-16/5 divided by 12/25

The probability that Samuel goes first and wins the game is 1/16 (0.0625). The Option B is correct.

The probability that Samuel goes first is 1/4, since there are four players and each is equally likely to go first.

The probability that Samuel wins the game, given that he is playing, is also 1/4, since each player is equally likely to win and there are four players in total.

To find the probability that Samuel goes first and wins the game, we need to multiply these two probabilities:

P(Samuel goes first and wins) = P(Samuel goes first) x P(Samuel wins | Samuel is playing)

= (1/4) x (1/4)

= 1/16

= 0.0625

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The total distance traveled by Max is approximately 2 + 4.5 + 4.5 = 11 feet/.

What is Cartesian plane?

The Cartesian plane, also known as the coordinate plane, is a two-dimensional plane that is used to represent and graph mathematical equations and functions. The plane is named after the French mathematician and philosopher René Descartes, who developed the concept in the 17th century.

We can use the Pythagorean theorem to find the distance between Max and Kenji, and between Max and Lindsey. Let's assume that the stage is a coordinate plane, with Max's original position at (0,0), Kenji's position at (0,2), and Lindsey's position at (-4,0).

The distance between Max and Kenji is the length of the hypotenuse of a right triangle with legs of length 2 and 4. Using the Pythagorean theorem, we have:

sqrt(2² + 4²) = sqrt(20) ≈ 4.5

So the distance between Max and Kenji is approximately 4.5 feet.

The distance between Max and Lindsey is the length of the hypotenuse of a right triangle with legs of length 4 and 2. Using the Pythagorean theorem, we have:

sqrt(4² + 2²) = sqrt(20) ≈ 4.5

So the distance between Max and Lindsey is also approximately 4.5 feet.

To find the total distance traveled by Max, we can add up the distances traveled during each part of his dance:

Twirling from Lindsey's position to Kenji's position: This distance is the same as the distance between Lindsey and Kenji, which is 2 feet.

Leaping from Kenji's position back to Max's original position: This distance is the same as the distance between Max and Kenji, which we found to be approximately 4.5 feet.

Walking from Max's final position back to his original position: This distance is the same as the distance between Max and Lindsey, which we also found to be approximately 4.5 feet.

So the total distance traveled by Max is approximately 2 + 4.5 + 4.5 = 11 feet. Rounded to the nearest tenth, this is 11.0 feet.

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B

East Indians and Chinese because they are both in the continent of Asia, which is where P and Q are located.

Answer:

A) -1

Step-by-step explanation:

[tex] \dfrac{i^{2n - 3} \times i^{3n - 1}}{i^{5n - 2}} = [/tex]

[tex] = i^{2n - 3 + 3n - 1 - (5n - 2)} [/tex]

[tex] = i^{2n - 3 + 3n - 1 - 5n + 2} [/tex]

[tex] = i^{-2} [/tex]

[tex] = \dfrac{1}{i^2} [/tex]

[tex] = \dfrac{1}{-1} [/tex]

[tex] = -1 [/tex]

Therefore, they will have paid the same amount after attending 9 games.

An equation is a mathematical statement that expresses the equality between two expressions or values. It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions. An equation typically includes an equal sign (=) that indicates that the two sides of the equation are equal in value.

Here,

Let's start by setting up an equation to represent the total cost for each person after attending a certain number of games:

For the season ticket holder: Total Cost = 136.98 + 2.5x, where x is the number of games attended

For the second person: Total Cost = 17.72x

To find the number of games at which they will have paid the same amount, we can set the two equations equal to each other and solve for x:

136.98 + 2.5x = 17.72x

136.98 = 15.22x

x = 9

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Answer:

The answer is B

Step-by-step explanation:

These are triangles are similar and because of that:

x/6 = (x+2.5)/(6+4)

x/6 = x/10 + 0.25

x = 6x/10 + 1.5

4x/10 = 1.5

4x = 15

x = 3.75

no

calculating the equation, you haft to simplify it gives 1.5

it's 1.5x

Answer:

[tex] {2}^{a} \times {2}^{b} = {2}^{a + b} = {2}^{0} [/tex]

From this, a + b = 0, meaning a and b are additive inverses of each other.

As an example, let a = 1, so b = -1.

Answer:

37 tens

Step-by-step explanation:

divide the numbers

For the given triangle, m∠CBD = 63 degrees.

What is triangle?

A triangle is a two-dimensional geometric shape with three sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points with line segments.

In a triangle, the sum of the angles is always 180 degrees.

So, we can write:

m∠ABD = m∠ABC + m∠CBD

Substituting the given values, we get:

96 = (7x - 9) + (6x + 27)

Simplifying the equation:

96 = 13x + 18

Subtracting 18 from both sides:

78 = 13x

Dividing by 13:

x = 6

Therefore:

m∠ABD = 96 degrees

m∠CBD = 6x + 27 = 6(6) + 27 = 63 degrees

m∠ABC = 7x - 9 = 7(6) - 9 = 33 degrees

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In the year 2015, the times ranking and average scores of math achievement for fourth-graders were option (c) Kuwait

According to the Trends in International Mathematics and Science Study (TIMSS) report for 2015, the lowest ranking and average scores of math achievement for fourth-graders were found in Kuwait. Kuwait ranked 48th out of the 49 countries that participated in the study.

It's worth noting that while Korea, Russia, and Iran also participated in the study, they did not have the lowest ranking or scores. Korea, in fact, ranked 5th overall with an average math score of 608, while Russia ranked 12th with an average math score of 544, and Iran ranked 24th with an average math score of 474.

The reasons for Kuwait's low ranking and scores in math achievement could be due to various factors, such as inadequate resources for education, lack of effective teaching methods, or low investment in STEM (science, technology, engineering, and mathematics) education.

Therefore, the correct option is (c) Kuwait

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The inverse of the provided graph is shown in the image attached below.

In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value). By critically observing the graph, we can logically deduce the following points;

Vertex (h, k) = (-4, 6)

y-intercept (x, y) = (0, 8)

y-intercept (x, y) = (0, 4)

Point (x, y) = (5, 9)

Point (x, y) = (5, 3)

By swapping both the input value (x-value) and output value (y-value), we have:

Vertex (h, k) = (6, -4)

x-intercept (x, y) = (8, 0)

x-intercept (x, y) = (4, 0)

Point (x, y) = (9, 5)

Point (x, y) = (3, 5)

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A a scale factor of 4/5 would be used to create a figure with an area of 16 square units from a figure with an area of 25 square units.

The scale factor to create a figure with an area of 16 square units from a figure with an area of 25 square units can be found using the formula:

scale factor = √(new area / original area)

Plugging in the given values, we get:

scale factor = √(16/25)

So, we have

scale factor = 4/5

Therefore, a scale factor of 4/5 would be used to create a figure with an area of 16 square units from a figure with an area of 25 square units.

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Answer: 4/5

The first person to answer was correct.

Step-by-step explanation:

I took the quiz so you don't have to! <3

Answer:

12,750,000ft

Step-by-step explanation:

1,500 * 8,500 = 12,750,000

A quadratic equation is a type of polynomial equation of degree 2, which means the highest power of the variable in the equation is 2.

The general form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants and x is the variable. The coefficient a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.

We know that;

y = (x - 3)^2+ 36

y = x^2 -3x + 9 + 36

y = x^2 - 3x + 45

y = -3[(x + 4) (x - 5)

y = -3[x^2 - 5x + 4x - 20]

y = -3[x^2 -x - 20]

y = -3x^2 + 3x + 60

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Nolan has 270 different outfits to choose from.

What is permutation?

Ways" or permutation refers to the number of different possible outcomes or arrangements in a situation. For example, if you have 3 different shirts and 4 different pants, there are 12 ways (3 x 4) to choose one shirt and one pant. The concept of "ways" is often used in combinatorics, which is the branch of mathematics that deals with counting and arranging objects.

To find the total number of different outfits that Nolan can choose from, we need to multiply the number of options for each clothing item:

Total number of outfits = number of pants x number of t-shirts x number of sweaters or hoodies x number of shoes

Total number of outfits = 6 x 3 x 3 x 5 = 270

Therefore, Nolan has 270 different outfits to choose from.

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Answer:

The scale factor would be 3,000

Step-by-step explanation:

3(3000) = 9000 millimeters

9000 x [tex]\frac{1}{1000}[/tex] = 9 to convert to meters

Helping in the name of Jesus.

Answer:

the amount at the end of the third year is A3 = $11,330.40.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For the first year, the interest rate is 10%, so we have:

A1 = 8000(1 + 0.1/1)^(1*1)

A1 = 8800

After the first year, the principal becomes 8800. For the second year, the interest rate is 12%, so we have:

A2 = 8800(1 + 0.12/1)^(1*1)

A2 = 9856

After the second year, the principal becomes 9856. For the third year, the interest rate is 15%, so we have:

A3 = 9856(1 + 0.15/1)^(1*1)

A3 = 11330.4

Therefore, the amount at the end of the third year is A3 = $11,330.40.

In summary, the initial amount of $8,000 is compounded annually for three years at different interest rates. By using the formula for compound interest, we find that the amount at the end of the third year is $11,330.40.

Answer:

To find the original price of the dress, we can use the following formula: Original price = Sale price / Discount rate In this case, we know that the sale price was $17, and the discount rate was 85%. So we can substitute these values into the formula: Original price = $17 / 0.85 Simplifying this expression, we get: Original price = $20 Therefore, a dress originally cost $20.

The solutions to the equation are x = -11/3 and x = 6.

In mathematics, an equation is a statement that two expressions are equal. It consists of two sides separated by an equal sign (=). The expression on the left side of the equal sign is usually called the left-hand side (LHS), while the expression on the right side is called the right-hand side (RHS).

Equations can take many different forms and can involve various types of functions and operators, such as addition, subtraction, multiplication, division, exponentiation, logarithms, trigonometric functions, and more. They can also involve one or more variables, which can be solved for to obtain a specific value or range of values that make the equation true. Equations are used extensively in mathematics, science, engineering, economics, and many other fields.

To solve the equation for x, we can start by simplifying both sides of the equation and bringing all the terms to one side:

(1)/(x²-6x) - (x)/(x²-36) = 2

We can simplify the left side of the equation by finding a common denominator:

[(1)(x-6) - (x)(x+6)] / [(x-6)(x+6)] = 2

Expanding the numerator and simplifying, we get:

(-x² + 7x - 6) / [(x-6)(x+6)] = 2

Multiplying both sides by the denominator, we get:

-x² + 7x - 6 = 2(x-6)(x+6)

Expanding the right side, we get:

-x² + 7x - 6 = 2(x² - 36)

Simplifying and rearranging, we get:

3x² - 7x - 66 = 0

We can solve this quadratic equation by factoring or using the quadratic formula:

3x² - 7x - 66 = (3x + 11)(x - 6) = 0

So either 3x + 11 = 0 or x - 6 = 0:

3x + 11 = 0 => x = -11/3

x - 6 = 0 => x = 6

Therefore, the solutions to the equation are x = -11/3 and x = 6.

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To take a systematic sample of 100 companies from a population of 1,803 companies, determine the sampling interval (k) which is N/n, choose a random starting point between 1 and k, and select every kth company until 100 companies are sampled.

To take a systematic sample of 100 companies from the 1,803 companies that are members of an industry trade association, follow these steps

Determine the sampling interval (k), which is the number of companies in the population divided by the desired sample size. In this case, k = 1803/100 = 18.03. Round this number up or down to the nearest whole number based on your sampling preferences.

Choose a random starting point between 1 and k. For example, you could randomly select a number between 1 and 18.

From the starting point, select every kth company in the list of members until you have 100 companies. For example, if the starting point is 4, you would select companies 4, 22, 40, 58, 76, 94, 112, and so on until you reach 100 companies.

Important numerical values used in this process are:

Population size (N) = 1,803 companies

Desired sample size (n) = 100 companies

Sampling interval (k) = N/n = 1803/100 = 18.03

Random starting point (any number between 1 and k, depending on sampling preference)

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Answer:

we know the area of the parallelogram is given by a=b×h

The solution is that the rancher should buy 26 steers and 13 cows

Let's start by setting up a system of equations based on the given information.

The total amount of money the rancher has is $1000, and they plan to buy steers at $25 each and cows at $26 each. Let's say they buy s steers and c cows, then we have:

$25s + $26c = $1000 (Total amount spent)

We also know that s and c are both positive integers (whole numbers greater than zero).

We can solve for s and c by using some algebraic techniques. First, let's simplify the equation by dividing both sides by $1 to get rid of the dollar sign

25s + 26c = 1000

Now we can use a technique called "integer division" to solve for s and c. We'll start by assuming that the rancher buys all steers and no cows, which gives us

25s + 26(0) = 1000

25s = 1000

s = 40

So the rancher could buy 40 steers with their $1000. However, we need to account for the fact that they can also buy cows. Let's say they buy c cows, then we can set up another equation based on the total number of animals they buy

s + c = Total number of animals

Since we don't know the total number of animals, we'll leave that as a variable for now. We can use this equation to solve for c in terms of s:

c = Total number of animals - s

Now we can substitute this expression for c into the first equation:

25s + 26c = 1000

25s + 26(Total number of animals - s) = 1000

25s + 26Total number of animals - 26s = 1000

-Taking 25s to the right side

26Total number of animals = 1000 + s

dividing both sides by 26

Total number of animals = 38 + s/26

So the total number of animals must be a whole number, which means that s/26 must be a positive integer. We can try different values of s to see which ones work

If s = 26, then s/26 = 1 and Total number of animals = 39. This gives us c = 39 - 26 = 13, so the rancher would buy 26 steers and 13 cows.

If s = 52, then s/26 = 2 and Total number of animals = 40. This gives us c = 40 - 52 = -12, which doesn't make sense since c must be a positive integer.

If s = 78, then s/26 = 3 and Total number of animals = 41. This gives us c = 41 - 78 = -37, which again doesn't make sense.

So the only solution that works is when the rancher buys 26 steers and 13 cows. This would cost

25(26) + 26(13) = $650 + $338 = $988

So the rancher would have $12 left over from their $1000 budget.

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The given question is incomplete, the complete question is:

With $1000 a rancher is to buy steers at  $25 each and cows at $26 each. If the number of steers s and the number of cows c are both positive integers, what is the solution?

A Magic Square is a square grid of numbers in which the sum of every row, column, and diagonal is equal.

One way to approach this is to start with the center number and work outwards.

Since every row, column, and diagonal adds up to 0, the center number must be 0.

From there, we can fill in the rest of the numbers systematically.
For example, in the top row, we need to find two numbers that add up to 0.

We could choose 1 and -1, or 2 and -2, or any other pair of opposite numbers.

Let's choose 1 and -1 for the top row.

Then, we can fill in the bottom row with the same numbers in reverse order.
Next, we can fill in the left and right columns.

Since every column must add up to 0, we need to choose numbers that add up to 0 in each column.

Let's choose 3 and -3 for the left column, and 2 and -2 for the right column.

Finally, we can fill in the diagonals with the remaining numbers.

In this particular Magic Square, every row, column, and diagonal adds up to 0.

We can choose 4 and -4 for one diagonal, and 5 and -5 for the other diagonal.
By following this systematic approach, we can complete the Magic Square with the following numbers:
           3  2 -1
           0  0  0
          -3 -2  1
This Magic Square is a great example of the fascinating patterns and mathematical properties that can be found in numbers. It is also a fun puzzle to solve and can provide hours of entertainment for people of all ages.

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Based on the information provided by the question, we found the following solutions:

An event is considered dependent if the outcome of one event affects the probability of the outcome of another event. Conversely, events are considered independent if the outcome of one event does not affect the probability of the outcome of another event.

Therefore, in the case of selecting lollipops with or without replacement, the distinction between dependent and independent events lies in whether or not the lollipop selection process affects the probability of future selections.

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Answer:

To find out for what mileages Company A will charge less than Company B, we need to set up an inequality using the given prices and the number of miles driven, m.

For Company A, the cost is a flat rate of $104 regardless of the number of miles driven. Therefore, the inequality is simply:

104 < 65 + 0.60m

We can simplify this inequality by subtracting 65 from both sides:

39 < 0.60m

To isolate m, we can divide both sides by 0.60:

65 < m

So, Company A will charge less than Company B for any mileage greater than 65 miles. If Rachel plans to drive more than 65 miles, she should choose Company A to save money. However, if she plans to drive less than 65 miles, Company B may be the cheaper option.

Answer:

h = 9km

Step-by-step explanation:

area of a trapezoid= ½ x (a+b) x h

117 = (2+2+11 +11) / 2 x h

h = 117 / 26÷2

h = 9km

a) For a 90% confidence interval [22.25, 23.55].

For a 95% confidence interval [22.10, 23.70].

For a 99% confidence interval [21.97, 23.83].

b) For a 90% confidence interval [22.25, 23.55].

a) To construct a confidence interval for the population mean age, we can use the formula: CI = x* ± tα/2 * (σ / sqrt(n)), where x* is the sample mean age, σ is the population standard deviation, n is the sample size, and tα/2 is the critical value of the t-distribution with n-1 degrees of freedom and a given level of confidence α/2.

For a 90% confidence interval, α = 0.1 and tα/2 = 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].

For a 95% confidence interval, α = 0.05 and tα/2 = 2.093, so the interval is: 22.9 ± 2.093 * (1.5 / sqrt(20)) = [22.10, 23.70].

For a 99% confidence interval, α = 0.01 and tα/2 = 2.861, so the interval is: 22.9 ± 2.861 * (1.5 / sqrt(20)) = [21.97, 23.83].

b) If the given standard deviation of 1.5 years came from the sample instead of the population, we need to use a t-distribution with n-1 degrees of freedom to construct the interval. The formula is the same as before, but we replace σ with s, the sample standard deviation.

For a 90% confidence interval, the critical value is still 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].

c) If the distribution of the population is not specified, we can still form a confidence interval if we have a large enough sample size (typically, n >= 30) due to the central limit theorem. In this case, we have n = 20, so we may not have enough information to form a confidence interval if we cannot assume the population is normally distributed.

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