peter's international barbershop is a popular haircutting and styling saloon near the campus of the brooklyn college. one barber is available to work full time and spend an average of 4 minutes on each customer. customers arrive all day long at an average rate of 5 minutes arrivals tend to follow the poisson distribution, and service times are exponentially distributed. explain your results. [5 points]

The dimensional analysis conversion of 100 inch to feet is 8.33 feet.

Dimensional analysis is the study of the relationships between different physical quantities in engineering and science by identifying their base quantities and units of measurement and tracking these dimensions as calculations or comparisons are performed. when there is insufficient information to set up precise equations, a method of analysis in which physical quantities are expressed in terms of their fundamental dimensions. Dimensional Analysis (also known as the Factor-Label Method or the Unit Factor Method) is a problem-solving strategy that takes advantage of the fact that any number or expression can be multiplied by one without changing its value.

Here,

100 inch to feet,

=100/12

=8.33 feet

The conversion of 100 inch to feet using dimensional analysis is 8.33 feet.

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Answer: 7/12 can't be simplified anymore. Have a nice day ;)

For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.

What is function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.

A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).

Four orders of functions live functions with return values and arguments.

This function accepts arguments and gives back a result.

functions that take arguments but have no return values.

functions with return values and no arguments.

functions that have no arguments or return values.

we are given two function f( x) and g( x);

f( x) = 3x- 2 and

g( x) = x2

So, for fg( x), we've to put value of g( x) into f( x);

Hence, the equation will be;

fg( x) = 3x2- 2.

thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.

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The transverse axis has a length of 5 units.

A transverse axis is a line that divides a conic section (such as an ellipse or hyperbola) into two symmetric parts. In the case of an ellipse, the transverse axis is the major axis, and it runs perpendicular to the minor axis.

To find the length of the transverse axis, we can use the equation (x − 1)²/a² + (y + 3)²/b² = 1, where a and b are the lengths of the major and minor axes, respectively.

The given equation is :

(x−h)²/a² + (y−k)²/b² = 1

Where h and k are the coordinates of the center of the ellipse.

Now we can substitute the given values in the equation

(x−1)²/25 + (y+3)²/9 = 1

To find the length of the transverse axis, we can take square root of the major axis value, a² = 25

√25 = 5

So the length of the transverse axis is 5 units.

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The migration matrix that has been found is

                [0.98033     0.00179

                 0.01967      0.99821 ]       by matrix method.

The 2012 populations of California and the US minus California are 38,041,430 and 275,872,610, respectively, according to the exercise statement. Let's represent these quantities by the variables c and u. What we want are two vectors m1 and m2 such that

cm 1+um 2 ​=     [ 2013 population of California

                       2013 population of US minus California ]

m1 = [ 0.98033   0.01967 ]      and    m2 = [ 0.00179   0.99821]

Now that we have the two vectors for equation ,we use the fact that a vector equation of the form

                             au + bv = w

is equivalent to a matrix equation of the form  

                              [ u  v ] [a b] = w

to get our migration matrix for this system.

[0.98033     0.00179

0.01967      0.99821 ]

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The complete question is :

In 2012 the population of California was 38,041,430, and the population living in the United States but outside California was 275,872,610. During the year, it is estimated that 748,252 persons moved from California to elsewhere in the United States, while 493,641 persons moved to California from elsewhere in the United States. Set up the migration matrix for this situation, using five decimal places for the migration rates into and out of California. Let your work show how you produced the migration matrix.

​

For the given system of inequalities y < -x + a and y > x + b in the xy-plane , the solution represents the relation between a and b is given by :

Option A. a > b.

In the xy -plane given system of inequalities are :

y < -x + a

y > x + b

⇒ x + b < y < -x + a

⇒ x + b < -x + a

⇒ 2x < a - b

Now ( 0, 0 ) is the solution of the given system of inequalities represents :

2(0) < a - b

⇒ a - b > 0

⇒ a > b

Therefore, the relationship between the  'a' and 'b' for the given system of inequalities is given by :

Option A. a > b

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Answer:

  a1 = 16

  a(n) = a(n-1) -3   for n ≥ 2

Step-by-step explanation:

You want a recursive formula for the arithmetic sequence 16, 13, 10, 7, ....

The given sequence has a first term of 16. The common difference is ...

  13 -16 = -3

Each successive term is found by adding this difference to the one before. That describes the relation expressed by the recursive formula.

  [tex]\begin{cases}a_1=16\\a_n=a_{n-1}-3&\text{for $n\ge2$}\end{cases}[/tex]

Answer:

The volume of the prism is 6.186

Step-by-step explanation:

1. The volume of a cylinder can be calculated using the formula V = πr^2h where r is the radius of the cylinder base, h is the height and π is a mathematical constant.

2. The diameter of the cylinder base is given as 19.8 cm and the base area of the cylinder is given as 307.8 cm^2.

3. The volume of the cylinder is given as 9.234 cm^3.

4. If the cylinder and the prism share the same height, the volume of the prism can be calculated by using the base area of the prism.

5. The base area of the prism is given as 196 cm^2.

6. The volume of the prism can be calculated by multiplying the base area with the height of the prism.

7. The volume of the prism is 196cm^2 * h = 6.186 cm^3

8. So the volume of the prism is 6.186 cm^3

Answer: 38 toys

If each of the smaller boxes has 10 toys, and Martin's mom added 28 more toys into only one of the boxes, that box would have a total of 38 toys.

10 + 28 = 38 toys

The accurate of the function is calculated using the fomula O(n).

Function in math is known as an equation that has only one answer for y for every x and it assigns exactly one output to each input of a specified type.

Here we have given that maximum distance is less than 10%.

As we all know that the basic approach is to check only consecutive pairs of x and y.

Here we have given that for every element x or y, then we have to check the index of the previous occurrence of x or y and if the previous occurring element is not similar to current element update the minimum distance.

Here we have a question arises what if an x is preceded by another x and that is preceded by a y for that situation we have to know how to get the minimum distance between pairs.

Hereby analyzing closely it can be seen that every x followed by a y or vice versa can only be the closest pair so ignore all other pairs.

Complete question:

Write the function to calculate the accuracy? show that maximum distance is less than 10%.

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The solution to the equation is 6.24

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

o/3.9=1.6

Express the variable as x for proper identification

So, we have the following representation

x/3.9=1.6

Multiply both sides of the equation by 3.9

This gives

x = 3.9 * 1.6

Evaluate

x = 6.24

Hence, the solution is 6.24

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Complete question

Solve the following equation

o/3.9=1.6

The equation of the graph that passes through the points (4, 24) and (6, 30) is y = 3x + 12

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

The point-slope form is expressed as;

y - y₁ = m( x - x₁ )

Given that the the graph passes through the points (4, 24) and (6, 30).

First, determine the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 30 - 24 )/( 6 - 4 )

Slope m = ( 6 )/( 2 )

Slope m = 3

Next, plug the slope m = 3 and point 1 ( 4,24) into the point-slope form and simplify.

y - y₁ = m( x - x₁ )

y - 24 = 3( x - 4 )

y - 24 = 3x - 12

y = 3x - 12 + 24

y = 3x + 12

Therefore, the equation of line is y = 3x + 12,

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Answer: According to Mars, the makers of M&Ms, their factory produces 25% blue, 25% orange, and 12.5% for each of the remaining colors, which are yellow, green, brown, and red.

The observed values based on the entire lasso are 25 blue, 25 orange, 12.5 yellow, 12.5 green, 12.5 brown, and 12.5 red. These values match the expected values according to the manufacturer, which is 25% blue, 25% orange, and 12.5% for each of the remaining colors.

So, the observed values based on the entire lasso compare to the expected values from the manufacturer. The proportion of colors in the observed sample is the same as the proportion of colors that the factory produces, meaning that the factory is producing the expected ratio of colors.

Step-by-step explanation:

The volume of the solid generated by revolving about the line y=-1 is 324π cubic units and the volume of the solid generated by revolving about the line y=-2 is 216π cubic units.

To find the volume of the solid generated by revolving the region bounded by the parabola y=-(x^2)/9 and the lines y=-1 about a line, we can use the method of cylindrical shells.

a) The line y=-1 is the axis of revolution, so the volume of the solid generated by revolving the region about this line is:

V = ∫[(-1-(x^2)/9)^2 - (-1)^2] * 2πx dx

where the integral is taken over the interval for which the parabola y=-(x^2)/9 is above the line y=-1. So the limits of the integral are from -3 to 3, the volume is:

V = ∫[(-1-(x^2)/9)^2 - (-1)^2] * 2πx dx from -3 to 3 = 324*π cubic units

b) The line y=-2 is the axis of revolution, so the volume of the solid generated by revolving the region about this line is:

V = ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx

where the integral is taken over the interval for which the parabola y=-(x^2)/9 is above the line y=-2. So the limits of the integral are from -3 to -sqrt(92) = -3 to -3sqrt(2) and 3*sqrt(2) to 3 , the volume is:

V = ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx from -3 to -3sqrt(2) + ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx from 3sqrt(2) to 3 = 216*π cubic units

c) The line y=1 is not on the same side of the parabola y=-(x^2)/9 as the region bounded by the parabola and the lines y=-1 so there is no solid generated by revolving about this line.

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Answer:

The equation Jared can use to find the rate at which he drove is:

rate (r) = distance (d) / time (t)

So in this case, Jared can plug in the values he knows into the equation:

r = 15 miles / 0.5 hours

Solving for r, he can find the rate at which he drove:

r = 30 miles per hour.

So Jared drove at a rate of 30 miles per hour.

Step-by-step explanation:

PLEASE GIVE BRAINLIEST

The coordinates of X are (-6.4, 5.75)

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

A = (-10,7)

B = (8,-5).

m : n = 1 : 4

The coordinate is then calculated as

X = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

X = 1/5 * (1 * 8 + 4 * -10, 1 * -5 + 4 * 7)

Evaluate

X = (-6.4, 5.75)

Hence, the coordinate is (-6.4, 5.75)

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Complete question

given directed line segment ab determine point x on the graph such that x partitions the segment from a(-10,7) to b(8,-5) in the ratio 1:4 and give it's coordinates

The radius of curvature is 1410 ft, the velocity is 5.48 ft/s, the normal acceleration is 0.0213 ft/s2, and the magnitude of the acceleration is 0.500 ft/s2 after the particle travels 30 ft along the path to (2.806, 142).

The radius of curvature, r, can be calculated using the formula r = v2/a, where v is the velocity and a is the normal acceleration. The velocity is calculated by integrating the acceleration with respect to time. The normal acceleration is calculated by taking the derivative of the velocity with respect to time. The magnitude of the acceleration is the same as the acceleration given in the problem.

1. Calculate the velocity, v, by integrating the acceleration (0.5 ft/s2) with respect to time:

v = 0.5 * t = 0.5 * 30 s = 15 ft/s

2. Calculate the normal acceleration, a, by taking the derivative of the velocity with respect to time:

a = dv/dt = 0.5 ft/s2

3. Calculate the radius of curvature, r, using the formula r = v2/a:

r = 15 ft/s2/0.5 ft/s2 = 30 ft = 1410 ft

4. The magnitude of the acceleration is the same as the acceleration given in the problem, 0.5 ft/s2.

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The simplification of the trigonometric function tan x csc x is;  sec x

The six trigonometric functions are defined as;

sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Now, we know that;

cot x = cos x/sin x

sec x = 1/cos x = (cos x)⁻¹

csc x = 1/sin x = (sin x)⁻¹

tan x = sin x/cos x

Thus;

tan x csc x = (sin x/cos x) * (1/sin x)

= 1/cos x = (cos x)⁻¹

= sec x

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Consequently, b must have a value of -3.The following points should be located on the cartesian plane: (0,a), (a,0), (-a, 0), (0,-a)..

How to calculate a line's equation given two points:Make use of the slope formula to determine the slope.

To find the y-intercept (b), use one of the points and the slope.

The slope-intercept form of a line is y = mx + b, and you may obtain the equation for the line by plugging in the values for m and b once you have those values.

On the graph of 2x + 3y = - 5, 2,b) is located.

To estimate

The amount b

Given that (2,b) is located on the graph of 2x + 3y = 5,

hence, we do

( 2 × 2 ) + ( 3 × b ) = - 5

⇒ 4 + 3b = - 5

⇒ 3b = - 9

⇒b = - 3

Consequently, b must have a value of -3.

The following points should be located on the cartesian plane: (0,a), (a,0), (-a, 0), (0,-a)...

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Correct option is C, The information about the acids that are created from the sugar in sweets and bacteria from teeth comes from Jaws.

gum, lollipops, and hard sweets without additional sugar.

Gum with a high Xylitol content, like Icebreaker Ice Cubes, makes you salivate more, which helps kill dangerous bacteria. Hard sweets and sugar-free lollipops can also stimulate the salivary glands.

Black chocolate offers more antioxidants than milk chocolate and less sugar.

As long as it is eaten in moderation and leaves your teeth bushed, the occasional candy piece is acceptable.

The greatest strategy to stop sugar's harmful effects on teeth is to always pay close attention. We advise you to limit your sugar intake, regularly brush away the bacteria-filled plaque on your teeth, and consume nutritional meals to maintain strong teeth.

Combining routine dental exams with fluoride treatments from our dental team will give you and your family the best chance of preventing tooth decay.

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Answer: 1

Step-by-step explanation:

1 + 0 = 1

The value of the expression when e = 12 and f = 1/2 is 1

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

e/4 + 2f - 3

Also, from the question, we have the following values:

e = 12 and f = 1/2

substitute the known values in the above equation, so, we have the following representation

e/4 + 2f - 3 = 12/4 + 2 * 1/2 - 3

Evaluate the expression

e/4 + 2f - 3 = 1

Hence, the solution is 1

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The company, under the new president, is most likely, earning a profit of $ 10, 000 per month.

When a person is said to have done a 180, it means that they are now doing the opposite of what they used to do. For example, a person who was eating only fast foods doing a 180 would end up eating only healthy food.

This means that the new president doing a 180, means that the company is doing the opposite of what they were doing and instead of making losses of $ 10, 000 monthly, they are making profits of $ 10, 000 every month.

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The observational unit is Harley and the variable is 0, 1, 2, ..., 10.

When gathering statistical data, information is gathered and statistics are compiled on an observation unit, which is also known as a statistical unit occasionally. An observation is the value of a certain variable at a specific time.

The observational unit in this scenario is Harley and the variable is the number of times Harley chose the correct cup out of 10 trials. The variable can take on the values of 0, 1, 2, ..., 10, where 0 represents the number of incorrect choices and 10 represents the number of correct choices.

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The line represents 1 foot, so 4 feet would require a line that is 4 times as long as the 1/4 inch line, which is 1 inch.

The formula for finding the length of a line to represent a certain number of feet is L = (1/4)*F, where L is the length of the line, and F is the number of feet. In this case, to find the length of a line to represent 4 feet, the calculation would be L = (1/4)*4 = 1. Therefore, the line would need to be 1 inch long to represent 4 feet. This is because 1/4 inch of the line represents 1 foot, so 4 feet would require a line that is 4 times as long as the 1/4 inch line, which is 1 inch.Therefore, to represent a length of 4 feet on the same drawing, a line 1 inch long needs to be drawn. The calculation is as follows: 1/4 inch line = 1 foot, therefore 4/4 inch line = 4 feet. Therefore, 1 inch line = 4 feet.

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The set of all differentiable real-valued functions defined on the real line. Proved that V is a vector space with the operations of addition and scalar multiplication defined as:

(f + g)(s) = f(s) + g(s)

(c f)(s) = c[f(s)].

Let V denote the set of all differentiable real-valued functions defined on the real line. Prove that V is a vector space with the operations of addition and scalar multiplication defined as:

(f + g)(s) = f(s) + g(s)

(c f)(s) = c[f(s)].

To prove vector space, we need to hold eight properties of vector space.

1) Closed

 (f + g)(s) = f(s) + g(s) (given)

so, closed holds with respect to given defined operation.

2) Associative law

let defined three function, f,g,h in V,

(f+g)(s)+h(s)=f(s)+g(s)+h(s)

                   = f(s)+(g+h)(s)

hence associative law hold.

3) Existence of identity,

(f+o)(s)=f(s)

f(s)+o(s)=f(s)

Hence, O(s) is identity for this function,

4) Existences of Inverse,

(-f)(s) is inverse for f(s)

5) Commutative law,

(f+g)(s)=(g+h)(s)

6)( cf)(s)=c[f(s)]g

7) c(f+g)(s)=cf(s)+g(s)

8) c(fg)(s)=(cf(s))g(s)

Hence, the given function is defined Operations.

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Answer:

Step-by-step explanation:oc (6,5), (3,2), (2,4) (6, 3), (1, 0)

The value of P(x < 1) is 0.5.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Mean = 1

Standard deviation = 0.05

The P-value of Z when x = 1.

z = (x - mean) / standard deviation

z = (1 - 1)/0.05

z = 0

The P-value when z = 0 is 0.5.

So,

P(x < 1) = 0.5

Thus,

P(x < 1) is 0.5.

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