the amount of time it takes john to wait in line at the bank is continuous and uniformly distributed between 7 minutes and 17 minutes. what is the probability that it takes john between 9 and 12 minutes to wait in line at the bank?

The difference in the price of a car worth £15,000 + VAT due to the increase in VAT is £250.

To calculate the difference in price due to the increase in VAT, first find the original amount of VAT on the car:

£15,000 x 17.5% = £2,625

Then find the new amount of VAT on the car:

£15,000 x 20% = £3,000

Finally, subtract the original amount of VAT from the new amount of VAT to find the difference:

£3,000 - £2,625 = £375

Therefore, the difference in the price of the car due to the increase in VAT is £375. However, this is only the difference in VAT. To find the total difference in price, you need to add the original price of the car:

£15,000 + £375 = £15,375

So the total difference in the price of the car due to the increase in VAT is £250 (£15,375 - £15,000).

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After considering the following hypothetical survey results of 18- to 34-year-olds in a certain country, in response to the question "Are you currently living with your family?" we get the following probabilities.

a. The joint probability table for the given data is:

             Yes      No      Totals

Men          0.212   0.282   0.494

Women        0.184   0.322   0.506

Totals       0.396   0.604   1

b. The marginal probabilities for living with family and not living with family are:

                 Yes No

Men        0.212 0.282

Women 0.184 0.322

Totals 0.396 0.604

c. The probability of living with family given you are an 18- to 34-year-old man in the U.S. is 0.212/0.396 = 0.5354 or approximately 53.54%.

d. The probability of living with family given you are an 18- to 34-year-old woman in the U.S. is 0.184/0.506 = 0.3636 or approximately 36.36%.

e. The probability of an 18- to 34-year-old in the U.S. living with family is 0.396 or 39.6%.

f. We cannot determine whether the sample is representative solely based on the percentage of males in the survey.

A good representative sample should be randomly selected to accurately reflect the population being studied. The percentage of males in the sample is relevant only if it differs significantly from the percentage of males in the population being studied.

The joint probability table was developed for the survey results of 18- to 34-year-olds on living with family. Marginal probabilities were calculated and the probability of living with the family was found for both men and women. The overall probability of living with the family was also determined. It is unclear if the sample is representative without additional information.

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the expectation of buying one ticket is $2

Expectation if a person buys one ticket A person is interested in buying a ticket for a lottery that offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. The expected return is calculated using the following formula:

Expectation = (Probability of winning Prize 1 × Value of Prize 1) + (Probability of winning Prize 2 × Value of Prize 2) + (Probability of winning Prize 3 × Value of Prize 3)To determine the expectation, we must first determine the probability of winning each of the three prizes.

Since one thousand tickets are sold and only one person can win the first prize, the probability of winning the $1000 prize is 1/1000 or 0.001. Similarly, the probability of winning the $500 prize is 1/1000 or 0.001. Since five $100 prizes are available and only one person can win each prize, the probability of winning any one of the five $100 prizes is 5/1000 or 0.005.

Therefore, the expectation is calculated as follows: Expectation = (0.001 × $1000) + (0.001 × $500) + (0.005 × $100)Expectation = $1 + $0.50 + $0.50Expectation = $2Thus, the expectation of buying one ticket is $2. This means that the average value of a ticket is $2, and a person can expect to win $2 on average by purchasing a ticket. Since the cost of a ticket is $3, the expected return is less than the cost of the ticket, and therefore, it is not a good investment from a financial standpoint.

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The point c satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5] is: c = 1.4697

The conclusion of the Mean Value Theorem says that there is a number

c in the interval (1, 5) such that:

f'(c) = (f(5) - f(1))/(5 - 1)

We are given the function f(x) = x⁻⁸

Thus:

f(1) = 1⁻⁸ = 1

f(5) = 5⁻⁸ = 0.00000256

Thus:

f'(c) = (0.00000256 - 1)/4

= -0.25

f'(c) = -8x⁻⁹

Thus:

-8c⁻⁹ = -0.25

c⁻⁹  = 0.25/8

c⁻⁹ = 0.03125

c = 0.03125^(-1/9)

c = 1.4697

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The number of fish caught by Ashraf and Khalid by solving the equation formed is 39 and 30 respectively.

What is the Substitution method for solving equations?

In a system of linear equations to solve, we have N variables and N equations between them to solve. In substitution, we represent one variable in terms of another and replace it in the equation to convert it to a 1-variable equation and solve it.

a) Given, the number of fishes caught by Ashraf is "x" and by Khalid is "y".

As the total number of fish caught is 69, the equation is :

              [tex]x + y = 69[/tex]

b) It is stated in the question that the number of fish caught by Ashraf i.e. x is 30% more than that caught by Khalid i.e. y.

The equation formed is :

           x = 30% greater than y

               [tex]= y + 30y/100[/tex]

               [tex]= (100+30)y/100[/tex]

               [tex]= 13y/10[/tex]

Hence, the equation is : [tex]10x = 13y[/tex]

c) Here, we have 2 equations and 2 variables. We use the substitution method to find the values of the variables :

                   [tex]y + 13y/10 = 69[/tex]

                   [tex](10+13)y/10 = 69[/tex]

                    [tex]23y/10 = 69[/tex]

                    [tex]y = 69 * 10 /23[/tex]

                     [tex]y = 30[/tex]

Putting the value of y in the first equation :

                  [tex]x + 30 = 69[/tex]

                  [tex]x = 39[/tex]

Hence, the number of fish caught by Ashraf is 39, and by Khalid is 30.

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The answer is 1 / 9.

Larry had 1/3 of a Submarine sandwich left over from the excursion. If sharing with 3 friends, they must divide equally.

To do this, 1/3 of the sandwich should be divided into three equal parts. This can be written as:

1/3÷3

To simplify this expression, division can be converted to multiplication by multiplying the reciprocal of the divisor (3) by the dividend (1/3). That is:

1/3 ÷ 3 = 1/3 × 1/3

Multiplying the numerator and denominator gives:

1/3 × 1/3 = 1/9  

Therefore, each person will get 1/9 of the original sandwich.

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Answer:

here is the ananswer

Step-by-step explanation:

red go to red and black to black

The number of cubic centimeters of paint that will fit in the cylindrical container is:

66.36 cm³

The volume of a cylinder can be determined by multiplying the area of the base by the height. It may be expressed using the formula:

V = πr²h

where π (pi) is approximately equal to 3.14, r is the radius, and h is the height.

You should also note that the radius of the cylinder is one-half of the diameter.

V = πr²h

Since the cylindrical container of paint has a diameter of 3 cm, its radius would be 1.5 cm. Furthermore, its height is around 7 cm. As a result, by substituting the given values into the formula, we may get the following result:

V = πr²hV = π(1.5)²(7)

V = 66.36 cm³

Therefore, the cylindrical container of paint can hold approximately 66.36 cubic centimeters of paint.

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The statement "The median number of minutes outside in the summer is equal to the maximum number of minutes outside in the winter" is best supported by the data (option B).

Looking at the plot;

Winter: Minimum= 0   Maximum= 60   Median= 30

Range = 60 - 0 = 60

Summer: Minimum= 20   Maximum= 90    Median= 60

Range = 90 - 20 = 70

So the median number of minutes outside in the summer is

equal to the maximum number of minutes outside in the winter.

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Missing information:

The question is incomplete and the complete question is shown in the attached image.

Answer:

b/c

Step-by-step explanation:

sin B = opp/hyp

sin B = b/c

the center of dilation for the triangle is (0,0)

The center of dilation is a point in a plane about which a dilation, a type of transformation, is performed. A dilation is a transformation that changes the size of a geometric figure, while preserving its shape and orientation. The center of dilation is the fixed point that serves as the reference for the scaling or shrinking of the figure.

In a dilation, each point of the original figure is moved away from or towards the center of dilation, by a certain factor called the scale factor.  

The coordinate of yellow triangle and scaled triangle both passes through center of axes.

So, the center of dilation is (0,0).

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The area of the polygon with vertices P(1,2), Q(1,4), R(-1,6), and S(-3,2) is given as 10 units. Option B

We can find the area of the polygon with the given vertices by dividing it into triangles and adding their areas.

One way to divide the polygon into triangles is to draw a diagonal from vertex P to vertex R. This creates two triangles, PQR and PRS.

[tex]\frac{1 }{2} ((4 - 2) + (6--4) + (-2 - - 18) + (-6 - 2)[/tex]

= 1 / 2 ( 2 + `10 + 16 - 8)

= 1 / 2 ( 20

= 10

The area of the polygon is 10 units

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Answer:

Step-by-step explanation:
To find the average number of days it takes for the sun to rotate once, we can add the three rotation periods and divide by 3:

Average rotation period = (24.5 + 24.8 + 34.3) / 3

Average rotation period = 83.6 / 3

Average rotation period = 27.87 days (rounded to two decimal places)

Therefore, the average number of days it takes for the sun to rotate once based on the given information is approximately 27.87 days.

The expression for the rate of thermal energy produced in the resistor as a function of time t is P(t) = V(t)²/R.

The thermal energy that is produced in a resistor can be determined by P = I²R, where P is the power, I is the current, and R is the resistance. The current is given by I = V/R where V is the voltage. Therefore, P = V²/R.

Using the Ohm's law, the voltage is V = IR, so P = I²R = (V/R)²R = V²/R.

Thus, the rate at which thermal energy is produced in the resistor as a function of time t can be expressed as: P(t) = V(t)²/R where P(t) represents the power or rate at which thermal energy is produced in the resistor, V(t) represents the voltage as a function of time t, and R represents the resistance of the resistor.

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Answer:

Of the given options, "an engine" is the most reasonable abstraction for a car.

An engine is a fundamental component of a car that powers its movement, and it is present in almost all cars. The number of miles driven and the driving car color are characteristics of a specific car rather than abstractions of a car itself. For example, a car can still be considered a car even if it has not been driven any miles yet or if it has no color at all.

Therefore, an engine is a more reasonable abstraction for a car as it captures an essential feature of a car that is present in all cars.

The solution is, D. Driving, a reasonable abstraction for a car includes. Driving is an action or behavior associated with a car, as it involves operating or using the car to travel from one place to another. It is an essential aspect of the car's purpose and function.

Here, we have,

we know that,

An engine is a machine designed to convert fuel into mechanical energy that can be used to power other machines or devices. In the context of automobiles, an engine is the primary source of power that drives the vehicle. It typically operates by burning fuel in a combustion chamber to generate high-pressure gases that drive a piston, which in turn rotates a crankshaft that ultimately powers the car's wheels.

Car color and number of miles driven are characteristics or properties of a car, while an engine is a component that helps to power the car. Driving, on the other hand, is an action or behavior associated with a car, as it refers to the act of operating or using the car to travel from one place to another.

Therefore, driving is a reasonable abstraction for a car, as it captures an essential aspect of the car's purpose and function.

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Answer:

The formula for the area of a circle is A = πr^2, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.

If the radius of the circle is 11 inches, then we can substitute this value into the formula:

A = πr^2

A = π(11)^2

A = π(121)

So the area of the circle is 121π square inches, which is approximately 380.1327 square inches when rounded to four decimal places.

She had 9 red candies, 43 orange candies, and 14 yellow candies. Therefore, there are total 66 candies.

In mathematics, total is the addition of a series of arbitrary numbers called addition or addition; the result is their sum. In addition to numbers, other types of values ​​can be added: functions, vectors, matrices, polynomials, and in general, elements of any type of mathematical object on which a "+" operation is defined. The sum of infinite sequence is called sequence. They involve the concept of limits and are not considered in this article.

Given that:

9 red candies

43 orange candies and 14 yellow candies.

Therefore, there are  = 9 + 43 + 14

                                   = 66 candies.

Therefore, there are total 66 candies.

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Answer:

If 5/6 of the employees in a company are male, then the fraction of male employees in the company is:

5/6

If 7/8 of the male employees wear spectacles, then the fraction of male employees who wear spectacles is:

7/8

To find the fraction of employees who are males and wear spectacles, we need to multiply the fractions:

(5/6) x (7/8) = 35/48

Therefore, the fraction of employees who are males and wear spectacles is 35/48.

Answer:

  y = csc(3x)

Step-by-step explanation:

You want an equation for a cosecant curve with vertical asymptotes at multiples of π/3.

The vertical asymptotes of the parent cosecant function are at multiples of π. Putting them at multiples of π/3 means compressing the graph horizontally by a factor of 3.

That compression means x will be replaced by 3x in the equation. You want ...

  y = csc(3x)

Answer:

Using the Pythagorean theorem, we know that:

a^2 + b^2 = c^2

where a and b are the legs of the right triangle, and c is the hypotenuse.

We can plug in the values given:

9^2 + b^2 = 18^2

Simplifying:

81 + b^2 = 324

b^2 = 243

b = sqrt(243) = 15.6 (rounded to the nearest tenth)

Therefore, the length of the other leg is approximately 15.6 cm.

Step-by-step explanation:

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The confidence interval for variance is (0.29,0.58)

A family of continuous probability distributions is known as the chi-square (X2) distribution. They are frequently employed in hypothesis tests, such as the chi-square test of independence and the goodness of fit test.

The parameter k, which stands for the degrees of freedom, determines the shape of a chi-square distribution.

The distribution of real-world observations rarely has a chi-square shape. Chi-square distributions are primarily used for testing hypotheses rather than for modeling actual distributions.

Since we have given that the sample size n= 54,

variance = 0.44

we need to find a 98% confidence interval to estimate the variance.

So, we will use Chi-square distribution,

For this, we will find

df=n-1 = 54-1 = 53,

the interval would be,

[tex]\frac{(n-1)s^2}{X^2_{\alpha/2}} < \sigma^2 < \frac{(n-1)s^2}{X^2_{1-\alpha/2}}\\\\\alpha=1-0.98=0.02\\\\\alpha/2=0.02/2=0.01\\X^2_{0.01,53}=79.84\\Similarly\\\\1-\alpha/2=0.99\\\\X_{1-\alpha/2}^2,df=X^2_{0.99,53}=40.308\\\\So,\\\frac{53*0.44}{79.84} < \sigma^2 < \frac{53*0.44}{40.308}\\\\0.29 < \sigma^2 < 0.58[/tex]

Hence the confidence interval is (0.29,0.58)

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The air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion.

According to Newton's Second Law of Motion, the rate of change of the airplane's momentum is equal to the sum of all the forces acting on the airplane. As the plane takes off and accelerates, the thrust of the engines acting in the forward direction causes the plane's momentum to increase. This increase in momentum results in an increase in air speed. The air resistance acting against the motion of the plane is another force that affects the plane's speed. As the plane accelerates, the air resistance increases, and the plane's speed decreases.

In summary, the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion, where the thrust of the engines and air resistance act as forces that influence the plane's air speed.

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The rate at which the side of the cube changes when the side of the cube is 4 m is -1/8 m/s (or approximately -0.125 m/s).

Let's use the formula for the volume of a cube:

V = s³

where V is the volume and s is the length of one side of the cube. To find the rate of change of the side length, we need to differentiate this formula with respect to time t:

dV/dt = d/dt (s³) = 3s² ds/dt

We know that dV/dt = -6 m³/s (the negative sign indicates that the volume is decreasing), and when s = 4 m, we have:

-6 = 3(4²) ds/dt

Simplifying this equation gives us:

ds/dt = -6 / (3*4²) = -1/8 m/s

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An arch top window is a window with a bottom in the form of a rectangle and the top in the form of a semicircle. The width of the window that lets in the most light is 6 meters.

The width of the window that lets in the most light is determined by the length of the base of the rectangle, which is equal to the diameter of the semicircle. The total length of the framing materials is 12 meters, so the base length of the rectangle should be 6 meters. Thus, the width of the window is 6 meters.

To explain further, the width of an arch top window is determined by the base of the rectangle that forms the bottom part of the window, and the top is a semicircle. To determine the width of the window that lets in the most light, the length of the base should be equal to the diameter of the semicircle. Since the total length of the framing materials is 12 meters, the base length of the rectangle should be 6 meters, and the width of the window should also be 6 meters.

This means that the width of the window that lets in the most light is 6 meters, as the length of the base of the rectangle is equal to the diameter of the semicircle.

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The total cost of the laptop with the sales tax included is 938.18.

The total cost of the laptop with the sales tax included is the sum of the original price and the tax amount. The formula to calculate the total cost is given below:

Total Cost = Original Price + (Original Price * Sales Tax Rate)

In this case, the Original Price is 882.99 and the Sales Tax Rate is 6.25%. Therefore, the Total Cost of the laptop with the sales tax included is calculated as follows:

Total Cost = 882.99 + (882.99 * 0.0625)

Total Cost = 882.99 + 55.19

Total Cost = 938.18

Rounding to the nearest cent, the total cost of the laptop with the sales tax included is 938.18.

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From the given information provided, there were 311 children who swam at the pool that day.

Let's use C to represent the number of children who swam at the pool and A to represent the number of adults who swam at the pool.

From the problem, we know that:

C + A = 402 (Equation 1) (The total number of people who used the pool was 402)

1.50C + 2.00A = 648.50 (Equation 2) (The total receipts from admission were $648.50)

To solve for C and A, we need to eliminate one of the variables. We can do this by multiplying Equation 1 by 1.50, which will give us:

1.50C + 1.50A = 603 (Equation 3)

Now we can subtract Equation 3 from Equation 2 to eliminate C:

2.00A - 1.50A = 648.50 - 603

0.50A = 45.50

A = 91

So there were 91 adults who swam at the pool that day. To find the number of children, we can substitute A = 91 into Equation 1:

C + 91 = 402

C = 311

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If a lawn sprinkler sprays water 7 feet in every direction as it rotates, the area of the watered lawn is approximately 153.94 square feet.

Assuming the sprinkler is placed at the center of the lawn, the area of the watered lawn can be found by calculating the area of a circle with a radius of 7 feet. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

Plugging in the given value of the radius, we get:

A = π(7 feet)^2

A = 153.94 square feet (rounded to two decimal places)

It's important to include the correct unit of measure, which is square feet in this case, to avoid confusion.

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