Consider the following sequence. 0​, 1​, 3​, 6​, 10​, 15​, 21​,...
​(a) List the next two terms of the sequence.
​(b) Assuming the sequence is denoted by A 1, A 2, A 3 ,​..., give an explicit formula for AN.
​(c) Assuming the sequence is denoted by P0, P1, P2,​..., give an explicit formula for PN.

By combining like terms, the equivalent of the given expression, [tex]-\frac{2}{3}a + \frac{5}{6}a-\frac{1}{6}[/tex] , is [tex]\frac{a}{6} -\frac{1}{6}[/tex] or [tex]\frac{a-1}{6}[/tex]

From the question, we are to combine like terms to create an equivalent expression of the given expression.

The given expression is

[tex]-\frac{2}{3}a + \frac{5}{6}a-\frac{1}{6}[/tex]

Combining like terms

[tex]\frac{2(-2a) + 1(5a)}{6} -\frac{1}{6}[/tex]

[tex]\frac{-4a + 5a}{6} -\frac{1}{6}[/tex]

[tex]\frac{a}{6} -\frac{1}{6}[/tex]

= [tex]\frac{a-1}{6}[/tex]

Hence, the equivalent expression is [tex]\frac{a}{6} -\frac{1}{6}[/tex] or [tex]\frac{a-1}{6}[/tex].

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The probability on a particular day that all machines will break down is 0.00060840. So the option b is correct.

In the given question,

A company has four photocopy machines A, B, C and D.

The probability that a given machine will break down on a particular day is;

P(A) = 13⁄100

P(B) = 9⁄50

P(C) = 1⁄5

P(D) = 13⁄100

We have to find the probability on a particular day that all machines will break down.

The required probability = P(A∩B∩C∩D)

The required probability = P(A)∙P(B)∙P(C)∙P(D)

The required probability = 13⁄100 × 9⁄50 × 1⁄5 × 13⁄100

The required probability = 1521/2500000

The required probability = 0.00060840

Hence, the probability on a particular day that all machines will break down is 0.00060840. So the option b is correct.

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Answer:

$14

Step-by-step explanation:

since there are 2 halves in a pound we just need to multiply 7 by 2

7x2

14

Hopes this helps please mark brainliest

It's $7 for 1/2 a pound so we have to double it to get our answer so...

$14 would be our answer.

[tex]1/2+1/2=1[/tex]

If the data collection contains the following numbers: 3, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 85 , Here 3 and 85 represents the outlier.

The important characteristics of Statistics are given as follows:

Outliers are the data's most wildly divergent values.

For instance, if the data collection contains the following numbers: 3 19, 25, 32, 36, 38, 31, 42, 57, 45, and 85

The display of data and outliers

The numbers 3 and 85, which are at the extremes and are hence outliers in the number line above, may be seen to be at these extremes.

The group's outliers are a part of it, but they are not close to the other group members.

Outliers are a concern since they cause an imbalance in the data set, which is why they are typically eliminated. Furthermore, an error can sometimes cause an outlier to appear in a data collection.

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Based on the probability values, the value of the probability notation P(B|A) is 9/11

The given parameters from the question are given as

P(A) = 2/3

P(B) = 3/5

P(AB) = 11/15

Before solving the probability notation P(B|A), we start by calculating the probability expression

This is represented as

P(B|A) = P(AB)/P(A)

Substitute the known values in the above equation, so, we have the following representation

P(B|A) = (3/5)/(11/15)

Express the quotient expression as products

So, we have the following representation

P(B|A) = 3/5 * 15/11

Divide 15 and 5 by 5

This gives

P(B|A) = 3/1 * 3/11

So, we have

P(B|A) = 3 * 3/11

Multiply 3 and 3

P(B|A) = 9/11

Hence, the value of the probability is 9/11

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Based on this information and the ratios given in the table, I would say that skull B is most likely a human skull.

Given,

In the question:

A series of measurements were made on four skulls (descriptions of the measurements can be found in the Student Exploration Sheet).

To find the which is most likely a modern human skull?

Now, According to the question:

The cranium/face area ratio relates to the size of the cranium relative to the rest of the skull, and we would expect this ratio to be fairly large for a human. The face angle relates to human faces in relation to primate faces, which are less protruded forwards (i.e., we have relatively flat faces), and the foramen magnum is the hole in the base of the skull through which the spinal column connects to the skull. In bipeds, we would expect this hole to be fairly equally distant from the back of the skull to the front of the skull,

So this ratio would be closer to

Hence, Based on this information and the ratios given in the table, I would say that skull B is most likely a human skull.

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The line segment i rotated 270 degree clockwise about the origin to form P'Q' the statement describe P'Q'. The accurate alternative is (B) P'Q' is same in period to PQ.

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Answer:

y=-x+6

Step-by-step explanation:

For linear graphs, the slope of perpendicular lines must be of equal value but opposite in sign: ([tex]m_1=-m_2[/tex]).

The slope of y=x+1 is 1, therefore the slope of the perpendicular line must be -1.

Given (x,y)=(-2,8) the equation of the perpendicular line can be obtained by substituting these values into the slope-intercept form y=mx+b.

8=(-1)(-2)+b

8=2+b

6=b

So, the perpendicular line has a slope-intercept form of y=-x+6 or y=6-x.

If solving an equation, put it in standard form with 0 on one polynomial side and simplify.

If you're down to a linear or quadratic equation (degree 1 or 2),

Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.

Put the equation in standard form with 0 on one side to simplify it while solving it.

Know the anticipated number of roots.

If you're left with a linear or quadratic equation of degree 1 or 2, use the quadratic formula or visual inspection to solve it.

Identify one logical cause or source.

Subtract from your factor.

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For the month of November, there has been a depreciation of almost $1,089.60.

By deducting the expected residual value from the cost of the tractor and dividing the result by the total projected operational life in hours, let's first get the depreciation per hour:

A tractor's depreciation per hour is calculated by deducting the residual value from the purchase price, and multiplying the result by the number of hours the tractor will be in use.

[tex]\rm D = \dfrac {136,700 - 14,500} { 18,800}\\D = \$6.81[/tex]

Multiplying the depreciation per hour by the number of hours the tractor was used to get the depreciation for the month of November

[tex]D_m = 6.81 \times 160\\D_m = \$1,089.60[/tex]

Therefore, for the month of November, there has been a depreciation of almost $1,089.60.

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The total value of Dan's piggy bank coins is worth 2844 cents.

What is currency?

Currency is defined as a unit of account that is issued by a government and is accepted at face value. Commodities and services can be exchanged using money.

As we know, each penny is worth 1 cent

Then, 14 pennies = 14 cents

And, a nickel worth 5 cents

Then, 12 nickles = 12*5 = 60 cents

And, a dime worth 10 cents

Then, 32 dimes = 32*10 = 320 cents

And, a quarter worth 25 cents

Then, 48 quarters = 48*25 = 1200 cents

And, a half dollar worth 50 cents

Then, 7 half dollars = 7*50 = 350 cents

And, a dollar worth 100 cents

Then, 9 dollars = 9*100 = 900 cents

Now,

Total coins worth = 14 + 60 + 320 + 1200 + 350 + 900

                             = 2844 cents

Hence, the total value of coins is 2844 cents.

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The problem that looks like after that he implifie the factor is 3/5.

A factor is a number that divides another number with no residual. In other words, if multiplying two whole numbers yields a product, then the numbers we are multiplying are factors of the product since they are divisible by the product.

Factors are numbers that can divide a number exactly. As a result, there is no leftover remaining after division. Factors are the numbers that you multiply together to get another number. As a result, a factor is the divisor of another integer.

Given, Yen calculates the product 5/8 times 24/25.

The product 5/8 times 24/25

=(5/8)(24/25)

Now, we have to factor the terms.

=(5/2×2×2)×(2×2×2×2)/(5×5)

=(5×2×2×2×3)/(2×2×2×5×5)

=3/5

The problem that looks like after that he implifie the factor is 3/5.

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By applying a translation of 5 units down, we will find the translated function:

g(x) = 3x - 7

Here we have the function:

y = f(x) = 3x - 2

And we want to apply a shift (translation) of 5 units downwards.

For any function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N > 0, the translation is upwards.

if N < 0, the translation is downwards.

Here we want to apply a translation of 5 units downwards, so we will write:

g(x) = f(x) - 5

Replacing f(x) we get:

g(x) = 3x - 2 - 5

g(x) = 3x - 7

That is the translated function.

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Hence, we proved that if n is an integer, then either n= 2mod3 or n^2=n mod6.

In the given question we have to prove that prove if n is an integer, then either n= 2mod3 or n^2=n mod6.

If n=2mod3 then tere is nothing to prove.

If n≠ 2mod3 then either n=0mod3 or n=1mod3

Case (1)

n=0mod3 ⇒ 3 | n⇒n=3m for mϵZ

n^2-n=(3m)^2-3m

n^2-n=9m^2-3m

n^2-n=3m(3m-1)

So, 3|3m, in this case 3m is even or 3m-1 is even.

i.e. 2|3m(3m-1) and also 3|3m(3m-1)

⇒6|3m(3m-1)

⇒6|n(n-1)

⇒6|(n^2-n)

⇒n=n mod6 (Proved)

Case (2)

n=1mod3 ⇒ 3 | (n-1)⇒n=3m+1 for mϵZ

n^2-n=(3m+1)^2-(3m+1)

n^2-n=9m^2+6m+1-3m-1

n^2-n=9m^2+3m

n^2-n=3m(m+1)

So, 3|3m, in this case 3m is even or 3m+1 is even.

i.e. 2|3m(3m+1) and also 3|3m(3m+1)

⇒6|3m(3m+1)

⇒6|n(n-1)

⇒6|(n^2-n)

⇒n=n mod6 (Proved)

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The write question is

Prove that if n is an integer, then n = 2 mod 3 or n^2 = n mod 6.

Answer:

z=1

Step-by-step explanation:

2.2(z+3)-1.93=6.87

2.2z+6.6-1.93=6.87

2.2z+4.67=6.87

       -4.67. -4.67

2.2z=2.2

/2.2. /2.2

z=1

Hopes this helps please mark brainliest

Answer:

z = 1

Step-by-step explanation:

2.2(z + 3) − 1.93 = 6.87

1. Distribute

2.2z + 6.6 - 1.93 = 6.87

2. Combine Like Terms

2.2z + 4.67 = 6.87

3. Subtract 4.67 on both sides

2.2z + 4.67 = 6.87

        - 4.67  - 4.67

2.2z = 2.2

4. Divide both sides by 2.2

[tex]\frac{2.2z}{2.2} = \frac{2.2}{2.2}[/tex]

z = 1

These are the preposition for the given conditions:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

The domain of the propositional P(x, y) consists of pairs x and y, where x is 1, 2, 3 and y is 1, 2, 3.

What are the disjunction and conjunction?

In logic functions, there are two kinds of compound statements. These are referred to as conjunction and disjunction. A conjunction implies that both statements are correct, whereas a disjunction implies that at least one of the statements is correct. A conjunction connects statements with the word "and," whereas a disjunction connects statements with the word "or."

By using disjunction and conjunction we get,

a) ∀x∀y P(x, y) is written as:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

b) ∃x ∃y P (x, y) is written as:

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

c) ∃x∀y P(x, y)  is written as:

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

d) ∀y∃x P(x, y)  is written as:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

Hence, these are the preposition for the given conditions:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

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2x+y-3 = 0 iS a linear function with coefficient as 2 and 1 with constant part c = 3.

In a graph, a linear function is one that generates a straight line. The degree of the polynomial function is often either maximum 1 or minimum 0. Despite the fact that both calculus and linear algebra can be used to express linear functions. The function notation is the only thing that differs. Also required is the ability to read an ordered pair expressed in function notation. A function is denoted by the notation f(a), where an is an independent variable on which the function depends. The straight line on the linear function graph contains the expression or formula;

Linear function can be always represented in the format of ax + by + c = 0.

Here,

a € ( -∞, +∞)

b € ( -∞, +∞)

c € ( -∞, +∞)

Hence, Linear expression always contains y¹ and x¹.

and can always be represented in the form of y = mx.

So it always represents the straight line.

For example: 2x+y-3 = 0 ia a linear expression with coefficient as 2 and 1 with constant part c = 3.

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We can determine which table represents a function by, verifying each input value's pairing with a single output value.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given,

We can determine which table represents a function by,

Determine whether a table of input and output values constitutes a function. Determine the values for the input and output. Verify each input value's pairing with a single output value. In that case, the table is a function.

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Answer:

x=30°

Step-by-step explanation:

Find angles of the triangles:

Angles on a straight line:

180°-120°=60°

Opposite angles(intersection property):

55°= 55°

Sum of angles in a triangle = 180°

So:

------>60°+55°+2x+5=180°

------>120°+2x=180°

------>2x=180°-120°

------>2x=60°

------>x=60/2°

------>x=30°

let an agle be 'a' and 'b' ,

120°+a=180° ( linear pair )

a=120°-180°

a=60°

b=55°(opposite angle )

a+b+2x+5=180°(angle sum property)

60°+55°+2x+5=180°

120°+2x=180°

2x=180-120

2x=60

x=60/2

x=30

hence, the value of x is 30

By using the z value, it can be calculated that

P value for upper tail = 0.0455

P value for lower tail = 0.9545

P value for two tail  = 0.091

What is z value?

z value determines the number of standard deviation, the event is above the mean value. That means z value determines the distance of the event from the mean and it is measured in terms of Standard Deviation.

z value = 1.76

From the z table

P value for upper tail = 1 - 0.9545 = 0.0455

P value for lower tail = 0.9545

P value for two tail = 0.0455 [tex]\times[/tex] 2 = 0.091

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Answer:

Curtis spent 14 dollars

Step-by-step explanation:

3x-29=13

   +29. +29

3x=42

/3.  /3

x=14

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The equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

According to the question,

We have the following information;

Point thorough which line is passing = (8,2)

Equation of the line:

x+4y = 28

Now, we will convert this equation into the slope-intercept form:

4y = -x+28

Dividing by 4 on both sides of the equation:

y = -x/4+28/4

y = -x/4+7

Slope of the line = -1/4

We know that the following formula is used to find the equation of the line:

(y-y') = m(x-x')

(y-2) = -1/4(x-8)

y-2 = -x/4+2

Adding 2 on both sides:

y = -x/4+4

Hence, the equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

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It has 816 ways to 3-element subsets, such that no two consecutive integers are in the subset.

You need three digits from 1 to 20, but you don't want any consecutive ones. You should call them a, b, and c.

Without loss of generality, a < b < c.

We use combinations,

Remember that we can write a + 1 b if a b and they're not sequential. With the aid of this insight, we can see the number of desired the number of methods for choosing a, b, and c from among the integers so that,

(1 ≤ a) & (a + 1 < b) & (b + 1 < c) & (c ≤ 20)

In other words, you want to know how many possibilities there are to choose the three numbers a, b, and c so that;

1 ≤ a < b − 1 < c − 2 ≤ 18

As a result, the question is equal to asking how many ways there are to select three integers (a, b - 1, and c - 2) from a range of 1 to 18. In other words, we are interested in how many ways we can select three items from a total of 18 options.

So, the response is:

[tex](^1^8_3)[/tex] = 816 ways

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The bearing of A route from C is  67.2°.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Here, we have

B traveled on a bearing of 150 and A traveled on the north side of B.

To find angle C, we have to use the cosine rule and we get

12² = 8² + 10² - 2 × 8 × 10 × cosC

C = 82.8°

The bearing of A from C will be

= 150° - 82.8°

= 67.2°.

Hence, the bearing of the A route from C is  67.2°.

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Lacy's blue fish tank has now 3 2/3 gallons of water.

If Lacy has 10 gallons of water and she pour an equal number of gallons of water into each of her 3 fish tanks, then the amount of water each tank will have is equal to the quotient of 10 divided by 3.

amount of water poured in each tank =  10 gallons / 3

amount of water poured in each tank = 10/3 gallons

If Lacy's blue fish tank already has 1/3 gallon of water in it, then the total amount of water the blue fish tank has is the sum of the two fractions.

Add the initial amount and the amount poured in after.

1/3 + 10/3 = 11/3 =  3 2/3 gallons

Simplifying the fraction, Lacy's blue fish tank has now 3 2/3 gallons of water.

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Brackets go first, then you have to do the multiplication and division, then addition and subtraction:

-42/5÷(-5) = (-42/5)÷(-5) = -42/(5 x -5) = -42/(-25) = 42/25

If the firm increases its production and sales from 3 to 4 units per day, the profit margin increases.

The correct answer option is option B

Total profit = Total revenue - Total cost

Total revenue = number of units × price of each Units

At 3 units:

Total profit = Total revenue - Total cost

= (3 × 2500) - $3000

= $7,500 - $3000

Total profit = $4,500

At 4 units:

Total profit = Total revenue - Total cost

= (4 × $2,500) - $4,100

= $10,000 - $4,100

= $5,900

In conclusion, the profit margin when production is increased from 3 to 4 units will also increase.

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The equations of the electric curve using the coordinates x₁ and x₂ are:

For AB:

y₁= (1/EI) [-M₀x₁³/6L  + M₀ Lx₁/6]

For CB:

y₂= (1/EI) [-M₀x₂²/2   + 3M₀Lx₂/2  - M₀L]

The elastic curve of a beam is the curve formed by the intersection of the neutral surface and the side of the beam when the longitudinal stresses on the fibers.

An Elastic curve is flatter, resembling the horizontal lines in the letter E. Price elasticity of demand, also known as demand elasticity, relates to the degree of responsiveness in demand quantity with respect to price.

For AB:

[tex]M_{x}[/tex]= - [tex]A_{y}[/tex]x₁

By using double integration method,

EI y₁"=[tex]M_{x}[/tex]= - [tex]A_{y}[/tex]x₁

EI y₁'=- [tex]A_{y}[/tex](x₁)²/2   +C₁   -------(1)

EI y₁=- [tex]A_{y}[/tex](x³/6)+C₁ x +C₂   -------(2)

The boundary conditions are:

At x₁=0, y₁=0

At x₁=L, y₁=L

y₁=0,

=- [tex]A_{y}[/tex](0)+C₁ (0) +C₂

Then, C₂=0

y₁=L,

=- [tex]A_{y}[/tex](L³/6)+C₁ (L) +0

Then, C₁= [tex]A_{y}[/tex](L²/6)

C₁=M₀L/6

EIy₁'= -M₀L((x₁)²/2) ------(3)

EIy₁ = -M₀L((x₁)³/6)+(M₀L/6)x₁   -----(4)

For CB:

Mₓ= -M₀

x₂ is in opposite direction to x₁

So the integration with respect to x₂ will be alternately signed.

EI y₂"=Mₓ= -M₀

EI y₂'= -(-M₀x₂)+C₃

EI y₂'=M₀x₂+C₃ ------(5)

EI y₂= -M₀((x₂)²/2)-C₃x₂+C₄ ------(6)

The boundary conditions are:

x₂=L, y₂'=y₁'

y₂=y₁=0

At x₂=L,

y₂'= M₀L²+C₃

y₂'= y₁'= -M₀L/2

C₃= -3M₀L/2

y₂= -M₀L₂/2-(-3M₀L/2)+C₄

C₄= -M₀L

The equation of the electric curve is,

For AB:

y₁= (1/EI) [-M₀x₁³/6L  + M₀ Lx₁/6]

For CB:

y₂= (1/EI) [-M₀x₂²/2   + 3M₀Lx₂/2  - M₀L]

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The allowable child and dependent care credit considering their pre-credit tax liability is $0

The following chart illustrates how their authorized child and dependent care credit was calculated:

If the revenue is less than $22,000, the full 22% would be permitted.

However, the eligible kid expense would only be allowed up to $7,000.

Consequently, the sum would be

= $7,000 × 22%

= $1,540

Since there is already a pre-credit tax liability, $0 should be taken into account because there would be no credit.

Due to their pre-credit tax liability, the available child and dependent care credit is therefore $0.

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Answer:

(8,2), (12,2),(10,10)

Step-by-step explanation:

any coordinate that means the two sides will have the same length

first, we know that the length is twice the amount of the width

so any coordinate we pick must be twice the length

pick a coordinate that is quite high up ( so we don't get into negatives)

so let's say (10,10)

then we want to go a positive number down - don't want to deal with fractions.

so e.g 8

so 6 down would be (10,2)

then the width is half the length so it has a 4cm wide base

and put an equal amount on each side to the left and the right to get the base co-ordinates

to the left : (8,2)
plus to the right: (12,2)

2+2= make a 4cm base

put these coordinates together and presto! you have coordinated proofs!