Problem
You're playing a game where you defend your village from an orc invasion. There are
3
33 characters (elf, hobbit, or human) and
5
55 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.

Answer:

Option D.

Step-by-step explanation:

To find hypotenuse [tex]c[/tex] use formula:

                                    [tex]\text{Cos(B)}=\frac{a}{c}[/tex]

       After substituting [tex]B=62^0[/tex]  and a = 7 we have:

                                 [tex]\text{cos}(62^o)=\frac{7}{c}[/tex]

                                     [tex]0.4695=\frac{7}{c}[/tex]

                                         [tex]c=\frac{7}{0.4695}[/tex]

                                          [tex]c=14.9104[/tex]

The CPA Practice Advisor reports that the mean preparation fee for federal income tax returns was 261. Use this price as the population mean and assume the population standard deviation of preparation fees is 120.

We need to find the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.

We use the central limit theorem that states that, regardless of the shape of the population, the sampling distribution of the sample means approaches a normal distribution with mean μ and standard deviation

σ/√n

where μ is the population mean, σ is the population standard deviation, and n is the sample size.

Therefore, we have:

[tex]\mu = 261\]\\sigma = $120\]\\n = 20\][/tex]

[tex]S.E.= \frac{\sigma}{\sqrt{n}}\\S.E =\frac{\ 120}{\sqrt{20}}\\S.E =26.83[/tex]

The probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is given by:

[tex]P(Z < \frac{X - \mu}{S.E})\][/tex]

where X is the sample mean, μ is the population mean, and S.E is the standard error of the mean.

To calculate the probability, we standardize the distribution of the sample means using the z-score formula, i.e.,

[tex]\[z = \frac{X - \mu}{S.E} = \frac{\50 - \261}{\26.83} = -7.91\][/tex]

Therefore, the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is zero because the z-score is less than the minimum z-score (i.e., -3.89) that corresponds to the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.

Thus, it is impossible to obtain such a sample.

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The system of equation with the same solution with 2x + 2y = 16 3x  - y = 4 is 2x + 2y = 16, 6x - 2y = 8. Therefore, the answer is 2.

System of equation can be solved using different method such as elimination method, substitution method and graphical method.  Therefore, let's solve the system of equation as follows;

2x + 2y = 16

3x  - y = 4

multiply equation(ii) by 2

2x + 2y = 16

6x - 2y = 8

add the equations

8x = 24

x = 24  / 8

x = 3

y = 3x - 4

y = 3(3) - 4

y = 9 - 4

y = 5

Therefore,

2x + 2y = 16

6x - 2y = 8

add the equation

8x = 24

x = 24  / 8

x = 3

Therefore,

2(3) + 2y = 16

6 + 2y = 16

2y = 16 - 6

2y = 10

y = 5

Therefore, the equation with the same solution is 2x + 2y = 16

6x - 2y = 8.

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Answer:

290

Step-by-step explanation:

Step-by-step explanation:

2(x+10y)+2(7x^2-x+9y)

= 2x+20y+14x^2-2x+18y

= (14x^2+38y) units^2

the missing dimension of the triangle is the base, which has a length of 21 feet. To find the missing dimension of the triangle, we will use the formula for the area of a triangle, which is:

Area = 1/2 x base x height

We know that the area of the triangle is 14 ft squared and the height is 6 ft. We can substitute these values into the formula and solve for the base:

14 = 1/2 x base x 6

Multiplying both sides by 2/6 (or simplifying to 1/3) gives:

14 x 3/2 = base

21 = base

Therefore, the missing dimension of the triangle is the base, which has a length of 21 feet.

This means that the triangle has a height of 6 feet and a base of 21 feet, and its area is 14 square feet. The height of a triangle is the perpendicular distance from the base to the opposite vertex, and in this case, it is given as 6 feet. The base of a triangle is the side opposite the height, and we have found that it has a length of 21 feet.

In summary, we can find the missing dimension of a triangle by using the formula for the area of a triangle and the given dimensions. In this case, we found that the missing dimension is the base, which has a length of 21 feet, and we know that the height is 6 feet.

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The first four terms of the sequence are 3, -15, 75, and -375.

In a arithmetic sequence, the common difference is the fixed value that is added to (or subtracted from) each term to get the next term in the sequence.  

To find the first four terms of the sequence given by aₙ= 3(-5)ⁿ⁻¹, we simply substitute n = 1, 2, 3, and 4, respectively, into the formula for an and evaluate:

a₁= 3(-5)¹⁻¹ = 3(-5)⁰= 3(1) = 3

a₂ = 3(-5)²⁻¹ = 3(-5)¹= -15

a₃ = 3(-5)³⁻¹ = 3(-5)²= 75

a₄= 3(-5)⁴⁻¹ = 3(-5)³= -375

Therefore, the first four terms of the sequence are 3, -15, 75, and -375.

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The solution to the equation is x = -2 if x ≠ 0.

The equation  -1/x-1+2/x+5=1 can be rearranged to 2/x+1/x+5 = 0. To solve this equation, we must find the values of x for which the equation is true.
Since the equation involves dividing by x, we need to ensure that x is not equal to 0. Therefore, the restriction on the variable is x ≠ 0.
To solve the equation, we can first add -1/x to both sides to get 2/x + 5 = 1. Then, we can subtract 5 from both sides to get 2/x = -4. Finally, we can divide both sides by 2 to get x = -2.
Therefore, the solution to the equation is x = -2 if x ≠ 0.
To solve the given equation, we need to first find a common denominator. Here, the common denominator is (x - 1)(x + 5).-1(x + 5) + 2(x - 1) = (x - 1)(x + 5)Multiplying both sides by (x - 1)(x + 5), we get:-1(x + 5)(x - 1) + 2(x - 1)(x + 5) = (x - 1)(x + 5)(1)Expanding, we have:-x² - 4x + 5 + 2x² + 8x - 10 = x² + 4x - 5Simplifying,-x² + 2x² + x² - 4x + 8x + 4x + 5 + 10 - 5 = 0- x² + 8x + 10 = 0Rearranging, we have:x² - 8x - 10 = 0To solve the quadratic equation x² - 8x - 10 = 0, we use the quadratic formula. The formula is given byx = [-b ± sqrt(b² - 4ac)] / 2a Where a = 1, b = -8, and c = -10.Substituting these values, we get:[tex]x = [8 ± sqrt((-8)² - 4(1)(-10))] / 2(1)[/tex]

Simplifying = [8 ± sqrt(64 + 40)] / 2x = [8 ± sqrt(104)] / 2x = 4 ± sqrt(26)Therefore, the restrictions on the variable Are's ≠ 1 and x ≠ -5.

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Answer:

A

Step-by-step explanation:

Since both the x and y coordinates changed signs, this is a reflection over the origin. A reflection over the origin is a reflection across both axes.

Answer: A

Answer:

Step-by-step explanation:

Option 3

Answer:

Step-by-step explanation:

yes

I think it equals 18 tens

Answer:

3 x 60 x 30 = 5400

Step-by-step explanation:

The probability of winning is 1/42 expressed as a fraction.

Given that the odds on a bet are 41:1 against, we are to find the probability of winning.

We know that odds against = (Number of unfavorable outcomes) : (Number of favorable outcomes).

Thus, odds against = 41:1. This implies that the number of unfavorable outcomes is 41 and the number of favorable outcomes is 1.Probability of winning is given by the formula P(winning) = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is the sum of the number of favorable and unfavorable outcomes.

Number of favorable outcomes = 1 and Number of unfavorable outcomes = 41

Therefore, the total number of possible outcomes = 1 + 41 = 42

Thus, P(winning) = Number of favorable outcomes / Total number of possible outcomes

P(winning) = 1 / 42

Therefore, the probability of winning is 1/42 expressed as a fraction.

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The probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is used to quantify uncertainty and to make informed decisions in the face of incomplete or uncertain information.

We can assume that the heights of male passengers follow a normal distribution with a mean of 69.0 in and a standard deviation of 2.8 in. Let X be the height of a male passenger in inches. Then, we need to find the probability that X is less than or equal to 74 in, which represents the height of the airliner's doors.

(a) Using the standard normal distribution, we can standardize X as follows:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution, and z is the corresponding z-score.

Substituting the values, we get:

z = (74 - 69.0) / 2.8 = 1.75

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than or equal to 1.75:

P(Z ≤ 1.75) ≈ 0.9599

Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

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De acuerdo con la información, podemos inferir que el volumen total de la figura sería 1,476.58 cm³

To find the volume of the figure we must divide it into different sections because it has cones, pyramids, hemispheres, cylinders, and rectangular cubes. Below is the procedure:

Volume of rectangular segments:

Volume of the pyramids:

First we must calculate the height of the pyramids.

Cone volume:

First we need to calculate the height of the cone.

Cylinder volume:

Volume of the hemisphere:

Finally we just have to add all the values and we will obtain the total volume of the figure:

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Answer:

between 15 and 16

Step-by-step explanation:

31÷2=15.5 meaning 15.5 is between 15 and 16

Answer:

x=5 or x=-5

Step-by-step explanation:

[tex]x^{2} -25=0[/tex]

[tex](x-5)(x+5) =0[/tex]

[tex]x=-5 \\x=5[/tex]

The volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant is π units cubed. The curve is not provided here. Therefore, it is impossible to solve this question. We are unable to determine the function whose graph is being revolved around the y-axis based solely on the information given.If the curve had been given, we would have used the disk method, which states that the volume of a solid of revolution generated by rotating a plane figure about a line is equal to the sum of the volumes of an infinite number of infinitesimally thin disks perpendicular to that line. If f(x) is a non-negative function defined on [a, b], then the volume V of the solid generated by revolving the region between the curve y = f(x), the x-axis, x = a, and x = b about the y-axis is given by:V = π∫ab[f(x)]2 dxWhere π is the constant π = 3.14159..., a and b are the limits of integration, and f(x) is the function whose graph is being revolved.

It is also important to avoid ignoring any typos or irrelevant parts of the question and to not repeat the question in the answer unless necessary. Finally, when using math terminology or solving math problems, it is important to show all work and use proper notation.

For example, when solving a problem such as "find the volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant. if the answer does not exist, enter dne. otherwise, round to four decimal places," one might use the formula for finding the volume of a solid of revolution:V=π∫abf(x)2dxwhere f(x) is the function defining the curve, and a and b are the limits of integration. The limits a and b can be found by setting the equation defining the curve equal to zero and solving for x.

Once the limits are found, the function can be integrated and the result can be multiplied by π to find the volume of the solid. The answer should then be rounded to four decimal places and, if the answer does not exist, the answer should be entered as dne.

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lets use the two given points to form a system of equations and solve for the values of a and b.

Starting with the given equation:

y = ab

At point (2, 60):

60 = ab^(2)

At point (4, 960):

960 = ab^(4)

Now we can solve for a and b using algebraic manipulation.

First, we can divide the second equation by the first equation:

960/60 = (ab^(4))/(ab^(2))

16 = b^(2)

Taking the square root of both sides, we get:

b = 4

Substituting b = 4 into either of the two equations, we can solve for a:

60 = a(4^(2))

60 = 16a

a = 60/16

a = 15/4

Therefore, the values of a and b are:

a = 15/4

b = 4

So the exponential function is:

y = (15/4) * 4^x

"another way, same answer "

Experiment Random Variable (x)Possible values of the random variable Discrete or Continuous.

a) Take a 20-question examination Number of questions answered correctly Discrete (0, 1, 2, 3, ..., 20)

b. Observe cars arriving at a tollbooth Number of cars arriving at tollbooth for 1 hour Discrete (0, 1, 2, 3, ...)

c. Audit 50 tax returns Number of returns containing errors Discrete (0, 1, 2, 3, ...)

d. Observe an employee’s work Number of nonproductive hours in an eight-hour workday Continuous

e.Weigh a shipment of goods Number of pounds Continuous Random variables are numerical values that are a result of a random experiment. Random variables are generally classified into two categories

Solution:

discrete random variables and continuous random variables

.Discrete random variables

 When a random variable can assume only a countable number of values, it is called a discrete random variable.

Examples: the number of cars passing by a particular point of a highway in a day or the number of customers served by a shop in a day.

Continuous random variables: 

When a random variable can assume any value within a given range or interval, it is called a continuous random variable.

Examples: temperature, the weight of a person, or the height of a person.Tax returns: The random variable is discrete, as it can only take certain values (0, 1, 2, 3, and so on) since the number of tax returns containing errors is an integer.The shipment of goods: The random variable is continuous because it can assume any value between the minimum and maximum weight of the shipment, and the weight of the shipment can be any value.

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The equation of  line of reflection that transforms shape P into shape Q is y=7.

a reflection is known as a flip. A reflection is a mirror image of its shape. An image will reflect through the line, known as the line of reflection. Every point in a figure is said to mirror the other figure when they are all equally spaced apart from one another.

In the given figure, Shape P and Shape Q touches the line y=7 and Shape Q forms exact reflection of Shape P

Hence, the equation of the line of reflection that

transforms shape P into shape Q. is y=7.

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The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

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In the multiple regression model with k regressors, the variance of the stochastic errors in the population can be estimated by the residual mean square (MSE).

         Multiple regression is a statistical tool that allows the researcher to estimate the relationship between multiple independent variables and a dependent variable. It measures the impact of a given independent variable on the dependent variable after controlling for the other independent variables.

        In simple linear regression, there is only one independent variable, whereas, in multiple linear regression, there is more than one independent variable.

         Residual mean square (MSE) is the variance of the error term (the difference between the predicted and observed values). It represents the average variance of the errors or the average deviation of the dependent variable from its predicted value.

         The MSE can be used to estimate the variance of the stochastic errors in the population. It is calculated by dividing the sum of squared residuals by the degrees of freedom (n-k-1)

           Where n is the sample size and k is the number of regressors.

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The total number of listings possible for the 14 teams in the local little league is 11,664. This is because there are 14 teams, so the number of possible listings is equal to 14! (14 factorial). 14! is equal to 1x2x3x4x5x6x7x8x9x10x11x12x13x14, which equals 11,664.

To further explain, 14! is the number of ways to arrange 14 items. This is because the first item can be arranged in 14 ways, the second item in 13 ways, the third in 12, and so on. This means that the total number of possible arrangements is 14x13x12x11x10x9x8x7x6x5x4x3x2x1, which equals 11,664.

Therefore, the total number of listings possible for the 14 teams in the local little league is 11,664.

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Answer: 540 cm²

Step-by-step explanation:To find the area of the dilated rectangle, we need to first find the dimensions of the new rectangle after it has been dilated by a factor of 3.

The length of the new rectangle will be 3 times the original length, which is:

10 cm x 3 = 30 cm

The width of the new rectangle will also be 3 times the original width, which is:

6 cm x 3 = 18 cm

Therefore, the area of the dilated rectangle will be:

30 cm x 18 cm = 540 cm²

a) The linear function that gives the sales in x years after 2011 is of: S(x) = 18x + 191.

b) The slope of the graph of S(x) is of 18, meaning that the sales increase by 18 million a year.

c) The online sales were of 227 billion in the year of 2013.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

We take 2011 as the reference year, when the sales were of 191 billion, hence the parameter b is given as follows:

b = 191.

In 3 years, the sales increased by 54 billion, hence the slope m is given as follows:

m = 54/3

m = 18.

Hence the function modeling the sales in x years after 2011 is given as follows:

y = 18x + 191.

The sales were of 227 billion x years after 2011, for which y = 227, hence:

227 = 18x + 191

18x = 36

x = 2.

2 + 2011 = 2013.

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The graph showing one cycle of the trigonometric function y = 8 cos 8x is plotted and attached

Trigonometric graphs are graphical representations of trigonometric functions, which are functions that relate the angles of a right triangle to the ratios of its sides. The three most commonly used trigonometric functions are

The graphs of these functions are periodic, meaning they repeat themselves over a regular interval.

In the problem, the graph plotted is that of cosine function and the amplitude of is 8

The 5 points marked are

(-π/16, 0) - the first point

(0, 8) - showing the amplitude and 1/4 cycle

(π/16, 0) - 1/2 cycle

(-π/16, -8) - 3/4 cycle

(3π/16, 0) - one complete cycle

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No, we cannot conclude that 90% of households have between .7 and 2.1 children based on the confidence interval alone.

Based on the confidence interval alone, we cannot come to the conclusion that 90% of households have a number of children between .7 and 2.1. A confidence interval only provides a range of values that likely contains the true population parameter (in this case, the average number of children per household) with a certain level of confidence (in this case, 90%). It does not provide information about the distribution of the variable within the population. Therefore, we cannot make any conclusions about what percentage of households have a certain number of children based on the confidence interval alone.

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Regional identities have led to independence movements in the United Kingdom but not in Mexico because of the history of the regions' existence as separate states in the United Kingdom.

Reason of regional identities:

In the United Kingdom, there are four countries with distinct regional identities: England, Scotland, Wales, and Northern Ireland. Each of these countries has a unique culture, language, and history, which has led to a sense of national pride and identity.Regional identities in the United Kingdom have played a significant role in independence movements.

        For example, Scotland has a long history of wanting independence from the United Kingdom. The country was an independent state until it joined the United Kingdom in 1707.

              However, many Scottish people feel that their cultural and political identity is different from the rest of the United Kingdom and have called for a referendum on Scottish independence.Mexico, on the other hand, is a unitary state with a strong central government. The country has a long history of political and cultural unity, which has led to a sense of national identity.

      Therefore, the history of the regions' existence as separate states in the United Kingdom best explains why regional identities have led to independence movements in the United Kingdom but not in Mexico.

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