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According to the question we can say that it will take the artist 72 hours to paint 9 pictures for the art show.

If the artist can draw one-eighth of a picture in one hour, then he can draw one complete picture in 8 hours (since 8 x 1/8 = 1).

Therefore, to draw 9 pictures, the artist will need 9 x 8 = <<9*8=72>>72 hours.

So, it will take the artist 72 hours to paint 9 pictures for the art show.

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Ted's claim is correct - the two shaded triangles must be congruent.

We can prove this using the following reasoning:

The two triangles share the same base, segment BC.

The two triangles have the same height, as the height of a triangle is measured as a perpendicular line from the base to the opposite vertex, and the perpendicular line from B to segment AD is the same length as the perpendicular line from C to segment AE.

Therefore, the two triangles have the same area.

If two triangles have the same area and share a common side (in this case, segment BC), they must be congruent by the Side-Area-Side (SAS) congruence theorem.

Therefore, we can conclude that the two shaded triangles are congruent.

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The value of x in the given figure on the basis of chords intersecting in a circle at an anle of 65° and the intercepted arcs being (4x) and (2x+10) is 20.

What is chord?

A chord is a line segment which joins any two points on the circle. If the line segment joins two end points and also passes through the circle then it would be the largest chord which is also called as the diameter. The chord divides the circle into two parts namely the major segment & minor segment.

Here two chords intersect inside the circle at 65° and the measure of the intercepted arcs are given as (4x)° and (2x+10)°

As per the thoerem of circles, the angle of intersection of chords is equal to half of the sum of the values of intercepted arcs.

Angle of intersection= [tex]\frac{1}{2}[/tex]  (sum of intercepted arcs)

                             65° = [tex]\frac{1}{2}[/tex]  (sum of (4x)° and (2x+10)°)

                              65° = [tex]\frac{1}{2}[/tex] ((4x)° + (2x+10)°)

                              65° = [tex]\frac{1}{2}[/tex] (4x + 2x+10)

                              65° = [tex]\frac{1}{2}[/tex] (6x+10)

                         2 (65°) = (6x+10)

                              130 = 6x + 10

                              120 = 6x

                                 x = 20

The value of x = 20

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Therefore, the value of F is approximately 18.92 degrees.

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees or radians and can be classified based on their measure as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (between 90 and 180 degrees), or straight (exactly 180 degrees). Angles are an important concept in geometry and have many real-world applications, including in physics, engineering, and architecture.

Here,

If we look at the diagram, we can see that angles d° and e° are vertical angles, which means they are equal in measure. Similarly, angles (9-86)° and 45° are supplementary angles, which means they add up to 180°. Using this information, we can set up an equation:

d = e (since they are vertical angles)

(9-86) + 45 + e + (6f) + 15 = 180 (since the sum of angles in a triangle is 180°)

Simplifying the equation, we get:

-32 + e + 6f + 60 = 180

e + 6f + 28 = 180

e + 6f = 152

Substituting d = e, we get:

d + 6f = 152

But we know that d + e + (9-86) = 180 (since the sum of angles in a straight line is 180°)

Substituting d = e, we get:

2d + (9-86) = 180

2d = 77

d = 38.5

Substituting d = e = 38.5 in the equation e + 6f = 152, we get:

38.5 + 6f = 152

6f = 113.5

f = 18.92

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We can conclude that C. the neighborhood is significantly less likely to be Democrat.

The null hypothesis was that there is no difference between the proportion of Democrats in the sample and the population. Since the null hypothesis has been rejected, it means that there is a significant difference between the sample and the population proportions. In this case, 60% of the respondents in the random sample are Democrats, which is lower than the 75% Democrat proportion in the community as a whole. Therefore, we can conclude that the neighborhood from which the sample was drawn is significantly less likely to be Democrat compared to the overall community.

The other options are not supported by the given information:

A type I error might or might not have occurred. We cannot determine this based on the information provided. A type I error refers to the incorrect rejection of a true null hypothesis. Without knowing the true proportions of the neighborhood, we cannot determine if a type I error has been committed. Whether a one-tailed test or a two-tailed test was used is not specified in the question.

However, the conclusion that the neighborhood is significantly less likely to be Democrat can be derived from either type of test. Therefore, the correct option is C.

The question was incomplete, Find the full content below:

sixty percent of the respondents in a random sample drawn from a neighborhood are democrats. the community as a whole is 75% democrat. the difference between sample and population has been tested and the null hypothesis has been rejected. what might we conclude? select one:

a. a type i error has been committed

b. a one-tailed test has definitely not been used

c. the neighborhood is significantly less likely to be democrat

d. the difference is not significant

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The indefinite integral of [tex]xsin(x^2)[/tex] with respect to x is [tex]-(1/2)cos(x^2) + C[/tex], where C is the constant of integration.

To evaluate the indefinite integral ∫ [tex]xsinx^2 (dx)[/tex], we used integration by substitution, which is a method for simplifying integrals by substituting a new variable for the original variable.

We can use integration by substitution to evaluate this integral.

Let u = [tex]x^2[/tex], then du/dx = 2x, or equivalently, dx = du/(2x).

Substituting, we have:

∫ [tex]xsinx^2 dx[/tex] = ∫ sin(u) * (du/2)

Now we can integrate with respect to u:

∫ sin(u) * (du/2) = -(1/2)cos(u) + C

We then integrated the resulting expression with respect to u, obtaining -(1/2)cos(u) + C, where C is the constant of integration.

∫ [tex]xsinx^2 dx = -(1/2)cos(x^2) + C[/tex]

Finally, we substituted back u = [tex]x^2[/tex], obtaining [tex]-(1/2)cos(x^2) + C[/tex] as the indefinite integral of [tex]xsinx^2 (dx)[/tex] with respect to x.

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Answer:

How many times can 3 go into 64?

21 times

3 x 21

Step-by-step explanation:

You're welcome.

Answer: 21.3333333333

Step-by-step explanation:

64 / (Divided by) 3 equals 21.3333333...(Recurring, Meaning to go on for infinity)  

With the help of the volume and radius of the cylinder, we know that the height is 18.01 in.

A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions.

In elementary geometry, it is regarded as a prism with a circle as its basis.

A cylinder can instead be described as an infinitely curved surface in a number of modern domains of geometry and topology.

So, in the given situation use the formula:

V=πr²h

Now, calculate as follows:

V=πr²h

h = V/πr²

h = 2772/π7²

h = 18.00724in

Rounding off: h = 18.01 in

Therefore, with the help of the volume and radius of the cylinder, we know that the height is 18.01 in.

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With given expression error=2%,  the filling machine is not working within specifications for this container of oats.

What exactly are expressions?

In mathematics, an expression is a combination of symbols, numbers, and operators (such as + and -) that represents a value or a quantity. It can contain variables, which are symbols that represent unspecified values, and constants, which are fixed values. Expressions can be simple, like "5 + 3", or more complex, like "3x² - 2xy + 7".

Now,

The oat-filling machine must fill each container with 16 ounces of oats with a 2% margin of error, according to the requirements. This means that the acceptable range of oat quantity in a container is from 16 - 0.0216 = 15.68 ounces to 16 + 0.0216 = 16.32 ounces.

Since the container in question has been filled with 16.5 ounces of oats, we can see that it is outside the acceptable range specified by the machine's specifications. Therefore, the filling machine is not working within specifications for this container of oats.

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Mrs. Hernandez's section has sold 12 fruit pies and Mr. Kane's class had sold 17 bottles of fruit juice.

Let's use the variables 'x' and 'y' to represent the number of fruit pies sold by Mrs. Hernandez's class and the number of bottles of fruit juice sold by Mr. Kane's class, respectively.

From the problem, we know that:

Each fruit pie sold for $5, so the revenue from Mrs. Hernandez's class is 5x.

Each bottle of fruit juice sold for $2, so the revenue from Mr. Kane's class is 2y.

The total number of items sold is 29, so x + y = 29.

The total revenue earned is $94, so 5x + 2y = 94.

Our system of equations is:

x + y = 29

5x + 2y = 94

To solve the system, we can use the substitution method. Solving the first equation for y, we get:

y = 29 - x

Substituting this expression for y into the second equation, we get:

5x + 2(29 - x) = 94

Simplifying and solving for x, we get:

3x = 36

x = 12

Substituting x = 12 into the equation y = 29 - x, we get:

y = 29 - 12 = 17

Therefore, it can be concluded that Mrs. Hernandez's class sold 12 fruit pies and Mr. Kane's class sold 17 bottles of fruit juice.

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Step-by-step explanation:

The total cost of c pens is $cd. The total cost of e pencils is $0.01ef. Thus, the formula for the total cost is:

$T = cd + 0.01ef

Answer:1:3

Step-by-step explanation:

we can show this as 4:12=1:3

so ratio of bikes to children is 1:3

On solving the provided question we can say that

1. circle centered at the origin with a radius of 10 is:

[tex]x^{2} +y^{2} =100[/tex]

2. circle with center R(-1, 8) and a radius of 5 is:

[tex](x + 1)^2 + (y - 8)^2 = 25[/tex]

3. center P(8, -5) and a radius of 24.5 is:

[tex](x -8)^2 + (y +5)^2 = 24.5[/tex]

4. the origin and passing through the point (9, -2) is:

[tex]x^{2} +y^{2} -18x+4y+85=0[/tex]

5. center B(0, -2) and passing through the point (-6, 0) is:

[tex](x )^2 + (y +2)^2 = 40[/tex]

6. center F(11, 4) and passing through the point (-2, 5) is:

[tex](x -11)^2 + (y - 4)^2 = 1708[/tex]

A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.

circle centered at the origin with a radius of 10 is:

[tex]x^{2} +y^{2} =100[/tex]

circle with center R(-1, 8) and a radius of 5 is:

[tex](x + 1)^2 + (y - 8)^2 = 25[/tex]

center P(8, -5) and a radius of 24.5 is:

[tex](x -8)^2 + (y +5)^2 = 24.5[/tex]

the origin and passing through the point (9, -2) is:

[tex]x^{2} +y^{2} -18x+4y+85=0[/tex]

center B(0, -2) and passing through the point (-6, 0) is:

[tex](x )^2 + (y +2)^2 = 40[/tex]

center F(11, 4) and passing through the point (-2, 5) is:

[tex](x -11)^2 + (y - 4)^2 = 1708[/tex]

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Check the picture below.

so hmmm the square inscribed in the circle, we can see it as two congruent triangles, whose base is 28 and height is 14.  Now, if we get the whole area of the circle with radius of 14, and subtract the area of those triangles, what's leftover is the shaded area.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ circle }{\pi (14)^2}~~ - ~~\stackrel{ \textit{two triangles} }{2\left[\cfrac{1}{2}(\underset{b}{28})(\underset{h}{14}) \right]}}\implies 196\pi -392 ~~ \approx ~~ \text{\LARGE 223.75}[/tex]

There are a total of 36 boxes of popcorn with each box containing 2 popped kernels except for the last box which contains 1 popped kernel.

If there are 85 kernels in a pound of popcorn, then we can assume that there are 84 boxes of popcorn with each box containing one kernel less than the previous box. The last box will contain only one kernel.

Following formula should be used to find the sum of the first n natural numbers:

n(n+1)/2.

Therefore, the number of boxes required to hold all the popped kernels is given by solving the equation:

n(n+1)/2 = 84

Solutions for the quadratic equation can be found as:

n = -9 or n = 8

Since we cannot have a negative number of boxes, therefore, we take:

n = 8.

Therefore, there are a total of 36 boxes of popcorn with each box containing 2 popped kernels except for the last box which contains 1 popped kernel.

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The number of boxes required for the popped corn can be calculated by dividing the total number of popped kernels by the capacity of each box. To do this, we need to know the yield of the popcorn, which means the ratio of popped kernels to unpopped kernels.

Let's assume that the yield of the popcorn is 10:1, which means that for every 10 unpopped kernels, 1 kernel pops. Therefore, there would be 10 x 16 = 160 unpopped kernels in a pound of popcorn.

Assuming that each box can hold 100 popped kernels, we can calculate the total number of boxes required as follows: Total number of popped kernels = 1 lb of popcorn x 10 (yield) = 1600 popped kernels Number of boxes required = 1600 popped kernels ÷ 100 kernels per box = 16 boxes

Therefore, 16 boxes are needed to hold all the popped kernels. The last box will be partially filled, and the number of popped kernels in it can be calculated by subtracting the number of kernels in the other 15 boxes from the total number of popped kernels:

Number of kernels in the last box = 1600 popped kernels - (15 boxes x 100 kernels per box) = 100 popped kernels Hence, there are 16 boxes required to hold all the popped kernels, with the last box having 100 popped kernels in it.

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Therefore, the sides of the two triangles for x = 2 are approximately 106.099 and 22.317. After a few iterations, we get an approximate value of y for x = 2: y_1 = 9.618, y_2 = 9.614 and y_3 = 9.614

A triangle is a two-dimensional geometrical shape with three straight sides and three angles. It is one of the basic shapes in geometry and is commonly encountered in mathematics, science, and everyday life. Triangles can be classified based on the lengths of their sides and the measures of their angles. Some common types of triangles include equilateral triangles (all sides and angles are equal), isosceles triangles (two sides and two angles are equal), and scalene triangles (no sides or angles are equal). Triangles have many properties and relationships that are useful in solving problems involving angles, sides, and area.

Here,

Since the two triangles are similar and one triangle is inscribed in the other, the corresponding sides of the two triangles are proportional. That is,

(y² + 16) / (yx² + 9x) = (x² + 7x + y/2) / (3y/2 + 17)

Cross-multiplying and simplifying, we get:

(y² + 16)(3y/2 + 17) = (yx² + 9x)(x² + 7x + y/2)

Expanding and rearranging, we get a quadratic equation in y:

3y³ + 44y² + 102y - 816x³ - 5652x² - 7569x - 1836 = 0

This equation is difficult to solve explicitly for y, but we can use numerical methods or algebraic software to find an approximate value of y for a given value of x.

For example, let's assume x = 2. Using a numerical method such as Newton-Raphson, we can iteratively solve for y:

Let f(y) = 3y³ + 44y² + 102y - 816x³ - 5652x² - 7569x - 1836

Let f'(y) be the derivative of f(y): f'(y) = 9y² + 88y + 102

Let y_0 be an initial guess for y, such as y_0 = 10 (any positive value of y would work as an initial guess)

Iterate using the formula: y_n+1 = y_n - f(y_n) / f'(y_n), starting with n = 0

After a few iterations, we get an approximate value of y for x = 2:

y_1 = 9.618

y_2 = 9.614

y_3 = 9.614

Therefore, for x = 2, the positive value of y is approximately 9.614. We can then use this value to find the corresponding sides of the two triangles:

Side of big triangle: y² + 16

= 9.614² + 16

= 106.099

Side of small triangle: x² + 7x + y/2

= 2² + 7(2) + 9.614/2

= 22.317

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From the sign chart, we can see that the solution set is x < -5 or -5 < x < 7. Therefore, the solution to the original inequality is:

x < -5 or -5 < x < 7

In order to solve an inequality, you need to isolate the variable on one side of the inequality symbol (i.e., <, >, ≤, ≥) and determine the range of values for which the inequality holds true.

The process for solving an inequality depends on the specific type of inequality. Here are the general steps for solving different types of inequalities:

Solving linear inequalities:

a. Move all variable terms to one side of the inequality and all constant terms to the other side.

b. Divide or multiply both sides by a positive constant (i.e. not zero) to isolate the variable.

c. If you multiply or divide by a negative constant, flip the inequality symbol to maintain the inequality.

Solving quadratic inequalities:So, the inequality can be written as:

[tex](x - 7) (x + 5) < 0[/tex]

To solve this inequality, we need to consider the sign of the expression on the left-hand side for different values of x. We can do this by creating a sign table:

x      |   x - 7   |   x + 5   | (x - 7) (x + 5)

----------|-----------|-----------|----------------

-6 | -13 | -1 | +13

-4 | -11 | +1 | -11

-1 | -8 | +4 | -32

6 | -1 | +11 | -11

8 | +1 | +13 | +13

From the sign table, we can see that the expression (x - 7)(x + 5) is negative (i.e., less than zero) for values of x between -5 and 7. Therefore, the solution to the inequality is:

[tex]-5 < x < 7[/tex]

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Using the principle of inclusion-exclusion, 59 students took math only, 21 students took English only, and 40 students took history only.

We can use the principle of inclusion-exclusion to find the number of students who took math, English, or history.

The total number of students who took each course is,

131 (Math) + 151 (English) + 158 (History) = 440

Next, we subtract the number of students taking two courses at a time, since these students have been counted twice in the above totals,

Math and English = 67

Math and History = 55

English and History = 113

We then add back the number of students taking all three courses, since these students have been subtracted twice,

All three courses = 50

Using these values, we can calculate the number of students taking only one course as follows,

Math only = Math - Math and English - Math and History + All three courses = 131 - 67 - 55 + 50 = 59

English only = English - Math and English - English and History + All three courses = 151 - 67 - 113 + 50 = 21

History only = History - Math and History - English and History + All three courses = 158 - 55 - 113 + 50 = 40

Therefore, 59 students took math only, 21 students took English only, and 40 students took history only.

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Answer:

it equals 0

Step-by-step explanation:

3 + -3=0

(a) The probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013. (b) The expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes

a) The probability that a randomly selected customer spends less than 65 minutes at the gym is calculated using the standard normal distribution formula.

z = (x - μ) / σ

where,μ = 70 minutes, σ = 20 minutes, x = 65 minutes

Substituting the given values, we get

z = (65 - 70) / 20

z = -0.25

Using a standard normal table or calculator, the probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013.

b) The standard deviation (standard error) of the sample mean can be calculated using the formula:

SE = σ/√n

where,σ = 20 minutes, n = 49

Substituting the given values, we get

SE = 20/√49

SE = 2.857 minutes

Therefore, the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes, respectively.

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Answer: x - 15

Given:

     -9 + 4x - 3(x + 2)

Distribute the -3:

     -9 + 4x - 3x - 6

Combine similar terms:

     -15 + x

Answer:

[tex] \sf \: x - 15[/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ -9 + 4x - 3(x + 2)

Let's simplify the expression,

→ -9 + 4x - 3(x + 2)

→ -9 + 4x - 3(x) - 3(2)

→ -9 + 4x - 3x - 6

→ 4x - 3x - 9 - 6

→ (4x - 3x) + (-9 - 6)

→ (x) + (-15)

→ x - 15

Hence, the answer is x - 15.

The missing value in the given figure is 120 degree.

An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent.

The base angles of an isosceles trapezoid are congruent.

The converse is also true: If a trapezoid has congruent base angles, then it is an isosceles trapezoid.

In CFED,

As it is and isosceles trapezoid,

m∠C=m∠F

m∠D=m∠E

∴m∠F = 60 degrees

Now

m∠D+m∠E+m∠F+m∠C = 360 degree

2m∠D+120=360

m∠D=(360-120)/2

∴m∠D=120 degree

Thus the value of missing angle is 120 degree.

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Answer:

20 cars

Step-by-step explanation:

.4x = 8

x = 20 cars

To verify the answer, 40% of 20 is 8.

Step-by-step explanation:

$ 3.28 / 16 oz = $  .205  per ounce    which rounds to 21 cents per ounce

The value of the definite integral is -28/3

Using the power rule of integration, we can find the antiderivative of t^2 - 5 as follows:

∫(t^2 - 5) dt = (1/3)t^3 - 5t + C

where C is the constant of integration.

To evaluate the definite integral, we substitute the limits of integration into this expression and take the difference:

∫^-1_1 (t^2 - 5) dt = [(1/3)(1^3) - 5(1)] - [(1/3)(-1^3) - 5(-1)]

= (1/3 - 5) - (1/3 + 5)

= (-14/3)  (16/3)

= -28/3

Therefore, the value of the definite integral is -28/3.

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Answer:

QPS=110

m<2= 55

m<7=35

m<3=35

m<PQR=70

Step-by-step explanation:

the two lines interesting the rhombus were perfectly cut in half

The length of other leg of the triangle is 64√2 cm.

What is Pythagoras theorem?

For right angle triangle,

Hypotenuse² = Base²+Height ²

Here we have a right angle triangle.

It is given that height and base of the triangle is 8 cm.

Now we want to find other leg of the triangle.

It is clear that other leg means hypotenuse here because this is a right angle triangle.

We know,

Hypotenuse ²= Base²+Height ²

[tex] = {64}^{2} + {64}^{2} \\ = 4096+ 4096 \\ = 2 \times 4096[/tex]

So,

[tex]hypotenuse = \sqrt{2 \times 4096} \\ = \sqrt{64 \times 64 \times2 } \\ = 64\sqrt{2} [/tex]

Therefore, length of the third leg is 64√2 cm.

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Correct question is " There is a right angle triangle. Height and base of the triangle is 8 cm.What is the length of other leg of the triangle?

64 cm

64√2 cm

128 cm

128√2 cm"

The radius of the sphere is about 8 yards.

The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume, r is the radius, and π is the mathematical constant pi, approximately equal to 3.14.

We can rearrange the formula to solve for the radius:

r = ((3V)/(4π))^(1/3)

Substituting the given volume V = 2,143.57 yd³ and π = 3.14, we get:

r = ((3 x 2,143.57)/(4 x 3.14))^(1/3)

Evaluate

r ≈ 8.0

Rounding to the nearest yard, the radius of the sphere is approximately 8 yards.

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The area of the first triangle formed by points A, E, and B is 16 square units, the second triangle is formed by points B, C, and D, and the pentagon is formed by points B, C, and D the given points are 30 square units.

To plot and connect the given points in order, we first arrange them in a clockwise direction starting from point A(-5, 5).

The order is A, E, D, C, B, and A.

The rectangle is formed by the points C, D, and their respective y-coordinates. The length of the rectangle is 6 - 6 = 0 units, and the width is 5 - (-3) = 8 units.

The first triangle is formed by points A, E, and B. The base of the triangle is 4 units (the x-coordinate of E minus the x-coordinate of A), and the height is 8 units (the y-coordinate of A minus the y-coordinate of E).

The second triangle is formed by the points B, C, and D. The base of the triangle is 7 units (the x-coordinate of C minus the x-coordinate of B), and the height is 4 units (the y-coordinate of B minus the y-coordinate of D).

Therefore, the area of the rectangle is:

0 x 8 = 0 square units.

The area of the first triangle is:

0.5 x 4 x 8 = 16 square units.

The area of the second triangle is:

0.5 x 7 x 4 = 14 square units.

The total area of the pentagon is:

area of the rectangle + area of the first triangle + area of the second triangle

16 + 14 + 0 = 30 square units.

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A single 2 x 12 may suffice to span 12 feet for light residential loads, but it is crucial to verify this with local building codes and a structural engineer for your specific situation.

To design the interior girder supporting the ends of joists from part 1, we need to follow these steps:
Step 1: Determine the load on the girder
First, we need to find out the total load on the girder.

Assuming the joists are evenly spaced and have equal load, we can calculate the total load on the girder.
Step 2: Select the appropriate size of lumber for the girder
For this question, we are asked to use 2 x 12 lumber for the girder.

A 2 x 12 has a nominal size of 1.5 inches x 11.25 inches.
Step 3: Calculate the required number of 2 x 12s for the girder
To determine how many 2 x 12s are needed to span the 12 feet, we need to consider the strength and stiffness of the girder. To do this, we can refer to span tables or consult a structural engineer.

Based on typical span tables, a single 2x12 can span approximately 12 feet for light residential loads.
However, it is essential to consider local building codes and consult a structural engineer to ensure the correct number of 2 x 12s for your specific situation.

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