Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 22 feet and a height of 16 feet. Container B has a diameter of 18 feet and a height of 17 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.

After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?

To calculate the variances, we need to compare the actual costs and quantities with the standard costs and quantities. Let's calculate each variance step by step:

(a) Direct material price variance:

Actual cost of direct material = 160,000 litres x RM14/litre = RM2,240,000

Standard cost of direct material = 160,000 litres x RM15/litre = RM2,400,000

Direct material price variance = Actual cost - Standard cost

= RM2,240,000 - RM2,400,000

= -RM160,000 (unfavourable)

(b) Direct material usage variance:

Actual usage of direct material = 160,000 litres

Standard usage of direct material = 120,000 cans x 12 litres/can = 1,440,000 litres

Direct material usage variance = Standard cost - Actual cost

= RM2,400,000 - RM2,240,000

= RM160,000 (favourable)

(c) Direct labour rate variance:

Actual cost of direct labour = 55,000 hours x RM12.50/hour = RM687,500

Standard cost of direct labour = 120,000 cans x 4 hours/can x RM12/hour = RM5,760,000

Direct labour rate variance = Actual cost - Standard cost

= RM687,500 - RM5,760,000

= -RM5,072,500 (unfavourable)

(d) Direct labour efficiency variance:

Actual hours worked = 55,000 hours

Standard hours allowed = 120,000 cans x 4 hours/can = 480,000 hours

Direct labour efficiency variance = Standard cost - Actual cost

= RM5,760,000 - RM687,500

= RM5,072,500 (favourable)

(e) Variable overhead expenditure variance:

Actual variable overhead = RM828,000

Standard variable overhead = 55,000 hours x RM16/hour = RM880,000

Variable overhead expenditure variance = Actual variable overhead - Standard variable overhead

= RM828,000 - RM880,000

= -RM52,000 (unfavourable)

(f) Fixed overhead efficiency variance:

Actual hours worked = 55,000 hours

Standard hours allowed = 120,000 cans x 4 hours/can = 480,000 hours

Fixed overhead efficiency variance = Standard fixed overhead - Actual fixed overhead

= RM440,000 - (55,000 hours x RM10/hour)

= RM440,000 - RM550,000

= -RM110,000 (unfavourable)

(g) Fixed overhead expenditure variance:

Actual fixed overhead = RM440,000

Standard fixed overhead = 55,000 hours x RM10/hour = RM550,000

Fixed overhead expenditure variance = Actual fixed overhead - Standard fixed overhead

= RM440,000 - RM550,000

= -RM110,000 (unfavourable)

(h) Possible cause for favourable direct labour rate and efficiency variances:

One possible cause for favourable direct labour rate and efficiency variances could be improved productivity or efficiency in the production process. It could be due to employees working more effectively, reducing the time required to complete tasks and thus resulting in lower costs. Additionally, the company may have negotiated lower labour rates or implemented cost-saving measures in the labour component.

Note: It's important to consider the given units and values while performing the calculations, and to round the variances appropriately based on the given requirements.

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Hope it helps you! .....

Answer: $115

Step-by-step explanation:

From the question, we are informed that the expression that represents the total cost for a party with g guests was given as:

= 70 + 5g

Therefore, the total cost for a party

with 9 guests will be:

= 70 + 5g

= 70 + 5(9)

= 70 + 45

= $115

Answer:

The answer from using a graphing calculator would be B because I had gotten 11.24025147 and that would round up to 11

Step-by-step explanation:

I would suggest that you use your graphing calculator for this or calculator.

Given that the average time spent by a consultant with each customer is 10 minutes.We have been given the following data:

[\begin{aligned}\mu &=1 \\L_{q} &=? \\w_{q} &=?\end{aligned}\].

The given data doesn't give a clear picture of the service goal, therefore we need to find out the service goal.

This is nothing but the waiting time of the customer.

To calculate the waiting time of the customer we need to first find the average number of customers in the queue and then the average waiting time in the queue.

We know that the distribution of customers arriving at the consultant follows Poisson's distribution.  

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Taylor series expansion of f(x) = sin(x) centered at c = π/2 is sin(x - c) = x - c - (x^3 - 3x^2c + 3xc^2 - c^3)/6 + (x^5 - 5x^4c + 10x^3c^2 - 10x^2c^3 + 5xc^4 - c^5)/120 - ...

The Taylor series expansion of f(x) = sin(x) centered at c = π/2 can be found by using the Maclaurin series for sin(x) and substituting (x - c) in place of x. The Maclaurin series for sin(x) is:

sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...

Substituting (x - c) for x, we get:

sin(x - c) = (x - c) - ((x - c)^3)/3! + ((x - c)^5)/5! - ((x - c)^7)/7! + ...

Expanding the terms, we have:

sin(x - c) = x - c - (x^3 - 3x^2c + 3xc^2 - c^3)/3! + (x^5 - 5x^4c + 10x^3c^2 - 10x^2c^3 + 5xc^4 - c^5)/5! - ...

Simplifying the expression, we obtain:

sin(x - c) = x - c - (x^3 - 3x^2c + 3xc^2 - c^3)/6 + (x^5 - 5x^4c + 10x^3c^2 - 10x^2c^3 + 5xc^4 - c^5)/120 - ...

This is the Taylor series expansion of f(x) = sin(x) centered at c = π/2.

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The correct statement is B. The center of the circle is the midpoint of the given endpoints of the diameter.

In a circle, the center is located at the midpoint of any diameter. A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle. Therefore, if we are given the endpoints of a diameter, we can determine the center of the circle by finding the midpoint of these endpoints. This means that the x-coordinate of the center will be the average of the x-coordinates of the endpoints, and the y-coordinate of the center will be the average of the y-coordinates of the endpoints.

Option A is not necessarily true because the x-coordinate of the center may or may not be the same as the x-coordinates of the given endpoints.

Option C is incorrect because the center of the circle can be found by determining the midpoint of the diameter.

Option D is not necessarily true because the y-coordinate of the center may or may not be the same as the y-coordinates of the given endpoints.

Therefore, the correct statement is B. The center of the circle is the midpoint of the given endpoints of the diameter.

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The radius of the circle which is overlapping the square is 1.12.

The length of side of the square is 2. Let us say that the radius of the circle is R.

The circle and the square are overlapping on each other.

The area of the region that are outside the circle but inside the square are equal to the area of the region which are inside the circle but outside the square.

Let us name the area of the region that are outside the circle but inside the square as M.

Let us name the area of the region which are inside the circle but outside the square as N.

Let us say that the area that is common in both is C.

The area of the square is 4.

So, according to the question,

M + C = 4

And,

N + C = πR²

And we know, M = N,

So,

C - πR² = C - 4

R = 2/√π

R = 1.12.

So, the radius of the circle is 1.12

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Adding a quadratic term to data that shows a curve in the scatterplot will provide a better fit but not affect the residual plot in any way, this statement is false

A scatterplot is a type of data display that shows the relationship between two numerical variables. Each member of the dataset gets plotted as a point whose x-y coordinates relates to its values for the two variables.

When on adding a quadratic term to  data, is illustrated on a scatter plot, a quadratic equation will form a “U” shape that is either concave down or concave up.

Therefore, adding a quadratic term to data that shows a curve in the scatterplot will provide a better fit but not affect the residual plot in any way, this statement is false.

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Answer:

9 is 2

10 is 6

Step-by-step explanation:

The combined total of their contracts is $1,296,250

The values of the contracts are given as:

The combined total is represented as:

Total = Exxon Mobil + Aerospace

Substitute known values

Total = $756,733 + $539,517

Evaluate the sum

Total = $1,296,250

Hence, the combined total of their contracts is $1,296,250

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Answer:

Your answer would be D!

Step-by-step explanation:

\(\dfrac 25 (2x-5)\\\\\\=\dfrac 25 \cdot 2x - \dfrac 25 \cdot 5\\\\\\=\dfrac{4x}5 - 2\)

Answer:

It's A and the answer is 4^x

Step-by-step explanation:

The exponential function that models the data is f(x) = \(4^x\).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.

We have a table.

The given function is not a linear because the difference of two consecutive term is not constant.

Now, the ratio

1/(1/12)= 12

12/1= 12

144/12= 12

1728/ 144= 12

If the ratio is same then the function is Exponential.

So, the exponential function is

f(x) = \(4^x\)

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Answer:

2 radians

Step-by-step explanation:

The ratio of the arc length to the circumference is the same as the measure of angle AOB in radians to 2pi. 2pi radians is a full circle. We can now construct an equation, with x being our answer.

\(\frac{6}{6\pi } =\frac{x}{2\pi } \\\frac{1}{\pi } =\frac{x}{2\pi }\\1=\frac{x}{2} \\2=x\)

First, we try to simplify both sides. Next, we multiply both sides by pi. Then, we multiply both sides by 2. Finally, our answer is 2, so 2 radians.

The area of the sector is 16π square inches.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360) x \(\pi r^2\)

where r is the radius of the circle.

In this case, the radius is given as 8 inches.

We are also given that the central angle measures from 60 to 150 degrees. To calculate the area of the sector, we need to find the size of the central angle first.

To do this, we subtract the smaller angle from the larger angle:

150 - 60 = 90 degrees

So, the central angle is 90 degrees.

Now, we can substitute the values into the formula:

Area of sector = (90/360) x \(\pi 8^2\)

Area of sector = (1/4) x π(64)

Area of sector = 16π square inches

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The three points to plot for the equation 2y = 3x + 11 are (0, 5.5), (1, 7), and (-1, 4).

To graph the equation 2y = 3x + 11, we can choose any three points that satisfy the equation. Let's select three points and plot them on a coordinate plane:

Point 1:

Let's set x = 0 and solve for y:

2y = 3(0) + 11

2y = 0 + 11

2y = 11

y = 11/2 = 5.5

So, the first point is (0, 5.5).

Point 2:

Let's set x = 1 and solve for y:

2y = 3(1) + 11

2y = 3 + 11

2y = 14

y = 14/2 = 7

The second point is (1, 7).

Point 3:

Let's set x = -1 and solve for y:

2y = 3(-1) + 11

2y = -3 + 11

2y = 8

y = 8/2 = 4

The third point is (-1, 4).

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The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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Based on the information given, the area of the trapezoid will be 89.7cm².

It should be noted that the formula for calculating the area of a trapezoid will be:

= (a + b)/2 × h

where a = 8

b = 13

h = 7.8

Area = (13 + 8)/2 × 7.8

= 21/2 × 7.8

= 11.5 × 7.8

= 89.7cm²

Therefore, based on the information given, the area of the trapezoid will be 89.7cm².

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Answer:

It should be ≈ 6,6

calculated the angle <CAB and both are 90°. But that would mean BC is wrong

The possible definitions of f(x) and g(x), considering the composition of the functions, are given as follows:

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The functions for this problem are defined as follows:

As the composition of the functions is then given as follows:

\(h(x) = f(g(x)) = f(8x + 6) = \sqrt{8x + 6}\)

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Answer:

96730322328

Step-by-step explanation:

I hope this helps

The general solution to the differential equation. If initial conditions are given, we can solve for the constants C1 and C2.

The given differential equation is:

y ln x * (dx/dy) = [(y+1)/x]^2

We can solve this equation by separation of variables, which means we can rearrange the equation so that all the x terms are on one side and all the y terms are on the other side. Then, we can integrate both sides with respect to their respective variables.

First, we rewrite the equation in a form suitable for separation of variables:

y ln x dx = [(y+1)/x]^2 dy

Next, we separate the variables and integrate both sides:

∫y ln x dx = ∫[(y+1)/x]^2 dy

Integrating the left-hand side by parts, we have:

u = ln x dv = y dx

du/dx = 1/x v = (1/2) y^2

∫y ln x dx = (1/2) y^2 ln x - ∫(1/2) y dx

= (1/2) y^2 ln x - (1/4) y^2 + C1

where C1 is the constant of integration.

Integrating the right-hand side, we use the substitution u = y+1:

u = y+1 du = dy

∫[(y+1)/x]^2 dy = ∫(u/x)^2 du

= (1/x^2) ∫u^2 du

= (1/3x^2) u^3 + C2

where C2 is the constant of integration.

Substituting this back into the original equation, we have:

(1/2) y^2 ln x - (1/4) y^2 + C1 = (1/3x^2) (y+1)^3 + C2

This is the general solution to the differential equation. If initial conditions are given, we can solve for the constants C1 and C2.

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Answer:

12, 120,012

Step-by-step explanation:

Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,

and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.

They need to think about how their technology could be used, and whether it could be used to harm people or the environment.

They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,

and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.

For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.

In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.

This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.

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Answer:

x = 1.14

x = -1.47

Step-by-step explanation:

Use the quadratic formula.

x =  

-b ± √b2 - 4ac /2a

1 ± 6 √61  = x

Answer:

Equation of the line is 3y = -5x + 8

Step-by-step explanation:

Slope:

\({ \bf{m = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }}\)

substitute:

\({ \sf{m = \frac{1 - 6}{1 - ( - 2)} }} \\ { \sf{m = - \frac{5}{3} }}\)

General equation of a line:

\({ \boxed{ \pmb{y = mx + b}}}\)

b is the y-intercept.

Consinder point (1, 1):

\({ \sf{1 = ( - \frac{5}{3} \times 1) + b}} \\ { \sf{b = \frac{8}{3} }}\)

Substitute:

\({ \sf{y = - \frac{5}{3} x + \frac{8}{3} }} \\ \\ { \sf{3y = - 5x + 8}}\)