PLEASE HELP!! It's my unit test!!

Katherine is x years old. Mabel is 4 years younger than Katherine. Five times Mabel's age is equal to 400.

#1 Write an equation that solves for Katherine's age, x.

#2How old is Katherine? (Show your work.)

#3 How old is Mabel? (Show your work.)

The solution of Neumann problem, ∇²u= 0 if r < R , Uₙ (R,θ) = f(θ) is u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ) with boundary conditions uᵣ (r,θ) = ∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ) and

Aₙ=∫(f(θ)cosnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]

Bₙ=∫(f(θ)sinnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]

Given that

The solution of Numann problem

∇²u= 0 if r < R , Uₙ (R,θ) = f(θ)

Use polar co-ordinates (r,θ)

uᵣᵣ + 1/r uᵣ+ 1/uᵣ (uθθ) = 0 ,0 < r< R,

0 <θ <2π and ∂u/∂r(R,θ) = f(θ) is directional derivative

r²d²u/dr² + rdu/dr + d²u/dθ² = 0

Let , r = ε⁻ᵗ , u(r(t),θ)

uₜ = uᵣ(rₜ) = - e⁻ᵗ uᵣ

uₜₜ =( - e⁻ᵗ uᵣ )ₜ = ε⁻ᵗuᵣ + e⁻²ᵗ uᵣᵣ

= r uᵣ+ r²uᵣᵣ

Thus we have, uₜₜ + uθθ = 0

Let u(t,θ) = X(t)Y(θ)

Which gives X''(t)Y(θ) + X(t)Y"(θ) = 0

X"(t)/X(t) = - Y"(θ)/Y(θ) = λ

From Y"(θ) + λ Y(θ) = 0

We get, Yₙ(θ) = aₙ cosnθ + bₙ sinnθ

λ= n² , n =0, 1, ...

With these values of λn we solve,

X"(t) - n² X(t) = 0

If n = 0 , X₀(t) = c₀t + d₀

X₀(r) = -c₀log (r) + d₀

If n not equal to 0 then

Xₙ (t) = cₙeⁿᵗ + dₙ e⁻ⁿᵗ

Xₙ(r) = cₙ(r)⁻ⁿ + dₙ (r)ⁿ

We have u₀(r, θ) = X₀(r)Y₀(θ)

= a₀ ( - c₀(log r) + d₀)

uₙ(r,θ) = Xₙ(r) Yₙ(θ)

= (cₙ r⁻ⁿ+ dₙrⁿ)(aₙ cosnθ + bₙ sinnθ)

But u must be positive at t =0

So, cₙ = 0 ; n = 0,1,2....

u₀ (r,θ) = a₀ d₀

uₙ(r,θ) = dₙ rⁿ( aₙ connθ + bₙ sinnθ)

By superposition , we can write as

u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ)

Boundary conditions gives

uᵣ (r,θ)=∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ)

the coefficients aₙ , bₙ for n ≥ 1 are determined are Fourier series for f(θ)

but a₀ is not determined from f(θ) therefore , it may take arbitrary value. By using Fourier series,

Aₙ= Integration of(f(θ)cosnθ dθ/π n R⁽ⁿ⁻¹⁾) where θ∈[-π, π]

Bₙ= Integration of (f(θ) sinnθ dθ/π nR⁽ⁿ⁻¹⁾) where θ∈[-π, π]

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As a result, the second table agrees with the formula y= 3x -3.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

-3x - 3 = -6

y= 3x -3

Therefore, the second table matches the equation y= 3x -3.

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A and B are events defined on a sample space, with P(A) = 0.6 and P(BIA) = 0.3. then P(A and B) = 0.18

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

If A and B are events defined on the sample space with P(A) = 0.6 and P(BIA) = 0.3.

To find P(A and B),

we use the formula of conditional probability,

P( A and B ) = P (BIA) P(A)

P( A and B ) = 0.6 × 0.3

P( A and B ) = 0.18

Therefore, P ( A and B ) is 0.18.

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77532 is the total cost to Russell

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Russell Slater bought 700 shares of Disney stock at $106.50 per share

The amount for 700 shares is 700×106.5

74550

commission of 4% of the purchase price.

We have to convert 4% to decimal value by dividing 4 by 100

0.04

Now multiply 0.04 with 74550 to get the commission

0.04×74550

2982

Now add this commission amount with 74550 to find total cost,

2982+74550

77532

Hence, 77532 is the total cost to Russell

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The balance of Carlos account after this period, using simple interest, is of:

$2,339,488.08.

This is a simple interest problem, hence the balance of the account can be obtained using an exponential function, defined as follows:

[tex]B(n) = B(0)(1 + r)^n[/tex]

In which the parameters of the exponential function are defined as follows:

In the context of this problem, the values of these parameters are given as follows:

B(0) = 1500000, r = 0.025, n = 18, as one and a half year = 18 months.

Then the balance of Carlos account is obtained as follows:

B(18) = 1500000(1.025)^18 = $2,339,488.08

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Answer: Its -12

Step-by-step explanation:

In Algebra, a constant is a number on its own.

The number of seashells that Joan gave to Sam is 43   .

In the question ,

it is given that ,

the total number of seashell that Joan found on the beach is = 70 ,

let the  number of seashells that she gave to Sam be "x" .

the number of seashells that Joan has with her is = 27 .

So , the equation that represents the above situation about the number of seashells is

27 + x = 70

subtracting 27 from both sides of the equation ,

x = 70 - 27

Simplifying further ,

we get ,

x = 43

Therefore , the number of seashells given is 43 .

The given question is incomplete , the complete question is

Joan found 70 seashells on the beach . she gave Sam some of her seashells . She has 27 seashell . How many seashells did she give to Sam ?

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The fraction of height at which the collision occured is , y/y₀ = 1/2 + v₀²/(2 g y₀) .

For ball A

Given that the ball is dropped and its initial velocity is zero, the equation is

= - 2 g (y₀-y)

For ball B

v {B}^2 = v₀² - 2 g y

We swap out

2v {B}^2 = -2 g (y₀ -y)

g y0 + 2 g y = -v B2

v {B}^2 = v₀² - 2gy

It can be solved because it is a system of two equations with two unknowns. Let's add and multiply by -1.

0 = g y₀ + v₀² -2gy

Bypassing the height

y = (g yo plus v02) / 2g

y = yo / 2 + v₀² / 2g

In this exercise, we'll assume that the building's height and ball B's initial velocity are both known.

The percentage is

y/yo

= 1/2 + v₀²/(2gyo) (2gyo)

Velocity and speed describe how quickly or slowly an object is moving. We frequently encounter circumstances when we must determine which of two or more moving objects is going faster.

If the two are travelling on the same route in the same direction, it is simple to determine which is quicker.

It is challenging to identify who is moving the fastest when their motion is in the other direction.

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Answer:

The triangle was translated to the right by 4 points.

Step-by-step explanation:

If you look at the coordinates, the Y value does not change at all when comparing the original image to the translated image. Only the x value was translated. Since the problem told you it was a translation you can pick a point and subtract the value of the original image from the value of the translated image. If your answer to the subtraction problem is positive, the image moved to up or to the right (for the x-axis), if it is negative then your image moved down or to the left . Up and down is for translations along the Y-axis, and left and right are for translations along the X-axis. This works for both X and Y values. I know I just dumped a bunch of words on you, so to show you lets use points C and C'. C has an X value is 3 and C' has an X value of 7.

Subtract C (3) from C' (7) and that'll give you an answer of 4. Since the answer is positive it will move up or to the right. Since we used the X value, it moved to the right.

If you need a better explanation let me know and I'll try my best.

The reasonable 95% confidence intervals for the population mean difference is (7.83, 12.13) , the correct option is (a) .

In the question ,

it is given that ,

90% confidence interval is given as (8.21 , 11.75)

using this interval , we have to find the 95% confidence interval .

Now, [tex]x_{d}[/tex]  - E = 8.21

[tex]x_{d}[/tex] + E = 11.75 , where E is the margin of Error .

Solving the equations ,

we get ,

E = 1.77  and [tex]x_{d}[/tex] = 9.98

So , the margin of error E is given as

E = [tex]t_{\frac{0.10}{2},15 } \times \frac{S.D.}{\sqrt{n} }[/tex]

we have to find standard deviation from this ;

given n = 16 and [tex]t_{\frac{0.10}{2},15 }[/tex] = 1.7531

Substituting in the margin of error equation ,

we get ,

S.D. = (1.77 × 4)/1.7531

= 4.0386

So , the 95% confidence interval is given as [tex]x_{d}[/tex]  ± [tex]t_{\frac{0.10}{2},14 } \times \frac{S.D.}{\sqrt{n} }[/tex] .

from t table , [tex]t_{\frac{0.10}{2},14 }[/tex] = 2.1314

Substituting ,

we get ,

CI = (9.98 ± 2.1314×4.0386/√16)

= (9.98 ± 2.1519)

= ( 9.98 - 2.1519 , 9.98 + 2.1519)

= (7.83 , 12.13)

Therefore , the correct option is (a) (7.83 , 12.13)    .

The given question is incomplete , the complete question is

Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply:

(a) (7.83, 12.13)  

(b) (7.53, 11.83)

(c) (8.45, 11.51)

(d) (8.63, 11.33)

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The value of 2xx ÷ 3yy is 288/1225

In mathematics, simply or simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.

Given that, an expression 2xx ÷ 3yy, where x = 12 and y = 35

2x12x12/3x35x35 = 288/1225

Hence, The value of 2xx ÷ 3yy is 288/1225

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Answer: 2

Step-by-step explanation:

By using the fact that segment DC bisects the angle  BCA, we will see that:

m∠DCB =  67.38°

First, we know that the angle CDB is an angle of 90°, and the angle ACB has a measure of 134.76°.

Now, notice that the segment DC bisects that angle (bisects means that it "cuts it" right in half), then the angle BCD is half of that, we will have:

∠DCB = 134.76°/2 = 67.38°

In this way we conclude that the measure we wanted to find is  67.38°.

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Answer:

To test the researcher's claim, we need to conduct a hypothesis test. The null hypothesis, denoted as H0, is that the proportion of workers who are satisfied with their job is equal to 80%, and the alternative hypothesis, denoted as Ha, is that the proportion is significantly different than 80%.

To conduct the hypothesis test, we first need to calculate the sample proportion of workers who are satisfied with their job. To do this, we need to know how many of the 300 workers surveyed indicate that they are satisfied with their job. Without this information, it is not possible to conduct the hypothesis test.

Step-by-step explanation:

The average rate of change from 1992 to 2000 is -1.025 percent per decade.

What is the average rate of change?

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

the average rate of change :

A(x) = 34.5 - 42.7 / 2000 - 1992

A(x) = -8.2 / 8

A(x) = -1.025

Hence, the average rate of change from 1992 to 2000 is -1.025 Percent per decade.

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The possible domain of the convergence are b. (-1,3) and c. (-1,3]

Domain of convergence.

In statistics, domain of the convergence also known as interval of convergence means an interval associated with a given power series such that the series converges for all values of the variable inside the interval and diverges for all values outside it.

Given,

Here we need to identify in which of the options are domain of convergence.

As per the definition of domain of convergence, the interval of the convergence is (-∞ , ∞).

So, the possible convergence in the given options are (b) and (c).

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Answer:

  (b)  y=(x+1)²−9

Step-by-step explanation:

You want the vertex form equation of the graphed parabola, which opens upward and has its vertex at (-1, -9).

The vertex form equation for a parabola with vertex (h, k) is ...

  y = (x -h)² +k

The vertex of the parabola shown is (h, k) = (-1, -9). Using these values in the equation gives ...

  y = (x +1)² -9

__

Additional comment

The equation may include a scale factor that multiplies the square. Here, the curve rises 1 unit for 1 unit either side of the vertex, so the scale factor is 1. (The rise at ±1 from the vertex is the scale factor.)

Steps: (1) read the vertex coordinates from the graph; (2) put those coordinates in the vertex form equation; (3) check to see that the vertical scale factor is 1.

Answer:

transitive property

Step-by-step explanation:

An angle is formed when two lines or rays meet at a common point. The common point is known as the vertex.

An angle measurement can be defined as the measure of the angle formed by the two rays or arms at a common vertex. Angles are measures in degrees. There are many kinds of angles in geometry such as acute, obtuse, reflex, straight and right angle. Each angle has a different measure.

Angle relationship between the angles made when a line intersects a pair of parallel lines.

In geometry, there are five fundamental angle pair relationships such as complementary angles, supplementary angles, adjacent angles, linear pair, vertical angles.

The more familier unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°. Two angles are complementary if the sum of their measures is 90°.

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Answer:

55000 grams

Step-by-step explanation:

1 kg = 1000 grams  ==> kilo means 1000, so 1 kilogram = 1000 grams

Now multiply 55 kg with the grams-kilograms conversion factor to get the total number of grams Shaina weighs.

55 kg* 1000 grams / 1 kg =

55 * 1000 grams / 1 =  ==> cancel out the kg

55 * 1000 = 55000 grams

Answer:

b = a - 6

Step-by-step explanation:

Solve for b:

6 + b = a

6 + b - 6 = a - 6

b + 0 = a - 6

b = a - 6

Answer:

n = 16

Step-by-step explanation:

-1/2 n = -8

(-1/2 * n = -8) * 2  ==> multiply the equation by 2 to remove fractions

-1 * n = -16

-n = -16 ==> simplify

n = 16

Answer: 16

Step-by-step explanation:

-1/2n=-8

Divide by -1/2

n=16

The total amount of ticket sales on this day is $1900.

Math has several different subfields, including algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.

Elementary algebra is crucial for all mathematical applications since it deals with the manipulation of variables, which are frequently represented by Roman letters, as though they were numbers. The study of algebraic structures such as groups, rings, and fields is known as abstract algebra, mostly in education (the term is no more in common use outside educational context). In contemporary presentations of geometry, linear algebra—which deals with linear equations and linear mappings—is used.

Given,

Number of adult tickets sold by zoo=43

And number of child tickets sold by zoo=80

Also given that,

The cost of each adult ticket=$20

And the cost of each child ticket=$13

20 x 43 = 860

80 x 13 = 1040

860 + 1040 = 1900

Therefore, the total amount of ticket sales on this day is $1900

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The complete question is:

"Question A zoo sells 43 adult tickets and 80 child tickets in one day. Each adult ticket costs $20 and each child ticket costs $13.

What is the total amount of ticket sales on this day?

Enter your answer in the box.

$="

Answer:

Solution of the given equation by elimination method is x=0.5 and y=5.

Step-by-step explanation:

8x + 7y = 39 --------------(1)

4x - 14y = -68 ------------(2)

Multiply the equation 2 by -2, then add the equations along.

Equation (2) multiply by -2 :  -8x +28y = 136

8x + 7y = 39 --------------(1)

-8x +28y = 136-----------(2)

Add these equations to eliminate x:

0x+35y=175

35y=175

y=5

Substitute y=5 in 8x+7y=39:

8x+(7)(5) =39

8x+35=39

8x=39-35

8x=4

X=8/4

x=0.5

Solution of the given equation by elimination method is x=0.5 and y=5.

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Answer:

It is a observational study

Step-by-step explanation:

  We calculated from the graph that 10542719 people expected to have type O blood.

Generally, human body contains any of these four common types of blood. These are type A, B, O and AB.

If we want to estimate our population containing different blood group. we need to carry out survey study to colect data.

Given, Estimated population in 2010 =21515754

the population in percentage who may have O type blood =49%

Actual number of people who expected to have O type blood =

(21515754×49)/100

=10542719

hence, total 10542719 people expected to have O type blood.

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Total $234.95 is the cost of 5 band shirts and 5 pair of pants.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given, Molly bought 4 band shirts and 3 pair of pants for $159.99.

And Christian bought 3 band shirts and 2 pair of pants for $113.00.

Let x be the band shirts and y be the pair of pants.

So, according to the question;

4x + 3y = 159.99         equation 1

3x + 2y = 113                equation 2

Now, we have the system of the equations.

In order to solve the system of equations:

Multiply 4 to the equation 2 and multiply 3 to the equation 2.

12x + 9y = 479.97

12x + 8y = 452

Subtracting the transformed equation 2 to transformed equation 1.

y = 27.97

Then 12x = 479.97 - 251.73

 12x = 228.24

x = 228.24 / 12

x = 19.02.

To find the amount of 5 band shirts and 5 pair of pants:

5x + 5y

= 5 (19.02) + 5(27.97)

= 95.1 + 139.85

= 234.95

Therefore, 5 band shirts and 5 pair of pants cost $234.95.

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The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .

In the question ,

it is given that ,

the differential equation is

y'' + 9y + 5y³ = Cos(10t)   ...equation(1)

y(0) = 0, y'(0) = 1

for y = 0 , the differential equation is

y''(0) + 9y(0) + 5{y(0)}³ = Cos90)

y''(0) + 9 + 5 = 1 ;

y''(0) = 1.

differentiating equation(1) with respect to "t" , we have

y''' + 9y' + 15y²y' = -10Sin(10t)

y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)

y'''(0) + 9 + 0 = 0

y'''(0) = -9

The Taylor series is given by

y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....

Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have

y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....

= t + t²/2 - 3/2.t³ + ...

Therefore , the first three terms are t , t²/2 , -3/2.t³   .

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y = 3 + tan (π/4)x , this is the equation of transformed graph of tangent with period 4 that has been shifted vertically up 3 units.

Our parent function:

y = tan x

Let's apply the vertical shift now:

y = 3 + tan x

Now the period. This is a little tricky because we have to remember that the period is equal to π/b, because tangent functions normally have a period of π, and the b is the value placed in front of the x.

In this case, that value would have to be π/4

π/(π/4) = 4

Therefore, our b-value is π/4 and our final equation is as follows:

y = 3 + tan (π/4)x

The question is :

write the equation of the transformed graph of tangent with period 4 that has been shifted vertically up 3 units

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A relation R on N that is reflexive and symmetric but not transitive of example is { N , ME , MA } .

Given :

Let N be set of New England states {ME, NH, VT, MA, CT, RI }. (See map provided.) (Note that Maine is abbreviated as ME and Massachusetts as MA.) For each of the following parts, either give an example of a relation on the set of New England states N that has the noted properties, or else show that no such relation exists.

a )

A relation R on N that is reflexive and symmetric but not transitive of example is { N , ME , MA } .

b )

A relation S on N that is reflexive and transitive but not symmetric is { MA , CT , RI } .

c )

A relation T on N that is transitive and symmetric but not reflexive is { ME , NH , VT } .

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