The value of θ for which | r | has maximum value if r = sinθ is θ = π/2.
Given r = sinθ and the range of θ is 0 < θ < π
If 0 < θ < π the range of sinθ is:
0 ≤ sinθ ≤ 1
So, in 0 < θ < π, the maximum value of sinθ is 1 and this value occurs at θ = π/2.
Now, we are asked to determine the value θ for which | r | is maximum and it is also given that r = sinθ and we have already found out that the maximum of sinθ in 0 < θ < π is 1.
Therefore, the maximum value of | r | is 1 and this value occurs at θ = π/2.
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A car decreased in value by 38% to $9235 when it was resold. What was the original
price of the car to the nearest dollar?
the original price is really "x", which oddly enough is the 100%.
now it decreased to $9235, and we know that's 38% less than "x", so 100% - 38% = 62%, so $9235 is really the 62% of "x", hmmm what the dickens is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 9235& 62 \end{array} \implies \cfrac{x}{9235}~~=~~\cfrac{100}{62} \\\\\\ \cfrac{ x }{ 9235 } ~~=~~ \cfrac{ 50 }{ 31 }\implies 31x=461750\implies x=\cfrac{461750}{31}\implies x\approx 14895[/tex]
In ΔABC, a = 6 inches, m∠A=121° and m∠B=36°. Find the length of b, to the nearest 10th of an inch.
Answer:4.1
Step-by-step explanation:
Answer: 4.1
Step-by-step explanation:
each year, a magazine complies a list of the 400 richest americans. a of september 19,2012 the mean is
The mean of the 400 richest Americans as of September 19, 2012 is $4.25 billion.
The mean of the 400 richest Americans is calculated by summing up all of the net worth of each person on the list, and then dividing it by the total number of people on the list. The formula used to calculate the mean is:
Mean = (Sum of Net Worth) / (Total Number of People on the List)
For example, on September 19, 2012, the total net worth of the 400 richest Americans was $1.7 trillion. If we divide this by the total number of people on the list (400), then the mean net worth of the 400 richest Americans is $4.25 billion.
Therefore, the mean of the 400 richest Americans as of September 19, 2012 is $4.25 billion.
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a population of caribou have weights that are distributed like the bell shaped curve. the mean weight is 125 pounds with a standard deviation of 12 pounds. use the empirical rule to approximate the percent of weights that are between 101 and 137 pounds.
Approximately 68% of the weight fall between 101 and 137 pounds.
The empirical rule states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
To apply the empirical rule to this problem, we need to convert the weight range of 101 to 137 pounds into units of standard deviation. To do this, we subtract the mean weight of 125 pounds from each value and divide it by the standard deviation of 12 pounds.
So the weight range of 101 to 137 pounds corresponds to the standard deviation range of:
(101 - 125) / 12 = -2
(137 - 125) / 12 = 1
So the weight range of 101 to 137 pounds corresponds to the standard deviation range of -2 to 1.
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 68% of the weight fall between 101 and 137 pounds.
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Approximately 68% of the weight fall between 101 and 137 pounds.
The empirical rule states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
To apply the empirical rule to this problem, we need to convert the weight range of 101 to 137 pounds into units of standard deviation. To do this, we subtract the mean weight of 125 pounds from each value and divide it by the standard deviation of 12 pounds.
So the weight range of 101 to 137 pounds corresponds to the standard deviation range of:
(101 - 125) / 12 = -2
(137 - 125) / 12 = 1
So the weight range of 101 to 137 pounds corresponds to the standard deviation range of -2 to 1.
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 68% of the weight fall between 101 and 137 pounds.
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can you taste ptc? ptc is a substance that has a strong bitter taste for some people and is tasteless for others. the ability to taste ptc is inherited. about 75% of italians can taste ptc, for example. you want to estimate the proportion of americans who have at least one italian grandparent and who can taste ptc. how large a sample must you test to estimate the proportion of ptc tasters within 0.04 with 90% confidence? answer this question using the 75% estimate as the guessed value for .
The sample size of 470 people is required to estimate the proportion of PTC tasters within 0.04 with 90% confidence.
To estimate the proportion of Americans who have at least one Italian grandparent and can taste PTC with a 90% confidence interval of 0.04, we need to calculate the sample size required using the formula for a proportion. Using the estimate of 75% for the proportion of Italians who can taste PTC as the guess for p, we can calculate that a sample size of 470 people is required.
This means that we need to test 470 Americans who have at least one Italian grandparent to estimate the proportion of PTC tasters within 0.04 with 90% confidence. The formula for the sample size takes into account the desired level of confidence and the margin of error, which is the difference between the estimate and the true value that we are willing to accept.
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In a direct variation, y= 1 /7 when x= 8/7 Write a direct variation equation that how the relationhip between x and y
A direct variation equation is: [tex]y = \frac{1}{8} x[/tex].
Direct variation exists between two variables when one quantity is directly dependent on the other. One quantity increases with respect to the other quantity and vice versa.According to the question,
x and y vary directly proportional then the equation is
y =kx ( where k is the constant of variation)
If x is not equal to zero the value of the constant of proportionality can be given as k = y/x.To find k use the given condition y = 1/7 when x = 8/7
we know that,
[tex]k = \frac{y}{x} = \frac{1/7}{8/7} = \frac{1}{8}[/tex]
Hence, the equation is: [tex]y = \frac{1}{8} x[/tex] .
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What is the equation of the line that passes through the point (1,-3) and has a slope of -3?
An equation of the line that passes through the point (1, -3) and has a slope of -3 is y = -3x.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the information provided above, we have the following slope and data points on the line:
Points = (1, -3).Slope, m = -3At point (1, -3), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-3) = -3(x - 1)
y + 3 = -3x + 3
y = -3x + 3 - 3
y = -3x
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Graph 2 lines to find x and y values that make both y= -2/3x + 3 and y= 2x -5
The values of {x} and {y} for which both the equations are true are {x} = 3 and {y} = 1.
What is system of simultaneous equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given is the system of simultaneous equations as -
{y} = -{2/3}x + 3
{y} = 2x - 5
Refer to the graph of the equations attached. The value of {x} and {y} for which both the equations are true is given by the point of intersection of both lines.
Therefore, the values of {x} and {y} for which both the equations are true are {x} = 3 and {y} = 1.
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WILL MARK BRAINLIEST FIRST ANSWER, EASY POINTS
Which linear graph represents a proportional relationship?
The second one because it passes through (0,0)
The derivative of a function of f at x is given by f′(x)=limh→0f(x+h)−f(x)h provided the limit exists.
Use the definition of the derivative to find the derivative of f(x)=8x^2+2x+7.
Enter the fully simplified expression for f(x+h)−f(x). Do not factor. Make sure there is a space between variables.
f(x+h)−f(x)= ?
The derivative of a function of f at x is given by f′(x) = lim(h→0) f(x+h)−f(x)h provided the limit exists.
What is derivative of a function?A function's immediate rate of change at one particular location is referred to as the derivative of that function. At a certain point along the curve, the derivative provides the precise slope. The symbol for the derivative of a function is dy/d x, which stands for the derivative of the function with respect to the variable.
Given that,
f(x + h) - f(x) = 16xh + 8h² + 2h
f(x)=8x²+2x+7.
then derivative is given by:
f'(x) = lim(h→0) [f(x + h) - f(x)] / h
f'(x) = lim(h→0) [8(x + h)²+2 (x+h) + 7] - [8x²+2x+7] / h
f'(x) = lim(h→0) 8x² + 16xh + 8h² + 2x + 2h + 7 - 8x² - 2x - 7 / h
f'(x) = lim(h→0) 16xh + 8h² + 2h / h
f'(x) = lim(h→0) 16x + 8h + 2
f'(x) = 16x + 8
f(x + h) - f(x) = [8(x + h)²+2 (x+h) + 7] - [8x²+2x+7]
f(x + h) - f(x) = 8x² + 16xh + 8h² + 2x + 2h + 7 - 8x² - 2x - 7
f(x + h) - f(x) = 16xh + 8h² + 2h
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Can I have help please
Answer:
Of course you can :)
Answer provided in image !^^
Step-by-step explanation:
3. In the image shade 9 because 3/4x12=9
Use the map shown below to find the distance between cities A and B to the nearest tenth. point A is at (0,0) and point B is at (-5,3)
Answer:-5, 3
Step-by-step explanation:
its the answer. Period
perform each step to solve for x
3x-6+x-2
Based on the given expression representing each angle, the value of x is 47 and each angles are 135° and 45° respectively.
How to solve supplementary angles?Based on the given diagram; the angles represented by the expression are referred to as supplementary angles.
So, we can find the unknown variable x by adding the expressions and equating it to 80°
(3x - 6) + (x - 2) = 180
3x - 6 + x - 2 = 180
combine like terms
3x + x - 6 - 2 = 180
4x - 8 = 180
Add 8 to both sides
4x = 180 + 8
4x = 188
divide both sides by 4
x = 188/4
x = 47
Therefore, the respective angles are;
3x - 6
= 3(47) - 6
= 141 - 6
= 135°
x - 2
= 47 - 2
= 45°
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Find Sn for the arithmetic series where a1=3 , an=3 , n=14
The value of the sum of the series is 42
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
In this series, a1=3 , an=3 , n=14
Plugging these values into the formula, we get:
Sn = 14/2 * (3 + 3)
= 14/2 * 6
= 7 * 6
= 42
So, the sum of the first 14 terms of the arithmetic series is 42
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find the average value of the function f(x) = x3 8x 6 on [0, 4].
The average value of the function f(x) = x² - 8x + 6 on [0, 4] is 38.
Describe calculus.The two primary divisions of calculus, differential calculus and integral calculus, are concerned with rates of change and slopes of curves.
By dividing the definite integral of the function over the interval by the length of the interval, one can determine the average value of a function over the interval [a, b].
The function in this instance is f(x) = x3 - 8x + 6, and the range is [0, 4]. Using the definite integral of x3 and the definite integral of -8x, one can determine the definite integral of the function across the interval:
[tex]\int\limits^0_4 {x^{3} - 8x + 6 } \, dx[/tex]
= [tex]\frac{x^4}{4} - \frac{8x^2}{2} + 6x[/tex]
evaluated at x = 4 - x = 0 = [tex]0 - \frac{4^{4} }{4} - \frac{8.4^2 }{2} + 6.4\\[/tex]
= - 24
The length of the interval is b - a = 4 - 0 = 4. Hence, the average value of the function over the interval is given by:
Therefore, the average value of the function f(x) = x^3 - 8x + 6 on [0, 4] is 38.
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Determine which matrices are in reduced echelon form and which others are only in echelon form. 011 1 0 011 0000 1 1 40 0 1 011 b. 0010 Is matrix b in reduced echelon form, echelon form only, or neither? a.echelon form only b.reduced echelon form c.neither
Matrix b is in reduced echelon form.
Therefore the answer is b. reduced echelon form.
In a reduced echelon matrix, the leading entry (the first non-zero entry from the left in a row) in each non-zero row is 1, and all entries above and below the leading entry are 0. Matrix b satisfies these conditions, so it is in reduced echelon form.
Reduced echelon form is a special type of echelon form for matrices, which is used in linear algebra to solve systems of linear equations. In a reduced echelon form matrix, the following conditions are satisfied:
All non-zero rows are above any rows of zeros
The leading entry (the first non-zero entry from the left in a row) in each non-zero row is 1, and all entries above and below the leading entry are 0.
Each leading entry is the only non-zero entry in its column.
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1. A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches.
What is the surface area of the pyramid?
Enter your answer in the box.
2.A child's toy is in the shape of a square pyramid. The pyramid stands 20 inches tall and each side of the base measures 24 inches.
Half of the surface area of the pyramid is black and the remainder is yellow.
What is the surface area of the toy that is yellow?
Enter your answer, rounded to the nearest tenth, in the box.
3.A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 50 feet and the slant height of each lateral side of the pyramid is 40 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.
The total surface area of the hexagonal pyramid is 237.5 in²
How do equations work?An expression that depicts the relationship between two or more numbers and variables is called an equation. Depending on the degree, an equation may be linear, quadratic, cubic, or another type.
A solid figure's surface area is calculated by summing up all of its distinct surfaces.
Given the hexagonal pyramid with a base of 6 inches and each isosceles triangle having a height of 8 inches. Hence:
Area of pyramid base = 93.5 in²
The lateral face has 6 triangle faces, hence:
Area of each lateral face = 1/2 * base * height = 0.5 * 8 * 6 = 24 in²
Total area of lateral face = 6 * 24 in² = 144 in²
Total surface area = 144 in² + 93.5 in² = 237.5 in²
The surface area is 237.5 in²
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2. (10 points) Christine works in a medical lab. She has several blood samples. The volume of each sample was measured, and they are shown below. 2.350 milliliters 2.285 milliliters 2.332 milliliters 2.299 milliliters 2.317 milliliters A. Put the blood samples in order, from largest volume to smallest volume.
The volume of blood samples from smallest to largest can be ordered as 2.350 milliliters, 2.332 milliliters, 2.317 milliliters, 2.299 milliliters and 2.285 milliliters
What is Ordering of Numbers?Ordering of numbers is the listing of numbers in a specific order, may be from smallest to largest or from largest to smallest.
The given volumes are :
2.350 milliliters, 2.285 milliliters, 2.332 milliliters, 2.299 milliliters and 2.317 milliliters
We have to look at the decimal part because the real part is same 2 for all the values.
So the order is,
2.350 milliliters, 2.332 milliliters, 2.317 milliliters, 2.299 milliliters and 2.285 milliliters
Hence the order is 2.350 milliliters, 2.332 milliliters, 2.317 milliliters, 2.299 milliliters and 2.285 milliliters.
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The parametric equationsx = u, y = ucosv, z = usinv, with 0 ≤ u ≤ 2, 0 ≤ v ≤ 2π represent the cone that results when the line y = x (where 0 ≤ x ≤ 2) in the xy−plane is revolved about the x−axis. Sketch the cone, and calculate its surface area.
The surface area of the cone with the given parametric equation is (4π + 4π√2) square units.
The parametric equations describe a cone that is generated by rotating a line segment in the xy-plane about the x-axis. The result is a 3-dimensional surface that has a circular base with radius 2 and a height of 2.
The surface area of the cone can be calculated using the formula:
A = πr^2 + πrs
where r is the radius of the circular base and s is the slant height.
The slant height is equal to the distance from the center of the circular base to the tip of the cone, which can be calculated using the Pythagorean theorem: s = √(h^2 + r^2), where h is the height of the cone.
Therefore, for this cone with radius 2 and height 2, the surface area can be calculated as:
A = πr^2 + πrs
= π * 2^2 + π * 2 * √(2^2 + 2^2)
= 4π + 4π√2
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hey can you help me find the domain and range
The domain is all x-values or inputs of a function & the range is all y-values or outputs of a function.
How to find domain and range?The numbers you supply to the function are referred to as the domain. The numbers it returns to you are referred to as the "range."
Take y=3x as an illustration. The domain of this function is "all real numbers," so you can substitute any number you like for x. (or everything from negative infinity to positive infinity, if you like). Furthermore, as you can probably guess, any actual number could result from it. (You desire the release of a specific real-world number. To get there, enter x as one-third of that number. As a result, "all real numbers" are included in this function's range.
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let's let x represent the length of one of the sides of the cube (in cm), let s represent the surface area of the cube (in square cm), and let v represent the volume of the cube (in cubic cm).
Surface area of the cube can be S = 6x², if the side length of the cube is 7.7 cm, the surface area would be is S = 6(7.7)² = 391.16.
What do you mean by Surface Area?The surface area of an object refers to the total area of its exposed outer surface. It is a measure of the amount of space that an object's surface covers. Surface area is a two-dimensional concept, and is different from the object's volume, which is a three-dimensional concept.
The surface area of an object depends on its shape, and can be calculated using mathematical formulas specific to different shapes. For example, the surface area of a cube is the sum of the areas of its six faces, while the surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere.
Surface area is an important concept in a variety of fields, including physics, chemistry, and engineering. In physics, it is used to calculate the heat transfer between objects, while in chemistry it is used to calculate the amount of reactant needed to cover a given surface area in a reaction. In engineering, surface area is important in the design of heat exchangers, reactors, and other equipment where heat or chemical reactions take place on surfaces.
V = x³
So, if the side length of the cube is 7.7 cm, the volume would be:
V = (7.7)³ = 455.169
The surface area of the cube can be calculated as:
S = 6x²
So, if the side length of the cube is 7.7 cm, the surface area would be:
S = 6(7.7)² = 391.16
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The complete question is:
Allie is completing a long division problem that may or may not have a remainder. In each box, drag the appropriate digit to show the correct way to divide
Answer choices may be used more than once.
Follow the example of long division to understand the method and concept of the same.
Let us understand the long division with an example. For this, let us take 13032 as the dividend and 24 is the divisor. Now, performing long division.
On division the quotient will be 5. Now, subtracting 120 from 130, the remainder will be 10. Now, we will take the dividend 103.
Dividing 103 by 24, the overall quotient will be 54. On subtraction we get 7. Taking 2, thus, the combined dividend is 72.
Dividing 72 by 24, the quotient will be 3. Thus, overall quotient will be 543. The remainder will be zero. Thus, the long division of 13032 by 24 yields 543 as quotient without remainder.
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what is the formula to find the height of a cylinder via Surface Area (total) and radius?
Answer:
diameter=radius divided by 2
pls hurry this is urgent
The angle measures are ∠QRS = 66° and ∠SQR = 95°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
The triangle QRS with side SR on ray ST.
∠QRS + 114° = 180°
∠QRS = 66°.
Now, the sum of all the angles of the triangle is 180°.
5y + y + 66 = 180
6y = 114
y = 19
So, ∠SQR = 95°.
Therefore, ∠QRS = 66° and ∠SQR = 95°.
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Enter the numerator and the denominator of the fraction in simplest form that is equal to 0. 84 repeating
The fraction that is equal to 0.84 repeating is 8/9 in simplest form.
If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase "lowest words" when referring to the simplest form.
0.84 repeating can be represented as a fraction in simplest form by using the following method:
Let x = 0.84 repeating,
Then 10x = 8.4 repeating.
Subtracting the two equations,
we have 9x = 8.
Dividing both sides by 9,
we have x = 8/9.
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simplify 60 with [tex]\sqrt{x} 60[/tex]
the shorter diagonal of a rhombus with 70 degrees is 122 cm long, how long is the longer diagonal
The length longer diagonal is 174 cm.
In a rhombus, the diagonals bisect each other as well as the the vertex angles and adjacent angles are supplementary
So assuming that the 70 degree angle is opposite the 122 cm diagonal, we have
(1/2 length of the shorter diagonal) / sin (35) = (1/2 length of the longer diagonal) / sin(55)
Multiply both sides by 2
( length of the shorter diagonal) / sin (35) = ( length of the longer diagonal) / sin(55)
Multiply both sides by sin(55).
Length of the longer diagonal = sin (55) (122 cm) / sin (35) = 174 cm
Therefore, the length of the longer diagonal is 174 cm.
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What is the relation ship between angle 1 and 2? And why is it that.
Answers:
Congruent
Similar
Corresponding angles
Alternate interior angles
In given geometric shape, angle 1 and 2 are alternate interior angles.
What are geometric shapes?In mathematics, geometric shapes are the patterns that show how everyday objects are shaped. Shapes are the forms of objects in geometry that have boundaries, angles, and surfaces. Both 2D and 3D shapes come in a variety of forms.
Regarding their regularity or uniformity, shapes are also categorised. Regular shapes like a square, circle, etc. are typically symmetrical. Asymmetrical shapes are irregular. They are also referred to as organic shapes or freeform shapes. For instance, a tree's shape is atypical or organic.
Now,
The angles formed when a transversal intersects two coplanar lines are known as alternate interior angles. They are on the inside of the parallel lines, but on the outside of the transversal. The transversal cuts through two Coplanar lines at different points.
Hence,
angle 1 and 2 are alternate interior angles.
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in how many ways can 9 yellow marbles be divided among 4 distinguishable cups?
The number of ways 9 yellow marbles can be divided among 4 distinguishable cups is 126.
Dividing 9 marbles among 4 cups is a combination problem. The number of combinations is given by the formula C(n + r - 1, r - 1), where n is the number of items (marbles) and r is the number of groups (cups). In this case, n = 9 and r = 4. Plugging these values into the formula, we get:
C(9 + 4 - 1, 4 - 1) = C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1) = 220
This means that there are 220 ways to divide 9 yellow marbles into 4 distinguishable cups. However, since the cups are distinguishable, each combination is counted multiple times, once for each permutation of the cups. The number of permutations of n items taken r at a time is given by the formula n! / (n - r)!. In this case, the number of permutations is 4! = 4 * 3 * 2 * 1 = 24.
So, the total number of ways to divide 9 yellow marbles into 4 distinguishable cups is 220 / 24 = 9. This means that there are 126 distinct ways to divide 9 yellow marbles among 4 distinguishable cups.
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Your newspaper article will end with recommendations to fans about buying
tickets. Your research indicates the average local baseball fan plans to attend
67 games during the season. What are your recommendations to the average
fan about buying tickets? Should they buy season tickets or single-game
tickets?
Make a recommendation for fans buying tickets in each section:
• main box
• bleachers
• left field reserve
Include all necessary work to support your answer.
I recommend the average fan buy season tickets when purchasing seats.
Based on the research, the average local baseball fan plans to attend 67 games during the season. For a fan who is planning to attend this many games, it would be more cost-effective to purchase season tickets rather than individual game tickets.
For fans considering season tickets, here are some recommendations based on the seating section:
Main Box: If cost is not a concern and the fan is looking for a premium experience, purchasing season tickets in the Main Box section is the way to go. The fan will have the best view of the field and access to the best amenities.Bleachers: For the more budget-conscious fan who wants to attend the most games possible, purchasing season tickets in the Bleachers section is the best choice. These tickets are typically the least expensive and provide an energetic atmosphere with a close view of the field.Left Field Reserve: For fans who want a good balance between cost and comfort, season tickets in the Left Field Reserve section would be a good option. These tickets are often priced in between Main Box and Bleachers tickets and provide a good view of the field.Purchasing season tickets rather than individual game tickets is the most cost-effective choice for the average fan who plans to attend 67 games during the season. The best choice of section will depend on the fan's budget and personal preferences.
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