A steep mountain is inclined 74 degrees to the horizontal and rises to a height of 3,400 feet above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 940 feet out in the plain from the base of the mountain. Find the shortest length of cable needed. Round to two decimal places.

Answer:

Step-by-step explanation:

Answer:

Chloe is making a large table in the shape of a trapezoid, as shown. She needs to calculate the area of the table. She is making the longest side of the table twice as long as the table's width. Complete parts a and b below.

a) Write an expression for the area of the table in terms of the width x.

One possible expression is:

A = (x + 2x) * h / 2

where A is the area of the table, x is the width of the table, and h is the height of the table.

To get this expression, we use the formula for the area of a trapezoid    :

A = (a + b) * h / 2

where a and b are the lengths of the parallel sides of the trapezoid. Since Chloe is making the longest side of the table twice as long as the width, we can write:

a = x

b = 2x

Substituting these values into the formula, we get:

A = (x + 2x) * h / 2

b) Simplify the expression and find the area of the table if x = 3 feet and h = 4 feet.

To simplify the expression, we can combine like terms and apply the order of operations:

A = (x + 2x) * h / 2

A = (3x) * h / 2

A = 3 * x * h / 2

To find the area of the table if x = 3 feet and h = 4 feet, we can plug in these values into the simplified expression:

A = 3 * x * h / 2

A = 3 * 3 * 4 / 2

A = 9 * 4 / 2

A = 36 / 2

A = 18

Therefore, the area of the table is 18 square feet.

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Answer:

p =4

q = -2

Step-by-step explanation:

To mirror is to reflect.  See the picture

let's convert all mixed fractions to improper fractions, then add them up.

[tex]\stackrel{mixed}{2\frac{1}{10}}\implies \cfrac{2\cdot 10+1}{10}\implies \stackrel{improper}{\cfrac{21}{10}}~\hfill \stackrel{mixed}{1\frac{2}{7}} \implies \cfrac{1\cdot 7+2}{7} \implies \stackrel{improper}{\cfrac{9}{7}} \\\\\\ \stackrel{mixed}{4\frac{9}{10}}\implies \cfrac{4\cdot 10+9}{10}\implies \stackrel{improper}{\cfrac{49}{10}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{21}{10}+\left(\cfrac{9}{7}+\cfrac{49}{10} \right)\implies \cfrac{21}{10}+\left(\cfrac{(10)9~~ + ~~(7)49}{\underset{\textit{using this LCD}}{70}} \right)\implies \cfrac{21}{10}+\left(\cfrac{90+343}{70} \right) \\\\\\ \cfrac{21}{10}+\left(\cfrac{433}{70} \right)\implies \cfrac{21}{10}+\cfrac{433}{70}\implies \cfrac{(7)21~~ + ~~(1)433}{\underset{\textit{using this LCD}}{70}}\implies \cfrac{147+433}{70} \\\\\\ \cfrac{580}{70}\implies \cfrac{58}{7}\implies 8\frac{2}{7}[/tex]

Step-by-step explanation:

[tex]2 \frac{1}{10} + (1 \frac{2}{7} + 4 \frac{9}{10} )[/tex]

[tex]2 \frac{1}{10} = \frac{21}{10} [/tex]

[tex]1 \frac{2}{7} = \frac{9}{7} [/tex]

[tex]4 \frac{9}{10} = \frac{49}{10} [/tex]

[tex] \frac{21}{10} + ( \frac{9}{7} + \frac{49}{10} )[/tex]

[tex]( \frac{9}{7} + \frac{49}{10} ) = \frac{90 + 343}{70} = \frac{433}{70} [/tex]

[tex] \frac{21}{10} + \frac{433}{70} = \frac{147 + 433}{70} = \frac{580}{70} = 8 \frac{2}{7} [/tex]

The cost recovery deductions for the first 3 years under MACRS are as follows:

Year 1: $1,800

Year 2: $2,304

Year 3: $941 (rounded)

Let's determine the cost recovery deductions under MACRS for the first 3 years:

Lets determine the property class for the computers.

Since the computers are 5-year property, they fall under the "5-Year Property" class.

Now determine the MACRS depreciation percentages for the property class.

Referring to the MACRS table, the depreciation percentages for 5-Year Property are as follows:

Year 1: 20.00%

Year 2: 32.00%

Year 3: 19.20%

Calculate the cost recovery deduction for each year.

Year 1:

Cost Recovery Deduction = Cost of Computers × Depreciation Percentage for Year 1

= $9,000 × 20.00%

= $1,800

Year 2:

Cost Recovery Deduction = (Cost of Computers - Accumulated Depreciation)×Depreciation Percentage for Year 2

= ($9,000 - $1,800) ×32.00%

= $7,200× 32.00%

= $2,304

Year 3:

Cost Recovery Deduction = (Cost of Computers - Accumulated Depreciation) × Depreciation Percentage for Year 3

= ($9,000 - $1,800 - $2,304) × 19.20%

= $4,896 × 19.20%

= $940.99 (rounded to nearest dollar)

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The value of sin θ is equal to 3/5.

We have,

Given that θ is the angle for which [tex]cos^{-1}(4/5)[/tex] is equal to, we can determine the value of sin θ using the trigonometric identity:

sin²θ + cos²θ = 1

To find sin θ, we can rearrange the identity as:

sin θ = √(1 - cos²θ)

Since θ satisfies the condition 0 < θ < π/2, we know that cos θ is positive, and thus we can directly substitute [tex]cos^{-1}(4/5)[/tex] into the equation:

sin θ = √(1 - (4/5)²)

sin θ = √(1 - 16/25)

sin θ = √(9/25)

Since 0 < θ < π/2, sin θ is positive.

Therefore:

sin θ = 3/5

Hence,

The value of sin θ is equal to 3/5.

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to get the equation of any straight line, we simply need two points off of it.

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-4}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{5}}} \implies \cfrac{ -6 }{ -9 } \implies \cfrac{2}{3}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{5}) \\\\\\ y-2=\cfrac{2}{3}x-\cfrac{10}{3}\implies y=\cfrac{2}{3}x-\cfrac{10}{3}+2\implies {\Large \begin{array}{llll} y=\cfrac{2}{3}x-\cfrac{4}{3} \end{array}}[/tex]

The Distance around the track is 400.4 meters

In order to determine the distance around a track with two straight sections and two curved ends,

we must first determine the lengths of each section.

Let us consider the given diagram.The distance of the straight section can be determined by adding the length of two opposite sides together. Let us assume that each side of the straight section measures 50 meters. Thus, the total length of the straight section is:50m + 50m = 100mTo calculate the length of the curved sections, we must first determine the radius of each section.

This can be done by dividing the diameter by 2, since the diameter is not given,

we can divide the total length of each curved section by pi (3.14) and then divide the answer by 2 to get the radius of each section.

Let's say the total length of each curved section is 150 meters, therefore, the radius is:150m / 3.14 / 2 = 23.89m (rounded to the nearest hundredth)

Therefore, the circumference of each curved section is:2πr = 2 x 3.14 x 23.89 = 150.18m (rounded to the nearest hundredth)

So, the total distance around the track is:100m + 150.18m + 150.18m = 400.36 meters (rounded to the nearest tenth).

Therefore, the distance around the track is 400.4 meters (rounded to the nearest tenth).

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The population grew to 5650 in 13.48 years .

Given,

Population of town in 1940 is a function given by:

P= 1304 + 300t

Now,

Let total number of population after certain years be 5650.

Let t1 be the year in which the population reached a count of 5650. Solve for t1:

5650= 1304 + 300t1

t1 = 13.48 years

The population grew to the number 5650 in 13.48 years past 1940, approximately 1954 .

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Answer:

Melaine

Step-by-step explanation:

[tex]\text{Melaine's Total Earnings}=\$2500(1.05)^{15}=\$5197.32\\\text{Josiah's Total Earnings}=\$1000(1.10)^{10}=\$2593.74[/tex]

Therefore, Melaine will earn the most money over time

Answer:

Step-by-step explanation:

Thee percentage of 8th graders that prefer comedies is 44%

percentage is the ratio of required to the total number of samples in an experiment.

Here,

8th graders that prefer comedies = 18

Total number of 8th graders = (10+18+13) = 41

P(8th that prefer comedies) = (18/41) × 100% = 43.90

Therefore, the percentage of 8th graders that prefer comedies is 44%.

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Para encontrar el número que estás pensando, podemos plantear una ecuación. Denotemos al número desconocido como "x". Según la información proporcionada, podemos escribir la ecuación:

4x + 16 = 8

Ahora resolvamos la ecuación para encontrar el valor de "x":

4x = 8 - 16

4x = -8

x = -8/4

x = -2

Entonces, el número que estás pensando es -2.

Answer:

Step-by-step explanation:

V = width x length x height

   = 13 x 18 x 8

   = 1,872 in³

Answer:

A rectangular prism is a three-dimensional shape that has six rectangular faces. The volume of a rectangular prism is the amount of space inside it. To find the volume of a rectangular prism, we can use the formula: V = lwh, where l is the length, w is the width, and h is the height of the prism. In this case, we are given that the height is 8 in, the width is 13 in, and the length is 18 in. Plugging these values into the formula, we get:

V = lwh

V = (18)(13)(8)

V = 1872

Therefore, the volume of the rectangular prism is 1872 cubic inches.

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Answer:

[tex]y=3x+17[/tex]

Step-by-step explanation:

Use point-slope form

[tex]y-y_1=m(x-x_1)\\y-(-4)=3(x-(-7))\\y+4=3(x+7)\\y+4=3x+21\\y=3x+17[/tex]

Answer:

Step-by-step explanation:

3/4 hours=3/4×60=45 minutes

10:15+5.45 hrs=16:00+0:35=16:35=4.35 pm

so C

The monthly payment on the loan would be approximately $2,023.52.

To calculate the loan in detail, we need to determine the time period and the monthly payment. Let's break down the given information:

Loan amount: $17,000

Simple interest rate: 6.8%

Total interest: $867

First, we can calculate the interest amount using the formula for simple interest:

Interest = Principal × Rate × Time

We know the interest amount is $867, and the principal (loan amount) is $17,000. Let's solve for time (in years):

867 = 17,000 × 0.068 × Time

Dividing both sides of the equation by (17,000 × 0.068), we get:

Time = 867 / (17,000 × 0.068)

Time ≈ 0.7596 years

Since the loan term is usually expressed in months, we multiply the above result by 12 to convert it to months:

Time in months = 0.7596 × 12

Time in months ≈ 9.1152 months

Now that we have the time period in months, we can calculate the monthly payment (P) using the formula:

P = (Principal + Total Interest) / Time in months

P = (17,000 + 867) / 9.1152

P ≈ 2,023.52

Therefore, the monthly payment on the loan would be approximately $2,023.52.

To summarize, for a loan amount of $17,000 with a simple interest rate of 6.8% and a total interest of $867, the loan term would be approximately 9.1152 months, and the monthly payment would be around $2,023.52.

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we would expect m to be positive.

In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.

Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.

If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.

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The expression 81a² + 5b² cannot be factored

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

81a² + 5b²

using the above as a guide, we have the following:

The terms of the expression cannot be factored

This is so because they do not have any common factor

Hence, the expression 81a² + 5b² cannot be factored

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Step-by-step explanation:

First box contains 8 black and 12 white beads Second box contains 9 black and 6 white beads.

(a) One black bead from each box is taken.

Number of such cases = 8×9=72

Total number of possibilities = 20×15=300

Probablity of getting both black beads =

300

72

=

25

6

(b) One black and one white bead is taken.

So if one black bead is taken from first box then one white bead is taken from second box and if one white bead is taken from first box then one black bead is taken from second box.

Number of such cases = 8×6+12×9=48+108=156

Total number of possibilities = 20×15=300

Probablity of getting one black and one white bead =

300

156

=

25

13

The mean is 46.75, the median is 40, the mode is 42, the range is 41, and the standard deviation is approximately 13.12.

To find the mean, median, mode, range, and standard deviation of the given ages, let's organize the data in ascending order:

29, 34, 35, 38, 42, 42, 64, 70

Mean:

To find the mean, we sum up all the values and divide by the total number of values:

Mean = (29 + 34 + 35 + 38 + 42 + 42 + 64 + 70) / 8

= 374 / 8

= 46.75

Median:

The median is the middle value in a sorted dataset. In this case, we have an even number of values, so we take the average of the two middle values:

Median = (38 + 42) / 2

= 40

Mode:

The mode is the most frequently occurring value. In this case, the mode is 42 since it appears twice, more than any other value.

Range:

The range is the difference between the highest and lowest values:

Range = 70 - 29

= 41

Standard Deviation:

To find the standard deviation, we need to calculate the deviations from the mean, square them, take the average, and then find the square root:

Deviation from the mean: (29-46.75), (34-46.75), (35-46.75), (38-46.75), (42-46.75), (42-46.75), (64-46.75), (70-46.75)

Squared deviations: 339.2656, 167.5625, 122.0625, 71.0625, 21.0625, 21.0625, 340.5625, 527.0625

Average squared deviation: (339.2656 + 167.5625 + 122.0625 + 71.0625 + 21.0625 + 21.0625 + 340.5625 + 527.0625) / 8

= 172.6719

Standard Deviation: √172.6719 ≈ 13.12

Therefore, the mean is 46.75, the median is 40, the mode is 42, the range is 41, and the standard deviation is approximately 13.12.

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[tex]A'=\{3,6,7\}\\B'=\{2,4,6\}\\A'\cap B'=\{6\}[/tex]

Therefore, [tex]n(A'\cap B')=1[/tex].

Answer:

1 element

Step-by-step explanation:

A' means not A and B' means not B

∩ means both

so now we have how many elements are not in A and not in B

A has 1,2,4,5 so not A will be 3,6,7

B has 1,3,5,7 so not B will be 2,4,6

now we look at what not A and not B have together and that is 1 element {6}

The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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The Total amount paid by Peel is $8000. Peel must remit $13,333.33 to pay the balance of the debt at the end of the credit period.

(a) To determine the amount Peel must remit to pay the balance of the debt at the end of the credit period, we need to calculate the remaining balance after the two payments.

The original invoice amount is not given in the question, so we'll calculate it using the given discounts. Let's assume the original invoice amount is X dollars.

First, let's calculate the amount after a 25% discount:

Amount after 25% discount = X - 0.25X = 0.75X

Next, let's calculate the amount after a 20% discount:

Amount after 20% discount = 0.75X - 0.20(0.75X) = 0.75X - 0.15X = 0.60X

Now, let's consider the payment on September 30 to reduce the debt to $5000:

Remaining balance after September 30 payment = 0.60X - $5000

Finally, let's consider the payment on October 20 to reduce the debt by $3000:

Remaining balance after October 20 payment = (0.60X - $5000) - $3000

To find the amount Peel must remit to pay the balance, we set the remaining balance equal to zero and solve for X:

(0.60X - $5000) - $3000 = 0

Simplifying the equation:

0.60X - $8000 = 0

0.60X = $8000

X = $8000 / 0.60

X = $13,333.33

Therefore, Peel must remit $13,333.33 to pay the balance of the debt at the end of the credit period.

(b) To find the total amount paid by Peel, we sum the two payments made by Peel:

Total amount paid = $5000 + $3000

Total amount paid = $8000

Therefore, the total amount paid by Peel is $8000.

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Answer:

x = 20, y = -3

Step-by-step explanation:

Set both equations equal to each other

[tex]\displaystyle y=\frac{3}{5}x-15\\\\y=-\frac{3}{4}x+12\\\\\\\\\frac{3}{5}x-15=-\frac{3}{4}x+12\\\\\frac{12}{20}x-15=-\frac{15}{20}x+12\\\\\frac{27}{20}x-15=12\\\\\frac{27}{20}x=27\\\\x=20\\\\y=\frac{3}{5}x-15\\\\y=\frac{3}{5}(20)-15\\\\y=\frac{60}{5}-15\\\\y=12-15\\\\y=-3[/tex]

Answer:

0.75 = contraction

4/5 = contraction

-7 = expansion

11/9 = expansion

-4.3 = expansion

Step-by-step explanation:

The scale factor is a numerical value that expresses the proportional change in size between an original object or figure and a scaled version of it.

If the magnitude of the scale factor is greater than 1, it indicates an expansion, meaning the new size is larger than the original size.

If the magnitude of the scale factor is between 0 and 1, it indicates a contraction, meaning the new size is smaller than the original size.

If the scale factor is negative, it indicates a reflection in addition to the expansion or contraction.

[tex]\hrulefill[/tex]

As 0.75 is between 0 and 1, the scale factor of 0.75 would cause a contraction.

As 4/5 is between 0 and 1, the scale factor of 4/5 would cause a contraction.

As the magnitude of -7 is 7, and 7 is greater than 1, the scale factor of -7 would cause an expansion.

As 11/9 is greater than 1, the scale factor of 11/9 would cause an expansion.

As the magnitude of -4.3 is 4.3, and 4.3 is greater than 1, the scale factor of -4.3 would cause an expansion.

Answer:

0.75: Contraction

4/5: Contraction

-7: Expansion

11/9: Expansion

-4.3: Expansion

Step-by-step explanation:

The probability of winning is given as P(winning) = 1 / 4,469,850

C(45, 4) = 45! / [4!(45-4)!]

        = 45*44*43*42 / (4*3*2*1)

        = 148995

So, the total number of possible outcomes is 148995 * 30 = 4,469,850.

Now, we have to figure out the number of winning outcomes. In a lottery, there's typically only one winning combination (the numbers drawn), so the number of winning outcomes is 1.

This is an incredibly small probability, indicating that the chances of winning this kind of lottery on a single ticket are extremely low.

P(winning) = 1 / 4,469,850

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Answer:

11a)

A regular hexagon (6 sides) is given. Because it is regular, every interior angle has the same value.

We know that the sum of the interior angles of a triangle is 180°. Using this information, we can break this hexagon up into 4 triangles:

Given each triangle's interior angles sum to 180°, and we have 4 triangles, the total sum of the interior angles of the entire hexagon is

180*4 = 720

The sum of the interior angles of the hexagon is 720°.

11b)

The same idea can be applied:

This time a regular decagon (10 sides) is given. This shape can be broken up into 8 triangles (This value will always be the number of sides - 2).

We can now multiply to find the total sum of the interior angles.

180*8 = 1440

The sum of the interior angles of the decagon is 1440°.

(The formula to solve for interior angle sum of regular shapes is 180 * (number of sides - 2)

11c)

To find the measure of one interior angle of a regular octagon (8 sides), we must take the total sum of the interior angles and divide that by 8 (to find the value of 1 angle).

First, find the interior sum value using interior angle sum formula:

180 * (8-2) = 180 * 6 = 1080°

Now we can divide this by 8 to find the sum of one interior angle:

1080/8 = 135°

The value of one interior angle of a regular octagon is 135°.

(The formula to solve for one interior angle of a regular shape is

[180 * (number of sides - 2)] / number of sides

11d)

The sum of the exterior angles of any polygon is 360°.

An easy way to demonstrate this idea is with an equilateral triangle (every interior angle is 60°). If the interior angle is 60°, the exterior angle is 120° (supplemental theorem).

A triangle has 3 angles: 120 * 3 = 360°. The sum of exterior angles is 360°.

For a heptagon (7 sides), or any other polygon, the same result will be found.

(In order to algebraically solve this however, you would find the value of one interior angle using the formula above, subtract that value from 180 to find the value of one exterior angle, and then multiply the value of one exterior angle by 7 for a heptagon).

11e)

Given the sum of exterior angles is 360°, we can simply divide 360 by the number of sides to find the value of one exterior angle.

360 / 7 = 51.42857...

The measure of one exterior angle of the heptagon is about 51.4°.

Sherry Smith received 820 votes, the total Number of votes cast was 1000.

The total number of votes cast if Sherry Smith received 820 votes, you need to be provided with information on the percentage of votes Sherry Smith won. This is because knowing the percentage of votes Sherry Smith won would enable you to calculate the total number of votes cast, as follows:

If Sherry Smith won x percent of the total votes cast, then the total number of votes cast would be:

A total number of votes cast = (820 ÷ x) × 100We can use the formula above to calculate the total number of votes cast as follows:

If Sherry Smith won 82 percent of the total votes cast, then the total number of votes cast would be: Total number of votes cast = (820 ÷ 82) × 100Total number of votes cast = 1000 votes

Therefore, Sherry Smith received 820 votes, and the total number of votes cast was 1000.

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The true statement are:

Poster Perfect: Since Poster Perfect charges a setup fee of $10 plus $3 per poster, the total cost will increase linearly with the number of posters printed.

We can set up equation as

y= 10 + 3x where x is number of pieces

The graph will show a constant slope for PrintPro:

Since PrintPro charges a flat rate of $5 per poster with no setup fee, the total cost will increase at a constant rate as the number of posters printed increases.

We can set up equation as

y= 5x where x is number of pieces

For x = 5

Poster Perfect: y= 10+ 15 = $25

PrintPro: y = 25

and, for x= 6

Poster Perfect: y= 10 + 18 = $28

PrintPro: y = 30

So, the true statement are:

Both printers will print the same number of poster for $25.

Poster Perfect cost less if you want to print more than 5 posters.

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