Aria makes 12 dollars for each hour of work. Write an equation to represent her total pay, p, after working h hours.

Recall the power series expansions of [tex]\sin(x)[/tex] and [tex]e^x[/tex].

[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1}[/tex]

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{1}{n!} x^n[/tex]

By substituting [tex]3x[/tex] for [tex]x[/tex] in the latter series, we have

[tex]\displaystyle e^{3x} = \sum_{n=0}^\infty \frac{1}{n!} (3x)^n = \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

Then the series expansion of [tex]f(x)[/tex] is

[tex]\displaystyle f(x) = x^3 \sin(x) + e^{3x+2} \\\\ ~~~~~~~~ = x^3 \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2(n+2)} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.

In the question the given function is,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

We know that series representation of sin x and eˣ are:

   ⇒ [tex]e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]

             = [tex]\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Substituting the series representation in the function we get,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

⇒ [tex]f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Hence [tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]  is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².

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The area of the surface is 144.708

The equation of the given surface is,

z=g(x,y)=xy

Solving the partial derivatives,

∂g∂x=y,∂g∂y=x

Substituting to the formula

S=∬√1+( ∂g∂x)2+(∂g∂y)2dA

Thus,

S=∬√1+(y)2+(x)2dAS=∬√1+x2+y2dA

The region in the XY-plane is defined by the intervals  0≤θ≤2π,0≤r≤4

Converting the integral into polar coordinates,

S=∫2π0∫40√1+r2rdrdθ

Integrating with respect to r

S=∫2π0[13(1+r2)32]40dθ

S=∫2π0(17√173−13)dθ

Integrating with respect to θ

S=(17√173−13)[θ]2π0

S≈144.708

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Answer:

i think 80 copies

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

just because all three numbers are even

Hope this helps

The greatest common factor of 30, 22, and 8 will be 2.

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.

In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.

For example in 6 and 12 6 is the highest common factor.

The factor of 30 ⇒ 2,3,5

The factor of 22 ⇒ 2,11

The factor of 8 ⇒ 2,4

The only common factor among 30,22 and 8 is 2 so it will be the greatest common factor.

Hence "The greatest common factor of 30, 22, and 8 will be 2".

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The solution for the given differential equation is lnlxl = [tex]\frac{-x}{y} +C[/tex]

Given,

[tex](y^{2} +y^{x} )dx - x^{2} dy =0[/tex]

Here,

x = vy, dx = vdy + ydv

y = ux, dy = udx + xdu

Then,

[tex]((ux)^{2} +(ux)x)dx-x^{2} (udx+xdu)=0\\=u^{2} x^{2} dx+ux^{2} dx-x^{2} udx-x^{3} du=0\\=u^{2} x^{2} dx=x^{3} du\\=\frac{x^{2} }{x^{3} } dx=\frac{1}{u^{2} } du[/tex]

Now,

[tex]\int\limits^a_b {\frac{1}{x} } \, dx =\int\limits^a_b {u^{-2} } \, du[/tex]

l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{u^{-1} }{(-1)} +C[/tex]

l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{-1}{u} +C[/tex]

y = ux

u = [tex]\frac{y}{x}[/tex]

That is l[tex]n[/tex]l[tex]x[/tex]l [tex]=\frac{-x}{y} +C[/tex]

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Plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.

To plot the value(s) on the number line where the given function is equal to zero:

The equation is written as: y = (x+5)(x-1)

This is further written as:

The highest point occurs when x = 0, which is (5)(-1) = -5

Therefore, plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.

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The correct question is given below:

Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).

Answer:

Trapezoidal prism

Step-by-step explanation:

As long as only two sides of two of the faces are parallel, and the other four faces have two sets of parallel sides, this is a trapezoidal prism.

Answer:

it is a Trapezoidal prism

Answer:

j = 7.8.

Step-by-step explanation:

The slope of the line = difference in y-values / corresponding difference in x-values.

Slope = (7-3) / (j-5) = 10/7

so 10(j - 5) = 7*4

10j - 50 = 28

10j = 78

j = 7.8.

Using a calculator, the line of best fit for the function is given by:

y = 51.7x - 5.7.

To find the equation, we need to insert the points (x,y) in the calculator. For this problem, a linear regression is used because the data only increases.

From the given table, the points are:

(1, 68), (2,97), (3, 134), (4, 176), (5, 241), (6,335).

Inserting these points on the calculator, the line of best fit for the function is given by:

y = 51.7x - 5.7.

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The parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

For this question,

The curve is given as

x(t)=e^-t cos(t),

y(t) =e^-t sin(t),

z(t)=e^-t

The point is at (1,0,1)

The vector equation for the curve is

r(t) = { x(t), y(t), z(t) }

Differentiate r(t) with respect to t,

x'(t) = -e^-t cos(t) + e^-t (-sin(t))

⇒ x'(t) = -e^-t cos(t) - e^-t sin(t)

⇒ x'(t) = -e^-t (cos(t) + sin(t))

y'(t) = - e^-t sin(t) + e^-t cos(t)

⇒ y'(t) = e^-t ((cos(t) - sin(t))

z'(t) = -e^-t

Then, r'(t) = { -e^-t (cos(t) + sin(t)), e^-t ((cos(t) - sin(t)), -e^-t }

The parameter value corresponding to (1,0,1) is t = 0. Putting in t=0 into r'(t) to solve for r'(t), we get

⇒  r'(t) = { -e^-0 (cos(0) + sin(0)), e^-0 ((cos(0) - sin(0)), -e^-0 }

⇒  r'(t) = { -1(1+0), 1(1-0), -1 }

⇒  r'(t) = { -1, 1, -1 }

The parametric equation for line through the point (x₀, y₀, z₀) and parallel to the direction vector <a, b, c > are

x = x₀+at

y = y₀+bt

z = z₀+ct

Now substituting the (x₀, y₀, z₀) as (1,0,1) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get

x = 1 + (-1)t

⇒ x = 1 - t

y = 0 + (1)t

⇒ y = t

z = 1 + (-1)t

⇒ z = 1 - t

Hence we can conclude that the parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

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Answer:

NONE of these statements are true

[tex] \frac{d}{dx} (f(x).g(x)) = f'(x).g(x) + g'(x).f(x)[/tex]

[tex] \frac{d}{dx} ( \sqrt{x {}^{2} + x} ) {}^{2} = \frac{2x + 1}{2 (\sqrt{x {}^{2} + x}) {}^{2} } = \frac{2(2x + 1)(x {}^{2} + x) }{2|x²+x|} = \frac{(2x + 1)(x { }^{2} +x)}{|x²+x|} [/tex]

[tex] \frac{d}{dx} ( \sqrt{f(x)} ) = \frac{f'(x)}{2 \sqrt{f(x)} } [/tex]

Adam says that the number 4 has four factors. The above statement is incorrect as 4 only three factors 1,2, and 4.

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The conceptual and quantative relationship between  Alpha risk and Beta risk is related to the probability of accepting Null hypothesis. They are also known as Type 1 and type 2 error.

Alpha Risk:

Alpha risk is the risk that in statistical test a null hypothesis will be rejected when it is actually true. This is also known as a type I error, or a false positive. The term risk refers to chance or likelihood of making an incorrect decission.

Beta risk:

Beta risk represents the probability that a false hypothesis in a statistical test is accepted as true. Beta risk contrast with alpha risk, which measures the probability that a null hypothesis is rejected when it is actually true.

Determining the type of risk in a quantitative relationship is primarily based on sample size. The Sample Size directly affect the Alpha and Beta risk. If Sample size is larger, the Alpha and Beta risk will lower, and if the sample size is lower the risk of Beta and Alpha increases.

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Step-by-step explanation:

3×5×2 = 30 lorry trips to deliver 2,500 crates.

3 lorries, 5 trips per day, 2 days

that means that one lorry trip transports

2,500 / 30 = 250/3 = 83.33333... crates = 83 1/3 crates.

now we need x lorries each making 6 trips per day in 1 day (so, 6 trips, period) to transport 10,000 crates.

that looks like

x × 6 × 83.33333... = 10,000

x × 6 × 83 1/3 = 10,000

x × (6×83 + 6 × 1/3) = 10,000

x × (498 + 2) = 10,000

500x = 10,000

x = 20

so, we need 20 lorries each doing 6 trips in one day to transport 10,000 crates in one day.

these are altogether 20×6 = 120 lorry trips.

that is 4 times the number of the original scenario (30 trips).

and logically, when doing 4 times the work, we achieve 4 times the result (10,000 crates instead of 2,500).

Answer:

Short leg = 10

Longer leg = 10[tex]\sqrt{3}[/tex]

Hypotenuse = 20

Step-by-step explanation:

The given is a special right triangle, its angle measures are as follows:

30-60-90 and the side lengths will follow as:

x, x[tex]\sqrt{3}[/tex], 2x respectively.

The length of hypotenuse (sees angle measure 90) is represented with 2x and it's given as 20

We can conclude x = 10 from this

So the length of short leg is 10

Then the length of longer leg is 10[tex]\sqrt{3}[/tex]

The length of hypotenuse is already given as 20

2a is 2 x a

Substitute a =5

2 x 5 =10

Now we have:

10^2-c

Substitute c = 10

(2 - 10 = - 8)

So,it's now 10^ - 8 (10 to the power of - 8)

Ans: 10^ - 8 (or 1 x 10^ -8)

Hope this helps!

Answer:

The slope of line p is 3 and the slope of line q is -3.

Th find the kicker with the greatest goal success rate, Coach Salinas should:

Statistics refers to the method of collecting data for the purpose of analysis, making of inferences and drawing of conclusions about the data collected.

Statistics usually involve numerical data in large quantities.

Statistical data can be used to make predictions about future events. They are also used to make decisions. For example, the statistical data of soccer players such as games/goal ratio, number of complete dribbles per match, number of successful take-ons, number of tackle or interceptions per game can be used in deciding which soccer player a football team should buy.

In the given scenario, Coach Salinas wants to compare the kicking statistics for kickers on their team in order to find the kicker with the greatest goal success rate.

To do this, Coach Salinas should:

In conclusion, statistical data is important in making decisions.

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Answer:

A and D are the answers.

Step-by-step explanation:

Answer:

Step-by-step explanation:

let we suppose the ratios as x , 2x and 3x

we know that,

x + 2x + 3x = -----

6x= -------

x= -----/6

therefore x = ......

2x = 2 * x (value of x)

3x = 3 * x (value of x)

and the question is solved

Answer:

let the ratio be 1x,2x,3x

Now,

1x+2x+3x=180°(sum of angles of triangle are 180)

or,6x=180°

or,x=180/6

or,x=30°

Then,

1x=1*30

=30°

2x=2*30

=60°

3x=3*30

=90°

Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.

The surface area of a sphere is simply the total area that covers its outer surface.

The surface area of a sphere is expressed as;

A = 4πr²

Where r is radius and π is pi. ( π = 3.14 )

Given the data in the question;

We substitutes the given values into the equation above.

A = 4πr²

320cm² = 4 × 3.14 × r²

320cm² = 12.56 × r²

r² = 320cm² / 12.56

r² = 25.477707cm²

r = √25.477707cm²

r = 5.05cm

Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.

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Answer:

The radius is 5.05 centimeters.

Hope this helps!

Step-by-step explanation:

The area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex]

Given that the grid has squares with side lengths of 1.5 cm.

We are required to find the area of the composite figure.

The area of the composite figure is approximate to the area of the rectangle plus the are of the semicircle at the top of the rectngle plus the semicircle at the right side of the rectangle.

Finding the area of the rectangle.

A=(3*1.5)(4*1.5)=27 [tex]cm^{2}[/tex]

Finding the area of the semicircle at the top of the rectangle.

A=1/2 π[tex](2*1.5)^{2}[/tex]=4.5 π [tex]cm^{2}[/tex]

Finding the area of the semicircle at the right of the rectangle.

A=1/2 π[tex](1.5*1.5)^{2}[/tex]

=2.53π [tex]cm^{2}[/tex]

Total area =27+4.5π+2.53π

=27+7.03π

Use π=3.14

=27+7.03*3.14

=49.1 [tex]cm^{2}[/tex]

Hence the area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex].

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Using the Laplace transform, the value o y' − 2y = (t − 4), y(0) = 0 is⇒y(t) = 0 e^-t + u(t -1)e^1-t

Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in  regions of physics, electrical engineering, control optics, arithmetic and sign processing.

y' − 2y = (t − 4),

y(0) = 0

Taking the Laplace transformation of the differential equation

⇒sY(s) - y (0) + Y(s) = e-s

⇒(s + 1)Y(s) = (0+ e^-s)/s + 1

⇒y(t) = L^-1{0/s+1} + {e ^-s/s + 1}

⇒y(t) = 0 e^-t + u(t -1)e^1-t

The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.

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Step-by-step explanation:

the inner WU arc angle is 23x - 5.

the outer WU arc angle is 37x + 5.

together they must be 360°, as this is the full circle.

so, we have

360 = 23x - 5 + 37x + 5 = 60x

x = 6

therefore, the angle at V is

V = 5x + 17 = 5×6 + 17 = 30 + 17 = 47°

inner WU arc angle = 23x - 5 = 133°

outer WU arc angle = 37x + 5 = 227°

this also fits with

V = (outer arc angle - inner arc angle)/2 =

= (227 - 133)/2 = 94/2 = 47°

The probability that exactly 1 train will pass Mary's house is 0.00889.

According to the given question.

On average, 18 trains pass by Mary's house daily i.e. in 24 hours.

As, we know that "Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event".

Therefore,

The probability that exactly one train will pass Mary's house in a 3 hour period

= [tex]\frac{^{18C_{1} } }{^{24} C_{3} }[/tex]

[tex]= \frac{\frac{18!}{1!\times17!} }{\frac{24!}{3!\times 21!} }[/tex]

[tex]= \frac{18}{\frac{24\times23\times22}{3\times2\times1} }[/tex]

[tex]=\frac{18}{8\times23\times\ 11}[/tex]

= 18/2024

= 0.00889

Hence, the probability that exactly 1 train will pass Mary's house is 0.00889.

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√64 is rational.

Hope this helps :)

❄ Hi there,

let us consider this –

Is [tex]\sqrt{64}[/tex] a rational or irrational number?

Well, to answer that we need to work out [tex]\sqrt{64}[/tex].

And we know that

[tex]\sqrt{64} =8[/tex]

and 8 is a rational number.

That's it!

❄

The minimum number of cards which must be drawn to get atleast 3 cards of aces is 4.

According to the given question.

We have a deck of cards.

As, we know that

The total numbers of cards in a deck = 52

Since, we have to find the minimum number of cards to be drawn so that we will get atleast 3 cards of aces.

As they have used atleast in the question so the cards can be more also so we have to reach at minimum number of cards to be drawn to guarantee atleast 3 cards of aces.

Number of suits in a  standard deck= 4 (Clubs, Hearts, Diamond,  Spades)

Number of aces in a suit = 1

We need atleast three cards of aces. Which means that we have 4*1 =4 cards from each suit.

Thereofre, the minimum number of cards which must be drawn to get atleast 3 cards of aces is 4.

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Answer:

x^2/ 16 + y^2/4 = 1

Step-by-step explanation:

The major axis is 4 and that goes with the x variable.  It is the major axis because 4 is a larger value than 2.

4 x 4 = 16

2 x 2 = 4

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

In this problem we know the coordinates of a vertex, a co-vertex and the center of an ellipse. Based on this information, we find an ellipse whose major axis is parallel to the x-axis. whose formula in standard form is:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

The major semiaxis has a length of 4 units and the minor semiaxis has a length of 2 units. If we know that (h, k) = (0, 0), a = 4 and b = 2, then the equation of the ellipse is:

x² / 16 + y² / 4 = 1

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

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The claim is wrong, or your question is incorrectly entered.

[tex]x=1 \implies f(3) = f(3) + f(1) \implies f(1) = 0[/tex]

[tex]x=3 \implies f(9) = f(3) + f(3) = 2f(3)[/tex]

[tex]x=9 \implies f(27) = f(3) + f(9) = 3 f(3)[/tex]

[tex]x=27 \implies f(81) = f(3) + f(27) = 4f(3)[/tex]

Then

[tex]f(1) - f(3) - f(9) - f(27) = 0 - f(3) - 2f(3) - 3f(3) = -6f(3) \neq 4f(3) = f(81)[/tex]

at least if [tex]f(3)\neq0[/tex].

Answer:

1. 36 liters

2. 3 kg

Step-by-step explanation:

because 12 liters is 4kg if you multiply both by 3 you’ll get that 12 kg is equal to 36 liters

also, if you divide both by 4, you’ll see that 1kg is equal to 3 liters. Then with this knowledge, yiucc be an see that if you multiply both by 3; 3 kg will be 9 liters! :)

Answer:

1.) 36 litres

2.) 3 kg

Step-by-step explanation:

In this case there is a ratio of 1:3 of mass to volume.  If we know the mass, the volume is 3 times that.  If we know the volume, the mass is that divided by 3.