x/2 - (5x-3)/12 = 1/3 x - 0.75
solve for x

Answer:31

Step-by-step explanation:

Answer:

y=31

Step-by-step explanation:

-21 + y= 10

-21 + y + 21 =10 + 21

y = 10+21

y = 31

HOPE THIS ANSWER HELPS YOU :)))

The constant of variation is 1/3

In this question, a point (12, 4) lies on the graph of a direct variation.

we need find the constant of variation.

Let (x, y) = (12, 4)

We know that in direct variation if one value increases other also increases or vice versa.

In direct variation, the coordinate points can be written as:

y = k * x

where k is the constant of variation

For y = 4 and x = 12,

4 = k * 12

k = 4/12

k = 1/3

Therefore, the constant of variation is 1/3

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Answer:

the vertex is 89

Step-by-step explanation:

Answer:

\(X1/12=491/24\)

\(By \: cross \: multiplication,\)

\(24x=491×12\)

\(x=5892/24\)

\(x=245.5\)

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

What is Quadrant?

(i) When sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=41.81°,138.18°

So it lies in Ist and IInd quadrant.

A suitable graph is not provided here.

(ii) when cosФ=-1/2

Ф=cos^(-1)(-1/2)

Ф=120°,240°

So it lies in IInd and IIIrd quadrant.

A suitable graph is A and D.

(iii) when cotФ=3/4

Ф=cot^(-1)(3/4)

Ф=53.13°,233,13°

So it lies in Ist and IIIrd quadrant.

A suitable graph is E.

(iv) when cosecФ=3/2 or sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=0.729°

So it lies in Ist quadrant.

A suitable graph is not provided here.

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

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There are \(\frac{60!}{57!}\) ways we can do it.

Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,

the president can be select in 60c1 = \(\frac{60!}{1! 59!}\)

                                                           = \(\frac{60 *59!}{1*59!}\)

                                                           = 60 ways

After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.

and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.

∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58

              =  \(\frac{60 * 59 * 58 * 57!}{57!}\)

              =  \(\frac{60!}{57!}\)

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Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

The integrals are evaluated as, (-1/4)L - 7/8 and 24 - 4cos(8).

Double integrals are a mathematical tool used to integrate a function of two variables over a two-dimensional region. They are the generalization of single integrals to two dimensions and are an important tool in calculus and mathematical analysis.

To evaluate the double integral \(\int\int_L^{L+1} (y+1) dy dx\), we integrate first with respect to y and then with respect to x:

\(\int\int_L^{L+1} (y+1) dy dx\) = \(\int_L^{L+1} \dfrac{y^2}{2} + y dx\)

= \(\int_L^{L+1} (\dfrac{x^2}{2} + x)y + ydx\)

=\([(\dfrac{x^2}{2} + x)(\dfrac{y^2}{2} + y) + yx]_L^{L+1}\)

= ((3/8 + L^2/2)L + 5/4) - ((3/8 + (L+1)^2/2)(L+1) + 5/4)

= (-1/4)L - 7/8

To evaluate the double integral \(\int \int_0^S _8^0 x sin(y) dy du\), we integrate first with respect to y and then with respect to u:

\(\int \int_0^S _8^0 x sin(y) dy du = \int_0^8 \int_0^x x sin(y) dy du\)

= \(\int_0^8 [-x cos(y)] |_0^x du\)

= \(\int_0^8 (-x cos(x) + x) du\)

= \([\dfrac{1}{2} u^2 (-cos(u) + 2)] |_0^8\)

= 24 - 4cos(8)

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--The complete question is, Evaluate the following integrals,

a) ∫∫(L,L+1) (y+1) dy dx

b) ∫∫S 8 0 x sin(y) dy du--

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

We can Long Division method to solve quotients step by step

What is long division method and its steps ?

When splitting huge numbers, the task is divided into several sequential parts using the long division approach. The dividend is divided by the divisor, just as in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

We need to comprehend a few stages in order to divide. A vinculum or right parenthesis separates the dividend from the quotient, while a vertical bar separates the divisor from the dividend. Let's now go through the long division stages listed below to comprehend the procedure.

1. Take the dividend's first digit starting from the left . Verify if this digit exceeds or is equal to the divisor.

2. Next, divide it by the divisor, and write the result as the quotient on top.

3. Subtract the outcome from the digit, and then put the difference below.

Step 4: Decrease the dividend's subsequent digit (if present).

Step 5: Carry out Step 4 again.

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To solve the equation b/7.8 = -2.15, we need to multiply both sides of the equation by 7.8 to isolate the variable b. The solution is b = -16.77, rounded to two decimal places.

To solve the equation b/7.8 = -2.15, we need to isolate the variable b. We can do this by multiplying both sides of the equation by 7.8, which is the denominator of the fraction on the left-hand side. This gives:

b = -2.15 x 7.8

We can simplify the right-hand side by multiplying -2.15 and 7.8 to get:

b = -16.77

Therefore, the solution to the equation b/7.8 = -2.15 is b = -16.77. It is important to round the answer to two decimal places since the original equation has two decimal places.

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Answer:

35

Step-by-step explanation:

answer

hx2

Step-by-step explanation:

Answer:

-54

Step-by-step explanation:

-3 -3/4(c-4)=5/4

\(\\\)

Answer:

Exact Form:

c  = −5/3

Decimal Form:

c  = −1.¯6

Mixed Number Form:

c  = −1 2/3

Step-by-step explanation:

8400000cm

84 kilometer is 8400000 centimeter.

Here given 84 km ,

We know that 1 km = 1000 meter

               so 84 km  = 84 x 1000 meter

                                 = 84000 meter

 and 1 meter = 100 cm

 so here 84000 meter = 84000 x 100 cm

                                       = 8,400,000 Centimeters

∴ 84 km = 8400000cm

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Answer:

1 2/3 cm^2.

Step-by-step explanation:

Area = 1 2/3 * 1

= 1 2/3

John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Let's start by setting up the equations to solve for this problem.

Let x be the amount of money John had initially.

Then, Mary had (384 - x) initially.

After John gave Php 36 to Mary, John had (x - 36) left and Mary had (384 - x + 36) = (420 - x).

We are told that Mary had three times as much money as John after this transaction, so we can write:

3(x - 36) = 420 - x

Simplifying this equation gives:

3x - 108 = 420 - x

4x = 528

x = 132

Therefore, John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Answer: Mary had Php 252 at first.

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Integral is \(\int_0^{27} (sin x)/x dx\) ≈ 0.246918974 (rounded to nine decimal places).

To approximate the integral ∫₀²⁷ (sin x)/x dx with an error of magnitude less than 10⁻⁸ using series, we can use the Maclaurin series expansion of sin x:

sin x = x - (x³/3!) + (x⁵/5!) - (x⁷/7!) + ...

Substituting this series into the integral, we get:

∫₀²⁷ (sin x)/x dx = ∫₀²⁷ (x - (x³/3!) + (x⁵/5!) - (x⁷/7!) + ...) / x dx

= ∫₀²⁷ (1 - (x²/3!) + (x⁴/5!) - (x⁶/7!) + ...) dx

= [x - (x³/(33!)) + (x⁵/(55!)) - (x⁷/(7 × 7!)) + ...]

Evaluated from x = 0 to x = 0.27

Using the first four terms of this series, we get:

∫₀²⁷ (sin x)/x dx ≈ [0.27 - ((0.27)³/(33!)) + ((0.27)⁵/(55!)) - ((0.270)⁷/(7×7!))]

= 0.246918974

To estimate the error of this approximation, we can use the remainder term of the Maclaurin series:

|Rn(x)| ≤ M(x-a)ⁿ⁺¹/(n+1)!

M is an upper bound for the nth derivative of sin x, and a = 0 for the Maclaurin series.

The sin x Maclaurin series, we can use M = 1.

Using the fifth term of the series as the remainder term, we get:

|R5(0.27)| ≤ ((0.27)⁶)/(6!)

≈ 1.96 x 10⁻⁸

Since this is less than 10⁻⁸, we can conclude that our approximation is accurate to the desired level of precision.

\(\int_0^{27} (sin x)/x dx\) ≈ 0.246918974 (rounded to nine decimal places).

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The value of the integral, to an error of magnitude less than 10^-8, is approximately 0.24618491.

To approximate the value of the integral with an error of magnitude less than 10^-8, we can use the Taylor series expansion of sin x/x about x=0. We have:

sin x/x = 1 - x^2/3! + x^4/5! - x^6/7! + ...

Integrating this series term by term from 0 to 0.27, we obtain:

integral 0.27 0 sin x/x dx ≈ 0.27 - 0.27^3/3!/3 + 0.27^5/5!/5 - 0.27^7/7!/7 + ...

We can use the alternating series estimation theorem to estimate the error in the approximation. The terms of the series decrease in magnitude and alternate in sign, so the error is less than the absolute value of the first neglected term, which is 0.27^9/9!/9. This is less than 10^-8, so we can stop here and round the approximation to nine decimal places:

integral 0.27 0 sin x/x dx ≈ 0.24618491

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The pulse shape p(t) in the time domain can be found using the inverse Fourier transform of its Fourier transform P(f). The pulse shape is given by p(t) = A sinc(2πRb t)/(1 - 4Rb^2t^2).

To find the pulse shape p(t) in the time domain, given its Fourier transform P(f), we can use the inverse Fourier transform. Specifically, we can use the formula: p(t) = (1/2π) ∫ P(f) e^(j2πft) df, where the integral is taken over all frequencies f.

In this problem, the Fourier transform of the pulse shape p(t) is given by:

P(f) = A rect(f/Rb) = A rect(f/2Rb) * e^(-jπf/Rb)

where rect(x) is the rectangular function defined as 1 for |x| ≤ 1/2 and 0 otherwise.

To evaluate the integral, we can split the rectangular function into two parts, one for positive frequencies and one for negative frequencies:

P(f) = A rect(f/2Rb) * e^(-jπf/Rb) = A/2Rb [rect(f/2Rb) - rect(f/2Rb - 1/(2Rb))] * e^(-jπf/Rb)

We can then substitute this expression into the inverse Fourier transform formula to obtain:

p(t) = (1/2π) ∫ A/2Rb [rect(f/2Rb) - rect(f/2Rb - 1/(2Rb))] * e^(-jπf/Rb) e^(j2πft) df

Now, we can evaluate the integral using the properties of the rectangular function and the complex exponential:

p(t) = A/2Rb [(1/Rb) sinc(2Rbt) - (1/Rb) sinc(2Rb(t-1/(2Rb)))]

where sinc(x) is the sinc function defined as sinc(x) = sin(πx)/(πx).

Simplifying this expression, we get:

p(t) = A sinc(2πRb t)/(1 - 4Rb^2t^2)

Therefore, we have shown that the shape of the pulse in the time domain is given by:

p(t) = A sinc(2πRb t)/(1 - 4Rb^2t^2)

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The values of the variables, the side lengths and the scale factors are calculated below

Question 11

The height is calculated as

Height : 44 = 5 : 4

So, we have

Height/44 = 5/4

Evaluate

Height = 55

Question 12

The length BE is calculated as

BE : 3 = 10 : 12

Evaluate

BE = 4

Question 13

The scale factor of dilation (k) is calculated as

k = B/A

So, we have

k = 6/4

k = 1.5

Question 14

The perimeter of FGH is calculated as

Perimeter = 35 * 6/10

Perimeter = 21

Question 15

The value of x is calculated as

x : 10 = 24 : 16

So, we have

x/10 = 24/16

Evaluate

x = 15

Question 16

The length KL is calculated as

KL : 28 = 3 : 12

Evaluate

KL = 7

Question 17

The value of x is calculated as

x : 9 = 10 : 16

So, we have

x/9 = 10/16

Evaluate

x = 5.625

Question 18

The value of x is calculated as

x : 24 = 15 : 18

Evaluate

x = 20

Question 19

The scale factor of dilation (k) is calculated as

k = A'/A

So, we have

k = 3/1

k = 3

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The correct option is D. the number of sweatshirts for which cost and income are equal.

Any equation that contains only one element which squares the variable and none that raises it to a higher power.

The general form form of quadratic equation is-

ax² + bx + c = 0

According to the question;

Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.

Step 1: Write the following system of equations as the first step.

\(\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}\)

Step 2: Replace the value of "y" in the equation (2).

\(35 x=-0.05(x-400)^{2}+9492\)

Step 3: Make the equation above simpler.

\(35 x=-0.05 x^{2}-8000+40 x+9492\)

Step 4: Write the preceding equation in generalised quadratic form.

\(0.05 x^{2}-5 x-1492=0\)

The processes above lead to the conclusion that option D provides the proper statement.

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The complete question is-

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

y=35x

y=-0.05(x-400)^2+9,492

A. the number of sweatshirts that generate the maximum income

B. the number of sweatshirts that generate the minimum cost

C. the number of sweatshirts for which the difference between cost and income is greatest.

D. the number of sweatshirts for which cost and income are equal

Answer:

D

Step-by-step explanation:

He said so

Answer:

$8421.60

Step-by-step explanation:

First, we need to convert the dimensions of the deck from yards to square yards, since the cost is given per square yard.

The area of the deck is the product of its length and width:

8 yards * 12 yards = 96 square yards

So, the cost to build the deck is:

$87.85/square yard * 96 square yards = $8421.60

Therefore, it cost $8421.60 to build the deck.

Answer:

The answer is C

I did the quiz on edge

Answer:

D

Step-by-step explanation:

ello

-_-

just work hard and help others as much as they help you:)

Y = ( 6 + E X ) X Using Logarithmic Differentiation  D Y D X is `dy/dx = YX[Eln(6 + EX) + (6 + EX)/6 + 1/x]`

Therefore, `dy/dx = YX[Eln(6 + EX) + (6 + EX)/6 + 1/x]`.

To find `dY/dx`, use logarithmic differentiation.

Given: `Y = (6 + EX)X` Differentiate each side concerning `x` using logarithmic differentiation.

Applying logarithmic differentiation:  

`ln y = ln (6 + EX)X` Differentiate both sides concerning `x`.

Differentiating both sides concerning `x`, we get:

`1/y dy/dx = X(ln(6 + EX)X)' + (lnX)'(6 + EX)

= X[(6 + EX)' ln(6 + EX) + (6 + EX)/6 + lnX]`

Now, we need to simplify this expression:`(6 + EX)' = E`

Using the chain rule of differentiation,

we can solve `(6 + EX)' = E` as follows:

`(6 + EX)' = 6'(1 + EX)' = 0 + E = E`

Therefore, we have `(6 + EX)' = E`

Again, differentiate concerning `x`.So, `E' = dE/dx`.

We also have `(lnX)' = 1/x`.

Substituting these values in the previous expression, we get:

`1/y dy/dx = X[Eln(6 + EX) + (6 + EX)/6 + 1/x]`

Multiplying both sides by `y`, we get:

`dy/dx = YX[Eln(6 + EX) + (6 + EX)/6 + 1/x]`

Therefore, `dy/dx = YX[Eln(6 + EX) + (6 + EX)/6 + 1/x]`.

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The cost to cover the garden with mulch will be $12.00, as the area of the rectangular garden is 12 ft.².

The cost of one bag of mulch is given as $5.00.

The area covered by one bag of mulch is 5 ft.².

Therefore, the cost to cover 1 ft.² of the garden with mulch is $(5/5) = $1.00.

To find the area of the rectangular plot representing the garden, we do the follows:

The distance formula between two points (x₁, y₁) and (x₂, y₂) is,

d = √((x₂ - x₁)² + (y₂ - y₁)²).

The length of the rectangular plot between points (3, 9) and (5, 9):

Length = √((5 - 3)² + (9 - 9)²) = √(2² + 0²) = √(4) = 2.

The width of the rectangular plot between the points (3, 3) and (3, 9):

Width = √((3 - 3)² + (9 - 3)²) = √(0² + 6²) = √(36) = 6.

Therefore, the area of the rectangular plot = Length*Width = 2*6 = 12 ft.².

Therefore, the cost to cover the rectangular plot with mulch, at the cost of $1.00 per 1 ft.² = $1*12 = $12.00.

Therefore, the cost to cover the garden with mulch will be $12.00, as the area of the rectangular garden is 12 ft.².

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The algorithms are a problem solving tool in Python because it  provides a wide range of built-in algorithms that can be used to solve many common problems.

The Algorithms are a fundamental problem solving tool in Python . An algorithm is a set of instructions that are executed in a specific order to solve a particular problem. In Python, algorithms can be implemented in the form of functions or methods.

So , In addition to the built in algorithms, Python also provides a rich collection of third party libraries that contain various algorithms that can be used to solve complex problems.

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The given question is incomplete , the complete question is

How are algorithms a problem solving tool in Python ?

Answer:

Answer is 690 every month

Step-by-step explanation:

The total cost is $23,500

Scholarship:8200$

2nd scholarship:7400$

Grandparents: 1000$

23,500-8,200-7400-1000=6900÷10=690

He will have to save up 690 every month for 10 months

The mutually exclusive events are A) A car buyer is female and chose "fuel efficiency" as their most important factor, and B) A car buyer is male and chose "manufacturer reputation" as their most important factor. Event C is not mutually exclusive with any of the other events since it involves a combination of factors and does not include gender.

The mutually exclusive events are events that cannot occur at the same time.

Based on the options:

A) A car buyer is female and a car buyer chose "fuel efficiency" as their most important factor for their purchase.

B) A car buyer is male and a car buyer chose "manufacturer reputation" as their most important factor for their purchase.

D) A car buyer is female and a car buyer chose "looks" as their most important factor for their purchase.

From these options, events A and B are mutually exclusive because they represent different combinations of gender and most important factor.

Event D is also mutually exclusive with events A and B because it represents a different combination of gender and most important factor.

Event C, however, is not mutually exclusive with any of the other events because it represents a combination of factors and does not involve gender.

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Suppose $2000 is deposited in a bank account with an annual compound interest rate of 3%. After two years, we will have accumulated 121.80 in interest on your initial 2000 deposit.

Compound interest is, to put it simply, interest that is earned on interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.

There may be a difference in the timing of when interest is paid out and compounded. For instance, interest on a savings account may be paid monthly but compounded daily. The account balance plus any interest that has accrued but has not yet been paid out are used by the bank to determine your daily interest earnings.

For the above question:

Account Balance = Principal x (1 + interest rate (decimal))^number of the years. With given information this is:  \(2000 (1.03)^2\) = 2,121.80.  So we will earn 121.80 in interest after the 2 years on your original 2000 deposit.

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