The function f(x) = 1. 25x2 models the packaging costs, in cents, for a box shaped like a rectangular prism. The side lengths are 2x in. , 2x in. , and 0. 5x in. What are reasonable domain and range values for this function, if the longest side length of the box can be no greater than 20 in. ? Write the answers in interval notation

Answer:

The answer is £52.8

Step-by-step explanation:

Answer: this answer makes no sense

Step-by-step explanation:

The expression is equivalent to 45m^-6p^2v^12/15m^-2p^8v^-4 is Option b 3v^16/m^4p^6 .

Given :

expression is equivalent to for all values of m , p , and v where the expression is defined

= ( 45m^-6 ) * p^2 * v^12 / 15m^-2 * p^8 * v^-4

= ( 45 / 15 ) ( m^-6 / m^-2 ) ( p^2 / p^8 ) ( v^12 / v^-4 )

= 3 ( m^-6 - ( -2 ) ( p^2 - 8 ) ( v^12 - ( - 4 )

= 3 ( m^-6 + 2 ) ( p^-6 ) ( v^12 + 4 )

= 3 ( m^-4 ) ( p^-6 ) ( v^16)

= 3 * v^16 / m^4 * p^6

= 3v^16 / m^4p^6

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Answer: 21.182

Step-by-step explanation:

The following triangles are congurent

Yes SAS

Answer:

Mo is sharing the sweets between 5 friends

Step-by-step explanation:

An important thing to note is that whichever way Mo shares the sweets, the total number of sweets he has does not change. It means that if he chooses the first method to share the sweets, or the second method, he still has the same number of sweets. This will be helpful in setting up an equation that will help us solve the problem.

If he chooses the first way to share the sweets:

7x + 2 = total number of sweets available.

This is because each of his friends gets 7 sweets each, with 2 leftovers. If we add them up, it will give the total number of sweets available to be shared.

If he chooses the second way to share the sweets:

6x + 7 = total number of sweets available.

This is because each of his friends gets 6 sweets each, with 7 leftovers. If we add them up, it will give the total number of sweets available to be shared.

because the total number of sweets do not change, we have

7x +2 = 6x +7

Grouping like terms,

7x - 6x = 7 - 2

x = 5.

Therefore, Mo is sharing the sweets between 5 friends

the solution to the given system of linear equations using matrix inversion is x = 1.5 and y = -1.5.

To solve the given system of linear equations using matrix inversion, we can represent the system in matrix form as follows:

AX = B

where A is the coefficient matrix, X is the column matrix of variables (x and y), and B is the column matrix of constants.

The given system of equations is:

x + y = 4    ...(Equation 1)

x - y = 1    ...(Equation 2)

In matrix form, this becomes:

⎡ 1  1 ⎤   ⎡ x ⎤   ⎡ 4 ⎤

⎢      ⎥ * ⎢   ⎥ = ⎢   ⎥

⎣ 1 -1 ⎦   ⎣ y ⎦   ⎣ 1 ⎦

To find the solution, we need to calculate the inverse of the coefficient matrix A and multiply it by the constant matrix B. The solution is given by:

X = A^(-1) * B

To proceed, let's find the inverse of matrix A:

A = ⎡ 1  1 ⎤

     ⎣ 1 -1 ⎦

To find the inverse of A, we can use the formula for a 2x2 matrix:

A^(-1) = (1/det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate of A.

Calculating the determinant of A:

det(A) = (1*(-1)) - (1*1) = -1 - 1 = -2

Now, let's find the adjugate of A:

adj(A) = ⎡ -1  1 ⎤

             ⎣  1  1 ⎦

Using these values, we can find the inverse of A:

A^(-1) = (1/det(A)) * adj(A) = (1/-2) * ⎡ -1  1 ⎤ = ⎡ 1/2  -1/2 ⎤

                                                                     ⎣ -1/2 1/2 ⎦

Next, we multiply A^(-1) with the constant matrix B:

⎡ 1/2  -1/2 ⎤   ⎡ 4 ⎤   ⎡ (1/2)*4 + (-1/2)*1 ⎤   ⎡ 2 - 1/2 ⎤

⎢           ⎥ * ⎢  ⎥ = ⎢                   ⎥ = ⎢         ⎥

⎣ -1/2 1/2  ⎦   ⎣ 1 ⎦   ⎣ (-1/2)*4 + (1/2)*1 ⎦   ⎣ -2 + 1/2 ⎦

Calculating the resulting values:

X = ⎡ 2 - 1/2 ⎤ = ⎡ 3/2 ⎤ = ⎡ 1.5 ⎤

   ⎣ -2 + 1/2 ⎦   ⎣ -3/2 ⎦   ⎣ -1.5 ⎦

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There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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Answer:

17 floors

Step-by-step explanation:

1 floor every 4 seconds.

90/4 = 22.5

40 - 22.5 = 17.5

17.5 is 17ish floors, and is the only answer that is close to 17 floors.

Solution:

First, we need to find out the amount for one kilogram. Since 100 grams = 30 pesos, and 1000 grams = 1 kilogram, we need to multiply it by 10.

30 x 10 = 300

Now we have the amount for 1 kilogram. Now in order to get the amount for 8 kilograms, we need to multiply it by 8.

300 x 8 = 2400 pesos

Answer:

The answer is 2,400 pesos.

Check:

30 x 10 = 300 So 300 pesos for a kilogram

300 x 8 = 2400 So 2400 pesos for 8 kilograms.

Answer:

1) 4.2 inches

2) 63 inches²

Step-by-step explanation:

If the base is 15 inches, we can assume that the opposite side is also 15 inches. 15 + 15 = 30. If we subtract 30 from the total perimeter, we will have the sum of the last two sides.

38.4 - 30 = 8.4

Now that we have the sum we can now find the exact length with division:

8.4/2 = 4.2 inches

To find the area, we multiply these together.

4.2 * 15 = 63

Answer:

51

Step-by-step explanation:

Control charts are used to monitor and identify when a process is out of control. There are several situations that indicate an out-of-control process, and these can be recognized on a control chart. Here are five such situations:

A point falls outside the control limits: If a data point falls above the upper control limit or below the lower control limit, it indicates that the process is out of control. This suggests that there may be a significant change or variation in the process.

Nonrandom patterns: Nonrandom patterns in the data points on a control chart, such as a consistent upward or downward trend, cycles, or oscillations, suggest that the process is not stable. These patterns indicate the presence of special causes of variation.

Runs and streaks: A run or streak refers to a series of consecutive data points that are either above or below the central line on the control chart. Runs or streaks suggest a lack of randomness and indicate that the process is not in control.

Lack of points within control limits: If there are long stretches of data points that are consistently clustered near one control limit or the central line without points within the control limits, it suggests that the process is not stable and may be exhibiting a systematic bias or shift.

Excessive variation: If there is excessive variation in the data points on the control chart, indicated by a wide spread of points around the central line, it suggests that the process is not under control. This can be recognized when the data points exceed the expected range of variation. These situations provide clear indications that a process is out of control and requires investigation and corrective actions to address the underlying causes of the variations. Control charts help in quickly identifying these situations and facilitating timely interventions to maintain process stability and quality.

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490

472 <490<500

it fits the criteria

Answer:

1. 105/12

2. 4/3

3. 600/5

4. 52/1

5. 1/4

Step-by-step explanation:

Marissa's shape is classified as a scalene and obtuse triangle, considering it's concepts presented in this problem.

The triangle has three sides of unequal length, as the opposite angle measures are different, hence it is classified as an scalene triangle.

(it would be equilateral if all had the same length, and isosceles if two sides have the same length).

The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.

(acute with no angles of 90º or greater, right with one angle of exactly 90º).

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f'(x) = 6 * (1/(sec(x) + tan(x))) * (sec(x)tan(x) + sec^2(x)).

f(x) = 6 ln(sec(x) + tan(x))

f'(x) = 6 * (1 / (sec(x) + tan(x))) * (sec(x) * tan(x) + sec^2(x))

f"(x) = 6 * [-(sec(x)*tan(x) + sec^2(x))^2 + (sec(x)*tan(x) + sec^2(x)) * (2*sec^2(x))] / (sec(x) + tan(x))^2

Now, to find the third derivative, we differentiate f"(x) with respect to x.

f"'(x) = [12*sec^4(x) - 6*sec^2(x)*tan^2(x) - 12*sec^2(x)*tan^2(x) + 6*tan^4(x)] / (sec(x) + tan(x))^3

Simplifying this expression, we get:

f"'(x) = [12*sec^4(x) - 18*sec^2(x)*tan^2(x) + 6*tan^4(x)] / (sec(x) + tan(x))^3

Therefore, f"'(x) = [12*sec^4(x) - 18*sec^2(x)*tan^2(x) + 6*tan^4(x)] / (sec(x) + tan(x))^3.

Let f(x) = 6 ln(sec(x) + tan(x)). To find f'(x), we'll first use the chain rule:

f'(x) = 6 * (1/(sec(x) + tan(x))) * (sec(x) + tan(x))'.

Now, we'll find the derivatives of sec(x) and tan(x):

(sec(x))' = sec(x)tan(x) and (tan(x))' = sec^2(x).

So, (sec(x) + tan(x))' = sec(x)tan(x) + sec^2(x).

Now, substitute this back into our expression for f'(x):

f'(x) = 6 * (1/(sec(x) + tan(x))) * (sec(x)tan(x) + sec^2(x)).

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To determine whether the given sequence converges or diverges, we will examine each of the provided sequences and find their respective limits as n approaches infinity.

1. an = (-1)^n

The sequence alternates between -1 and 1 as n increases. Since it does not approach a specific value, the sequence diverges. Your answer for this sequence is NONE.

2. an = n^2 * e^(-n)

To find the limit as n approaches infinity, we can apply L'Hopital's Rule:

lim (n^2) / (e^n) as n approaches infinity.

Applying L'Hopital's Rule twice, we get:

lim (2n) / (e^n) and then lim (2) / (e^n).

As n approaches infinity, the denominator (e^n) increases without bound, so the limit becomes 0. The sequence converges to 0.

3. an = (3n - 1)! / (3n + 1)!

To find the limit as n approaches infinity, let's rewrite the sequence as:

an = 1 / [(3n)(3n + 1)]

As n approaches infinity, the denominator (3n)(3n + 1) increases without bound, and the sequence converges to 0.

In summary:
1. The sequence (-1)^n diverges (NONE).
2. The sequence n^2 * e^(-n) converges to 0.
3. The sequence (3n - 1)! / (3n + 1)! converges to 0.

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The displacement of the compressor is 628 cubic centimeters. Other factors that affect the performance of a compressor include its operating pressure, flow rate, efficiency, and power consumption.

To find the displacement of the compressor, we need to use the formula:
Displacement = (pi/4) x bore^2 x stroke
Here, the bore is 8 centimeters and the stroke is 10 centimeters. So, substituting these values in the formula, we get:
Displacement = (pi/4) x 8^2 x 10
Displacement = (3.14/4) x 64 x 10
Displacement = 628.32 cubic centimeters

A compressor is a mechanical device that is used to increase the pressure of a gas or air by reducing its volume. It works by compressing the gas or air in a cylinder and then transferring it to a storage tank or other equipment. The displacement of a compressor is a measure of the volume of gas or air that is displaced or compressed during one complete cycle of the compressor. Therefore, the displacement of the compressor is 628 cubic centimeters. This means that during one complete cycle of the compressor, it displaces or compresses 628 cubic centimeters of gas or air. The displacement is an important parameter of a compressor, as it determines its capacity or the amount of gas or air that it can compress in a given time.

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The displacement of the compressor is 160π cubic centimeters.

To find the displacement of the compressor, we first need to understand what displacement means. Displacement is the change in position of an object in a specific direction. In this case, the compressor has a bore of 8 centimeters and a stroke of 10 centimeters. The displacement of the compressor can be calculated as the product of the bore area (πr^2) and the stroke length.

Displacement = π(4^2) * 10 = 16π * 10 = 160π cubic centimeters.

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Answer:

x= 104

Step-by-step explanation:

Angle in a triangle is 180

35+41+x=180

76+x=180

x=180-76

x=104

Answer:

60% of 20 pages = .6  * 20 = 12 pages

Step-by-step explanation:

Given:

One of the angle of a triangle is 104°.

The objective is to find the missing angle x.

If two sides of a triangle are equal, then it is an isosceles triangle.

In an isosceles triangle, the angle formed by the equal sides is also equal.

Then, the value of angle x can be calculated angle sum property of triangle.

Hence, option (A) is the correct answer.

Answer:

Pretty sure its B

Step-by-step explanation:

Trust me

Answer:

yes they are the same

Step-by-step explanation:

2x + 28 =40

you subtract 28 from both sides

2x + 28 - 28 = 40 - 28

2x=12

divide 12 by 2 and get 6

2(6)=12

2(x + 14)= 40

So, 2(x) + 2(14)

2x + 28 = 40

So they're both the same, just with 2 different ways to solve the same equation...Hope this helps!!

The solution for 2x + 28 = 40 is 6.

The solution for 2(x + 14) = 40 is 6.

Yes, they have the same solution.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

2x + 28 = 40

Solve for x.

2x = 40 - 28

2x = 12

x = 6

2(x + 14) = 40

Solve for x.

2x + 28 = 40

2x = 40 - 28

2x = 12

x = 6

Thus,

The solution for both equations is the same.

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If these two numbers F(51) and F(52) are added together. Then the number of results will be 53,316,291,173.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Two large numbers of the Fibonacci are given below.

F(51) = 20,365,011,074 and F(52) = 32,951,280,099.

The sum of the F(51) and F(52) will be

     20, 365, 011, 074

  + 32, 951, 280, 099

      53, 316, 291, 173

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By using Venn Diagram, it can be calculated

I) The number of students taking all courses = 2

II) The number of students taking mathematics biology and chemistry = 2

III) The number of students taking biology and chemistry = 5

What is a Venn Diagram?

Venn Diagram is a diagram used to show the relationship between two or more sets.

This problem can be solved using Venn diagram

The Venn diagram has been attached here

Number of students taking maths and biology =7

Number of students taking chemistry and biology = 7

Number of students taking maths and chemistry = 7

Let the number of students taking all three courses be x

Number of students taking Maths = 40

Number of students taking maths only = 40 - 7 - 7 + x = 26 + x

Number of students taking Biology = 35

Number of students taking Biology only = 35 - 7 - 7 + x = 21 + x

Number of students taking Chemistry = 38

Number of students taking chemistry only = 38- 7 - 7 + x = 24 + x

Number of students taking maths and biology only = 7 - x

Number of students taking maths and Chemistry only = 7 - x

Number of students taking chemistry and biology only = 7 - x

Total number of students = 26 + x + 21 + x + 24 + x + 7 - x + 7 - x + 7 - x + x

                                           = 92 + x

By the problem,

92 + x = 94

x = 94 - 92

x = 2

I) The number of students taking all courses = 2

II) The number of students taking mathematics biology and chemistry = 2

III) The number of students taking biology and chemistry = 7 - 2 = 5

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Answer:

The truck can deliver up to 209 boxes without exceeding a mass of 4700.

Step-by-step explanation:

To solve this problem, we need to use the formula:

\(\sf:\implies Total_{(Mass)} = Number_{(Boxes)} \times Weight_{(Per\: Box)}\)

We know that each box weighs 22.5, so the formula becomes:

\(\sf:\implies Total_{(Mass)} = 22.5 \times Number_{(Boxes)}\)

We want to find the maximum number of boxes that the truck can deliver without exceeding a mass of 4700. So we set up an inequality:

\(\sf:\implies 22.5 \times Number_{(Boxes)} \leqslant 4700\)

To solve for number of boxes, we isolate it by dividing both sides by 22.5:

\(\sf:\implies Number_{(Boxes)} \leqslant 4700 \div 22.5\)

\(\sf:\implies Number_{(Boxes)} \leqslant 209.33\)

Since we can't have a fraction of a box, we round down to the nearest integer:

\(\sf:\implies \boxed{\bold{\:\:Number_{(Boxes)} \leqslant 209\:\:}}\:\:\:\green{\checkmark}\)

Therefore, the truck can deliver up to 209 boxes without exceeding a mass of 4700.

Answer:

32 cubic feet

Step-by-step explanation:

To know the volume of a figure we have to calculate the area of its "base" and then multiply it by its height.

In this case we have a rectangular hole that has an area of 8 square feet.

As we said before:

Volume = Area x height.

If we substitute the value of the area of the rectangle and the height (or depth in this case) we would get:

Volume = 8 x 4 = 32 cubic feet.

Thus, the volume of John's hole is 32 cubic feet.

Answer:

32 cubic feet

Step-by-step explanation:

The volume of a rectangular prism is given by;

Length*width*Height

or, Area*height

Height = 4 feet

Area= 8 square feet

Conversion to Cubic feet is given by;

(cubic feet) = (square feet) × (height in feet)

Therefore,

Cubic feet = 8 square feet*4 feet

= 32 cubic feet.

Answer:

D

Step-by-step explanation: