MAKE SURE TO SAY HOW TO GOT THE ANSWER SO I CAN HELP OTHERS AND SHOW MY MOM THIS!

Answer:

the answer is

Step-by-step explanation:

replace n with 5 and you got 3200

The 5th term of the sequence is 3200 therefore the correct option is option D.

A sequence is a collection of numbers (or other items such as geometric objects) that follow a pattern or function.

The function for a sequence is f(n) \(=200\times2^{n-1}\)

Where n represents the term.

So for the 5th term

f(5) \(=200\times2^{5-1}\\\)

     \(=200\times2^{4}\)

     = 200 × 16

     = 3200

Hence the 5th term of the sequence is 3200.

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The extreme points (x, y) along the curve are (-1, -1) and (0, 0).

The given function f(I, y) = e² x² + xy + y² = 1 represents a quadratic equation in two variables, x and y. To find the extreme points, we need to determine the values of x and y that satisfy the equation and minimize or maximize the function.

a) The function defined by f(x, y) = e² x² + xy + \(y^2\) - 1 takes on a minimum and a maximum value along the curve.

To find the extreme points, we need to find the critical points of the function where the gradient is zero.

Step 1: Calculate the partial derivatives of f with respect to x and y:

∂f/∂x = 2\(e^2^x\) + y

∂f/∂y = x + 2y

Step 2: Set the partial derivatives equal to zero and solve for x and y:

2\(e^2^x\) + y = 0

x + 2y = 0

Step 3: Solve the system of equations to find the values of x and y:

Using the second equation, we can solve for x: x = -2y

Substitute x = -2y into the first equation: 2(-2y) + y = 0

Simplify the equation: -4e² y + y = 0

Factor out y: y(-4e^2 + 1) = 0

From this, we have two possibilities:

1) y = 0

2) -4e²  + 1 = 0

Case 1: If y = 0, substitute y = 0 into x + 2y = 0:

x + 2(0) = 0

x = 0

Therefore, one extreme point is (x, y) = (0, 0).

Case 2: If -4e^2 + 1 = 0, solve for e:

-4e²  = -1

e²  = 1/4

e = ±1/2

Substitute e = 1/2 into x + 2y = 0:

x + 2y = 0

x + 2(-1/2)x = 0

x - x = 0

0 = 0

Substitute e = -1/2 into x + 2y = 0:

x + 2y = 0

x + 2(-1/2)x = 0

x - x = 0

0 = 0

Therefore, the second extreme point is (x, y) = (0, 0) when e = ±1/2.

b) The equation (1+x)e = (1+y)e* is satisfied along the line y = x.

To find a critical point on this line where the equation is neither locally uniquely solvable for x nor y, we need to find a point where the equation has multiple solutions.

Substitute y = x into the equation:

(1+x)e = (1+x)e*

Here, we see that for any value of x, the equation is satisfied as long as e = e*.

Therefore, the equation is not locally uniquely solvable for x or y along the line y = x.

c) Taylor expansion up to degree 2:

To understand the solution set of the equation in the vicinity of the critical point, we can use Taylor expansion up to degree 2.

2. Expand the function f(x, y) = e²x²  + xy + \(y^2\) - 1 using Taylor expansion up to degree 2:

f(x, y) = f(a, b) + ∂f/∂x(a, b)(x-a) + ∂f/∂y(a, b)(y-b) + 1/2(∂²f/∂x²(a, b)(x-a)^2 + 2∂²f/∂x∂y(a, b)(x-a)(y-b) + ∂²f/∂y²(a, b)(y-b)^2)

The critical point we found earlier was (a, b) = (0, 0).

Substitute the values into the Taylor expansion equation and simplify the terms:

f(x, y) = 0 + (2e²x + y)(x-0) + (x + 2y)(y-0) + 1/2(2e²x² + 2(x-0)(y-0) + 2(\(y^2\))

Simplify the equation:

f(x, y) = (2e² x² + xy) + ( x² + 2xy + 2\(y^2\)) + e² x² + xy + \(y^2\)

Combine like terms:

f(x, y) = (3e² + 1)x² + (3x + 4y + 1)xy + (3 x² + 4xy + 3 \(y^2\))

In the vicinity of the critical point (0, 0), the solution set of the equation, given by f(x, y) = 0, looks like a second-degree polynomial with terms involving  x² , xy, and  \(y^2\).

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Answer: x=10

Step-by-step explanation:

\(4(x+3)=x+42\\4x+12=x+42\\4x-x=42-12\\3x=30\\x=10\)

A graph's correlation between two variables reveals the relationship between them. The correlation is given a name based on the characteristics of the variables represented on the graphs.

What does the term correlation mean?

The data points of a person with two different factors are related in a scatterplot. The term "correlation" refers to this connection.

A correlation is the relationship between any two variables represented on any graph.

The correlation is divided into three main categories based on the sort of relationship between the variables. Those are

i) Positively correlation

ii) Negative correlation

iii) No correlation

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Answer:

w= 59/5 or 11.8

Step-by-step explanation:

-3(w+4)+8(w-6)=1/2(18-20)

-3w-12+8w-48=9-10

5w-60=-1

5w=-1+60

5w=59

w=59/5

Answer:

See below

Step-by-step explanation:

geckos are  1  out of (1+3)  = 1/4 th

1/4th * 80 = 20 geckos

Answer:

0.875

Step-by-step explanation:

you just divide 7 by 8, and you would get 0.875

7/8=0.875

Answer:

Step-by-step explanation:

6x = 54

x = 54 /6

x=9

therefore value of x is 9

Answer:

6x=54 if x =9 because 54/6 equals nine

Step-by-step explanation:

Amanda should save $115 each month for retirement .Answer A is correct

To calculate how much Amanda should save each month, we need to determine 5% of her monthly income as a dental assistant.

A 5% savings rate means she needs to save 5% of her monthly income, which is $2300. To find this amount, we can multiply her income by 5%:

$2300 * 0.05 = $115

Therefore, Amanda should save $115 each month for retirement.

Option (d) $115 is the correct answer. The other options, (a) $11500, (b) $460, and (c) $46, are incorrect because they do not correspond to 5% of Amanda's monthly income.

By saving $115 each month, Amanda will accumulate savings for her retirement over time. It's important to note that retirement savings should be tailored to individual circumstances, goals, and any additional financial commitments or considerations. Amanda may want to consult with a financial advisor to discuss her specific retirement plans and determine the most suitable savings strategy for her long-term financial security. Answer A is correct

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Answer:

258.39 m^2

Step-by-step explanation:

Solve for the rectangle:

18 • 12= 216

Now solve for the 3 semi circles:

A = 3.14(3)^2= 28.26/2 = 14.13 •3 = 42.39

Add up the areas:

216 + 42.39 = 258.39

Answer:

It is a little hard to see where your steps are for the equation, but x = 4, and I will explain:

Step-by-step explanation:

We know y = -1.5x +4, so we plug that into the equation

6x - 5(-1.5 + 4) = 34

6x +7.5x - 20 = 34    Here we distributed the -5 into the parenthesis.

13.5x -20 = 34

13.5 = 54

x = 4

Hope this helps!

Lin got it wrong when solving the system of equations because;

She made the mistake of leaving 7.5x as negative instead of making it positive after multiplying out the bracket.

6x - 5y = 34   ---(eq 1)

3x +2y = 8  ---(eq 2)

2y = 8 - 3x

divide each term by 2 to get;

y = 4 - 1.5x

This corresponds to what she got and it is correct.

6x - 5(4 - 1.5x) = 34

Multiplying out the bracket gives;

6x - 20 + 7.5x = 34

Let's simplify the left side by adding terms with x to get;

13.5x - 20 = 34

Add 20 to both sides to get;

13.5x = 54

x = 54/13.5

x = 4

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The x-intercept for the given equation is x = -3.

Given is an equation 2x-y = -6, we need to find the x-intercept for the line,

So the x-intercept of a line is the point where it cuts the x-axis,

To find the x-intercept we will put y = 0,

So,

2x - 0 = -6

2x = -6

x = -3

Or, you can just see the points from which it is passing the x-values will be the x-intercept,

Hence the x-intercept of the line is x = -3.

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Answer:

Step-by-step explanation:

We can use the quadratic formula to get the answer to this

Quadratic Formula: -b +- √b² - 4ac/2a

Once we input A, B, and C into this, and solve any multiplication, we get

x = -1  +- √1 + 20/2

We divide by 2a, which 2a = 2.

-0.5 +- 10.5.

these are the following values of x:

x = 10

x = 11

Pretty sure this is it, hope it helps!

y(x) = (1/6)x^2 - (8/9)x - 127/18.

Find the function of y(x) ?

To find the function y(x) that satisfies the given differential equation and initial condition, we can integrate the equation with respect to x.

Starting with the given differential equation:

dy/dx = (3x - 8)/9

We integrate both sides with respect to x:

∫dy = ∫(3x - 8)/9 dx

Integrating, we get:

y = ∫(3x - 8)/9 dx

Now, let's integrate each term separately:

y = (1/9) ∫(3x - 8) dx

= (1/9) [(3/2)x^2 - 8x] + C

Where C is the constant of integration.

To find the value of C, we can use the initial condition y(-1) = -6. Plugging in x = -1 and y = -6 into the equation, we have:

-6 = (1/9) [(3/2)(-1)^2 - 8(-1)] + C

-6 = (1/9) [(3/2) + 8] + C

-6 = (1/9) [3/2 + 16/2] + C

-6 = (1/9) (19/2) + C

-6 = 19/18 + C

To isolate C, we can subtract 19/18 from both sides:

C = -6 - 19/18

C = -108/18 - 19/18

C = -127/18

Now we substitute the value of C back into the equation:

y = (1/9) [(3/2)x^2 - 8x] - 127/18

Simplifying further, we have:

y = (1/6)x^2 - (8/9)x - 127/18

Therefore, the function y(x) that satisfies the given differential equation dy/dx = (3x - 8)/9 and the initial condition y(-1) = -6 is:

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Answer:

xy^7 - x^a y^b = 0

The exact values are:

a. sin2θ = -8√209/225

b. cos2θ = 193/225

c. tan2θ = -349448 × √209 / 8392633

To find the values of sin2θ, cos2θ, and tan2θ, we can use the double angle identities. Let's start by finding sin2θ.

Using the double angle identity for sine:

sin2θ = 2sinθcosθ

Since we know sinθ = 4/15, we need to find cosθ. To determine cosθ, we can use the Pythagorean identity:

sin²θ + cos²θ = 1

Substituting sinθ = 4/15:

(4/15)² + cos²θ = 1

16/225 + cos²θ = 1

cos²θ = 1 - 16/225

cos²θ = 209/225

Since θ lies in quadrant II, cosθ will be negative. Taking the negative square root:

cosθ = -√(209/225)

cosθ = -√209/15

Now we can substitute the values into the double angle identity for sine:

sin2θ = 2sinθcosθ

sin2θ = 2 × (4/15) × (-√209/15)

sin2θ = -8√209/225

Next, let's find cos2θ using the double angle identity for cosine:

cos2θ = cos²θ - sin²θ

cos2θ = (209/225) - (16/225)

cos2θ = 193/225

Finally, let's find tan2θ using the double angle identity for tangent:

tan2θ = (2tanθ) / (1 - tan²θ)

Since we know sinθ = 4/15 and cosθ = -√209/15, we can find tanθ:

tanθ = sinθ / cosθ

tanθ = (4/15) / (-√209/15)

tanθ = -4√209/209

Substituting tanθ into the double angle identity for tangent:

tan2θ = (2 × (-4√209/209)) / (1 - (-4√209/209)²)

tan2θ = (-8√209/209) / (1 - (16 ×209/209²))

tan2θ = (-8√209/209) / (1 - 3344/43681)

tan2θ = (-8√209/209) / (43681 - 3344)/43681

tan2θ = (-8√209/209) / 40337/43681

tan2θ = -8√209 × 43681 / (209 × 40337)

tan2θ = -349448 ×√209 / 8392633

Therefore, the exact values are:

a. sin2θ = -8√209/225

b. cos2θ = 193/225

c. tan2θ = -349448 × √209 / 8392633

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Answer:

3 terms, trinomial

Step-by-step explanation:

Answer:

Huh?

Step-by-step explanation:

I don't get question

Answer:

Point form:

(1, -1)

Equation form:

x=1, y=-1

Step-by-step explanation:

I hope the work wasnt part of the assignment cause i really have trouble showing mine.

Answer:

2, 10, 50, 250

Step-by-step explanation:

Using the formula with a₁ = 2 , then

a₂ = 5a₁ = 5 × 2 = 10

a₃ = 5a₂ = 5 × 10 = 50

a₄ = 5a₃ = 5 × 50 = 250

The first 4 terms are 2, 10, 50, 250

The correct option is False. The standard formulas for the derivatives of sine and cosine are true when the angle is in radians. These formulas are derived based on the properties of the trigonometric functions in the context of radians. The derivatives of sine and cosine with respect to an angle measured in radians are as follows:

\(\[\frac{d}{dx}(\sin(x)) = \cos(x)\]\)

\(\[\frac{d}{dx}(\cos(x)) = -\sin(x)\]\)

If the angle is measured in degrees, these formulas would not hold true. To differentiate trigonometric functions when the angle is measured in degrees, conversion factors and additional adjustments would be necessary.

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According to Dr. Aguilera's findings, excessive levels of anxiety are associated with poor academic performance. Sleep duration, on the other hand, is unrelated to excellent or poor academic performance.

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Apply the exponent rule x^a /x^b = x ^(a-b)

10^15 / 10^5 = 10^(15-5) = 10^10

Apple exponent rule: a^x/a^b = a^x-y

10^15/10^5 = 10^15-5 = 10^10

Best of Luck!

Therefore, the correct option is b. 0.317.

We are given that a bag contains 8 purple marbles and 12 green marbles.

A marble is drawn and then replaced.

This is done 40 times.

We need to find the probability that a purple marble is drawn at most 15 times.

Let X be the number of purple marbles drawn in 40 draws.

Then, X is a binomial random variable with n = 40 and p = 8/20 = 0.4

We are to find the probability that X ≤ 15.

Using the binomial probability formula, we have:P(X ≤ 15)

= ∑P(X = r),

where the summation is taken over all possible values of r from 0 to 15.

P(X = r) = nCr p^r (1-p)^(n-r),

where nCr = n!/[r!(n-r)!]

Hence,P(X ≤ 15) = ∑P(X = r) (for r = 0, 1, 2, ..., 15)

= P(X = 0) + P(X = 1) + P(X = 2) + ....... + P(X = 15)

We can use binomial probability tables or a calculator to find the above probabilities and sum them up.

After rounding to three decimal places, we get :P(X ≤ 15) = 0.317

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Average of given n numbers X1,X2,.........,Xn is x= £xi/n

Let the my number be x

Given:- The average of 3,15,x is 40

£xi/n =40

3+15+x/3=40

Multiplying 3 both side

18+x=120

x=120-18

x=102

Hence, my number is 102

We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

File < Options < (A) Formulas < Automatic

We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

Therefore, File < Options < (A) Formulas < Automatic

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The complete question is given below:

What would you choose as X in the given series of clicks to calculate formulas automatically: File < Options < X < Automatic?

a. Formulas

b. Language

c. Proofing

d. Advanced

We are given a problem regarding trigonometric identities and asked to resolve for theta.

Recall that:

Therefore, we have:

In radians, we have: