Debra is going to build some large wooden storage boxes. The boxes are shaped like rectangular prisms with lengths of 6, widths of 6, and heights of 3. She wants to cover all the sides of each box with special wallpaper. If she has a total of 1152ft of wallpaper, how many boxes can she cover?

Answer:

120

Step-by-step explanation:

Answer: 87.96 mm^2

Step-by-step explanation:

The formula is 2 π r h + 2 π r^2

So then just substitute the variables.

The time for the trough to have 80 gallons of water is 5 minutes.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of minutes be represented as m.

The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. This will be:

25 + 11m =80

Collect like terms

11m = 80 - 25

11m = 55

Divide

m = 55 / 11

m = 5

Therefore, there will be 5 minutes.

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The graph of a proportional relationship is a line through the origin or a ray whose endpoint is the origin

3. No because it's a line that doesn't go through the origin

4. Yes because it's a line through the origin

5. Yes because 1/3 = 2/6 = 3/9 = 4/12

6. No because 4/2 isn't equal to 8/5

7. Draw a graph just like 4., but change the y-axis

8. a. Let the equation be y = ax. 27 = 3a. a = 9. Therefore the equation is y = 9x.

8. b. 9

8. c. 9 * 5 = 45

9. a. The car travels 25 (> 18) miles per gallon of gasoline.

9. b. 25 * 8 - 18 * 8 = 7 * 8 = 56

Answer:

Step-by-step explanation:

diagonal  = 32 cm

Area of square = \(\dfrac{d^{2}}{2}\)

                        \(=\dfrac{32*32}{2}\\\\=512 \ cm^{2}\)

Diagonal separate the square into two equal triangles.

Area of upper triangle that is shaded black = area of lower triangle = 512/2

= 256 cm²

Isosceles triangle:

a = 6 cm  ; b = 6 cm c = 8cm

\(s = \dfrac{a+b+c}{2}\\\\=\dfrac{6+6+8}{2}\\\\=\dfrac{20}{2}\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = \sqrt{s*(s-a)(s-b)(s-c)}\\\\=\sqrt{10*4*4*2}\\\\=\sqrt{2 * 2 * 4 * 4 * 5}\\\\=4*2\sqrt{5}\\\\=8\sqrt{5}\\\\=8*2.24\\\\=17.92 \ cm^{2}\)

Area of black shade paper = 256 + 17.92 =  273.92 cm²

Area of white shade paper = 256 cm²

Area of the isosceles triangle = s(s-a)(s-b)(s-c)

Answer:

56

Step-by-step explanation:

Apply PEMDAS:

\(72 / 4.5*3+8\\\\16*3+8\\\\48+8\\\\\boxed{56}\)

The probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75.

To find the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A, we first need to determine the proportion of plumbing jobs done by Plumber A that result in consumer dissatisfaction.

Given that half the complaints dealt with Plumber A and that Plumber A does 40% of the plumbing jobs in the town, we can calculate this proportion as follows:

Proportion of unsatisfactory plumbing jobs done by Plumber A = (Half the complaints / Total number of plumbing jobs done by Plumber A)

= (Half the complaints / 40% of the total plumbing jobs in the town)

= (Half of 10% / 40%)

= 10% / 2 / 40% = 1 / 4 = 0.25

Therefore, the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A is 0.25.

To find the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A, we subtract the probability of obtaining an unsatisfactory plumbing job from 1:

Probability of a satisfactory plumbing job given that the plumber was Plumber A = 1 - Probability of an unsatisfactory plumbing job

= 1 - 0.25

= 0.75

Therefore, the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75.

In conclusion, given that Plumber A does 40% of the plumbing jobs in the town and that half the complaints dealt with Plumber A, the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A is 0.25, and the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75. These probabilities can be used to make informed decisions about which plumber to choose for plumbing jobs in the community.

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Answer:

(0, -12)

Step-by-step explanation:

Using the slope-intercept form, the y-intercept is 12.

The balloon is  above 17.7180 the ground

What is the trigonometry ?

A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical studies led to the development of the field in the Hellenistic world during the third century BC.

Given

The angle Ф  is 32°

The hypotenuse becomes 24 feet

Let AB be the opposite side

Using trigonometric function of sinФ

ie sinФ = Opposite / hypotenuse

  sin Ф = AB / 24

   AB = sin Ф * 24

  AB =  sin 32° * 24

   AB = 12.7180

As that person is 5 feet tall we have to add 5 to the value

ie

12.7180 + 5

= 17.7180

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Answer:

Step-by-step explanation:

the third one is correct

\(6 \times 3 - \frac{18}{9} \\ (6 \times 3) - (18 \div 9)\)

The maximum area of the rectangle inside the ellipse is 2ab.

Given that,

Ellipse = x2 / a2 + y2 / b2 = 1

we know the general coordinates of any point in an ellipse of the equation

x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)

So, we take general vertices of rectangles as

(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)

So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ

So, its area will be ab4sinθcosθ (Length x Breadth)

Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A

Now A=2absin2θ

Now as the area is the maximum given in the question, we have to differentiate it with respect to θ

dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)

Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ =  π / 2 and θ=π / 4

So now we to put θ=π / 4 in the equation of area which is A=2absin2θ

We get as A=2absin2π / 4=2absinπ / 2=2ab

Hence the max area of the rectangle inside the ellipse is 2ab.

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An equation that could represent a linear combination of the given system of equations is: B. 0 = -78.

In Mathematics, no solution is also referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

Generally speaking, a linear combination of any system of equations can be obtained by either adding or subtracting a multiple of the equations of the system.

2x/3 + 5y/2 = 15      ......equation 1.

4x + 15y = 12       ......equation 2.

By multiplying equation 1 with 6 and equation with 1, we have the following system of equations:

4x + 15y = 90       ......equation 3.

4x + 15y = 12          ......equation 4.

By subtracting equation 3 from equation 4, we have the following:

0 = -78

In this context, we can reasonably infer and logically conclude that 0 = -78 is an equation that would most likely represent a linear combination of the given system of equations.

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Complete Question:

The system of equations below has no solution.

2x/3 + 5y/2 = 15

4x + 15y = 12

Which equation could represent a linear combination of the system?

A) 4/3x=42

B) 0= -78

C)15/2y=33

D)0=0

Answer:

3418.05 (not rounded)

Step-by-step explanation:

Volume = Area * height

V =pi*(8)^2*17

Answer:

i dont know :(

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

5-3(5x+2)+15x

Distribute

5 - 3*5x - 3*2 +15x

5 - 15x -6+15x

Combine like terms

5-6 -15x+15x

-1

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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Hello !

it is an equilateral triangle (3 equal sides). In an equilateral triangle the angles are all equal so a = b = c.

The sum of the angles of a triangle is always equal to 180°.

so a = b = c = 180°/3 = 60°

it is an equilateral triangle (3 equal sides). In an equilateral triangle the angles are all equal so a = b = c.

A straight angle measures 180°, so b = 180° - 120° = 60°.

so a = b = c = 60°

Answer:

Step-by-step explanation:

This is an equilateral triangle (all angles are equal).

Angles in a triangle add up to 180°.

           \(a=b=c=\frac{180}{3} =60\)

Answer:

the  next year population is 122,689      

Step-by-step explanation:

The computation of the next year population is as follows:

= This year population × increase percentage

= 119,000 × (1 + 0.031)

= 119,000 × 1.031

= 122,689

Hence, the  next year population is 122,689

The above formula is applied so that the correct value of the population could come

and the same is relevant

Step-by-step explanation:

\(5x+3y+4\)

There are two variables, x and y.

There are two coefficients, 5 and 3.

There are no exponents in the following expression.

A radical equation is √(x + 2) = 4 - x and the extraneous solution is x = 7

From the question, we have the following parameters that can be used in our computation:

The solution to a radical equation

In step 4 and 5, we have

x = ∛5 * 5 * 5 * 5

x = 5∛5¬ * 5¬ * 5¬ * 5

The above steps are carried out because it would simplify the radical expression to its simplest form

The reason it is done is to have the value of x in its simplest form

Here's an example of a radical equation:

√(x + 2) = 4 - x

Square both sides

x + 2 = 16 - 8x + x^2

Evaluate the like terms

x^2 - 9x + 14 = 0

Factor the quadratic equation

(x - 2)(x - 7) = 0

Solve for x:

x = 2 or x = 7

For x = 2:

√(2 + 2) = 4 - 2

√4 = 2

2 = 2

This is true, so x = 2 is a valid solution.

For x = 7:

√(7 + 2) = 4 - 7

√9 = -3

3 = -3

This is not true, so x = 7 is not a valid solution.

So, there is an extraneous solution

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∫CF⋅dr = 171,

B. In this case, the line integral does not depend on the path joining (0, 0) to (1, 3) because the condition Nx ≠ My is not satisfied.

What is path?

In mathematics and physics, a path refers to a continuous curve or trajectory along which an object or point moves. It can be described by a set of coordinates or parametric equations that specify the position of the object at different points in time or space. A path can be one-dimensional (such as a straight line) or multi-dimensional (such as a curve in a plane or a three-dimensional space).

Given:

F = 6xyi +\(6y^2j\) (vector field)

C is the path y = 3 joining (0, 0) to (1, 3)

A. To evaluate ∫CF⋅dr, we need to parameterize the path C and compute the line integral along that path. Since C is defined by y = 3, we can parameterize it as r(t) = ⟨t, 3⟩, where t ranges from 0 to 1.

Using the formula for the line integral, we have:

∫CF⋅dr = ∫CMdx + Ndy

We need to calculate M and N:

M = 6xy

N =\(6y^2\)

Substituting the parameterization into M and N:

M = 6(t)(3) = 18t

N = \(6(3)^2 = 54\)

Now we can calculate the line integral:

∫CF⋅dr = ∫CMdx + Ndy = ∫(18t)dt + ∫54dy

Evaluating the integrals:

∫CF⋅dr = \(9t^2 + 54y\)

Substituting the limits:

∫CF⋅dr = \([9(1)^2 + 54(3)] - [9(0)^2 + 54(0)]\)

= 9 + 162 - 0 - 0

= 171

Therefore, ∫CF⋅dr = 171.

B. In this case, the line integral does not depend on the path joining (0, 0) to (1, 3) because the condition Nx ≠ My is not satisfied. The vector field F = 6xyi +\(6y^2j\) has continuous partial derivatives, and the line integral along any path joining the given points will yield the same result.

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Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The unit price is given by the cost divided by the number of ounces, and the better deal is given by the deal with the lowest unit price.

Hence, for the 11.3 ounce package:

u = 3.68/11.3 = $0.33 per ounce.

For the 29.3 ounce package:

u = 8.98/29.3 = $0.31 per ounce.

Due to the lower unit cost, the 29.3 ounce package is the better deal.

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Answer:

it should be 680

Step-by-step explanation:

1 kilogram is 1000 grams

720*6=4320

5000-4320=680

Answer:

x=1

Step-by-step explanation:

7x-12 = x-6

First, add 12 to both sides of the equation and then simplify

Now subtract x from both sides of the equation and then simplify

Divide 6 from both sides of the equation and then simplify

The value of x in the given equation 7x - 12 = x - 6 is 1.

An equation, in mathematics, is a collection of numbers, mathematical operations, variables, functions, and often symbols. An equation comprises two expressions on either side of the equality sign(=). The sides are termed left-hand side and right-hand side abbreviated as LHS and RHS.

The given equation is 7x - 12 = x - 6.

7x - 12 = x - 6

7x - x = 12 - 6

6x = 6

\(\frac{6}{6}\)x = \(\frac{6}{6}\)

x = 1.

Thus, in the given equation, the value of x is 1.

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Answer: sqrt(102)

Step-by-step explanation:

We know that triangles GFE and DCE are similar by AA.

If we let CD=FE=x, then we can set up a proportion. Namely,

CE/FE = CD/FG

17/x = x/6

x^2 = 102 -> x=sqrt(102)

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm not sure, but I think its 5

Step-by-step explanation:

10x² - 5x + 10

x = -3

10(-3)² -5(-3) + 10

= (10×9) + 15 + 10

= 90 + 15 + 10

= 115

Answer:

its a translation

Step-by-step explanation:

Triangle B slid to the left to get to triangle A

Not my best subject so I'm pretty sure the other person got it right!

Yes, the equation y = 5x represents a proportional relationship

Two or more expressions with an Equal sign is called as Equation.

The given equation is y=5x.

In a proportional relationship, the ratio of y to x is constant.

In the given equation the variable x and y has a proportional relationship.

The equation is in the form of y=mx+b

the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.

Hence,  Yes, the equation y = 5x represents a proportional relationship

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