

When a shape undergoes reflection, every point on the shape is mapped to a corresponding point on the opposite side of the line of reflection, maintaining the same distance from the line.

For example, if you have a triangle and reflect it across a line of reflection, the resulting image will be a triangle with the same size and angles, but it will be facing in the opposite direction.

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Step-by-step explanation:

triangle BCA=BAL bcoz Angle BCA= Angle BAL

Isoquants for f(K, L) = 1/2 min{K, L} that produce exactly 10 goods and 25 goods can be graphed, with labeled points.

For function f(K, L) = 1/2 min{K, L}, we can graph the isoquants that represent the combinations of capital (K) and labor (L) that produce exactly 10 goods and 25 goods.

An isoquant represents all the combinations of inputs (K and L) that yield the same level of output. In this case, the isoquants will be curves that connect different combinations of K and L, where the output is constant at either 10 goods or 25 goods.

To graph the isoquant for 10 goods, we plot points where f(K, L) = 10. For example, if we let K = 4 and L = 4, the minimum of K and L is 4, so f(K, L) = 1/2 * 4 = 2 goods.

Since this is less than 10, we need to increase either K or L. We can try K = 8 and L = 4, where the minimum of K and L is still 4, and f(K, L) = 1/2 * 4 = 2 goods. Again, this is less than 10, so we increase K or L further.

Continuing this process, we can plot a few more points and connect them to obtain the isoquant for 10 goods.

Similarly, we can graph the isoquant for 25 goods by plotting points where f(K, L) = 25. For each point, we determine the minimum of K and L, multiply it by 1/2, and check if the result is equal to 25. By plotting and connecting several such points, we obtain the isoquant for 25 goods.

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The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.

To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.

The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.

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Answer:

292

Step-by-step explanation:

Answer:

i took the test and the person above me is correct

Step-by-step explanation:

Answer:

s= number of shirts

3/2= constant of proportionality

Step-by-step explanation:

Josh takes a load of dress shirts to the dry cleaners. The amount he pays for dry cleaning (

f. is given by the equation f=3/2s, where s is the number of shirts. What is the constant of proportionality in terms of the cost per shirt?

Given:

f= 3 / 2s

Where,

f= amount Josh paid for dry cleaning

s= number of shirts

3= constant of proportionality

2= amount paid per shirt

For example, if Josh took 3 shirts to the dry cleaner, the amount Josh will pay is

f= 3 / 2s

= 3 / 2(3)

= 3 / 6

= 1 / 2

f= 1 /2

The probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

Let X denote the time required to process a package of five tasks. X is an exponentially distributed random variable with mean 2 minutes.

The probability of X being less than 8 minutes is given by:

P(X ≤ 8) = 1 - P(X > 8)

= \(1 - (1 - e^{(-8/2)}^{5}\)

= 0.963

Therefore, the probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

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The inverse equations are F(x)⁻¹ = ( x - 2 ) / 5and F(x)⁻¹ = 5x + 2.

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. In an inverse function, the value of two variables x and y are interchanged, and then the value of y is given an inverse function.

Given that the two equations are y= 1/2X+10 and y= -8X+3. The value of inverse functions will be calculated by replacing the x and y values and solving for y,

f(x)=5x+2

x = 5y + 2

y = ( x - 2 ) / 5

The inverse of the second equation is calculated as,

g(x)=(x-2)/5

x = ( y - 2 ) / 5

y = 5x + 2

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Sasha should use 2 desired outcomes in her probability calculation to determine that she has a 1/3 chance of winning the game.

To calculate Sasha's probability of winning, we need to determine how many desired outcomes she has. In this game, Sasha needs to spin a number higher than both of her friends' spins, which means she needs to spin a number greater than 1 and 4.

Let's analyze the spinner pictured. From the image, we can see that the spinner has numbers ranging from 1 to 6. Since Sasha needs to spin a number higher than 4, she has two options: 5 or 6.

Now, let's consider the desired outcomes. Sasha has two desired outcomes, which are spinning a 5 or spinning a 6. If she spins either of these numbers, she will have a number higher than both of her friends and win the game.

To calculate Sasha's probability of winning, we need to divide the number of desired outcomes by the total number of possible outcomes. In this case, the total number of possible outcomes is the number of sections on the spinner, which is 6.

Sasha's probability of winning is 2 desired outcomes divided by 6 total outcomes, which simplifies to 1/3.

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.

The answer should be 25 unites

Answer:

\(x=-1\)

Step-by-step explanation:

1) Subtract 9x from both sides.

\(14x+2-9x=-3\)

2)  Simplify  14x+2-9x to 5x+2.

\(5x+2=-3\)

3) Subtract 2 from both sides.

\(5x=-3-2\)

4) Simplify  -3-2 to  -5.

\(5x=-5\)

5) Divide both sides by 5.

\(x=-1\)

Therefor, the answer is x = -1

The average length of the queue and the Average number in the system.

the average time spent in the system can be calculated as:

W = Wq + (1 / μ)

The  M/G/1 system, we need to calculate the following parameters:

a. The probability that the system is idle.

b. The average length of the queue.

c. The average number in the system.

Let's solve each part step by step:

a. Probability that the system is idle (ρ):

The utilization factor (ρ) represents the ratio of the average arrival rate (λ) to the average service rate (μ). In an M/G/1 system, the probability that the system is idle can be calculated as:

P(Idle) = 1 - ρ

In this case, λ = 6 and μ = 9, so:

ρ = λ / μ = 6 / 9 = 2 / 3

Therefore,

P(Idle) = 1 - ρ = 1 - 2/3 = 1/3

b. Average length of the queue (Lq):

The average length of the queue can be calculated using Little's Law, which states that Lq = λ * Wq, where Wq represents the average time spent in the queue.

In an M/G/1 system, the average time spent in the queue (Wq) can be calculated using the Pollaczek-Khinchine formula:

Wq = ρ^2 / (2 * (1 - ρ)) * (σ^2 + (μ^2 / λ^2))

In this case, σ = 0.03, λ = 6, and μ = 9, so:

Wq = (2/3)^2 / (2 * (1 - 2/3)) * (0.03^2 + (9^2 / 6^2))

Simplifying the equation will give us the value of Wq.

c. Average number in the system (L):

The average number in the system (L) can be calculated as L = λ * W, where W represents the average time spent in the system. In an M/G/1 system,

Substituting the values of Wq and μ into the equation will give us the value of W. Then, we can calculate L by multiplying λ and W.

Lq and L, we can determine the average length of the queue and the average number in the system, respectively.

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Answer:

x = -4

Step-by-step explanation:

\(y = 9-7x\\37 = 9 - 7x\\28 = -7x\\x = -4\)

Answer:

-2, -1

Step-by-step explanation:

Answer:  A. 62 m

Step-by-step explanation:

Perimeter is the sum of all of the sides

Top = 20

Sides = 2(8) = 16

Bottom = 20 + 2(3) = 26

Total = 62

Answer:

use the top and bottom

Step-by-step explanation:

x-axis && y - axis

Answer:

Step-by-step explanation:

Key: So α is \(45:12\) and β is \(45:18\).

Proportionality means: "the quality of corresponding in size or amount to something else. the requirement of proportionality of punishment to offense"

the fact of a variable quantity having a constant ratio to another quantity."

Ok so now you have to answer the following question using that key.

1. False.

2.True

3.False

4.False

I hope this helps a bit.....I think I  got them right. :)

Domain: The domain of the function is \(\(-\infty < x \leq 5\) (excluding \(x = 0\)).\)

Range: The range of the function is \(\(1 \leq f(x) < \infty\)\).

To sketch the graph of the function \(\(f(x) = \begin{cases} |\!x\!| + 2 & \text{if } x < 2 \\ \dfrac{x+3}{x} & \text{if } 2 \leq x \leq 5 \end{cases}\)\), we'll consider the two cases separately.

Case 1: x < 2

In this case, the function is defined as f(x) = |x| + 2. The graph of f(x) = |x| + 2 is a V-shaped graph with the vertex at the point (0, 2) and opening upwards. It consists of two lines intersecting at the vertex. For x < 2, the absolute value function \(\(|\!x\!|\)\) is equal to (-x), so the graph of f(x) in this range is a line with a negative slope passing through the point (0, 2). The graph extends to negative infinity as x approaches negative infinity.

Case 2:  \(\(2 \leq x \leq 5\)\)

In this case, the function is defined as \(\(f(x) = \dfrac{x+3}{x}\)\). The graph of this function is a hyperbola with vertical asymptotes at x = 0 and a horizontal asymptote at y = 1. It starts from positive infinity as x approaches 0 from the right, passes through the point (1, 4), and approaches 1 as x goes towards positive infinity.

The domain of the function is \(\(-\infty < x \leq 5\) (excluding \(x = 0\))\) as the function is not defined at x = 0.

The range of the function is \(\(1 \leq f(x) < \infty\)\) since the function approaches 1 as x approaches infinity and takes on all positive values greater than or equal to 1.

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