in the geometric sequence with a first term of $6$ and a second term of $-6$, what is the $205^{th}$ term?

On solving the provided question, we can say that a set's elements can be arranged in any sequence.

A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,

Set Representation

A capital letter indicates a set. For instance, consider sets A, B, N, etc.

Small letters are used to identify the components of a set. Each element is written using curly brackets and a comma in between.

Elements are not repeated in set notation.

A set's elements can be arranged in any sequence.

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There are 15 ways to put 4 indistinguishable balls in 3 indistinguishable boxes.

Since the balls and boxes are indistinguishable, we only need to count the number of ways to distribute the 4 balls among the 3 boxes.

We can use the concept of stars and bars. The number of ways to distribute n indistinguishable items into r distinguishable boxes is given by (n+r-1) choose (r-1).

Here, the number of ways to distribute 4 indistinguishable balls into 3 distinguishable boxes is (4+3-1) choose (3-1) = 6 choose 2 = 15

So, there are 15 ways to put 4 indistinguishable balls in 3 indistinguishable boxes.

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Answer:

Below in bold.

Step-by-step explanation:

m < DAC  = 360 -15 - 155 - 166

                = 24⁰

The bearing of D from A

                = 180 + 15 + 24

                 =  219⁰

or S 39⁰ W.

The rate of change of volume with respect to R is 4πR².

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another. The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity. The rate of change from the coordinates of y to the coordinates of x can be found out as Δy/ Δx = (y2 - y1 )/ (x2 - x1 ). For a linear function, the rate of change m is represented in the slope-intercept form for a line: y=mx+b whereas the rate of change of functions is otherwise defined as, (f(b)-f(a))/ b-a.

The volume of the sphere is:

V = (4π/3)(R³)

Differentiating volume with respect to radius gives:

dV/dR  = (4π/3)× (3R²) = 4πR²

Thus, the rate of change of volume with respect to R is 4πR².

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Answer:

Step-by-step explanation:

3a-7=-4b+1

3a=-4b+1-7

simplify:

3a=-4b-6

divide by 3:

a=-4b-6/3

The title is explains what the graph is about. Scale: The scale is the numbers that show the units used on the bar graph. Labels: Both the side and the bottom of the bar graph have a label that tells what kind of data is shown.

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Using the formula of volume of a cone, the diameter of the cone is 5cm

The volume of a cone is a measure of the amount of space inside the cone. It can be calculated using the formula:

Volume = (1/3) * π * r^2 * h

Where:

The formula for the volume of a cone is a product of 1/3 and the product of π, radius square and height. The unit of measurement of the volume will be the cube of the unit of measurement of the radius and height.

It's important to note that a cone has a circular base, the radius of which is the distance from the center of the base to its edge. The height of the cone is the distance from the tip of the cone to the center of the base.

In this problem, we can simply find the diameter by calculating the radius.

V = 1/3(πr²h)

Substituting the values into the formula

42.5 = 1/3(3.14 * r² * 6.5)

42.5 * 3 = 20.41 r²

127.5 = 20.41r²

r² = 6.2469

r = 2.5

But the radius of a circular body is always half the length of it's diameter

d = 2 * r

d = 2 * 2.5

d = 5

The diameter is 5cm

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Answer:

π /5

Step-by-step explanation:

Use the form a * cos(bx−c) + d

Yes, the  intersection of all of those intervals always be ope

The mathematical concept of well-defined groupings of objects, or sets, that are referred to as members or elements of the set. The only sets that are taken into consideration are those whose members are also sets because pure set theory only deals with sets.

Any union of open sets, or an unlimited number of open sets, is open. It is open where a finite number of open sets intersect.

A closed set is the complement of an open set (according to the space that the topology is specified on).

Thus, the intersection of all of those intervals always be open.

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One is not considered a prime factor.

One has only a single element, which is itself, hence it is not regarded as a prime number. A prime number is a positive integer greater than 1 with just itself and the number one as its other positive divisors. Since there is only one divisor of one, one is not regarded as a prime number. Additionally, 1 does not adhere to the conventional characteristics of prime numbers and is regarded as a unit in mathematics.

For instance, a number's value is unaffected by division or multiplication by one, and it is always one when raised to any power. Since one does not meet the criteria for primes and does not share their characteristics, it is likewise excluded from the set of prime numbers.

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Answer:

16 ounces of $400 alloy

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

Using the Pythagorean Theorem, a^2 + b^2 = c^2, this would not be possible, because 4 + 9 does not equal 16.

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16

Answer:

No.

Step-by-step explanation:

the Pythagorean Theorem states that a²+b²=c²

where a and b are the legs and c is the hypotenuse of a right triangle

in this case we need to know if 2²+3²=4²

2²=4

3²=9

4²=16

4+9=13

13≠16

so no, the hypotenuse cannot be 4 inches long.

Answer:

Step-by-step explanation:

Density is a measure of how much mass is contained in a given volume. It is calculated by dividing the mass of an object by its volume.

To find the density of the cow's leg bone, we can use the following formula:

Density = mass / volume

In this case, the mass of the bone is 18 g, and the volume is 10 cm3. So we can plug in these values into the formula:

Density = 18 g / 10 cm3

The density of the bone is 1.8 g/cm3.

It's important to note that this is the density of the bone, but it's not the same density as a whole cow. Also, density can also change depending on the bone and the species.

The 40 randomly selected teachers: sample.

The list of all teachers in the school district: frame.

The 245 teachers in the school district: population.

A sample is a subset of a population that is selected for research purposes. In this case, the school board has randomly selected 40 teachers out of the 245 teachers in the district as a sample to survey their opinions on the new professional development plan.

A population is the entire group of individuals or objects that researchers are interested in studying. In this case, the population is all 245 teachers in the school district.

A frame is the list or method used to define the population. In this case, the frame is the list of all 245 teachers in the school district that was used as the basis for selecting the random sample of 40 teachers.

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Answer

a=3/2

b=1/2

Step-by-step explanation:

let f(x)=ax+b

f(2x-3)=a(2x-3)+b

f(2x-3)=2ax-3a+b

3x-4=2ax-3a+b

3x=2ax

3=2a

a=3/2

b-3a=-4

b-3(3/2)=-4

b=1/2

Since Paul's English class is located in the same quadrant as the library, the coordinates of the English classroom include the following: B: (−4, 5).

In Mathematics, the translation of a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image or function.

On the other hand (conversely), the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

Since the library is located in the fourth quadrant in which the value on the x-coordinate (x-axis) is positive while the value on the y-coordinate (y-axis) is negative, we can reasonably infer and logically deduce that its coordinates would be translated to the right and then downward.

In conclusion, the coordinates of the English classroom would most likely have negative x-coordinate (x-axis) and a positive y-coordinate (y-axis);

Coordinates of the English classroom = (-4, 5).

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Complete Question:

The map shows the location of four places in a school.

A coordinate plane is shown. There is a point at 5, 2 labeled Front office. There is a point at negative 6, 4 labeled Gym. There is a point at negative 4, negative 3 labeled Auditorium. There is a point at 6, negative 4 labeled Library.

Paul's English class is located in the same quadrant as the library. Which of the following could be the coordinates of the English classroom?

A: (4, 5)

B: (−4, 5)

C: (−4, −5)

D: (4, −5)

The Partitions occur on the line segments that Partitions are referred or called  as directed line segments .

What are Directed Line Segments  ?

The Directed Line Segments are defined as the line segments that has distance (length) and direction .

A line segment can be partitioned into many smaller segments which are compared/called as ratios and the Partitions that occur on line segments  are referred to as Directed segments .

The Simple Definition of Partition means to separate or to divide .

let AB be any line segment and we Partition the line AB in the ratio a:b , it means that we are dividing it into (a + b) equal parts and then we find a  point C which is "a" equal parts from A and "b" equal parts from B .

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Answer:

obviously 16 meters to the west

The  expression that shows how many minutes it will take to complete an order, assuming there are x parts in an order is 2x+10y = x

The statement states that  it takes 2 minutes to manufacture each part and 10 minutes to pack all the parts for an order.

Also, it is stated that there are  x parts in an order

This implies that  2(x) + 10(y) = x

Opening the brackets to have

2x + 10y = x

This is to say that 2 minutes of manufacture and 10 minutes of packing will give all the parts.

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Answer:

by finding the angles and sides using law of sines

Step-by-step explanation:

basically you have to use the law of sines to find the angles and sides, after that you will find the angles and sides using law of sines

the area of the shaded regions of all circles in terms of pi is a = 253.42 in², a = 215.98 yd², a = 25.13 ft², a = 201.06 yd² and a = 64.14 ft² respectively.

What is the shaded region?

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon.

The formula for calculating the area of a shaded segment of a circle is:

a = π ∗ r² ∗ angle/360

The area of the sector depends on the radius of the circle r and the measure of the angle t.

The area of a sector for angle t is  A = t/360 ⋅ π ⋅ r²

We have given the figures with their radius and shaded region angles,

In the first figure:

radius r =  11 in and  shaded region angle = 260°

so, a = π ∗ r² ∗ angle/360

a = π ∗ (11)² ∗ 260/360

a =  π ∗ 121 ∗ 2/3

a = 253.42 in²

In the second figure:

radius r =  15 yd and  shaded region angle = 110°

so, a = π ∗ r² ∗ 110/360

a = π ∗ (15)² ∗ 110/360

a =  π ∗ 225 ∗ 11/36

a = 215.98 yd²

In the third figure:

radius r =  6 ft  and  shaded region angle = 80°

so, a = π ∗ r² ∗ 80/360

a = π ∗ (6)² ∗ 80/360

a =  π ∗ 36 ∗ 2/9

a = 25.13 ft²

In the fourth figure:

radius r =  16 yd  and  shaded region angle = 90°

so, a = π ∗ r² ∗ 90/360

a = π ∗ (16)² ∗ 90/360

a =  π ∗ 256 ∗ 1/4

a = 201.06 yd²

In the fifth figure:

radius r =  7 ft  and  shaded region angle = 150°

so, a = π ∗ r² ∗ 150/360

a = π ∗ (7)² ∗ 150/360

a =  π ∗ 49 ∗ 5/12

a = 64.14 ft²

Hence, the area of the shaded regions of all circles in terms of pi is a = 253.42 in², a = 215.98 yd², a = 25.13 ft², a = 201.06 yd² and a = 64.14 ft² respectively.

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We can see here that assuming is solving a linear system and in the process of solving it, the person gets a final statement of 5 = 0, the true statement will  be: D. None of these statements are true.

A linear system is a set of one or more linear equations involving the same variables. The goal is to find the values of the variables that simultaneously satisfy all the equations in the system.

A linear equation of the form 5 = 0 has no solutions, since 5 is not equal to 0. In this case, if you graph the equation on a coordinate plane, it will be a straight line with no points on the line satisfying the equation.

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An average swimmer covers a distance of 1 / 30 miles in a minute, while an Olympic swimmer covers a distance of 1 / 10 miles.

This is a classic example of an open question, since there are answers as many as possible assumptions. In this case, answer change if swimmer's speed is changed. We shall consider two cases: (i) Average swimmer (v = 2 miles per hour), (ii) Olympic swimmer (v = 6 miles per hour).

Under the assumption of uniform motion, distance (s), in miles, is the product of speed (v), in miles per hour, and time (t), in hours (please notice that an hour is equal to 60 minutes):

s = v · t

Average swimmer (v = 2 mi / h, t = 1 / 60 h)

s = 2 · (1 / 60)

s = 2 / 60

s = 1 / 30 mi

Olympic swimmer (v = 6 mi / h, t = 1 / 60 h)

s = 6 · (1 / 60)

s = 6 / 60 mi

s = 1 / 10 mi

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The amount of each solution that should be mixed together to obtain the desired target solution is;

160 quarts of the solution that contains 3 parts salt to 5 parts water

120 quarts of the solution that contains 2 parts salt to 8 parts water

The parameters are;

Solution A contains 2 parts salt to 8 parts water

Solution B contains 3 parts salt to 5 parts water

Target Mixture contains 3 parts salt to 7 parts water:

Expressing the salt concentration in decimal form;

Solution A: 2/(2 + 8) = 2/10

= 0.20 salt

Solution B: 3/(3 + 5) = 3/8

= 0.375 salt

Mixed Solution: s/(3 + 7) = 3/10

= 0.30 salt

Since target mixture is 280 quarts;

If the amount of 0.375 salt present in mixed solution is denoted by x

Then, the amount of 0.20 salt is expressed as;

y = 280 – x

Using a general mixture equation, we will have;

0.375x + 0.20(280 - x) = 0.30(280)

0.375x + 56 - 0.20x = 84

Subtract 56 from both sides of the equation

0.375x - 0.20x + 56 – 56 = 84 – 56

0.375x - 0.20x = 28

0.175x = 28

Divide both sides of the equation by 0.175

0.175x/0.175 = 28/0.175

x = 160

Thus;

y = 280 – x

y = 280 – 160

y = 120

Therefore,

x = 160 quarts of the solution that contains 3 parts salt to 5 parts water

y = 120 quarts of the solution that contains 2 parts salt to 8 parts water

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The expression for a  90% confidence interval, given a sample of 50 people with a sample proportion of 0.65 is B. [tex]0.65\pm1.645\sqrt{\frac{0.65(1 -0.65)}{50}[/tex].

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

We know the confidence interval for a population proportion is given by the formula [tex]p\pm{Z_\frac{\alpha}{2}}\sqrt{\frac{p(1 -p)}{n}[/tex], where p = population proportion,

n = The number of samples and [tex]Z_\frac{\alpha}{2}[/tex] is the area value corresponding to the context.

Given, The 90% confidence interval, given a sample of 50 people with a sample proportion of 0.65.

We know at 90% confidence interval [tex]Z_\frac{\alpha}{2}[/tex] = 1.645.

Therefore it should be [tex]0.65\pm1.645\sqrt{\frac{0.65(1 -0.65)}{50}[/tex].

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Answer:

All I know is:

Step-by-step explanation:

You have to Graph

Then Find the Empirical/Simplest Formula

After you have to Calculate the Formula Weights

Then Find the Derivative - d/dx

Last, Find the Derivative - d/dy

Sorry I don't know the real answer.

The equation has one extraneous solution which is n is approximately 2.38

Here we have the following equation

=> 9/n²+1 = n+3/4

Now, we have to find the value of n by simplifying the given equation,

In order to so the simplification we have to do the cross multiplication on then, then we get the resulting expression as,

=> n²+1(n + 3) = 36

When we expand it then we get,

=> n²+1(n) + n²+1(3) = 36

=> n³ + n + 3n² +3 - 36 = 0

=> n³ + 3n² +  n - 33 =  0

Here we have to find the roots are the  x  values where the graph intersects the x-axis.

And then we have to find the roots replace y with  0  and solve for  x.

Then the value of n is obtained as

=> n  ≈  2.38

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0.115 is the quotient of  9.43/82

A division is a process of splitting a specific amount into equal parts.

In division, we divide a number by any other number to get another number as a result.

The number which is getting divided here is called the dividend.

The number which divides a given number is the divisor.

The number which we get as a result is known as the quotient.

9.43/82 we have to find quotient

9.43 is the dividend and 82 is the divisor

9.43/82=0.115

Hence, 0.115 is the quotient of  9.43/82

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