Walt's haircut costs $32. He leaves a 15% tip. How much does he pay for the haircut, including the tip?

Answer:

5 but fair losing would be three-fifths

Step-by-step explanation:

The laplace transform of f(t) is

F (s) =  2/s³ - 2e^{-2s}/s³ + e^{-2s}/s²  + 2e^{-2s}/s  -  3e^{-3s}/s²  + 7e^{-3s}/s

In order to answer the question, we need to know what Laplace transform is.

Laplace transform is a way on transforming a function from the time domain, t to the complex variable frequency domain, s.

Since f(t) = t² 0 < t < 2,

= t - 1 for 2 < t < 3 and

= 7 for t > 3

f(t) is a discontinuous function at t = 0, t = 2, t = 3,. So, we thus express f(t) in terms of the unit step function. We will then have

t² = t²u(t) - t²u(t - 2)

t - 1 = (t - 1)u(t - 2) - (t - 1)u(t - 3)

=  (t - 1 + 1 - 1)u(t - 2) - [(t - 1 + 3 - 3)u(t - 3)]

=  (t - 2 + 1)u(t - 2) - [(t - 3 + 2)u(t - 3)]

= (t - 2)u(t - 2) + u(t - 2) - (t - 3)u(t - 3) + 2u(t - 3)

f(t) = 7 = 7u(t - 3)

So, f(t) =  t²u(t) - t²u(t - 2) + (t - 2)u(t - 2) + u(t - 2) - (t - 3)u(t - 3) - 2u(t - 3) +  7u(t - 3)

\(L[u(t - c)f(t - c)}] = e^{-cs} F(s)\)

and \(L[t^{n}] = \frac{n!}{s^{n + 1} }\)

So, we take the laplace transform, then it becomes

L{f(t)} = L{t²u(t)} - L{t²u(t - 2)} + L{(t - 2)u(t - 2)} + L{u(t - 2)} - L{(t - 3)u(t - 3)} - L{2u(t - 3)} +  L{7u(t - 3)}

\(F(s) = \frac{2!}{s^{3} } - \frac{e^{-2s} 2!}{s^{3} } + \frac{e^{-2s} 1!}{s^{2} } + \frac{e^{-2s} 1!}{s } - \frac{e^{-3s} 1!}{s^{2} } - \frac{2e^{-3s} 1!}{s^{2} } + \frac{7e^{-3s} 1!}{s} \\= \frac{2!}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{e^{-3s}}{s^{2} } - \frac{2e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

\(F (s) = \frac{2}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{e^{-3s}}{s^{2} } - \frac{2e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

Hence, the laplace transform of f(t) is \(F (s) = \frac{2}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{3e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

Learn more about Laplace transform here:

https://brainly.com/question/2272409

#SPJ1

The function y = 3x + 5 can be written as:

x = (y - 5) / 3

To find the inverse function, we need to solve for y:

y = 3x + 5

Interchange x and y:

x = 3y + 5

Solve for y:

3y = x - 5

y = (x - 5) / 3

Therefore, the inverse function of y = 3x + 5 is:

y = (x - 5) / 3

For more questions like  inverse function visit the link below:

https://brainly.com/question/29215000

#SPJ11

Answer: (4,-11)

Step-by-step explanation: To perform a 180 degree rotation we switch the signs of the coordinates

Answer:

4,-11

Step-by-step explanation:

The answer is 4,-11 because if you think that you go over -4 and go up 11. Now switch the negative sign to the y coordinate because it is a 180 degree turn then you have your answer. 4,-11

pls mark as brainliest!!

Answer: BC = 24

Step-by-step explanation:

Given:

AB = x+33

AC = 3x - 15

BC = x

<B = <C

Solution:

Because <B = <C, you can say the corresponding sides AB and AC are equal as well

AB = AC

x + 33 = 3x -15  

48 = 2x

x = 24

Since x = BC

BC = x

BC = 24

Answer:

the equation is y=3

Since it's a horizontal slope line and is placed on the point of positive 3

Answer:

y=3

Step-by-step explanation:

Answer:

x = (v - u) / a

Step-by-step explanation:

v = u + ax.

subtract u from both sides:

v - u = ax.

divide both sides by a:

(v - u) / a = x.

so x = (v - u) / a.

this can also be written v/a - u/a

Answer:

A

Step-by-step explanation:

A is corrects since -13 is in the the domain of g(x) and 20 is in the range of g(x):

B is also false since 4 is in the domain of g(x)) and -11 isn't in the range of g(x)

C is also false since it's mentioned that g(0) = -2  

D is false since 7 isn't in the domain of g(x)

Answer:

60.96cm

Step-by-step explanation:

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Answer:

59

Step-by-step explanation:

6 plus 4 equals 8 plus 9

Answer:

Subtract

(a) 19xy - 8xy = 11xy

(b) \((2x^2-3y^2+7) - (x^2-y^2)\) = \(x^{2}+2y^{2} +7\)

Simplify by combining like terms:

(a) \((3x^2-5x+7) + (-38x^2+4x-3)+(11x^2+7x+8)\) = \(-26x^2+6x+12\)

(b) \((x^2y^2 + 2x^2y+5) + (x^2y^2-3x^2y-11)\) = \(2x^2y^2-x^2y-8\)

Find the value of the expression:

\(25x^2 + 9y^2+30xy\) when x = -8 and y -10

= \(25(-8)^2+9(-10)^2+30*-8*-10\)

= 4900

Answer:

Subtract

(a) 19xy - 8xy = 11xy

(b) (2x^2-3y^2+7) - (x^2-y^2)(2x2−3y2+7)−(x2−y2) = x^{2}+2y^{2} +7x2+2y2+7

Simplify by combining like terms:

(a) (3x^2-5x+7) + (-38x^2+4x-3)+(11x^2+7x+8)(3x2−5x+7)+(−38x2+4x−3)+(11x2+7x+8) = -26x^2+6x+12−26x2+6x+12

(b) (x^2y^2 + 2x^2y+5) + (x^2y^2-3x^2y-11)(x2y2+2x2y+5)+(x2y2−3x2y−11) = 2x^2y^2-x^2y-82x2y2−x2y−8

Find the value of the expression:

25x^2 + 9y^2+30xy25x2+9y2+30xy when x = -8 and y -10

= 25(-8)^2+9(-10)^2+30*-8*-1025(−8)2+9(−10)2+30∗−8∗−10

= 4900

Answer:

expression.

2(4x+3y)

2(4(4)+3(7))

2(16+21)

2( 37)

74

The probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (u) is 47 words per minute and the standard deviation (o) is 4 words per minute is; 68%

The empirical rule in statistics states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

x' = 51

μ = 47

σ = 4

Thus;

z = (51 - 47)/4

z = 1

From empirical formula at 1 standard deviation above the means, the probability is 68%.

Read more about empirical formula at; https://brainly.com/question/10093236

#SPJ1

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

For more questions on prime number

https://brainly.com/question/145452

#SPJ8

Problem

x^2 - 8x + 16

Solution

For this case we need to find two numbers a and b that added would be -8 and multiplied 16 and then we see that the two numbers are:

a= b= -4

because a+b = -4-4=-8

a*b= -4 (-4) = 16

And then the best answer for this case is:

(x-4)²

Answer:

Corresponding angles

\((2x + 35) \degree = 103\degree \\ 2x = (103 - 35)\degree \\ 2x = 68\degree \\ x = 34\degree\)

(a) The mean of the relevant distribution is 2.4 defective pistons.

(b) The standard deviation of the distribution is 1.539.

The mean of the relevant distribution is the expected number of defective pistons that we would expect to get from a sample of 80 pistons produced by this machine. The mean is calculated by multiplying the probability of a defective piston (3%) with the number of pistons in the sample (80). In this case, the mean is 2.4 defective pistons. The standard deviation of the distribution quantifies the uncertainty of our estimate. It is calculated by taking the square root of the variance, which is the expected value of the squared differences between the number of defective pistons in the sample and the mean. In this case, the standard deviation is 1.539. This means that, in theory, we would expect 68% of the samples to contain between 0.861 and 4.139 defective pistons.

Learn more about standard deviation here

https://brainly.com/question/13905583

#SPJ4

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Answer:

Step-by-step explanation:

i need help on that too

Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

When budgeting for housing, it is generally recommended to allocate a certain percentage of your income towards housing expenses. The recommended percentage varies depending on factors such as location, personal financial goals, and individual circumstances.

A common guideline is to spend no more than 30% of your monthly income on housing expenses. To determine the maximum amount Freya should budget for housing, we can calculate 30% of her monthly income:

Maximum housing budget = 30% of $1575

Maximum housing budget = 0.30 × $1575

Maximum housing budget = $472.50

Therefore, Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

for such more question on income

https://brainly.com/question/15169974

#SPJ8

Step-by-step explanation:

y = ax + b => ax +b = y

-5= a.1+ b => a + b = -5

-9= a.2+b => 2a+b = -9

________-

-a = 4

=> a = -4

a+b=-5 => b = -5 -a

b = -5+4 = -1

so, the Equation : y = -4x -1

The graph of y = x^2 should be translated by 1 unit to the right and 3 units up.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

Therefore, we have the following:

f(x) = x^2

g(x) = f(x - 1) + N

g(x) = (x - 1)^2 + 3

Read more on translation here: brainly.com/question/16486008

#SPJ1

Answer:

sorry

Step-by-step explanation:

Answer:

y=15

∠P=113

∠Q=67

∠R=113

∠S=67

Step-by-step explanation:

10y-37+4y+7=180

14y=210

y=15

∠P=10(15)-37=113

∠Q=180-113=67

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

for such more question on linear function

https://brainly.com/question/9753782

#SPJ8

Answer:

The circumference of a circle is given by the formula "C = pi x d" where "d" is the diameter and "pi" is the mathematical constant with an approximate value of 3.14.

In this problem, the diameter of the bicycle wheel is 60 centimeters, so its circumference is:

C = pi x d = 3.14 x 60 = 188.4 centimeters

When the wheel makes one revolution, it travels one circumference distance. Therefore, when the wheel makes 35 revolutions, it will travel:

distance = 35 x circumference = 35 x 188.4 = 6584 centimeters

We can convert centimeters to meters by dividing the distance by 100:

distance = 6584 ÷ 100 = 65.84 meters

Therefore, the wheel travels 65.84 meters when it makes 35 revolutions.

60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).

An expression is combination of variables, numbers and operators.

The given expression is (9.42×10⁴)(6.45×10²)

We have to find the value of the expression.

9.42×6.45×10²×10⁴

60.759×10²×10⁴

Bases are same then the powers will be added.

60.759×10⁶

Hence, 60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

The recursive formula of the geometric sequence is a(n) = 3a(n - 1) where a(1) = 2

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

\(a(n) =2 * 3^{n-1\)

Set a = 1

So, we have

\(a(1) =2 * 3^{1-1\)

a(1) = 2

Next, we have

Common ratio, r = 3

This means that a(n) = 3a(n - 1) where a(1) = 2

Read more about sequence at

https://brainly.com/question/30499691

#SPJ1