When used in a particular DVD player, the lifetime of a certain brand of battery is normally distributed with a mean value of 12 hours and a standard deviation of 0.8 hours. Suppose that two new batteries are independently selected and put into the player. The player ceases to function as soon as one of the batteries fails. (You may need to use a table.) in USE SALT (a) What is the probability that the DVD player functions for at least 10 hours? (Round your answer to four decimal places.) (b) What is the probability that the DVD player works for at most 13 hours? (Round your answer to four decimal places.) (c) Find a number ** such that only 15% of all DVD players will function without battery replacement for more than x* hours. (Round your answer to two decimal places.) x* = hr

69.1° is the value of C by Law of Cosines .

What is the cosine law?

The formula for the Law of Cosines is c2=a2+b22ab cosC. With the exception of the third component, which equals 0 if C is a right angle because the cosine of 90° is 0 and we have the Pythagorean Theorem, this is similar to the Pythagorean Theorem.

The Law of Cosines is given as

c² = a² + b² - 2ab-cosC

substitute the values in a, b, c

Plugging in given values, we get

  16² = 8² + 17² - 2 . 8 . 17 . cosC

   256 = 64 + 289 - 272. CosC

    256 = 353 - 272 . cosC

     256 - 353 = 272 . CosC

         -97 =   272 . CosC

            cosC = -97/-272

          C = across(97/272)

            C  = 69.1°

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Answer:

C= 83.04

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

x² - 36 = 0

x = 6

6² = 6 x 6 = 36

So..

36 - 36 = 0

As there are so many equations in mathematics, it is a very broad subject. These are a few illustrations of typical mathematical equations: [tex]x = -6; x = 6[/tex]. Thus, option C is correct.

To solve the equation [tex]x² - 36 = 0[/tex]  , we can use the difference of squares formula:

A, B, and C are constants in the quadratic equation: ax2 + bx + c = 0. A quadratic function, often known as a function with the form f(x) = ax2 + bx + c, can be solved using this equation to get its roots.

[tex]a² - b² = (a + b)(a - b)[/tex]

In this case, a² = x² and b² = 36, so we can write:

[tex]x² - 36 = (x + 6)(x - 6)[/tex]

Setting this expression equal to 0 and solving for x, we get:

[tex](x + 6)(x - 6) = 0[/tex]

[tex]x + 6 = 0 or x - 6 = 0[/tex]

[tex]x = -6 or x = 6[/tex]

Therefore, the solutions to the equation [tex]x² - 36 = 0[/tex] are  [tex]x = -6[/tex] and [tex]x = 6.[/tex]

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y = 5x² + 25x + 100 is the quadratic function that models the data.

x ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0.Since it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

We must employ the quadratic equation's general form in order to identify the quadratic function that best represents this data:

y = ax²+ bx + c

Three data points are available from the table: (0, 100), (1, 130), and (2, 140).

100 = a(0)² + b(0) + c

130 = a(1)² + b(1) + c

140 = a(2)² + b(2) + c

Simplifying each equation, we get:

c = 100

a + b + c = 130

4a + 2b + c = 140

Substituting c = 100 into the second and third equations, we get:

a + b = 30

4a + 2b = 40

The first equation's solution for b in terms of an is as follows:

b = 30 - a

This results from substituting this into the second equation:

4a + 2(30 - a) = 40

By condensing and figuring out a, we get at:

a = 5

Adding a = 5 to the first equation results in:

b = 25

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Step-by-step explanation:volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length

The solution is {y} = (2311, 2557, 2015) and hence the original message is CAT.

Suppose Alice uses the RSA methods as follows. She starts with a message consisting of several letters, and assigns a = 1,b=2, -2=26. She then encrypts each letter separately. For example, if her message is cat, she calculates 3 = mod n 19 = 2 mod n and 209 = mod n. Then she sends the encrypted message {G}=1,2,3 to Bob.The solution to the given question is as follows:Eva knows that n = 8881 = 79 × 112, where p = 79 and q = 112 are primes.Using the extended Euclidean algorithm and the fact that 13*5081 = 1 (mod 8880), one can compute the inverse of e modulo 8880 as d ≡ 5081 ≡ -3805 (mod 8880).To compute the message, Alice encrypts each letter of the message separately using the encryption function y ≡ x13 (mod 8881).Eva receives {G}=1,2,3 from Alice, and hence she wants to decipher it by computing 13 ≡ y ≡ G13 (mod 8881), where y is the message.To compute y, we have 1^{13} ≡ 1 (mod 8881), 2^{13} ≡ 8192 ≡ - 6889 + 2 (mod 8881) since 8192 = 2 × 4096 and 4096 = 8881 - 4785, hence, 2^{13} ≡ - 4785 × 2 + 2 (mod 8881), i.e., 2^{13} ≡ 2311 (mod 8881), and 3^{13} ≡ 3 × 3^{12} ≡ 3 × (3^{4})^{3} ≡ 3 × 6561^{3} ≡ 3 × 4299 ≡ 12897 ≡ 2557 (mod 8881).Therefore, the decrypted message is {y} = (2311, 2557, 2015) and hence the original message is CAT.Hence, the solution is {y} = (2311, 2557, 2015) and hence the original message is CAT.

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The possible echelon forms of the given matrix are:

A matrix is in echelon form when it has leading nonzero entries in each row, with each row starting further to the right than the row above it. In the given matrix, the first row does not have any nonzero entries, so it does not meet this criterion. The second row does have a nonzero entry (x) so it can meet the criterion, provided that it is the leading entry.

This is the case for b. 0 x
0 0, c. x *
0 0, and d. x *
0 x.
The other criterion for echelon form is that all starred entries (*) may have any value including zero. This criterion is met in all three cases.

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Answer: 1. Here is a sketch of the overlapping triangles ΔEBT and ΔELH:

         H

        /|

       / |

      /  |

     /   |

    / θ  |

   /____|L

       E

       |

       |

       |

       |

       T

       |

       |

       |

       |

       B

2. ΔEBT~ΔELH because they have the same shape (both are right triangles with angle θ in common) and their corresponding sides are proportional. Specifically, angle θ is shared by both triangles, angle EBT is a right angle, and angle ELH is a right angle. Therefore, by the Angle-Angle Similarity Theorem, the two triangles are similar. Corresponding sides are proportional because EB/EL = BT/LH (by definition of similar triangles).

3. We are given that BT (the length of the thumb) is about 2 inches. We are also told that the distance from the eye to the landmark (EL) is unknown, but that the distance from the eye to the thumb (EB) is 10 inches (estimated by the person). We are given that LH (the height of the landmark) is 604 feet, or 604*12=7248 inches (since there are 12 inches in a foot). Therefore, we can label the diagram as follows:

         7248

        /|

       / |

      /  | EL

     /   |

    / θ  |

   /____|L

       E

       |10

       |

       |

       |

       T

       | 2

       |

       |

       |

       |

       B

4. To solve for EL, we use the fact that the triangles are similar: EB/EL = BT/LH. Substituting in the known values, we get:

10/EL = 2/7248

5. Multiplying both sides by EL and dividing both sides by 2, we get:

EL = 7248*5 = 36240 inches

Therefore, the distance from the eye to the landmark is 36240/12 = 3020 feet (rounded to the nearest foot).

Step-by-step explanation:

The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection

The probability of choosing a red card or a king from a deck of 52 cards is 8/52 or 2/13. To calculate this, we first need to determine the number of cards that are either red or a king. There are 26 red cards in a deck of 52 cards, so the probability of choosing a red card is 26/52 or 1/2. There are four kings in a deck of 52 cards, so the probability of choosing a king is 4/52 or 1/13.

However, we need to be careful to avoid counting the red kings (two of which exist in a deck of 52 cards) twice. To account for this, we subtract the probability of choosing a red king from the sum of the probabilities of choosing a red card and a king. The probability of choosing a red king is 2/52 or 1/26, so the probability of choosing a red card or a king is:

P(red card or king) = P(red card) + P(king) - P(red king)
P(red card or king) = 26/52 + 4/52 - 2/52
P(red card or king) = 28/52
P(red card or king) = 2/13

The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection (i.e., the probability that they occur jointly).

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Answer:

Step-by-step explanation:

150

Answer:

Step-by-step explanation:

we have perimeter 16

for perimeter 4+4+4+4 we add together it's 16

for area we have 4 times 16

The area of the base of the prism is 7-½ cm³/h cm².

Area is two-dimensional space defined by a boundary. It is measured in square units, such as square feet, square meters, and acres. Area can be used to measure the size of a shape, such as a circle or a triangle, or the size of a piece of land. It can be used to calculate the area of a room or the area of a city. Area is an important concept in mathematics, and can be used in a variety of applications, from construction to engineering.

The volume of a right rectangular prism is the product of its length, width, and height. In this case, the prism has a volume of 7-½ cm³, so the equation for calculating its area of base is 7-½ cm³ = lwh. Since the height of the prism is not given, we can solve for it by dividing both sides of the equation by lw, resulting in the equation: 7-½ cm³/lw = h. The area of the base of the prism is then lw, which can be calculated by multiplying both sides of the equation by lw, resulting in lw = 7-½ cm³/h. Therefore, the area of the base of the prism is 7-½ cm³/h cm².

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The area of the base of the prism is 92/cm².

Area is two-dimensional space defined by a boundary. It is measured in square units, such as square feet, square meters, and acres. Area can be used to measure the size of a shape, such as a circle or a triangle, or the size of a piece of land. It can be used to calculate the area of a room or the area of a city. Area is an important concept in mathematics, and can be used in a variety of applications, from construction to engineering.

To find the area of the base of a right rectangular prism, we need to know two of its dimensions, such as the length and width. Since we only know the volume, we can use the formula V = lwh to solve for the unknown dimension.

We can rearrange this equation to solve for either the length or the width:

V = lwh
l = V/wh

or

V = lwh
w = V/lh

Since we know the volume (7-½ cm³) and the height (h) of the prism, we can use the formula V = lwh to solve for the length (l) or the width (w).

For example, if we solve for the length, we can substitute the known values into the equation:

l = V/wh
l = 7-½ cm³/wh

Since the height (h) is unknown, we can solve for it
by rearranging the equation:

7-½ cm³/l = wh
h = 7-½ cm³/wl

Now that we know the length (l) and the height (h), we can use the formula for the area of a rectangle to find the area of the base of the prism:

A = lw
A = l(7-½ cm³/wl)
A = (7-½ cm³/l)²
A = 92/cm²

Therefore, the area of the base of the prism is 92/cm².


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Answer: 54 square in

Step-by-step explanation:

I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation

The given conditional statements are false, true, false, True.

They are determined by following:

(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.

Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.

The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.

If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.

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(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.

(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.

The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.

(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.

(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.

Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.

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To work out the mean cost of a present in pounds (£), we need to divide the total cost of the presents (£80.52) by the number of presents (4).

The calculation will look like this:

£80.52 ÷ 4 = £20.13

Therefore, the mean cost of a present in pounds (£) is £20.13.

This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.

Tangent is a line or plane that touches a curve or surface at a single point. It is a measure of the steepness of a curve or surface at a particular point. It is equal to the ratio of the change in the y-coordinate to the change in the x-coordinate of a point on the curve. Tangent is used in many areas of mathematics and physics, including calculus, geometry, and mechanics. It is also used to describe the rate of change in a function, as well as to define the angle between two intersecting lines.

The tangent line equation for a line with a slope of 50 degrees is y = tan(50°)x.
To solve for x, you must rearrange the equation to isolate x on one side of the equation.
To do this, divide both sides of the equation by tan(50°), giving the equation x = y/tan(50°). This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.

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Answer:

x = 45.

Step-by-step explanation:

Given a straight line with the equation.

First collect like terms:

2x + x = 180 - 45

Then calculate:

3x = 135

Finally after dividing both sides by 3:

x = 45

80 middle school students prefer the documentaries television genre.

None of the given options match exactly, but the closest one is 76.

A circle graph, also known as a pie chart, is a type of chart that displays data as a circular diagram, divided into slices to represent proportions of a whole. Each slice of the circle represents a percentage of the total data being represented, and the entire circle represents 100% of the data.

Based on the circle graph, the percentage of students who prefer documentaries is 16% (as the percentage for documentaries is missing from the given options, we need to calculate it).

To find out the actual number of students who prefer documentaries, we need to multiply this percentage by the total number of students in the sample:

16% of 500 = (16/100) x 500 = 80

Therefore, 80 middle school students prefer the documentaries television genre.

None of the given options match exactly, but the closest one is 76.

Circle graphs are commonly used to show proportions or percentages of different categories within a dataset. They are useful for displaying data in a way that is easy to understand, and they are often used in business and finance, as well as in education and research.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Cant really graph since we don't have access, but here are some pointers.

The relationship in the table is a function because each input (x) has exactly one output (y). The equation for the relationship is y = 4 - x. The points (1, 3), (2, 2), and (3, 1) would all fall on this line.

In mathematics, an equation is a statement that shows the equality between two expressions, usually with one or more variables. An equation is typically represented using an equals sign (=) between the two expressions.

For example, the equation 2x + 5 = 11 shows that the expression 2x + 5 is equal to 11. This equation has one variable, x, which can be solved to find its value. In this case, we can subtract 5 from both sides of the equation to get 2x = 6, and then divide both sides by 2 to get x = 3.

The relationship in the table is a function because each input (x) has exactly one output (y).

Using words, the relationship could be described as "y is equal to 4 minus the value of x."

The equation for the relationship is y = 4 - x.

The graph of the relationship would be a straight line that starts at the point (0, 4) and slopes downward to the right. The points (1, 3), (2, 2), and (3, 1) would all fall on this line.

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The option a. S-(red,red), (red,black), (black,red), (black,black) is the most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards

The most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards and observing the color of each (26 cards in the deck are red and 26 are black) is given by option a. S-(red,red), (red,black), (black,red), (black,black).

Sample space S in probability theory denotes the set of all possible outcomes of an experiment.

In other words, the sample space S represents all possible outcomes of an experiment under consideration. For instance, in the current scenario,

These four possible outcomes are independent and equally likely events, and the sample space S for the possible outcomes is given by option a. S-(red,red), (red,black), (black,red), (black,black).

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The conversion of the statement of the expression into inequality form in terms of x is given by 1/2 × 3^x + 2^(2 - x) - 2 ≤ x ≤ 3

Using the details of the inequality,

1 half left parenthesis 3 right parenthesis to the power of x is,

1/2 × 3^x

Plus space 2 end exponent minus space 2 , negative 1 space  is written as ,

+ 2^(2 - x) - 2

less or equal than space x space less or equal than space 3

≤ x ≤ 3

Now, combine all to get the required inequality,

1/2 × 3^x + 2^(2 - x) - 2 ≤ x ≤ 3

Therefore, the required inequality for the given expression is equal to

1/2 × 3^x + 2^(2 - x) - 2 ≤ x ≤ 3

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The given question is incomplete, I answer the question in general according to my knowledge:

If left parenthesis x right parenthesis space equals space 1 half left parenthesis 3 right parenthesis to the power of x space plus space 2 end exponent minus space 2 , negative 1 space less or equal than space x space less or equal than space 3.

Represent the expression in the inequality form of x.

Answer:

We know that (23x)² + (1y)² = 7133029. From the right hand side of the equation, we can see that the last digit of 7133029 is 9. Using this information, we can deduce that the last digit of (23x)² must be 9, because (1y)² can only end in 1, 4, 5, 6 or 9.

Now we know that the last digit of (23x)² is 9 and the last digit of 23x is 3. Therefore the last digit of x is 3.

So, the last digit of the first number is 3. And the answer is (A) 3

Lightbulbs act as resistors. Janine is building a circuit that contains two lightbulbs in parallel. One of the lightbulbs has a resistance of 120 ohms, but the resistance of the second lightbulb is unknown. Therefore, The inverse of Janine's equation is r = -120/(t - 120).

Equation:

An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign. An equation is a formula that expresses that two expressions are equal by joining them with the equal sign =.The word comparison and its cognates in other languages ​​may have subtly different meanings; for example, in French, an equation is defined to contain one or more variables, and in English any well-formed formula composed of two expressions linked by equal signs is an equation.

According to the Question:

In algebra, an equation is a mathematical statement that determines whether two mathematical expressions are equal.

The type of comparison is identity or conditional comparison.

For each potential value, the variable provides an identifier. Only certain combinations of variable values ​​allow conditional comparisons to be true.

In order to  find the inverse of Janine's equation, we will to solve for r in terms of t.

First, we can rearrange the equation to get

⇒ t - 120 = 1/r.

divide both sides of the equation by 1/r to get

⇒ t/r - 120/r = 1.

divide both sides of the equation by -120/r to get

⇒ r = -120/(t - 120).

Therefore, the inverse of Janine's equation is r = -120/(t - 120).

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Answer:

53 miles per hour

Step-by-step explanation:

To calculate Jennifer's average rate of speed in miles per hour, we can use the formula:

average speed = total distance / total time

In this case, Jennifer drove a total distance of 265 miles and it took her a total time of 5 hours, so:

average speed = 265 miles / 5 hours

Simplifying the expression, we get:

average speed = 53 miles per hour

Therefore, Jennifer's average rate of speed in miles per hour is 53 miles per hour.

Answer: 53 miles per hour

Step-by-step explanation:

To find Jennifer's average rate of speed in miles per hour, we divide the distance she traveled by the time it took her:

Average speed = distance ÷ time

Average speed = 265 miles ÷ 5 hours

Average speed = 53 miles per hour

Therefore, Jennifer's average rate of speed was 53 miles per hour.

The probability of guessing randomly at least 8 correct answers in a 10 question multiple choice test where each question has 4 choices is 0.0385 or approximately 3.85%.

To find the probability of guessing at least 8 correct answers, we need to use the binomial probability formula:

P(X ≥ k) = 1 - P(X < k)

where

P(X ≥ k) is the probability of getting k or more correct answers

P(X < k) is the probability of getting less than k correct answers

n is the total number of questions in the test = 10

p is the probability of guessing the correct answer = 1/4

q is the probability of guessing the incorrect answer = 3/4

Now, we need to find the probability of getting less than 8 correct answers:

P(X < 8) = Σ P(X = k) for k = 0 to 7

P(X = k) = nCk * p^k * q^(n-k)

where nCk is the binomial coefficient for choosing k items from a set of n items.

P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 7)

P(X = k) = nCk * p^k * q^(n-k)

P(X = 0) = 10C0 * (0.25)⁰ * (0.75)¹⁰ ≈ 0.0563

P(X = 1) = 10C1 * (0.25)¹ * (0.75)⁹ ≈ 0.1875

P(X = 2) = 10C2 * (0.25)² * (0.75)⁸ ≈ 0.2813

P(X = 3) = 10C3 * (0.25)³ * (0.75)⁷ ≈ 0.2503

P(X = 4) = 10C4 * (0.25)⁴ * (0.75)⁶ ≈ 0.1450

P(X = 5) = 10C5 * (0.25)⁵ * (0.75)⁵ ≈ 0.0586

P(X = 6) = 10C6 * (0.25)⁶ * (0.75)⁴ ≈ 0.0161

P(X = 7) = 10C7 * (0.25)⁷ * (0.75)³ ≈ 0.0028

Therefore, P(X < 8) = 0.0563 + 0.1875 + 0.2813 + 0.2503 + 0.1450 + 0.0586 + 0.0161 + 0.0028 ≈ 1.0 - 0.0385 = 0.9615 or approximately 96.15%

The probability of guessing at least 8 correct answers:

P(X ≥ 8) = 1 - P(X < 8) ≈ 1 - 0.9615 = 0.0385 or approximately 3.85%

The problem seems incomplete, it must have been...

"Steve is taking a 10-question multiple choice test where each question has 4 choices. What is the probability that guessing randomly will give him at least 8 correct answers?"

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Answer:

10 sides

Step-by-step explanation:

We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:

S = (n - 2) x 180 degrees

If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:

1440 = (n - 2) x 180

Dividing both sides by 180, we get:

8 = n - 2

Adding 2 to both sides, we get:

n = 10

Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.

Answer:

Order is important: If allowed 11881376

Order is important:If rep. Is not allowed 7893600

Step-by-step explanation:

If the order isnt important and repetition is not allowed 65780

If order isn’t important and repetition is allowed 142506