What is the area of the following trapezoid in the following graph (there is an attachment)

Since the second derivative of the cost function is zero, the critical point obtained in step 4 is a saddle point.

There is no minimum or maximum cost of materials that can be used to make a box of 16 ft³.

The objective of the problem is to find the minimum cost of material required to make a closed rectangular box that can contain 16 ft³ of material. Three kinds of materials are required to make the box. The costs of the material for the top and bottom are Php18 per square foot, the cost of the material for the front and the back is Php16 per square foot, and the cost of the material for the other two sides is Php12 per square foot.To solve the problem, the following steps are taken:

Step 1: Label the dimensions of the rectangular box.

Assume that the length, width, and height of the box are represented by x, y, and z, respectively. This implies that the volume of the box is given by V = xyz, which is 16 ft³.

Therefore, the objective of the problem is to find the minimum cost of the materials required to make the box.

Step 2: Determine the cost function. The total cost of the materials is the sum of the cost of each material.

Therefore, the cost function C is given by

C = 2(18xy) + 2(16xz) + 2(12yz)

Step 3: Simplify the cost function.

C = 36xy + 32xz + 24yz

Step 4: Determine the critical points. To find the critical points, take the partial derivative of C with respect to x, y, and z. dC/dx

= 36y + 32z

= 0;

dC/dy

= 36x + 24z

= 0;

dC/dz

= 32x + 24y = 0. Solving these equations simultaneously, we have x = 3, y = 2, and z = 4/3.

Step 5: Find the second derivative. To determine whether the critical point obtained in step 4 is a minimum, maximum, or saddle point, find the second derivative.

The second derivative test is used to classify the critical point as a minimum, maximum, or saddle point. To find the second derivative, take the partial derivative of dC/dx, dC/dy, and dC/dz with respect to x, y, and z respectively.

Thus, d²C/dx² = 0,

d²C/dy² = 0, and

d²C/dz² = 0.

Step 6: Conclusion. Since the second derivative of the cost function is zero, the critical point obtained in step 4 is a saddle point.

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Answer:

Step-by-step explanation:

Answer:

Find the retail sale price of each item below. Round to two decimal places when necessary. Original price : $325.50; Markdown: 15%.

A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.

----------------------

The car is 120 miles away when the motorcycle starts.

The bike gains on the car at 30 mph (70-40).

It takes 4 hours for the bike to close the gap (120/30).

In 4 hours, the bike and the car are 280 miles from the starting point.

---------

4*70 = 280

7*40 = 280

Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)

70T = 40T + 120

30T = 120

T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).

It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.

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Answer:

323

Step-by-step explanation:

Answer:

its $458.57 on edg

Step-by-step explanation:

Answer:

The expression 103 is called the exponential expression. ... The exponent applies only to the number that it is next to. ... If −3 is to be the base, it must be written as (−3)4, which means −3 • −3 • −3 ... From row 1 to row 2, the exponential form goes from 105 to 104. ... Following the pattern, you see that 100 is equal to 1.

Step-by-step explanation:

A ratio displays the multiplicity of two numbers, the total number of employees is 187.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were going to compare one data point (A) to another data point (B). This indicates that you are multiplying data A by data B.

So the ratios are-

men : women

4:7

x:119

Now, relationship between 7and 119 is -

men : women

4:7

7*17

x:119

Now,

men : women

4:7

4*17 :7*17

68:119

Total number

68+119= 187

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False. The metric system is a decimalized system of measurement, but it is not used exclusively in the United States.

In fact, the United States primarily uses the U.S. customary system, while the metric system is widely used in most other countries around the world.

Most nations throughout the world use the metric system, a decimal-based measurement system that is universally recognised. It offers a standardised method for gauging temperature, length, mass, and other physical attributes. The metre (for length), kilogramme (for mass), second (for time), ampere (for electric current), kelvin (for temperature), mole (for amount of material), and candela (for luminous intensity) are the basic units of the metric system. Because the metric system is based on powers of 10, converting between units is simple. Global communication and trade are made easier by its promotion of usability, consistency, and compatibility across scientific, industrial, and everyday uses.

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The estimation of 0.000007328 is \(7\times10^{-6\).

Estimation is he ability to guess the amount of anything without actual measurement.

The number (n) is given as:

\(\text{n}=0.000007328\)

Multiply by 1

\(\text{n}=0.000007328\times1\)

The number is to be rounded to the nearest millionth.

So, we substitute \(\frac{1000000}{1000000}\) for 1

\(\text{n}=0.000007328\times1\)

\(\text{n}=0.000007328\times\dfrac{1000000}{1000000}\)

This becomes

\(\text{n}=7.328\times\dfrac{1}{1000000}\)

Express the fraction as a power of 10

\(\text{n}=7.328\times10^{-6\)

Approximate to a single digit

\(\rightarrow\bold{n=7\times10^{-6}}\)

Therefore, the estimation of 0.000007328 is \(7\times10^{-6}\).

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The area of the largest triangle is 48 square inches

The formula for calculating the area of a triangle is expressed as:

Area = 1/2 * base * height

Determine the height using Pythagoras theorem

h² = 20² -16²

h² =  400 - 256

h² = 144

h = 12in

Determine the area of largest triangle = 1/2 * 12 * 16

Area of largest triangle = 1/2 * 6 * 16

Area of largest triangle = 48 square inches

Hence the area of the largest triangle is 48 square inches

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Answer:

43.8

Step-by-step explanation:

Remark

Are there ever a lot of assumptions!!

Area of the rectangles

A = L * W

L = 4 m

W = 3 m

Area = 4*3 = 12

There are 3 rectangles so the total area = 3*12 = 36

Area triangles

Area = 1/2 b * h

b = 3

h = 2.6

Area = 1/2 * 2.6 * 3

Area = 1/2 7.8

But there are 2 of them so the area for the 2 is

Area = 2* 1/2 7.8

Area = 7.8

Total area = 36 + 7.8

Total area = 43.8

Answer:

2.08 this is answer

The height of the triangle is 8root3 meters.

We have given that,

A tree breaks due to a storm and the broken part bends,

So that the top of the tree touches the ground making an angle of 60 degrees with the ground.

The distance between the feet of the tree to the point where the top touches the ground is 16m.

Let the Height of the Tree =AB+AD

and given that BD=8 m

Now, when it breaks a part of it will remain perpendicular to the ground (AB) and the remaining part (AD) will make an angle of 30 degrees.

Now, in △ABD

cos(30)=BD/AD=BD=root3AD/2

AD=2(8)/root3

also in the same triangle

\(tan(30)=AB/BD\implies 8/\sqrt{3}\)

Height of the tree=AB+AD

\(=\frac{16}{\sqrt{3} }+\frac{8}{\sqrt{3} } }\)

\(=\frac{24}{\sqrt{3} } \\=8\sqrt{3}m\)

Therefore the height of the triangle is 8root3.

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Answer:

-16, -15, -14, -13

Step-by-step explanation:

True. Nonsampling errors refer to errors that occur during the data collection process that are not related to the sampling method used. These errors can occur in any type of data collection method, whether it be through surveys, experiments, or observational studies.

Nonsampling errors can arise due to a variety of reasons, such as poor survey design, biased sampling methods, inadequate training of surveyors, errors in data entry or processing, or even deliberate fraud.

Nonsampling errors can have a significant impact on the quality of the data collected, as they can introduce biases and inaccuracies into the results. These errors can result in incorrect conclusions and decisions based on the data, which can have serious consequences. Therefore, it is important to take steps to minimize nonsampling errors during the data collection process, such as carefully designing surveys, ensuring proper training of surveyors, and conducting thorough quality checks on the data collected.

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Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

\($(a-b)(a+b)=a^2-b^2$\)

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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Answer:

photosynthesis is a processes by which plants get their proteins

Answer:

Adult: $ 4

Student: $ 7

Step-by-step explanation:

Adult: x

Students: y

a) 3x + 9y = 75

b) 8x + 5y = 67

Substitution:

a) 3x = -9y + 75

x = (-9y + 75)/3

x = -3y + 25

Substitute:

b) 8(-3y+25) + 5y = 67

-24y + 209 + 5y = 67

-19y = -209 +67

y = -133/-19

y = 7

Substitute:

x = = 3(7) + 25

x = -21+25

x = 4

49 - 2/3 x = 32 - 1/6 x

Move the constant terms to one side and the terms containing x to the other:

49 - 32 = 2/3 x - 1/6 x

Simplify the left side, and pull out the common factor of x on the right side:

17 = (2/3 - 1/6) x

Write the fractions in terms of a common denominator. In this case, you would take

2/3 = 4/6

so that

(2/3 - 1/6) x = (4/6 - 1/6) x = 3/6 x = 1/2 x

Then the equation is

17 = 1/2 x

Multiply both sides by 2:

2 × 17 = 2 × 1/2 x

34 = x

The student should stand at 2L/9 you will see it tip over so as to weigh of 60kg.

Due to the fact that mass is the quantity of matter contained in an item and does not change with gravity, mass is always the same. As long as the amount of matter in an object doesn't change, its mass will remain constant. In contrast, an object's weight refers to the force of gravity acting on it.

No matter where you are in the cosmos, you have the same mass since mass is a measurement of how much matter is in an object. But because weight measures the force between an object and the body it is resting on, it fluctuates (whether that body is the Earth, the Moon, Mars, et cetera).

Given : A mass of student 40 kg

length is represented by l

Position of the pivot point from the board = l/3

The student should stand at 2L/9 you will see it tip over so as to weigh of 60kg.

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Answer:

The vertical angles theorem

Step-by-step explanation:

The Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.

Angles ∠JKN and ∠MKL fit the criteria of the vertical angles theorem, meaning they are congruent.

Step-by-step explanation:

x^2 +4x +4 -7 is

y=x^2+4x-3

Answer: g(x)=(x+2)²-4.

Step-by-step explanation:

g(x)=f(x)+3

g(x)=(x+2)²-7+3

g(x)=(x+2)²-4.

Answer:

The train traveled 60 kilometers per hour.

Step-by-step explanation:

300/5=60

Answer:

60 km/hours

Step-by-step explanation:

in the picture above.

Answer:

C. (1, –1); minimum

Step-by-step explanation:

The answer to your question is letter “C”

The correct answer is c

The product between the two fractions is equal to 1/15.

When we want to take the product between two fractions, we need to multiply the numerators and the denominators together.

This means that if we have two fractions (a/b) and (c/d), the product between them is written as:

(a/b)*(c/d) = (a*c/b*d)

In this case we have:

(1/3)*(1/5)

Using the above rule we can solve the product as:

(1/3)*(1/5) = (1*1)/(3*5)

(1/3)*(1/5) = 1/15

That is the solution for the product.

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Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

Answer:

What is the average time that Larry rises from bed in the morning

Step-by-step explanation:

Because the answer isn't definite, you have to collect data and analyze to find the answer.