inverse of f(x)=3/2x +6

The concept of mathematical harmony was most directly incorporated in the Parthenon in the use of columns.

The term harmony has to do with tunes that are concordant and make meaning to the ears. The search for patterns and sequences is what introduced harmony to mathematics.

Hence, the concept of mathematical harmony was most directly incorporated in the Parthenon in the use of columns.

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Answer:

39.6534

Step-by-step explanation:

You divide 4005 by 101 and find the numbers that repeat as a decimal. In this case, the repeating decimals are 6534.

a. Ava's gross weekly income is $706.80. b.  $194.76 is deducted from Ava's gross weekly income as tax.

In Australia, a retirement savings programme called superannuation mandates that companies pay contributions to a fund on the employees' behalf. The payments are invested and grow over time, and when the employee retires, the fund gives them a lump amount or an ongoing income stream. In addition to the Age Pension offered by the government, superannuation is meant to provide income for people in retirement.

Given that, Ava earns $18.60 per hour for a 38-hour week.

Thus, gross weekly income is:

Gross weekly income = Hourly rate * Number of hours worked

Gross weekly income = $18.60 * 38

Gross weekly income = $706.80

b. The tax deducted is:

Taxable income = Gross weekly income - After-tax deductions

Taxable income = $706.80 - $34.20 - $23.40

Taxable income = $649.20

Now, the tax deducted is:

Tax deducted = Taxable income * Tax rate

Tax rate = 30% = 0.3

Now,

Tax deducted = $649.20 * 0.3

Tax deducted = $194.76

Hence, a. Ava's gross weekly income is $706.80. b.  $194.76 is deducted from Ava's gross weekly income as tax.

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Answer:

do u have a graph

Step-by-step explanation:

Answer:

The expression of density of the material with a density of 6 pound per pint in grams per liter (g/L) is 5756.75 g/L

Step-by-step explanation:

The density of the material is 6 pounds per pint of volume

The given conversion factors are;

1 pint (pt) = 2 cups (cups)

1 cup (cup) = 8 fluid ounces (fl oz)

Therefore;

2 cups (cups) = 2 × 8 fluid ounces = 16 fl oz

Also given;

1 fluid ounce = 29.574 mililiters (mL)

16 fl oz = 16 × 29.574 mL = 473.184 mL

1 liter (L) = 1000 mililiters (mL)

∴ 1 mL = 1/1000 L = 0.001 L

473.184 mL = 473.184 ×  0.001 L = 0.473184 L

1 pound (lb) = 0.454 kilograms (kg)

6 lb = 6 × 0.454 kg = 2.724 kg

1 kg = 1000 grams (g)

2.724 kg = 2.724 ×  1000 grams (g) = 2724 g

Therefore, with 6 lb = 2724 g and 1 pt = 0.473184 L, the density, d, of the material in grams per liter that has a density of 6 pounds per pint is given as follows;  

d = 2724 g/(0.473184 L)= 5756.75 g/L

The expression of density of the material with a density of 6 pound per pint in grams per liter (g/L) = 5756.75 g/L = 5756.75 g/L.

The z-score of an appliance that failed after 64 months is 2.

To find the z-score:

The given parameters are:

The z-score is then computed as follows:

We have the following for an appliance that stopped working after 64 months:

So, the equation becomes:

Compare and contrast the differences:

Calculate the quotient:

Therefore, the z-score of an appliance that failed after 64 months is 2.

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Step-by-step explanation:

Calculate 3/1 x 5/12 = 15/12

The denominator is constant, 12. Think of numbers that multiply the numerator.

What do you multiply by 1/12 to get 15/12?

Ans 15

What do you multiply by 3/12 to get 15/12

Ans 5

Answer:

they are not parallel

Step-by-step explanation:

they intersect eachother

Answer:

Step-by-step explanation:

Since AB is parallel to DE, we know that:

(ABC + BCD) = (CDE + EDC)

Substituting the given values, we get:

800 + BCD = 280 + EDC

Simplifying, we get:

BCD = EDC - 520

We also know that:

(BCD + CDE + DCE) = 180

Substituting BCD = EDC - 520 and CDE = 280, we get:

(EDC - 520 + 280 + DCE) = 180

Simplifying, we get:

EDC + DCE - 240 = 0

EDC + DCE = 240

Now we can solve for DCE in terms of BCD:

DCE = 240 - EDC

DCE = 240 - (BCD + 520)

DCE = 760 - BCD

Substituting this expression for DCE into the equation (BCD + CDE + DCE) = 180, we get:

BCD + 280 + (760 - BCD) = 180

Simplifying, we get:

1040 - BCD = 180

BCD = 860

Therefore, (DCB) = 180 - (BCD + CDE) = 180 - (860 + 280) = -960. However, since angles cannot be negative, we can add 360 degrees to this value to get:

(DCB) = -960 + 360 = -600

Therefore, (DCB) = -600 degrees.

Answer:

Option B

Step-by-step explanation:

Property of the multiplicative inverse,

A × A⁻¹ = I

Here A⁻¹ is the inverse of matrix A and I = Identity matrix.

Option A

\(\begin{bmatrix}1 & -3\\ 1 & -4\end{bmatrix}\times \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}1 & -6\\ 0 & -7\end{bmatrix}\)

False

Option B

\(\begin{bmatrix}1 & 3\\ 1 & 4\end{bmatrix}\times \begin{bmatrix}4 & -3\\ -1 & 1\end{bmatrix}=\begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}\)

True

Option C

\(\begin{bmatrix}-1 & 3\\ -1 & 4\end{bmatrix}\times \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}-1 & 6\\ 0 & 7\end{bmatrix}\)

False

Option D

\(\begin{bmatrix}1 & -3\\ -1 & 4\end{bmatrix}\times \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}1 & -6\\ 0 & 7\end{bmatrix}\)

False

Option B is the correct option.

There are 28,434 4-permutations of the positive integers not exceeding 100 that contain three consecutive integers in the correct order.

We want to find the number of 4-permutations containing three consecutive integers in the correct order.

Let's break this down step-by-step.

Identify the possible sets of consecutive integers:

Since we are looking for sets of three consecutive integers not exceeding 100, the highest possible set is (98, 99, 100). Therefore, we have a total of 98 sets (from 1-2-3 to 98-99-100).
Determine the number of ways to arrange each set within a 4-permutation:

Each set of consecutive integers can appear at the beginning, in the middle, or at the end of the permutation. So, there are 3 different positions for each set.

Calculate the remaining integer's options:

For each of the 3 positions, we have 97 options for the remaining integer since it must be different from the three consecutive integers in the set.

Multiply the number of sets, positions, and remaining integer options: 98 sets * 3 positions * 97 remaining integer options = 28,434 possible 4-permutations.

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Answer:  The total number of colored papers is 18.

Step-by-step explanation:

Given: The ratio of coloured papers to wight papers is 3:8.

Let total number of colored papers = 3x

and total number of wight papers = 8x

Since, there are 48 wight papers , then

\(8x=48\)

\(\Rightarrow\ x=6\)

Now , number of colored papers = 3(6)=18

Hence, the total number of colored papers is 18.

A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...

Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.

The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

Example'

The cumulative distribution function for the above probability distribution is calculated as follows:

The probability that \(X\) is less than or equal to is 0.1,

the probability that \(X\) is less than or equal to 2 is 0.1+0.3 = 0.4,

the probability that \(X\) is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and

the probability that \(X\) is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.

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Answer:

the answer is 6xy , hopefully that helped you

Answer:

2x^9 x

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x3"   was replaced by   "x^3".  

STEP  1 :

Multiplying exponential expressions :

1.1    x4 multiplied by x3 = x(4 + 3) = x7

The Equation at the end of step  1 :

 ((2x7 • x) • x) • y

STEP  2:  Final result :

 2x^9 y

Hope this helps!

Brain-List?

there are 128 different bit strings of length 7. To calculate the number of bit strings of length 7, we need to consider that each position in the bit string can either be 0 or 1.

Since there are 7 positions in the string, we have 2 options (0 or 1) for each position. Therefore, the total number of bit strings of length 7 is 2^7 = 128.To calculate the number of bit strings of length 7 that start with 0110, we need to fix the first four positions as 0110. The remaining three positions can have either 0 or 1, giving us 2 options for each position. Therefore, the total number of bit strings of length 7 that start with 0110 is 2^3 = 8.

To calculate the number of bit strings of length 7 that contain the string 0000, we need to consider the possible positions for the string 0000. It can occur in five different positions: at the beginning, at the end, or in any of the three middle positions. For each position, the remaining three positions can have either 0 or 1, giving us 2 options for each position. Therefore, the total number of bit strings of length 7 that contain the string 0000 is 5 * 2^3 = 40. However, we need to subtract the cases where the string 0000 occurs in both the beginning and end positions, as they were counted twice. So, the final answer is 40 - 24 = 16.

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(A) In this case, Paul deposits $4,500 into the account, so the present value (P) is $4,500. The annual percentage rate ® is given as 5%. The interest is compounded semi-annually, which means it is compounded twice a year.

Therefore, the number of times each year that the interest is compounded (n) is 2.

So, P = $4,500, r = 5%, and n = 2.

(B) To calculate the future value after 10 years, we can use the formula S(t) = P(1 + nr)^nt, where t is the time in years.

Substituting the values into the formula, we have:

S(10) = $4,500(1 + 0.05/2)^(2 * 10)
     = $4,500(1 + 0.025)^20
     ≈ $4,500(1.025)^20
     ≈ $4,500(1.5604)
     ≈ $7,022.80

Therefore, Paul will have approximately $7,022.80 in the account after 10 years.

(c)  The Annual Percentage Yield (APY) represents the actual or effective annual percentage rate, which takes into account compounding over the year.

The formula to calculate APY is APY = (1 + r/n)^n – 1, where r is the annual percentage rate and n is the number of times the interest is compounded per year.

Substituting the values into the formula, we have:

APY = (1 + 0.05/2)^2 – 1
   = (1 + 0.025)^2 – 1
   ≈ (1.025)^2 – 1
   ≈ 0.050625

Rounding to 3 decimal places, the APY is approximately 0.051.


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The parameterization of a circle of radius r in the xy-plane, centered at (a, b), and traversed once in a clockwise fashion can be represented by the following equations:

\(\[ x = a + r \cos(t) \]\[ y = b - r \sin(t) \]\)

where:

- (a, b) represents the center of the circle,

- r represents the radius of the circle,

- t represents the parameter that ranges from 0 to 2π (or 0 to 360 degrees) to traverse the circle once in a clockwise fashion.

In the equation for x, the cosine function is used to determine the x-coordinate of points on the circle based on the angle t. Adding the center's x-coordinate, a, gives the correct position of the points on the circle in the x-axis.

In the equation for y, the sine function is used to determine the y-coordinate of points on the circle based on the angle t. Subtracting the center's y-coordinate, b, ensures that the points are correctly positioned on the y-axis.

Together, these equations form a parameterization that represents a circle of radius r, centered at (a, b), and traversed once in a clockwise fashion.

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Assuming about the marginal pmf fx(X) and the conditional pmf h(y|x) for  given the random variables X and Y, we get P(x + y > 4) = 4/3.

To compute P(x + y > 4) given the random variables X and Y, we need to consider the joint probability distribution of X and Y, as well as the given conditions.

Let's assume the marginal probability mass function (pmf) of X, denoted as fX(x), is uniform on the interval [0, 4]. Since X is chosen randomly from this interval, we can assume that fX(x) = 1/5 for x in [0, 4], and 0 elsewhere.

Next, let's assume the conditional pmf of Y given X, denoted as h(y | x), is uniform on the interval [0, x]. Given that X = x, the possible values of Y are uniformly distributed from 0 to x. Therefore, we can express h(y | x) as h(y | x) = 1/x for y in [0, x], and 0 elsewhere.

Now, let's compute P(x + y > 4) by considering all possible combinations of X and Y:

P(x + y > 4) = ΣΣ P(x, y)

= ΣΣ P(x) * P(y | x)

= ΣΣ fX(x) * h(y | x)

= ΣΣ (1/5) * (1/x)

We need to compute this sum over all valid values of x and y. However, there is a constraint on the valid values of y based on the observed value of X.

For x = 0:

P(x + y > 4) = P(0 + y > 4) = P(y > 4) = 0

For x = 1:

P(x + y > 4) = P(1 + y > 4) = P(y > 3) = 0

For x = 2:

P(x + y > 4) = P(2 + y > 4) = P(y > 2) = 1/2

For x = 3:

P(x + y > 4) = P(3 + y > 4) = P(y > 1) = 2/3

For x = 4:

P(x + y > 4) = P(4 + y > 4) = P(y > 0) = 1

Summing these probabilities:

P(x + y > 4) = 0 + 0 + 1/2 + 2/3 + 1

= 8/6

= 4/3

Therefore, P(x + y > 4) = 4/3.

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Answer:

4:5

Step-by-step explanation:

hope this helps

Answer: 2

Step-by-step explanation: It is 2. You can use the vertex formula x= (-b/2a) 4/2(1), which is 2 and x=2 is the x intercept.

Answer:

x=

y=31

Step-by-step explanation:

hope this helps

Add the 259 to the initial price:

10,000 + 259 = 10,259

Increase that price by 25%, so multiply by 1.25:

10259 x 1.25 = 12,823.75

The price is then increased by another 10%, multiply by 1.10:

12,823.75 x 1.10 = 14,106.13

List price = $14,106.13

The specific solution to the initial value problem y⁴ - 3y' + 2y" = 2x, with initial conditions y(0) = 0, y'(0) = 0, y"(0) = 0, and y''(0) = 0, is y(x) = \(-3e^x + 3e^2x + e^(0.618x) - e^(-1.618x).\)

To solve the given initial value problem, we'll start by finding the general solution of the differential equation and then apply the initial conditions to determine the specific solution.

Given: y⁴ - 3y' + 2y" = 2x

Step 1: Find the general solution

To find the general solution, we'll solve the characteristic equation associated with the homogeneous version of the differential equation. The characteristic equation is obtained by setting the coefficients of y, y', and y" to zero:

r⁴ - 3r + 2 = 0

Factoring the equation, we get:

(r - 1)(r - 2)(r² + r - 1) = 0

The roots of the characteristic equation are r₁ = 1, r₂ = 2, and the remaining two roots can be found by solving the quadratic equation r² + r - 1 = 0. Applying the quadratic formula, we find r₃ ≈ 0.618 and r₄ ≈ -1.618.

Thus, the general solution of the homogeneous equation is:

\(y_h(x) = c_{1} e^x + c_{2} e^2x + c_{3} e^(0.618x) + c_{4} e^(-1.618x)\)

Step 2: Apply initial conditions

Now, we'll apply the initial conditions y(0) = 0, y'(0) = 0, y"(0) = 0, and y''(0) = 0 to determine the specific solution.

1. Applying y(0) = 0:

0 = c₁ + c₂ + c₃ + c₄

2. Applying y'(0) = 0:

0 = c₁ + 2c₂ + 0.618c₃ - 1.618c₄

3. Applying y"(0) = 0:

0 = c₁ + 4c₂ + 0.618²c₃ + 1.618²c₄

4. Applying y''(0) = 0:

0 = c₁ + 8c₂ + 0.618³c₃ + 1.618³c₄

We now have a system of linear equations with four unknowns (c₁, c₂, c₃, c₄). Solving this system of equations will give us the specific solution.

After solving the system of equations, we find that c₁ = -3, c₂ = 3, c₃ = 1, and c₄ = -1.

Step 3: Write the specific solution

Plugging the values of the constants into the general solution, we obtain the specific solution of the initial value problem:

\(y(x) = -3e^x + 3e^2x + e^(0.618x) - e^(-1.618x)\)

This is the solution to the given initial value problem.

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Answer:

Given the sides of a triangle, the Pythagorean Theorem (its converse, really) lets us distinguish the right triangles from the other triangles. The right triangles are the ones where , where is the length of the longest sides and and are the other two. So the Pythagorean Theorem works for any triangle.

Step-by-step explanation:

Answer:

Pythagorean Theorem is used when you have to find a side length of right triangle. Leg 1 and Leg 2 could be labeled as A and B, doesn't matter which one is which. But C is always the hypotenuse which is the biggest side in the whole triangle. And to find the hypotenuse of the it is always the side length opposite to the right angle in the triangle. So the formula goes like;

A² + B² = C²

Hope this helps!

Answer: To find the range of the marks obtained, we need to find the difference between the highest and lowest marks:

Range = highest mark - lowest mark

To find the highest and lowest marks, we can simply sort the marks in ascending or descending order:

39, 48, 56, 75, 76, 81, 85, 85, 90, 95

So, the highest mark is 95 and the lowest mark is 39. Then, the range is:

Range = 95 - 39 = 56

To find the mean marks obtained by the group, we need to add up all the marks and divide by the number of marks:

Mean = (85 + 76 + 90 + 85 + 39 + 48 + 56 + 95 + 81 + 75) / 10

   = 745 / 10

   = 74.5

So, the mean marks obtained by the group is 74.5.

Step-by-step explanation:

Carla earned $27,500 during the year, while William attended law school full-time for 9 months and earned no income. They would not get dependent child care credit.

Credit for dependent care:

A married couple or single person who cares for his or her own or dependent child can earn this dependent care credit.

'The dependent tax credit is non-refundable.

* General credit qualifications.

- Employment-related care cost is required for a

= dependent under the age of 13 or

A dependent or spouse who lives with the taxpayer for more than half the year and is physically or mentally incapacited.

* amount of credit.

* applicable percentage - eligible care cost

- the appropriate percentage ranging from 20% to 35% depending on AGI

If your income is less than $15,000, the rate will be 35%. Income above $15,000 will decrease by 1% for every 2000.

* To get credit, married taxpayers must file a joint return.

*the cost of eligible care has been defined.

- costs for qualified individual care within the taxpayer's homr or outsider's home.

= if outside the home, the dependent or spouse must spend at least 8 hours per day within the taxpayer's home.

= unless the relative is a child under the age of 19, child care payments to a relative are eligible for the credit.

- The amount of costs that qualify is the lower of the actual cost or 3000 for one qualified individual and 6000 for two or more qualified individuals.

* Limitation on earned income.

- The amount of eligible care costs may not exceed the lower of the taxpayer's or spouse's earned income.

- Full-time students, disabled taxpayers, and spouses are deemed to have earned income up to the monthly limits of $250 for one child and $500 for two.

William and carla submit a combined tax return.

Carla earned $27,500 last year.

William attended law school full time for 9 months without earning any money.

They paid $3,500 for carl, their 3 year old child.

William and Carla are ineligible for dependent care credit. Because they should both have employment income.

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Answer: 3.42 miles

Step-by-step explanation:

5.5 cm converts to 3.41754e-5 miles