use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y '

The required original fraction is 3/7.

Given that the numerator of a fraction is four less than the denominator and suppose  17 is added to each, the value of the fraction is 5/6.

To find the equation, consider two numbers as x and y then write the equation to solve by substitution method.

Let  x be the denominator and y be the numerator of the fraction.

By the given data and consideration gives,

Equation 1: y = x - 4

Equation 2 :

(numerator + 17)/(denominator + 17) = 5/6.

(y +17)/ (x + 17) = 5/6.

On cross multiplication gives,

6(y+17)  = 5(x+17)

On multiplication gives,

Equation 2 : 6y - 5x = -17

Substitute Equation 1 in Equation 2 gives,

6(x-4) - 5x = -17.

6x - 24- 5x = -17

x - 24 = -17

On adding by 24  both side gives ,

x = 7.

Substitute the value of  x= 7 in the equation 1 gives,

y = 7 - 4 = 3.

Therefore, the fraction is y / x is 3/7

Hence, the required original fraction is 3/7.

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Answer:

Step-by-step explanation:

I don't see the choices, but I will make the equations that seems to be correct to me.

Known facts:

Let's make the equations:

m + n = 4.5

35m + 60n = 225

Hope that helps!

If the mpc increases in value, the consumption function will become steeper.

What is MPC ?

MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.

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The value of the expression -13x-7y is -8.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations are

-9x + y = 2   .....(i)

-4x - 8y = -10 ....(ii)

Solve the equation by using system of equations.

Multiply equation (i) by 8 and add with equation (ii)

-72x + 8y = 16

-4x - 8y = -10

___________

-76x = 6

x = 6/-76

x = - (3/38)

Putting x = - (3/38) in equation (i):

-9[- (3/38)] + y = 2

27/38 + y = 2

y = 2 - 27/38

y = 49/38

Putting x = - (3/38) and y = 49/38 in -13x-7y:

-13(-3/38)-7(49/38)

= 39/38 - 343/38

= -304/38

= -8

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The average of y is given x in the simple regression model OC. Hyjx = Bo +Byx. So the correct option is OC. Hyjx = Bo +Byx.

To determine the average of y given x in the simple regression model, we can use the equation for the regression line, which is given as:

y = b0 + b1*x

Here, y represents the average of y given x, b0 is the y-intercept, and b1 is the slope of the regression line. x is the independent variable.

Step 1: Gather the data points for x and y values.

Step 2: Calculate the mean of x and y values.

Step 3: Determine the deviation of each x and y value from their respective means.

Step 4: Multiply the deviations of x and y, and sum them up.

Step 5: Square the deviations of x, and sum them up.

Step 6: Divide the sum of the product of deviations by the sum of squared deviations of x to obtain the slope (b1).

Step 7: Substitute the mean values of x and y in the equation to find the y-intercept (b0).

Step 8: Finally, plug in the value of x in the equation y = b0 + b1*x to find the average of y given x.

From the given answer choices, the correct option is OC. Hyjx = Bo + Byx, which represents the simple linear regression model y = b0 + b1*x.

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The area of the resulting surface is approximately 22π square units.

Therefore, the correct option is option D.

The given curve is rotated about the x-axis.

We are supposed to find the area of the resulting surface.

Let us first obtain the differential element of the given curve.

We know that the area of a surface obtained by rotating a curve around the x-axis is given by:

S=2π∫abf(x)√(1+(dy/dx)²)dx

where f(x) is the function of the curve which is being rotated and dy/dx is its differential element obtained as:

dy/dx=−2x

Let us now substitute the values into the formula:

S=2π∫−325−x2​(1+(−2x)²)dx

=2π∫−324(1+4x²)dx

=2π[1x+4x3/3]−324

=2π(11/3)

≈22π

The area of the resulting surface is approximately 22π square units.

Therefore, the correct option is option D.

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The Maclaurin series for f(x) is:

f(x) = ∑[n=1 to infinity] (x^n)/n! * P_n(0)

= ∑[n=1 to infinity] (x^n)/n! * n!/n^8

= ∑[n=1 to infinity] (x^n)/n^8

To find the Maclaurin series of f(x), we can repeatedly differentiate f(x) and evaluate it at x=0 to find the coefficients of the series.

f(0) = 0

f'(x) = 1/(1 + x^7)

f''(x) = -7x^6/(1 + x^7)^2

f'''(x) = (42x^5 + 49x^13)/(1 + x^7)^3

f''''(x) = (-210x^4 - 637x^12 - 343x^20)/(1 + x^7)^4

and so on. The general formula for the nth derivative of f(x) is given by:

f^(n)(x) = P_n(x)/(1 + x^7)^(n+1)

where P_n(x) is a polynomial of degree at most 6n-1. We can find the coefficients of P_n(x) using the formula for the nth derivative and evaluating it at x=0:

P_n(0) = n!f^(n)(0) = n!/(1+0^7)^(n+1) = n!/n^8

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The meclauren series for the function f with f(0)=0 and derivative \(f'(x) = \frac{1}{1 + x⁷}\), is equals to \(f(x) = x - \frac{ x⁸}{8} + \frac{x¹⁵}{15} - \frac{x²²}{22} + .... \).

The Maclaurin series represents a function as an infinite sum of terms, each term being a derivative of the function evaluated at x = 0, 1,... Formula is written, \(\sum_{n= 0}^{\infty}\frac{ f^{n}(0)}{n!} x^n\)

where fⁿ(0) --> derivatives of f(x) at x = 0

n --> real numbers

We have a function, f(x) such that f(0) = 0 and derivative of f(x), i.e, \(f'(x) = \frac{1}{1 + x⁷}\).

We have to determine the meclauren series of function f(x). First we determine the value of f(x), so, expand the \(\frac{1}{1 + x⁷}\) as meclauren series. The meclauren series for \(\frac{1}{1 + x}\) is written, \( \frac{1}{1 + x} = 1 - x + x² - x³ + ......\)

Replace the x by x⁷, we result

\( \frac{1}{1 + x^{7} } = 1 - {x}^{7} + {x}^{14} - {x}^{21} + ......\)

Now, integrating the above series expansion, \(\int f'(x) dx= \int ( 1 - x⁷ + x¹⁴ - x²¹ + ......) dx\)

\(f(x) = x - \frac{ x⁸}{8} + \frac{x¹⁵}{15} - \frac{x²²}{22} + .... + c \\ \)

Using f(0) = 0

=> f(0) = 0 = 0 + 0 + 0 +.... + c

=> c = 0

Hence, required series is \(f(x) = x - \frac{ x⁸}{8} + \frac{x¹⁵}{15} - \frac{x²²}{22} + .... \).

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Answer:

1) See below for table.

2) Domain: \(\{1, 2, 3, 4\}\)

Range: \(\{160, 160, 205, 250\}\)

Yes, this is a function.

Step-by-step explanation:

We know that the electrician charges a base fee of $70 plus $45 for each hour of work.

We also know that the minimum the electrician charges is $160.

Let's write an equation. Let x denote the number of hours worked and y denote the total price. There's also a base fee of $70. So, we can write the following equation:

\(y=45x+75\)

Part 1)

Let's create our table for 1, 2, 3, and 4 hours. To do so, we simply need to substitute each value for x in our equation.

1 Hour:

We have:

\(y_1=45(1)+70\)

Multiply and add:

\(y_1=45+70=\$115\)

However, notice that the minimum the electrician charges is $160. Therefore, for one hour of work, the electrician will still charge $160. So:

\(y_1=\$160\)

2 Hours:

Substitute 2 for x:

\(y_2=45(2)+70=90+70=\$160\\\)

So:

\(y_2=\$160\)

3 Hours:

Substitute 3 for x:

\(y_3=45(3)+70=135+70=\$205\)

So:

\(y_3=\$205\)

4 Hours:

Substitute 4 for x:

\(y_4=45(4)+70=180+70=\$250\)

So:

\(y_4=\$ 250\)

Therefore, for 1, 2, 3, and 4 hours of work, the prices will be $160, $160, $205, and $250, respectively.

We can create the following table (please scroll down to see the table. Also, y is measured in dollars).

Part 2)

The domain of a relation are the input values.

In this context, our input values are the amount of hours worked, and we calculated for 1, 2, 3, and 4 hours of work.

Therefore, our domain in this context is:

\(\{1, 2, 3, 4\}\)

The range of a relation are the output values.

In this context, the output values are the price for x hours of work.

Therefore, our range in this context is:

\(\{160, 160, 205, 250\}\)

This relation does represent a function. Remember that a function cannot have repeating input values. In other words, no one input can be equal to two or more different outputs. However, one output can be mapped to two or more different inputs.

For our table, none of the inputs are repeating. So, our relation is a function.

And we're done!

Answer:

The correct answer is B $887.5

Answer:

B.

887.50

Step-by-step explanation:

\(si = p \times r \times t \div 100\)

\(si \: = 2500 \times 7.1 \times 5\div 100\)

\(25 \times 7.1 \times 5\)

\( = 887.50\)

Answer:

V = 654.255 in^3

Step-by-step explanation:

6.7 in x 9.3 in x 10.5 in = 654.255 in^3 (cubic inches)

Answer:

Desmond

Step-by-step explanation:

3 over 5 x 100% = 60%

20 over 25 x 100% = 80%

6.5 over 10 x 100% = 65%

38 over 50 x 100% = 76%

The wet towel hung on a clothesline will lose 90% moisture after 2.57 hours, based on the proportional rate of evaporation.

A proportional rate refers to a rate that is constant or proportional to the initial value.

Proportional rates are expressed as percentages of the proportions compared to the whole values.

The time it takes the wet towel to lose 35% moisture = 1 hour

Let the hours or time when it will lose 90% moisture = x

The percentage of  moisture lost after x hours = 90%

Proportional rate of moisture loss = 0.35 (35%) per hour

x = 90%/35%

x = 2.57 hours

Thus, proportionately, after 2.57 hours, the wet towel must have lost 90% of its moisture since it could lose 35% after 1 hour.

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The usefulness of quasi-experimental designs for advancing knowledge is directly related to how thoroughly an investigator examines and controls for the selection criteria used in forming the initial groupings.

By carefully considering and controlling for the factors that influence the assignment of participants to different groups, researchers can strengthen the validity of their findings and enhance the credibility of their conclusions. Examining and controlling for other factors such as the results of the posttest analysis, measures used in a questionnaire, and the method of statistical analysis are also important, but the selection criteria play a crucial role in ensuring the comparability of the groups being studied. The correct option is selection criteria used in forming the initial groupings.

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Answer:

The x-intercept is found by setting y = 0, because that will give us the x-value at which the line crosses the x-axis

Step-by-step explanation:

Answer: D. There are no x-intercepts

The first one is 3

1. True: If Spain has an absolute productivity advantage in producing shoes, then it will have a lower opportunity cost for producing shoes than the rest of the world, allowing them to sell them at a lower price, which would encourage exporting.

2. True: The Ricardian Model explains how nations can gain by specializing in the production of goods that they are relatively more efficient in producing and then trading. It can be used to explain how workers in the same sector can be differently affected due to international trade. 3. Uncertain: The extent to which a specific or mobile factor of production benefits from trade (or trade liberalization) depends on several factors, and cannot be generalized.

4. False: Suppose that Home has a relative abundance of L compared with Foreign, then it means that K is scarce relative to L in Home. Thus, K owners in Home will benefit from free trade policies as it will lead to an increase in the demand for K.

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Answer:

11/50

Step-by-step explanation:

Answer:

-1

-Step-by-step explanation:

Step-by-step explanation:

\((ii)\\24y=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot3\cdot\boxed{y}\\16xy=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot2\cdot\boxed{y}\\\\GCF(24x;\ 16xy)=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot\boxed{y}=8y\)

\((iii)\\14p^2=2\cdot\boxed{7}\cdot\boxed{p}\cdot p\\\\7pq=\boxed{7}\cdot\boxed{p}\cdot q\\\\28p=\boxed{7}\cdot2\cdot2\cdot\boxed{p}\\\\GCF(14p^2;\ 7pq;\ 28p)=\boxed{7}\cdot\boxed{p}=7p\)

\((v)\\6a^3b^2c=\boxed{2}\cdot\boxed{3}\cdot\boxed{a}\cdot a\cdot a\cdot\boxed{b}\cdot b\cdot\boxed{c}\\\\24ab^3c^4=\boxed{2}\cdot2\cdot2\cdot\boxed{3}\cdot\boxed{a}\cdot\boxed{b}\cdot b\cdot b\cdot\boxed{c}\cdot c\cdot c\cdot c\\\\12abc=\boxed{2}\cdot 2\cdot\boxed{3}\cdot\boxed{a}\cdot\boxed{b}\cdot\boxed{c}\\\\GCF(6a^3b^2c;24ab^3c^4;\ 12abc)=\boxed{2}\cdot\boxed{3}\cdot\boxed{a}\cdot\boxed{b}\cdot\boxed{c}=6abc\)

\((vi)\\16x^3=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot2\cdot\boxed{x}\cdot\boxed{x}\cdot x\\\\-40x^2=-\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot5\cdot\boxed{x}\cdot\boxed{x}\\\\32x^4=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot2\cdot2\cdot\boxed{x}\cdot\boxed{x}\cdot x\cdot x\\\\GCF(16x^3;\ -40x^2;\ 32x^4)=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot\boxed{x}\cdot\boxed{x}=8x^2\)

The quadrilateral is a parallelogram

We should know that in every parallelogram, opposite sides are equal and parallel

To find the lenghts of the parallelogram, we use the formula for distance between two pointsa to find the sides

d = √(x2-x1)²+(y2-y1)²

DE= √(3+5)²+(5-3)²

de= √8²+2²

de=√16+4

de=√20 = 4.5 units

To find ef

d = √(x2-x1)²+(y2-y1)²

Input the coordinates

√(2-3)²+(1-5)²

ef= √-1²+-4²

= √1+16 =

= √17 = 4.1

To find fg

d = √(x2-x1)²+(y2-y1)²

Input the coordinates

√(-6+2)²+(-1-1)²

ef= √-1²+-2²

= √1+4 =

= √5 = 2.2

To find gd

d = √(x2-x1)²+(y2-y1)²

Input the coordinates

√(-5+6)²+(3+1)²

ef= √1²+4²

= √1+16 =

= √17 = 4.1

From the calculations two opposite sides are equal with 4.1 therefore it is a parallelogram

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The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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Step-by-step explanation:

7b+2b-5

=9b-5

Thank you

Answer: 9b - 5 is our answer

Step-by-step explanation:

7b - 5 + 2b

==> 7b - 5 + 2b ( we can order the terms in such a way, than we can add like terms)

==> 7b + 2b - 5  (combine like terms)

==> 9b - 5 is our answer

Hope this helped! Have a good day :D

For each value of t, we can substitute it back into the parametric equations x = 4t^3 and y = 4t - 8t^2 to obtain the corresponding points on the curve where the tangent line has a slope of 1.

To find the points on the curve defined by x = 4t^3 and y = 4t - 8t^2 where the tangent line has a slope of 1, we need to find the values of t that satisfy this condition.

The slope of the tangent line at a point on the curve is given by the derivative of y with respect to x, dy/dx. In this case, we have the parametric equations x = 4t^3 and y = 4t - 8t^2.

Differentiating y with respect to x, we can find dy/dx:

dy/dx = (dy/dt) / (dx/dt)

      = (4 - 16t) / (12t^2)

To find the points where the tangent line has a slope of 1, we set dy/dx = 1 and solve for t:

(4 - 16t) / (12t^2) = 1

Multiplying both sides by 12t^2, we get:

4 - 16t = 12t^2

12t^2 + 16t - 4 = 0

Simplifying the equation, we have:

3t^2 + 4t - 1 = 0

Now we can solve this quadratic equation for t. By factoring or using the quadratic formula, we find two values for t.

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Answer:

\( \frac{1 - 2 {x}^{2} -2x }{ 2x + 2} \)

Step-by-step explanation:

\( \frac{2}{4x + 4} - \frac{2x}{2} \)

\( = \frac{2 \times 2}{(4x + 4) \times 2} - \frac{(2x) \times (4x + 4) }{2 \times (4x + 4)} \)

\( = \frac{4}{8x + 8} - \frac{8 {x}^{2} + 8x }{8x + 8} \)

\( = \frac{4 - (8 {x}^{2} + 8x) }{8x + 8} \)

\( = \frac{4 - 8 {x}^{2} - 8x }{8x + 8} \)

\( = \frac{4 \times (1 - 2 {x}^{2} -2x ) }{4 \times (2x + 2)} \)

\( = \frac{1 - 2 {x}^{2} -2x }{ 2x + 2} \)

Answer:

x=4

Step-by-step explanation:

This is most probably the answer because 3, 4, 5 is a pythagorean triple.

Answer:

Multiply the angle measure by two.

Step-by-step explanation:

Answer:

you would multiple the angle and measure by two

Answer:

Step-by-step explanation:

are there values for f or b or q? What are we trying to solve?

Answer:

232cm

Step-by-step explanation:

A cheese usually has the shape of a cuboid.

Characteristics of a Cuboid

The amount of paper that would be needed to cover the block of cheese can be determined by calculating the perimeter of the block of cheese which is shaped as a cuboid

Perimeter of a cuboid = 4 x (length + breadth + height)

4 x (30 + 20 + 8) = 232cm

Answer:

8.36

Step-by-step explanation:

\(-0.7-(-2.6+ -0.8) +7.1\\ (add inside the parenthesis)\\\\-0.7 - 3.4 + 7.1\\\\=8.36\)

Answer:

1/6

Step-by-step explanation:

Idk i just googled it

Answer:

4x² + 11x + 6 = (x + 2)(4x + 3)