a call center has analyzed the calls received in the last month and found that, on average, 64 calls were received per hour. assume that call arrivals follow poisson distribution and come from an infinite population. service times follow an exponential distribution with an average of 45 seconds per call served. assume the queue length can be infinite with fcfs discipline. a) what is the average number of people in line? (2.5 points) b) what is the average number of people in the system? (2.5 points) c) what is the average amount of time that a person can expect to spend in line? (2.5 points) d) on average, how much time will a person spend in the system? (2.5 points) e) during the weekends, the call arrival rate can be expected to increase to over 80 per hour. what effect will this have on the average number of people waiting in line? (2 points)

The profit made as of investor borrows $100 is $25.

Investing in foreign currencies can be a profitable venture, but it comes with a certain level of risk.

If an investor borrows $100, converts it to pesos, and invests the pesos in Mexico for one year, the profit made is $25.

This is calculated by borrowing $100 and converting it to 625 pesos at the spot rate of 6.25 pesos per dollar.

The 625 pesos are then invested in Mexico for a year at a 45% interest rate, resulting in 281.25 pesos.

The 281.25 pesos are then converted back to dollars at the forward rate of 7.25 pesos per dollar, resulting in $38.75.

The resulting profit is $38.75 - $100 = -$61.25.

Investing in foreign currencies is not without its risks.

When investing in foreign currencies, the exchange rate can change drastically over short periods of time, resulting in losses or gains.

Additionally,

The interest rate in the country of investment can also change, resulting in different levels of returns.

The profit made if an investor borrows $100, converts to pesos and invests in Mexico for a year is $25.

The calculation is as follows:

Borrow $100 and convert to pesos:

100 x 6.25 = 625 pesos

Invest 625 pesos in Mexico for one year:

625 x 45% = 281.25 pesos

Convert 281.25 pesos back to dollars at the forward rate:

281.25 / 7.25 = $38.75

Profit = $38.75 - $100 = -$61.25

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90  is the average score of these top students.

What is the average in mathematics?

Mean is defined as the average equal to the ratio of the total number of values ​​in a particular set to the total number of values ​​in the set.

                               The average in mathematics is the average of a data set obtained by adding all the numbers and dividing the sum of the numbers by the number of numbers. For example, using the following dataset:

8, 9, 5, 6, 7, 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7, so the average is 7. 

the average score of these top students = 95 + 86 +  87 +  91 + 94 + 87/6

                                                              = 540/6 = 90

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A sequence is arithmetic sequence when the first differences are all the same non-zero number.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.

As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.

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Answer:

Step-by-step explanation:

mean means to add them all up and divide by how many their are.

The equations for which 8 is a solution are: x - 4 = 4, 2x = 16, x/2 = 16, and x/8 = 1.

An equation is a mathematical statement that shows that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal is usually to solve for the value of the variable that makes the equation true.

In the given question,

The equations in which 8 is a solution are:

x - 4 = 8 (which simplifies to x = 12)

2x = 16 (which simplifies to x = 8)

x/2 = 16 (which simplifies to x = 32)

x/8 = 1 (which simplifies to x = 8)

Therefore, the correct answers are:

x - 4 = 8

2x = 16

x/2 = 16

x/8 = 1.

The equations for which 8 is a solution are: x - 4 = 4, 2x = 16, x/2 = 16, and x/8 = 1.

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x² - 16x + 64 = 0 is the equation whose solution is 8.

How to check for which equations is 8 a solution?

To check if 8 is a solution for each equation, we substitute x = 8 into each equation and see if the equation is true or not.

x + 6 = 8 + 6 = 14

and

2x + 2 = 2(8) + 2 = 18, which is not equal to the value of (x+6).

Therefore, 8 is not a solution to this equation.

4x - 4 = 4(8) - 4 = 28,

and

10 - 2x = 10 - 2(8) = -6, which is not equal to 28.

Therefore, 8 is not a solution to this equation.

2x - 4 = 2×8-4 = 12

and

3x-24 = 3×8-24 = 0 which is not equal to 12. Therefore, 8 is not a solution to this equation.

Now,

x² - 16x + 64 = 0 (which can be factored as (x-8)² = 0)

x = 8 (which is always true)

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Correct question is "For which equations is 8 a solution? Select the correct answers from the following,

1) x + 6 = 2 x + 2

2) 10 - 2x = 4 x - 4

3) 2 x-4 = 3 x - 24

4) x² - 16x + 64 = 0

The population of unionid mussels start decreasing approximately at the rate of 75% after zebra mussels were introduced .

The change occurs as zebra mussels consuming almost all the resources available  into the Hudson River.

Change in the population of the unionid mussels and zebra mussels over the course of six years are as follow,

population of unionid mussels in 1991 in number per square meter

= 8

Then in the year 1994 it become 3 number per square meter

And finally in the year 1994 it become 2 number per square meter

Change in population of unionid mussels from 1991 to 1997

= [( 2 - 8 )/ 8] × 100

= -75%

Negative sign indicate that decrease in the population.

Now ,

Change in population of zebra mussels is given by,

In 1991 in number per square meter = 4

In 1994 in number per square meter = 1,329

In 1997 in number per square meter = 3,181

Change in population of zebra mussels from 1991 to 1997

= [( 3181 - 4 )/ 4] × 100

= 79425%

There is increase in the population of zebra mussels in thousands.

Reason of change is zebra mussels introduced into the Hudson River

and they eating almost all the resources available in the area.

Zebra mussels consumes large amount of phytoplankton and other small organisms available in the water .

Due to lack of resource availability unionid mussels population decreasing year by year.

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The above question is incomplete, the complete question is:

Unionid mussels are native to the Hudson River in New

York State. In the early 1990s, zebra mussels were

introduced into the Hudson River. The table shows the

number of unionid mussels and zebra mussels over the

course of six years.

How did the population of unionid mussels change

after zebra mussels were introduced? Why did this

change occur?​

attached data.

The four angles are: A = 110 degrees, B = 10 degrees, C = 120 degrees,   D = 120 degrees

Angles are geometric shapes created when two lines, rays, or line segments cross at a single point.

The two lines or line segments that make up the angle are referred to as the sides or arms of the angle, and this shared point is known as the vertex of the angle.

The amount of rotation required to shift one side to overlap with the opposite side determines the magnitude of an angle.

Angles are commonly expressed in degrees, with 360 degrees representing a full rotation around a point.

Acute angles (less than 90 degrees),

right angles (exactly 90 degrees),

obtuse angles (more than 90 degrees but less than 180 degrees), and straight angles (exactly 180 degrees) are some frequent forms of angles.

What are degrees ?

Angles are measured in degrees, a unit of measurement. 1/360th of a full revolution around a point is equivalent to one degree (1°).

Two perpendicular lines can be used to create a right angle, which has a 90 degree angle.

A straight angle, created by a straight line, has a degree value of 180.

Angles, rotations, and slopes are frequently measured in degrees in the fields of mathematics, physics, engineering, and several others.

The freezing point of water is 0 degrees Celsius (or 32 degrees Fahrenheit), whereas the boiling point is 100 degrees Celsius. In daily life, degrees are frequently used to express temperatures. (or 212 degrees Fahrenheit).

According to question :-

Let the four angles be A, B, C, and D. We know that:

A + B + C + D = 360 (the sum of all angles in a quadrilateral is 360 degrees)

We also know that:

A + B = 120 (the sum of the first two angles is 120 degrees)

C + D = 130 (the sum of the last two angles is 130 degrees)

We can use these equations to solve for the individual angles. First, we can rearrange the equation A + B = 120 to get:

A = 120 - B

Similarly, we can rearrange the equation C + D = 130 to get:

D = 130 - C

Substituting these expressions for A and D in terms of B and C into the equation A + B + C + D = 360, we get:

(120 - B) + B + C + (130 - C) = 360

Simplifying, we get:

250 - B + C = 360

Subtracting 250 from both sides, we get:

C - B = 110

Now we have two equations with two unknowns:

C + B = 130 (from the equation C + D = 130)

C - B = 110

We can add these equations to eliminate B and get:

2C = 240

Dividing by 2, we get:

C = 120

Substituting this value for C into either of the equations above, we get:

B = 10

Now we can use the equation A + B = 120 to find A:

A + 10 = 120

A = 110

Finally, we can use the equation A + B + C + D = 360 to find D:

110 + 10 + 120 + D = 360

D = 120

Therefore, the four angles are:

A = 110 degrees

B = 10 degrees

C = 120 degrees

D = 120 degrees

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For the given circle the value of x = [tex]18^{0}[/tex] and the value of y = [tex]10^{0}[/tex] .

What about circle?

A circle is a two-dimensional geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius of the circle. The diameter of a circle is the distance across the circle passing through the center, which is equal to twice the radius.

The circumference of a circle is the distance around the outside edge of the circle and is given by the formula C = 2πr, where "r" is the radius of the circle, and "π" (pi) is a mathematical constant equal to approximately 3.14159. The area of a circle is given by the formula A = πr^2, where "r" is the radius.

The circle is a fundamental shape in geometry and is used in many areas of mathematics, science, and engineering. It has many properties that make it useful, such as being able to inscribe it in a square with equal sides, as well as being the shape that minimizes the perimeter for a given area.

According to the given information:

As, we know that when diameter passes through center of circle is form a right angle .

So,  

[tex]5x^{0} = 90^{0} \\\\x^{0} = 18^{0}[/tex]

In the same way as we know that sum of all angle of triangle is = [tex]180^{0}[/tex]

i.e.

[tex]5x^{0} + 50^{0} + 4y^{0} = 180^{0}\\\\90^{0} + 50^{0} + 4y^{0} = 180^{0} \\\\4y^{0} = 180^{0} - 90^{0} - 50^{0} \\\\y^{0} = 10^{0}[/tex]

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Therefore, the value of x in the circle with center O is x = 7.

A circle is a geometric shape consisting of all points that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius. A circle is a two-dimensional shape, and it is often represented by the symbol "O" or "⭕". The circumference of a circle is the distance around its edge or boundary.

Here,

If AB and BC are chords of a circle with center O, then we can use the intersecting chords theorem to find the value of x. According to the intersecting chords theorem, if two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. That is,

AB * BD = CB * BD

where BD is the length of the segment of chord AC that is inside the circle.

We can rearrange this equation to get:

AB * BD - CB * BD = 0

Factorizing BD from both terms, we get:

BD * (AB - CB) = 0

Since BD cannot be zero (as it is a positive length), we have:

AB - CB = 0

Substituting the given values, we get:

(4x-1) - (3x+6) = 0

Simplifying this equation, we get:

x - 7 = 0

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The true or false statements, given the function, would include:

True:

False :

The point of symmetry is the vertex of the given function f(x). The vertex of f(x) is (3, 6), so the point of symmetry on ƒ-¹(x) will be the inverse of the vertex, which is (6, 3).

The statement is incorrect because the correct representation of the domain of ƒ-¹(x) is (-∞, ∞). The cubic function f(x) is a one-to-one function, and its range is all real numbers.

The given function f(x) is a one-to-one function because it is a cubic function with a unique output for each input. The inverse of a one-to-one function is also a function.  

The domain of the given function f(x) is all real numbers, and since it is a one-to-one function, its range will be the domain of its inverse function, which is (-∞, 6).

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The area of the region is 6 square unit.

The base of the triangle is the distance between the x-coordinates where the curves y = √x and y = −x + 6 intersect, which is 2. The height of the triangle is the distance between the y-coordinate where y = 0 intersects the y-axis and the y-coordinate where the line y = −x + 6 intersects the y-axis. This distance is 6.

Therefore, the area of the region bounded by the curves y = √x, y = −x + 6, and y = 0 is:

Area = 1/2 * base * height

    = 1/2 * 2 * 6

    = 6

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The estimated radius of the circular object with an area of 40 cm² is 3.57 cm

To find the inverse function r(A), we can start by setting A = πr² and solving for r:

A = πr²

A/π = r²

r = √(A/π)

Therefore, the inverse function is r(A) = √(A/π).

To estimate the radius of a circular object with an area of 40 cm², we can simply substitute A = 40 cm² into the inverse function:

r(40) = √(40/π) ≈ 3.57 cm

Therefore, the estimated radius of the circular object with an area of 40 cm² is approximately 3.57 cm

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Answer: When looking for this graph on your work, it is a parabola opening upwards (positive) with a vertex at (-1,3)

Step-by-step explanation:

The fewest number of trips needed to get everything across the river without anything being eaten is 5 trips.

The problem requires Fanny to figure out a sequence of steps that will enable her to transport the fox, chicken, and bag of corn across the river without anything being eaten.

To solve this problem she must come up with a plan that allows her to transport all three items without putting any of them at risk.

Here we have

The named Fanny bought a specially-trained fox named Federico and a chicken and a bag of corn seeds

To safely transport the fox, the chicken, and the bag of corn across the river, Fanny must follow a specific sequence of steps to ensure that nothing is eaten. Here is one possible solution:

Therefore,

The fewest number of trips needed to get everything across the river without anything being eaten is 5 trips.

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Required error is the perimeter of the triangle is 60 cm, not 66 cm as Alfonso said.

What is perimeter of a triangle?

The perimeter of a triangle is the total length of the three sides of the triangle. It is a fundamental geometric concept that is important in many applications, including architecture, engineering, and construction.

To calculate the perimeter of a triangle, you simply add up the lengths of its three sides. This is expressed by the following formula,

Perimeter = side a + side b + side c

where "a," "b," and "c" are the lengths of the three sides of the triangle.

Here Alfonso's error is that he added the three side lengths incorrectly. The correct way to find the perimeter of a triangle is to add up all three sides.

In this case, the three side lengths are 22 cm, 11 cm, and 27 cm. Adding them up, we get,

22 cm + 11 cm + 27 cm = 60 cm

Therefore, the perimeter of the triangle is 60 cm, not 66 cm as Alfonso said.

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Correct question is " There is a triangle whose sides are 22 cm, 11 cm and 27 cm.

Alfonso said that the perimeter of this

triangle is 66 centimeters. What was his error?"

Boyle's law, which relates the pressure and volume of an ideal gas, has various applications in science, engineering, and everyday life. Some of the applications of this measuring technique include:

Gas storage: Boyle's law is used in designing and managing gas storage systems, such as gas cylinders and tanks. It helps in determining the volume of gas that can be stored at a given pressure and vice versa.

HVAC systems: Heating, ventilation, and air conditioning (HVAC) systems use Boyle's law to control the pressure and volume of gases in order to regulate temperature and air flow.

Scuba diving: Boyle's law is applied in scuba diving to calculate the changes in volume of gases in diving cylinders at different depths, which affects the diver's breathing and decompression requirements.

Medical applications: In respiratory therapy, Boyle's law is utilized in devices like ventilators, which deliver oxygen or other gases to patients at specific pressures and volumes.

Industrial processes: Boyle's law is used in industrial processes where gases are compressed or expanded, such as in manufacturing, chemical processing, and power generation.

As for measuring surfaces that are not flat, Boyle's law is not directly applicable for such measurements. It is a gas law that relates the pressure and volume of a gas, assuming the gas behaves as an ideal gas.

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The sample may not be representative of the population's preferences for frozen desserts.

Sampling technique that Keziah is using is convenience sampling. Convenience sampling is a non-probability sampling technique.

The researcher selects the easiest and most convenient individuals to participate in the study.

Keziah is simply surveying shoppers who are exiting a grocery store on the west side of her town without any predetermined criteria for selection.

As a result, the sample may not be representative of the population's preferences for frozen desserts.

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Answer:

3.535

Step-by-step explanation:

35% is the same as .35

therefore, you can multiply 10.1 by .35 to get 3.535

Therefore , the solution of the given problem of equation comes out to be 2.61, -6.61 is the answer's numerical component.

Regression modelling uses the polynomial solution, which is x = ax2 + b + c=0, to solve problems with a single variable. The First Principle of Algebra states that there can only be one solution because it contains an additional order. There are both simple and complex solutions available. As the name suggests, a "non-linear algorithm" comprises four variables.

Here,

The equation y = x² + 4x - 12 has a parabola as its graph. To graph the solution to the equation x² + 4x = 12,

Rewrite the equation in the following format: y = x² + 4x - 12

Locate the x-values where the graph and x-axis overlap.

These x-values, which stand in for the equation's solutions, are those when y = 0.

Read off the graph's x-values and write them down as the equation's answers.

The solutions to the equation x² + 4x = 12 are about x = 2.61

and x = -6.61 (rounded to two decimal places), according to the graph of the equation y = x² + 4x - 12.

As a result, "2.61, -6.61" is the answer's numerical component.

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The drive-thru with typically more wait time is Burger Quick, because it has a larger median. The Option A.

The median is a measure of central tendency that represents the middle value of a set of data. In this case, the median wait time at Burger Quick is 15.5 minutes, while the median wait time at Super Fast Food is 12 minutes.

This indicates that, on average, customers at Burger Quick experience a longer wait time compared to customers at Super Fast Food. The larger median at Burger Quick suggests that there may be some longer wait times skewing the data towards the higher end which could be due to various factors such as slower service, or other operational issues at Burger Quick resulting in a longer wait time for customers at their drive-thru.

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The variance is equal to the squared value of the standard deviation.(Option a)

The variance is a measure of how spread out a set of data is. It is calculated by taking the average of the squared differences of each data point from the mean. The standard deviation, on the other hand, is the square root of the variance and measures the spread of data in relation to the mean.

Therefore, the variance is equal to the squared value of the standard deviation. Mathematically, Var(X) = σ^2, where Var(X) is the variance and σ is the standard deviation.

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To solve for x, we can combine like terms on the left side of the equation:

0.35x + 0.40x + 0.05x + 1.2 = 7.12

0.8x + 1.2 = 7.12

Subtracting 1.2 from both sides:

0.8x = 5.92

Dividing both sides by 0.8, we get:

x = 7.4

Therefore, the value of x is actually 7.4

Answer:

Step-by-step explanation:

first you divide the shape into 3 parts ;a big triangle, and 2 little squares

after that to get the height of the triangle i gotten by adding

3+5+2+6=16yd

area of a triangle =1/2 × b×h

area =1/2×7×16

area=112/2

area=56yd²

small squre 1=

area=5×5

=25yd²

area of small rectangle=

area=LB

=3×2

=6yd²

total area =triangle+square+rectangle

=56+25+6

TA=87yd²

Ms. Wilson purchased 6 more glue sticks than Mr. Davis.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

Let's define:

A = number of glue sticks in package A (18)

B = number of glue sticks in package B (12)

p = number of packages purchased

Then, the equations for the total number of glue sticks are:

Package A: g = 18p

Package B: g = 12p

Mr. Davis buys 5 packages of the Package A glue sticks, so he purchased:

g = 18 x 5 = 90 glue sticks

Ms. Wilson buys 8 packages of the Package B glue sticks, so she purchased:

g = 12 x 8 = 96 glue sticks

The difference in the total number of glue sticks that each person purchased is:

96 - 90 = 6 glue sticks.

Therefore, Ms. Wilson purchased 6 more glue sticks than Mr. Davis.

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The probability that a 120 square foot roll will contain more than one flaw is approximately 0.0001, or 0.01%.

The number of flaws per square foot, denoted by X, as a Poisson distribution with parameter lambda = 1/40 (since there is an average of one flaw per 40 square feet).

To find the probability that a 120 square foot roll will contain more than one flaw, we need to calculate the probability of X > 1, where X is Poisson distributed with parameter lambda = 1/40.

Using the Poisson distribution formula, we have:

[tex]P(X > 1) = 1 - P(X < = 1)[/tex]

= [tex]1 - [P(X = 0) + P(X = 1)][/tex]

We can calculate P(X = 0) and P(X = 1) using the Poisson distribution formula:

P(X = k) = (e^(-lambda) * lambda^k) / k!

where k is the number of flaws and lambda = 1/40.

[tex]P(X = 0) = (e^(-1/40) * (1/40)^0) / 0! = e^(-1/40) = 0.9756[/tex]

[tex]P(X = 1) = (e^(-1/40) * (1/40)^1) / 1! = (1/40) * e^(-1/40) = 0.0244[/tex]

[tex]P(X > 1) = 1 - [P(X = 0) + P(X = 1)][/tex]

[tex]= 1 - (0.9756 + 0.0244)[/tex]

[tex]= 0.0001[/tex]

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The coordinate notation for a translation of 7 units right and 4 units  are:

Q: (5,-2)

R: (4,-8)

A: (8,-6)

To perform a translation of 7 units right and 4 units down on Triangle QRS, we add 7 to the x-coordinates and subtract 4 from the y-coordinates of each vertex. The coordinate notation for the translated triangle, denoted as Q'R'S', is:

Q': (−2 + 7, 2 - 4) = (5, -2)

R': (−3 + 7, −4 - 4) = (4, -8)

S': (1 + 7, −2 - 4) = (8, -6)

So, the coordinate notation for the translated triangle Q'R'S' is Q'(5, -2), R'(4, -8), and S'(8, -6).

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The area of the small triangle is 4 sq.cm.. The area of the medium triangle is 12 sq.cm. The area of the large triangle is 24 sq. cm.

With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.

Given data:

Dimensions-

area of triangle = 1/2 *base * height

The area of the small triangle = 1/2*2*4 = 4 sq.cm.

The area of the medium triangle = 1/2*4*6 = 12 sq.cm.

The area of the large triangle = 1/2*6*8 = 24 sq. cm

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Complete question:

Dimensions-

small triangle: base = 2 cm, height = 4cm

medium triangle: base = 4 cm , height = 6 cm

Larger triangle: base = 6 cm ,height = 8 cm

The area of the small triangle is_______

The area of the medium triangle is______

The area of the large triangle is______

As a result, the response is A .The number of dollars it costs to rent the bowling lane for 3 hours.

The US, Canada, Australia, and some nations in the Pacific, Caribbean, Southeast Asia, Africa, and South America all use the dollar as their primary unit of exchange It is a type of paper money, currency, and monetary unit used in the United States that is equivalent to 100 cents

The total cost (in dollars) for renting a bowling alley for x hours is represented by the function b(x) = 3x + 15.

We change x in the function to 3 to obtain b(3).

B(3) = 3(3) + 15 = 9 + 15 = 24 is the result.

Therefore, b(3) is the amount of money required to rent the bowling alley for three hours.

As a result, the response is A.

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The probability that the mean annual salary of a random sample of 64 teachers from state X is less than $52,000 is approximately 0.005 or 0.5%.

The sampling distribution of the mean is normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Here, we are given that the population mean is $54,000 and the population standard deviation is $5,000. We are also told that the sample size is n = 64.

To find the probability that the mean annual salary of a random sample of 64 teachers is less than $52,000, we need to standardize the sample mean using the sampling distribution of the mean.

Z = (x' - μ) / (σ / √n)

where x' is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

Z = (52,000 - 54,000) / (5,000 / √64)

= -2.56

We can then look up the probability of a standard normal variable being less than -2.56 using a standard normal table or calculator, which gives us a probability of approximately 0.005.

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Complete question is:

The annual salary of teachers in a certain state X has a mean of $54,000 and standard deviation of σ = $5,000. What is the probability that the mean annual salary of a random sample of 64 teachers from this state is less than $52,000?