a wireless carrier offers the following plans that a person is considering. the family plan: $100 monthly fee, unlimited talk and text on up to 5 lines, and data charges of $35 for each device for up to 2 gb of data per device. the mobile share plan: $140 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $15 for each device up to a shared total of 10 gb of data. find the model of the total cost of the family plan in dollars. use p for the number of devices that need data plans as part of their cost.

In summary This is the solution to the differential equation (2x-1)dx+(7y+3)dy=0.

Why is it?

To solve for (2x-1)dx+(7y+3)dy=0, we need to find a function whose differential is (2x-1)dx+(7y+3)dy.

We can do this by integrating both sides with respect to their respective variables:

∫(2x-1)dx + ∫(7y+3)dy = 0

Integrating the first term with respect to x gives:

x²2 - x + C1

where C1 is the constant of integration.

Integrating the second term with respect to y gives:

7/2 y²2 + 3y + C2

where C2 is the constant of integration.

So the general solution to the differential equation is:

x²2 - x + C1 + 7/2 y²2 + 3y + C2 = 0

We can simplify this by combining the constants into a single constant, say C:

x²2 - x + 7/2 y²2 + 3y + C = 0

This is the solution to the differential equation (2x-1)dx+(7y+3)dy=0.

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The mass of the solid sphere of radius 4 is (2048/9)kπ.

To find the mass, M, of the solid sphere with the given characteristics, we can integrate the mass density over the volume of the sphere.

Let's denote the mass density as ρ and the distance from the center of the sphere as r.

Given that the mass density is proportional to the square of the distance, we can write:

ρ = \(k * r^2\), where k is the constant of proportionality.

The volume of a sphere is given by V = (4/3)πr^3, where r is the radius.

In this case, the radius of the sphere is given as 4.

Substituting the expression for ρ into the volume integral, we have:

M = ∫ρ dV

 = ∫\((k * r^2)\) dV

 = ∫\((k * r^2) ((4/3)\pi r^3)\) dr

Now, let's substitute the given values:

M = k * (4/3)π * ∫\(r^5\) dr

 = k * \((4/3)\pi * [r^6/6]\)(from 0 to 4)

Evaluating the integral limits, we get:

M = \(k * (4/3)\pi * [(4^6)/6 - (0^6)/6]\)

\(= k * (4/3)\pi * (4096/6)\\ = k * (4/3)\pi * (2048/3)\)

Therefore, the mass of the solid sphere, M, is (2048/9)kπ.

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The required angular speed of the propeller in 4000 rev per min π radians per sec is approximately 133.333 radians per second.

Given that a 80-horsepower outboard motor at full throttle will rotate its propeller at exactly 4000 revolutions per min.

We need to find the angular speed of the propeller in 4000 rev per min π radians per sec

.To find the angular speed of the propeller in 4000 rev per min π radians per sec, we know that1 revolution = 2π radiansTherefore,4000 revolutions

= 4000 × 2π radians

= 8000π radians

∴ Angular speed of propeller in 4000 rev per min π radians per sec

= (8000π radians/minute)/(60 sec/minute)

= (8000π/60) radians per second

= 133.333 radians per second (approx)

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The sum of the fractions 1/3 + 2/5 + 1/6 is 9/10. .To calculate the sum of fractions mentally using the properties of fraction addition, we can utilize the property of a common denominator.

By finding a common denominator for the fractions, we can add them together. Here's an example:

Suppose we want to calculate the sum of the fractions 1/3 + 2/5 + 1/6.

Find the common denominator:

To add fractions, we need a common denominator. In this case, the least common multiple (LCM) of the denominators 3, 5, and 6 is 30. Therefore, we can use 30 as the common denominator for all the fractions.

Convert the fractions to have a common denominator:

To convert each fraction to have a denominator of 30, we need to multiply both the numerator and denominator of each fraction by a suitable factor. Let's do that for each fraction:

1/3 = (1 * 10)/(3 * 10) = 10/30

2/5 = (2 * 6)/(5 * 6) = 12/30

1/6 = (1 * 5)/(6 * 5) = 5/30

Now, all three fractions have a common denominator of 30.

Add the fractions together:

Now that the fractions have a common denominator, we can simply add the numerators together while keeping the denominator the same:

10/30 + 12/30 + 5/30 = (10 + 12 + 5)/30 = 27/30

Simplify the fraction (if needed):

If possible, simplify the fraction. In this case, the numerator and denominator have a common factor of 3:

27/30 = (9 * 3)/(10 * 3) = 9/10

So, the sum of the fractions 1/3 + 2/5 + 1/6 is 9/10.

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(i) The parameters of the MA(1) model are:

   θ: The coefficient of the lagged error term, representing the strength and direction of the dependence between the current observation and the previous one.

   σ^2: The variance of the white noise error term, representing the randomness or noise in the model.

(ii) In the MA(1) model, μ(t) is the mean of the process, which is typically assumed to be zero since the model assumes stationary data. P(s,t) represents the auto covariance between time points s and t. For the MA(1) model, P(s,t) = σ^2 * θ^|s-t| (|s-t| represents the absolute difference between s and t).

(iii) A typical plot of an MA(1) process would show a series of observations with a dependence on the previous observation, followed by a rapid decay in dependence as the lag increases.

The plot may appear to oscillate around a mean of zero, exhibiting short-term patterns or shocks that dissipate over time. The pattern would resemble a damped sinusoidal or wave-like behavior with decreasing magnitude.

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Answer:

I think A  but if im wrong tell me sorry if it wrong

Step-by-step explanation:

Answer:

8 is 2 answers. the answer is A

Answer:

look at the picture .......................

Answer:

A.]A chord of a circle of diameter 40 cm subtends an angle of 70° at the centre of the circle.

Solution given;

diameter [d]=40cm

centre angle [C]=70°

(a) Find the perpendicular distance be tween the chord and the centre of the circle.

Answer:

we have

the perpendicular distance be tween the chord and the centre of the circle=[P]let

we have

P=d Sin (C/2)

=40*sin (70/2)

=22.9cm

the perpendicular distance be tween the chord and the centre of the circle is 22.9cm.

(b) Using = 3.142, find the length of the minor arc.

Solution given;

minor arc=\(\frac{70}{360}*πd=\frac{7}{36}*3.142*40\)

=24.44cm

the length of the minor arc. is 24.44cm.

B.]In the diagram, XZ is a diameter of the cir cle XYZW, with centre O and radius 15/2 cm.

If XY = 12 cm, find the area of triangle XYZ.

Solution given:

XY=12cm

XO=15/2cm

XZ=2*15/2=15cm

Now

In right angled triangle XOY [inscribed angle on a diameter is 90°]

By using Pythagoras law

h²=p²+b²

XZ²=XY²+YZ²

15²=12²+YZ²

YZ²=15²-12²

YZ=\(\sqrt{81}=9cm\)

:.

base=9cm

perpendicular=12cm

Now

Area of triangle XYZ=½*perpendicular*base

=½*12*9=54cm²

the area of triangle XYZ is 54cm².

Answer:

a)

d = 40 cm ⇒ r = 20 cm

Let the perpendicular distance is x.

Connecting the center with  the chord we obtain a right triangle with hypotenuse of r and leg x with adjacent angle of 70/2 = 35°.

From the given we get:

b)

The minor arc is 70° and r = 20

The length of the arc is:

Since XZ is diameter, the opposite angle is the right angle, so the triangle XYZ is a right triangle.

Find the missing side, using Pythagorean:

The area of the triangle:

The closest answer choice to this result is C: 5%, which is not very close. Therefore, the correct answer is not given as a choice The total area of Kelly's home is: 2,100 square feet.

2,100 square feet

To find the percentage of Kelly's home that is taken up by her office, we need to calculate the area of her office and divide it by the total area of her home.

The area of Kelly's office is:

812 feet x 1214 feet = 986,768 square feet

The total area of Kelly's home is:

2,100 square feet

To find the percentage of Kelly's home taken up by her office, we divide the area of her office by the total area of her home and then multiply by 100 to convert the answer to a percentage.

(986,768 square feet / 2,100 square feet) x 100 = 469.41%

This means that Kelly's office takes up almost 470% of her home, which doesn't make sense because it's impossible for an office to take up more area than the entire home.

The error occurred because we calculated the area of Kelly's office in square feet, but we need to calculate it in square feet relative to her entire home.

To do this, we need to divide the area of her office by the area of her home and then multiply by 100 to convert the answer to a percentage.

(986,768 square feet / 2,100 square feet) x 100 = 47%

Therefore, approximately 47% of Kelly's home is taken up by her office.

The closest answer choice to this result is C: 5%, which is not very close. Therefore, the correct answer is not given as a choice

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Answer:

(a+4)(a-4)=a²-4²   ITS LIKE THIS BECAUSE ITS AN IDENTITY,

               ⇒a²-16

Even when we solve it by the regular method of solving polynomials we get a²-16 as answer as there and thats the proof for the identity.

(a+b)(a-b)=a(a-4)+4(a-4)

⇒a²-4a+4a-16

⇒a²-16[NOTE:-4a+4a=0]

Thus we can see that a²-16 is the answer we get when we try to solve it by regular polynomial solution tooo.

And a²-16 is the polynomial from which we get (a+4)(a-4)

Answer:

Step-by-step explanation:

Given:

This figure gives us 180 degrees of angles.

Calculate the angle of x in the figures according to the term x on one side of the equation.

The angle relationship should be represented by 2x.

2x+75=180

First, subtract by 75 from both sides.

2x+75-75=180-75

Solve.

Subtract the numbers from left to right.

180-75=105

2x=105

Divide by 2 from both sides.

2x/2=105/2

Solve.

Divide the numbers from left to right.

105/2=52.5

x=105/2=52.5

I hope this helps. Let me know if you have any questions.

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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Given an AR(1) process with drift X = α + βX_{t-1} + ε_t, where α = 2, β = 0.7, and ε_t ~ N(0, 1).To find the mean of the process, we note that the AR(1) process has a mean of μ = α / (1 - β).

So, the mean is 6.67, the variance is 5.41, the first three ACF are 0.68, 0.326, and 0.161, and the first three PACF are 0.7, -0.131, and 0.003.

So, substituting α = 2 and β = 0.7,

we have:μ = α / (1 - β)

= 2 / (1 - 0.7)

= 6.67

To find the variance, we note that the AR(1) process has a variance of σ^2 = (1 / (1 - β^2)).

So, substituting β = 0.7,

we have:σ^2 = (1 / (1 - β^2))

= (1 / (1 - 0.7^2))

= 5.41

To find the first three autocorrelation functions (ACF) and the first 3 partial autocorrelation functions (PACF), we can use the formulas:ρ(k) = β^kρ(1)and

ϕ(k) = β^k for k ≥ 1 and

ρ(0) = 1andϕ(0) = 1

To find the first three ACF, we can substitute k = 1, k = 2, and k = 3 into the formula:

ρ(k) = β^kρ(1) and use the fact that

ρ(1) = β / (1 - β^2).

So, we have:ρ(1) = β / (1 - β^2)

= 0.68ρ(2) = β^2ρ(1)

= (0.7)^2(0.68) = 0.326ρ(3)

= β^3ρ(1) = (0.7)^3(0.68)

= 0.161

To find the first three PACF, we can use the Durbin-Levinson algorithm: ϕ(1) = β = 0.7

ϕ(2) = (ρ(2) - ϕ(1)ρ(1)) / (1 - ϕ(1)^2)

= (0.326 - 0.7(0.68)) / (1 - 0.7^2) = -0.131

ϕ(3) = (ρ(3) - ϕ(1)ρ(2) - ϕ(2)ρ(1)) / (1 - ϕ(1)^2 - ϕ(2)^2)

= (0.161 - 0.7(0.326) - (-0.131)(0.68)) / (1 - 0.7^2 - (-0.131)^2) = 0.003

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Answer:

umm there is no answer u have to make a diagram of the rational and irratinal or the area of numbers its not a letter u have to make a diagram

Step-by-step explanation:

The scalar λ can be given a value of -15.

We apply the principle of dot product and cross product between vectors to arrive at the solution.

The Dot Product of two vectors A and B is defined as:

A.B = |A|*|B|*Cosθ

where |A| and |B| are the magnitudes of the respective vectors.

Similarly, the Cross Product is defined as:

A×B = |A|*|B|*Sinθ * n,

where n is a vector perpendicular to both A and B.

Thus, A.B is a scalar quantity, but A×B is a vector.

We will apply both principles to arrive at a solution.

A+B and A-λB are perpendicular to each other.

Thus,

(A+B).(A-λB) = 0, since Cos90 = 0

A.A - λ(A.B) + B.A - λ(B.B) = 0

The dot product of a vector with itself is just the product of their magnitudes, as the angle between them is 0.

|A|² - λ|B|² + (1-λ)A.B = 0

A.B = |A|*|B| Cos 120 = -|A||B|/2 = -3|B|²/2               (Since |A| = 3|B|)

=> The prior equation can be further simplified as:

9|B|² - λ|B|² +(1-λ)(-3|B|²/2 ) = 0

|B|² {9 - λ +(3λ - 3)/2} = 0

Since |B| cannot be zero for obvious reasons, the rest of the expression is zero.

9 - λ +(3λ - 3)/2 = 0

18 - 2 λ + 3 λ - 3 = 0

λ = -15

Thus the scalar λ is equal to 15 for the two vectors to be perpendicular.

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Answer:

Please check explanation for answers

Step-by-step explanation:

1. the three main functions of trigonometry are;

The sine

The cosine

The tangent

2. The hypotenuse is opposite the right angle. The opposite side is opposite the reference angle. The adjacent side is next to the reference angle

3. The opposite and adjacent are the sides which are interchangeable depending on the reference angle.

4. SOHCAHTOA

SOH means ;

Sine = opposite/hypotenuse

CAH;

cosine = Adjacent/Hypotenuse

TOA;

Tangent = opposite/adjacent

Answer:

x=6

Step-by-step explanation:

FG + GH = FH

4+x-3 = 2x-5

Combine terms

x+1 = 2x-5

Subtract x from each side

x+1-x = 2x-5-x

1 = x-5

Add 5 to each side

1+5 = x-5+5

6 =x

Answer:

x=6

Step-by-step explanation:

F G + G H = F H

4+x-3 = 2x-5

Answer:he can read 1 and 3/12 or 15/12 books in an hour.

Step-by-step explanation:

Answer:

He can read 1 and 3/12 or 15/12 book in an hour.

Step-by-step explanation:

Forgive me if i am wrong

Answer:

2

f(x)= -x + 1

2

g(x) = -x + 6x +5

2

h(x)= +ax + bx -c ( its form should be like that )

Answer:

18 = x

Step-by-step explanation:

BE bisects CBD so that means

1/2 CBD = CBE

1/2 (94) = 3x-7

47 = 3x-7

Add 7 to each side

47+7 = 3x-7+7

54 = 3x

Divide by 3

54/3 = 3x/3

18 = x

Answer:

if nth term of the AP 3,10,17.... is same as the nth term of the AP 63,65,67.... find n.

Step-by-step explanation:

please solve this also it's hard for me

Answer:

Step-by-step explanation:

By further evaluating your question, I concluded based on my observation that the equation you asked must be this one:

\(x^{2} -10x + y^{2} +6y -30\) = 0 or \(x^{2} -10x + y^{2} +6y = 30\)

by completing the square formula of the x and y, you can get the center point of the circle

(1) \([x^{2} -10x+25] +[y^{2} +6y+9] = 30 + 25 + 9\)

(2) \((x-5)^{2} +(y+3)^{2} = 64\)

this would give us the center point of (5,-3) and the radius of 8 units.

Area = \(\pi x 8^2\)

Area = 200.96 sq. units

The salaries will be the same in year 20 and she will be earning $80,000. So, the first option is correct.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

                  y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

We will first create an equation to represent the data.

To find the slope we use the formula

m = (y₂-y₁)/(x₂-x₁)

= (60,000-55,000) / (12-10)

= 5,000/2 = 2500

Writing this in point-slope form, we have

y-y₁ = m(x-x₁)

y-55,000 = 2500(x-10)

Converting to slope-intercept form,

y-55,000 = 2500 × x - 2500 × 10

y - 55,000 = 2500x - 25,000

y = 2500x + 30,000  

Now we set this equal to the equation from the graph:

2500x + 30,000 = 2000x + 40,000

Subtract 2000x from both sides:

2500x + 30,000 - 2000x = 2000x + 40,000 - 2000x

500x + 30,000 = 40,000

500x = 40,000 - 30,000

500x = 10,000

x = 10,000/500

x = 20

The salaries will be the same in year 20.

y= 2000(20) + 40,000

y= 40,000 + 40,000

= 80,000

The salary in year 20 will be $80,000.

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\(4a^4-8a^2+4=0\implies 4(a^4-2a^2+1)=0\implies a^4-2a^2+1=0 \\\\\\ (a^2)^2-2a^2+1=0\implies (a^2-1)(a^2-1)=0\implies a^2=1 \\\\\\ a=\pm\sqrt{1}\implies a=\pm 1\)

Answer:

See below

Step-by-step explanation:

The chi-squared analysis aims to check whether observed frequencies in one or more categories match up with expected frequencies. I don't see any answer choices, but hopefully this short explanation will help!

The maximum abundance of species 1 if 250 of species 2 coexists with it is B. 500.

Determine the carrying capacity ratio between species 1 and 2.
Carrying capacity of species 1 = 1000
Carrying capacity of species 2 = 500
Ratio = 1000 / 500 = 2

Calculate the abundance of species 1 considering the presence of species 2.
Abundance of species 2 = 250
Abundance of species 1 = 2 * 250 = 500

So, the maximum abundance of species 1 if 250 of species 2 coexists with it is 500 (Option B).

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The monthly salary of Ward based on this annual salary is 5.53k

Annual salary = 66.4k

There are 12 months in a year

Monthly salary= Annual salary / 12

= 66.4k / 12

= 5.533333333333333

Approximately,

5.53k per month

Therefore, Ward receives monthly salary of 5.53k

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