Write an explicit formula for a(n), the n(th) term of the sequence 11,4,-3, ....

As per the given limit, the rigorous assertion of the function is a − δ < x < a + δ

In math term function is called as  a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output

Here we have given that the distance between two points a and b on a number line is given by  |a−b|.

And we need to find the rigorous assertion of the function.

Then the statement is written as

=> |f(x)−L|<ε

And it can be be interpreted as the distance between f(x) and L is less than ε.

Here we have another statement that is written as  

=> 0<|x−a|<δ

And it ma be interpreted as the value of x≠a and the distance between x and a is less than δ.

Here we have also important to look at the following equivalences for absolute value that the statement  |f(x)−L|<ε  is equivalent to the  statement  L−ε<f(x)<L+ε.

And the statement  0<|x−a|<δ is also equivalent to the statement  a−δ<x<a+δ here we know that x≠a.

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Answer:

1.625 mL

Step-by-step explanation:

2.5 mg per lb

For 130 lb, 130 × 2.5 mg = 325 mg are needed.

1 mL has 200 mg

1 mL is to 200 mg as x ml is to 325 mg

1/200 = x/325

200x = 325

x = 1.625

Answer 1.625 mL

The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.

The product of the four and the edge length of the square or the sum of all the sides of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,

4(x + 2) = 40

Simplify the equation, then we have

4(x + 2) = 40

(x + 2) = 10

x = 10 - 2

x = 8

The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.

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Answer: AAS and both triangles are congruent

Step-by-step explanation: Hello! Since you are given two angles and one side that are congruent in both triangles, you know that they are either congruent by ASA (angle side angle congruence postulate) or AAS (angle angle side) congruence postulate.  The way you tell the difference between the two is by how the congruent angles and the congruent side is shown.  In ASA, the congruent side would be the included side between both congruent angles.  Since the congruent side is not in between both angles and both angles do not share the congruent side to the other triangle, the triangles are congruent by AAS. The triangles two given shared angle and given congruent side is in the order of angle angle side, so the triangles are related by AAS.  This means that the triangles are congruent.  

Fun fact:
By CPCTC, you know that corresponding parts are congruent in congruent triangles.  If you know two or more triangles are congruent, then each of their angles and sides are congruent as well.

I hope this helps you!

Answer:

200mph

Step-by-step explanation:

Yes, substitution can be used to solve a linear system of equations.

Linear System of Equations:

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution. For example, is a system of three equations in the three variables x, y, z.

The substitution technique involves separating out a single variable from one equation and utilizing that expression to replace the variable in the other equation (s). This will enable you to solve for the remaining variable or variables and discover the system's answer.

Yes, a linear system of equations can be solved via substitution.

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The probability that a student studied for exactly 1 hour is 0.23

Probability is a measure of the likelihood of a particular event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

From the given table, you need notice that the number of students who study for 1 hour is 8.

In order to determine the probability that a student studied for exactly 1 hour, we need to find total number of students. That is:

Total number of student = 1 + 8 + 2 + 5 + 9 + 7 + 3 = 35

probability (exactly 1 hour) =  number of exactly 1 hour/Total number

probability (exactly 1 hour) = 8/35 = 0.23

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Answer:

B

Step-by-step explanation:

The possible sets of five tiles that she could have pulled out are (2,3),(3,2)

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

Given;

Number of tiles asha pulled out=5

Bag contains only positive and negative x and x² tiles

So, the equation will be

-x^2+x=5

x^2-x+5=0

Now,

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

x= 1 +[tex]\sqrt{1-4*-1*-5}[/tex])/2

x=2,3

x=3,2

Therefore, the quadratic equation solution will be (2,3),(3,2)

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We can actually think that insurance companies offer uninsured/ underinsured coverage at a cheaper rate than collision coverage because the risk of a claim is typically lower for uninsured/underinsured coverage.

An agreement to provide compensation to another party in the event of a certain loss, damage, or injury is known as insurance, and it is a way to safeguard against financial loss. It is a type of risk management that is mostly applied to protect against the risk of a potential or unforeseen loss.

Collision coverage is for damage to the policyholder's own vehicle, while uninsured/underinsured coverage is for damage caused by another driver who does not have enough insurance to cover the costs of an accident. Since fewer drivers are uninsured or underinsured, the likelihood of a claim being made under that coverage is lower, and thus the cost is less.

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Option (b) is the correct option i.e. The height is 5 units.

The height of an object is determined by measuring the distance between its base and its top.

As opposed to length, width, and height for a rectangular shape's area, the basic formula for volume is length, breadth, and height. The calculation is unaffected by how the different dimensions are referred to; for example, "depth" can be used in place of "height."

Given, V = πr².H

          V/πr² = H

So, It can be written in terms of height, H as V/πr².

Now, If r = 3 units and V= 45π then,

H =   V/πr² = 45π / π(3)²

                = 45π/9π

                = 5 units.

Hence, height is 5 units.

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The meaning of a zero in this situation shows that there was a time the player was in a steady position or without movement.

A data set is defined as the number of variables that makes up the data of an event, research or an experiment.

The data sets that was given are {+3, -1, -2, +1} which represent the number of moves that was made by a player.

But when a zero is included in that data set, this means that the player didn't make a move at the particular point in time.

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The Federal Reserve uses three main tools to conduct monetary policy: Open Market Operations, the Discount Rate, and Interest on Reserves (IOR).

Open Market Operations involve the buying and selling of government securities in the open market, which impacts the money supply and interest rates. The Discount Rate is the interest rate the Federal Reserve charges commercial banks to borrow from it. A lower Discount Rate encourages borrowing, while a higher Discount Rate discourages borrowing. Interest on Reserves (IOR) is the interest rate the Federal Reserve pays commercial banks on their excess reserves. A higher IOR rate encourages banks to keep more of their funds in the form of reserves, while a lower IOR rate encourages banks to lend out more of their funds. The Required Reserve Ratio is also used to affect the money supply, as it determines the amount of reserves banks must keep on hand. An increase in the Required Reserve Ratio reduces the money supply, while a decrease in the Required Reserve Ratio increases the money supply.

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The graph of f(x) = 3x is a vertical stretch with a factor of 3 of the graph of the parent function f(x) = x.

The parent function for this problem is defined as follows:

f(x) = x.

The transformed function is given as follows:

f(x) = 3x.

The only transformation is a multiplication by the constant 3. As the constant has an absolute value greater than 1, the graph of f(x) = 3x is a vertical stretch with a factor of 3 of the graph of the parent function f(x) = x.

The problem asks for how the graph of f(x) = 3x compares to the graph of f(x) = x.

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Answer:

To find the average growth on Alexandra's total investment, we need to calculate the weighted average of the growth in each of the three investments. The weighted average is calculated by multiplying the growth of each investment by its proportion of the total investment and then adding them together.

First, we need to calculate the total amount of money that Alexandra invested. Since he invested 40% in mutual funds, 40% in real estate, and 20% in stocks, we can assume he invested $100.

So the amount invested in mutual funds is 40/100 * $100 = $40

The amount invested in real estate is 40/100 * $100 = $40

The amount invested in stocks is 20/100 * $100 = $20

Then we can calculate the growth of each investment using the percentages provided:

The growth of mutual funds is 2/100 * $40 = $0.80

The growth of real estate is 7/100 * $40 = $2.80

The growth of stocks is 11/100 * $20 = $2.20

Now we can add up the growth of each investment and divide it by the total investment to find the average growth:

($0.80 + $2.80 + $2.20) / $100 = $5.80 / $100 = 0.058 or 5.8%

So the average growth on Alexandra's total investment is 5.8%.

In a case whereby longer leg of a right triangle is 3cm longer than the shorter leg and hypotenuse is 6cm longer than the shorter leg then the side lengths of the triangle is  9 inches.

The concept that will be used is pythagoras theorem.

We can make s = the length of the shorter leg.

Where the longer leg  can be expressedas  (s + 3),

Then the hypotenuse is( s + 6).

From pythagoras theorem,  a^2 + b^2 = c^2.  

then we have s^2 + (s + 3)^2 = (s + 6)^2

[s^2 + (s + 3)(s + 3)] =[ (s + 6)(s + 6) ]

s^2 + s^2 + 6s + 9 = s^2 + 12s + 36

If we collect like terms we have

s^2 - 6s - 27 = 0

Then if we factorize we have

(x - 9)(x + 3) = 0

then

we can set the whole left side to equal 0.

x - 9 = 0, then  x = 9

x + 3 = 0, then  x = -3.  

But we can only have positive value which sis 9, hence shortest side is 9 inches.

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Answer:

In economics, the LOD or Law of Demand states that as the price increases on a good or service, there are less people that are willing and able to purchase that good or service.

Here is an example

On the image attached there is a Price Quantity Demanded Graph. The Line on the graph represents demand.  The furthur right the line of the graph goes, the larger the quantity of demand for a good is, vice versa. The Law Of Demand is demonstrated on the graph and the table, when price (Px) is at 5, then only Quantity Demanded (Dx) equals 100. When Px = 1 then Dx = 500. As price decreases, demand increases.

Hope this helped :)

The value of k for which the equation has imaginary roots is k > ±2.

For a quadratic equation of the form k²x²-8x+4 to have a real double root, the discriminant (b²-4ac) must be equal to zero. For this equation, the discriminant is (-8)² - 4 * k² * 4 = 64 - 16k².

For the discriminant to be equal to zero, 64 - 16k² = 0 and k² = 4. Therefore, the value of k for which the equation has a real double root is k = ±2.

For a quadratic equation of the form k²x²-8x+4 to have two different double roots, the discriminant (b²-4ac) must be greater than zero. For this equation, the discriminant is (-8)² - 4 * k² * 4 = 64 - 16k².

For the discriminant to be greater than zero, 64 - 16k² > 0 and k² < 4. Therefore, the value of k for which the equation has two different double roots is k < ±2.

For a quadratic equation of the form k²x²-8x+4 to have imaginary roots, the discriminant (b²-4ac) must be less than zero. For this equation, the discriminant is (-8)² - 4 * k^2 * 4 = 64 - 16k².

For the discriminant to be less than zero, 64 - 16k² < 0 and k² > 4. Therefore, the value of k for which the equation has imaginary roots is k > ±2.

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Answer:

area of sector = 49π/6 cm² ≈ 25.7 cm²

Step-by-step explanation:

area of sector = (n/360°)πr²

where n = central angle of sector, and r = radius of circle

Here, we have:

n = 60°

r = d/2 = 14 cm / 2 = 7 cm

area of sector = (60°/360°)π(7 cm)²

area of sector = (1/6)π(49 cm²)

area of sector = 49π/6 cm² ≈ 25.7 cm²

The coordinates of the ends of the image are J'(x, y) = (- 7, 7), K'(x, y) = (- 5, 2) and L'(x, y) = (- 2, 3), whose transformation formula is P'(x, y) = P(x, y) + (0, - 2 · p). A representation of the figures is in the image shown below.

In this problem we find a geometric locus generated by three points on Cartesian plane that is reflected over the x-axis, whose formula is shown below:

P'(x, y) = P(x, y) + (0, - 2 · p)

Where:

If we know that J(x, y) = (- 7, - 7), K(x, y) = (- 5, - 2) and L(x, y) = (- 2, - 3), then the coordinates of the image are:

J'(x, y) = (- 7, - 7) + (0, 14)

J'(x, y) = (- 7, 7)

K'(x, y) = (- 5, - 2) + (0, 4)

K'(x, y) = (- 5, 2)

L'(x, y) = (- 2, - 3) + (0, 6)

L'(x, y) = (- 2, 3)

Now we proceed to graph both the geometric locus and its image.

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The expression can be rewritten as -

y = (1/27)x - (8/27)

Given is the expression as -

x = 8 + 27y

We can rewrite the expression as -

x = 8 + 27y

27y = x - 8

y = (1/27)x - (8/27)

Therefore, the expression can be rewritten as -

y = (1/27)x - (8/27)

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Out of the following, the statement is It generates testable hypotheses, is supported by a large body of evidence, and is broad in scope is  true of a scientific theory.

A scientific theory is a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation. A scientific theory is not just an idea or speculation. It is a systematic way of organizing and interpreting observations that are based on facts and evidence. It is also open to being tested and disproved if new evidence arises.

A scientific theory must be supported by a large body of evidence from multiple sources to be considered valid. Furthermore, a scientific theory must be broad in scope and explain a wide range of phenomena. It must also generate testable hypotheses that can be tested and verified through experimentation and observation.

A scientific theory is not accepted until it is thoroughly tested and confirmed through numerous experiments and observations. Therefore, it is not accepted after the person who formulated it has died.

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Answer:

Step-by-step explanation:

Part one is when you need to do area/perimiter.

DO

When you know the tower's height, you may calculate your distance from it.The answer is 92.54 feet .

When you know the tower's height, you may calculate your distance from it.The tangent of the angle of elevation multiplied by the horizontal distance, or doing the calculation, is all that is required to manually determine the height.

30° vertical angle from A to the tower's summit

50 + x is the horizontal separation between A and the tower's base.

Call h to get the tower's height.

tan 30 = h / (50 + x) => 50 + x = h / tan 30 => x = h / tan 30 - 50 (1)

40° vertical angle from B to the tower's summit

The tower's base is x feet away from B in a horizontal direction.

ratio: x = h / tan40; tan40 = h / tan40 (2)

Consequently, (1) and (2) are equivalent.

Tan40 = Tan30 - 50 =

30 - 40 = 50 h/tan

1,7321h - 1,1918h = 50

0.5403h = 50

h = 50/0.5403 = 92.54

Response: 92.54 feet

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The correct option regarding the growth rate of the exponential function is given as follows:

For each x increase of 1, the y increases by a common factor of 3.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

As the function in this problem is exponential, the increase of the output y must be a common factor, purely.

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Answer:

So the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.

Step-by-step explanation:

We can use algebra to solve for the width and length of the rectangle. Let's call the width of the rectangle "w" and the length "l".We know that the perimeter of the rectangle is the sum of all four sides, so we can use the formula:P = 2l + 2wwhere P is the perimeter and l and w are the length and width of the rectangle. We know that P = 312 feet.Also, we know that the length is seven times the width, so we can express the length as:l = 7wNow we can substitute this value of l into the perimeter equation:312 = 2(7w) + 2w312 = 14w + 2w312 = 16ww = 19.5 feetNow we can use this value of w to find the length:l = 7w = 7(19.5) = 136.5 feetSo the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.