Leta1, a2 a3 be a sequence defined by a1 = 1 and ak = 2ak-1 . Find a formula for an and prove it is correct using induction.

Answer:

5

Step-by-step explanation:

Experimental probability = number of tunes an event occurred / total number of trials

Experimental probability of getting head :

10 /12 = 0.833333

Expected number of heads from next 6 flips :

Experimental probability = expected number of heads / number of trials

0.833333 = x / 6

0.83333 * 6 = 5

5 times

The total number of flops required to solve the system is approximately 2ns.

Let R be an n x n upper-triangular matrix with semiband width s. Show that the system Rx = y can be solved by back substitution in about 2ns flops. An analogous result holds for lower-triangular systems.Back substitution is an efficient technique for solving systems of linear equations in matrix form.

This is because back substitution only works on upper- or lower-triangular matrices, which have certain features that make solving systems of equations easier.The back substitution algorithm starts by solving the first equation of the system and obtaining a solution for the first variable. It then uses this value to solve the second equation and obtain a solution for the second variable.

This process is continued until all the variables are solved for.Let R be an n x n upper-triangular matrix with semiband width s. The semiband width of a matrix is the maximum number of nonzero entries in any row or column of the matrix. This means that all entries below the diagonal of R are zero. Let y be a vector of length n.

We want to solve the system Rx = y using back substitution.Since R is upper-triangular, we can solve for the last variable x_n first. This only requires one multiplication and one subtraction. We can then use the value of x_n to solve for the second-to-last variable x_{n-1}, which requires two multiplications and two subtractions.

Continuing in this way, we can solve for all the variables x_1, x_2, ..., x_n, each time requiring one more multiplication and subtraction than the previous step.In total, the number of flops required to solve the system Rx = y using back substitution is approximately 1 + 2 + 3 + ... + n, which is equal to n(n+1)/2.

Since R has semiband width s, this means that each row of R has at most s nonzero entries, so each variable requires at most s multiplications and s-1 subtractions.

Therefore, the total number of flops required to solve the system is approximately 2ns.

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Answer:

B

Step-by-step explanation:

You didn't write the full question but B is the only one that make since.

Answer:

46 + W = 231

Step-by-step explanation:

Answer:

231-W=amount of brown eggs (185)

Step-by-step explanation:

Given:

The quadratic equation is:

[tex]x^2+13x+k=0[/tex]

[tex]x_1=-9[/tex]

To find:

The value of k and [tex]x_1[/tex].

Solution:

We have,

[tex]x^2+13x+k=0[/tex]                ...(i)

Putting [tex]x=-9[/tex], we get

[tex](-9)^2+13(-9)+k=0[/tex]

[tex]81-117+k=0[/tex]

[tex]-36+k=0[/tex]

[tex]k=36[/tex]

Putting [tex]k=36[/tex] in (i), we get

[tex]x^2+13x+36=0[/tex]

Splitting the middle term, we get

[tex]x^2+9x+4x+36=0[/tex]

[tex]x(x+9)+4(x+9)=0[/tex]

[tex](x+9)(x+4)=0[/tex]

[tex]x=-9,-4[/tex]

Here, [tex]x_1=-9[/tex] and [tex]x_2=-4[/tex].

Therefore, the required values are [tex]k=36[/tex] and [tex]x_2=-4[/tex].

Answer:

297 sq mm

Step-by-step explanation:

Area of Rectangle: 22 x 18 = 396

Area of Triangle:  (1/2)(22)(9) = 99

Area of Rectangle - Area of Triangle = Area of Shaded area

396 - 99 = 297

Answer:

please what is the exact question

Answer:

161.56 ft^2

Step-by-step explanation:

base area = (leg 1 x leg 2)/2 = (5 x 5)/2 = 25/2 = 12.5 ft^2

base perimeter = 5 + 5 + 7.07 = 17.07 ft

lateral surface = (perimeter x height) = 17.07 x 8 = 136.56 ft^2

surface area = base area x 2 + lateral surface = (12.5 x 2) + 136.56 = 161.56 ft^2

Answer:

y=45u

Step-by-step explanation:

4 with a 5 try adding / bc its supposed to be like a check sin

Any mean weight falling outside the interval of (17.06, 18.94) would be considered evidence against the company's claim.

μ = 18 and σ = 0.68. n = 10. The formula for the z-test is given by:

z = (x - μ) / (σ/√n)

Where:

z = z-test score

x = sample mean

μ = population mean

σ = standard deviation

n = sample size

Let's calculate the upper and lower limits by using the above formula:

Lower limit = μ - z_(α/2) * (σ / √n)

Upper limit = μ + z_(α/2) * (σ / √n)

Where z_(α/2) is the standard normal variate which can be found from the standard normal table (at 5% significance level) to be 1.96.

Therefore,

Lower limit = 18 - 1.96 * (0.68/√10) = 17.06

Upper limit = 18 + 1.96 * (0.68/√10) = 18.94

Thus, any mean weight of 10 randomly selected bags that falls outside the interval of (17.06, 18.94) would be considered evidence against the company's claim.

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The yield to maturity of a(n) eight-year, if this bond is currently trading for a price of $4723.70 is  B) 5.26%

Time = 8 years

Coupon rate = 4.4%

Value of the bond = $5000

Yield to maturity is the overall return on investment that a bond will have earned once all required payments have been made and the principal has been repaid. Since the investor would receive the initial bond price plus the interest rate that was finalised at the time of the total bond purchase.

Calculating yield to maturity -

[tex]P = C * [1 - (1 + r/2)^(-2n)] / (r/2) + F / (1 + r/2)^(2n)[/tex]

Substituting the values -

$4723.70 =

[tex]($5000 * 0.044/2) * (1 - (1 + Y/2)^(-28)) / (Y/2) + $5000 / (1 + Y/2)^(28)[/tex]

= 0.0526, or 5.26%

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Answer:

4) 8

5) 135

6) -.5

Step-by-step explanation:

4) 33.6/4.2=8

5) 3*45=135

6)4/-8= -1/2 or -.5

To compute the integral ∫ fdx over the disk D of radius R centered at (0,0), we need to express the function f in terms of the given coordinate transformation.

In polar coordinates, a point (r, θ) in the disk D can be represented as (r cos(θ), r sin(θ)).

Now, let's substitute these polar coordinates into the integral. The differential element dx becomes r cos(θ)dr, and the integral becomes:

∫ fdx = ∫ f(r cos(θ), r sin(θ)) r cos(θ)dr dθ

We can now evaluate this integral by integrating over the range of r and θ. The range for r is from 0 to R, and the range for θ is from 0 to 2π (since we are integrating over the entire disk).

Thus, the integral becomes:

∫ fdx = ∫[0 to R] ∫[0 to 2π] f(r cos(θ), r sin(θ)) r cos(θ)dr dθ

By evaluating this double integral, we can find the value of ∫ fdx over the given disk D.

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Answer:

number of females =16

Step-by-step explanation:

100% + 25% =125%. 125%=number of males. 100\125 ×20=16. 20 - 16 =4

Answer:

(-1, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = 2x + 3

y = x + 2

Step 2: Solve for x

Substitution

Step 3: Solve for y

Answer:

x = -3, y = -1

Step-by-step explanation:

In order to solve an equation using substitution you need to make one of the variables values opposite of one another. For example, 4's opposite would be -4. Moving on, we multiply the bottom equation by -2. That gives us y = -2x -4. We combine like values and the remaing equation is y = -1. Finally, we can insert our value;-1 = x +2. We do inverse operations and we are left with x = -3.

Answer: 11 times

Step-by-step explanation:

Have a wonderful day!

Answer:8.75

Step-by-step explanation:

Answer: it’s B

Step-by-step explanation:

Answer:

(-2,3)

Step-by-step explanation:

Answer:

C. (-2,3)

Step-by-step explanation:

(-2,3)

Answer:

$5.25

Step-by-step explanation:

Given data

Original price= $35

Discount= 15%

let us find 15% of $35

=15/100*35

=0.15*35

=$5.25

Hence the amount of the discount is

$5.25

1. The general solution of the differential equation is:

y(x) = c₁x^(-3) + c₂x^(-2).

2.The general solution of the differential equation is:

y(x) = c₀x^(-1)ln(x) + c₁x^(-1),

To solve the given differential equations using the Frobenius method, we assume a power series solution of the form:

y(x) = ∑(n=0)^(∞) aₙx^(r+n),

where aₙ is the nth coefficient of the series, r is a constant, and x is the independent variable.

1. For the equation 2xy'' + 5y' + xy = 0:

Substituting the power series solution into the equation and simplifying, we obtain:

x²∑(n=0)^(∞) aₙ(r+n)(r+n-1)x^(r+n-2) + 5∑(n=0)^(∞) aₙ(r+n)x^(r+n-1) + x∑(n=0)^(∞) aₙx^(r+n) = 0.

Now, equating the coefficient of each power of x to zero, we get:

∑(n=0)^(∞) (aₙ(r+n)(r+n-1)x^(r+n-2) + 5aₙ(r+n)x^(r+n-1) + aₙx^(r+n)) = 0.

This gives us a recurrence relation:

aₙ(r+n)(r+n-1) + 5aₙ(r+n) + aₙ = 0.

Simplifying, we find:

aₙ[(r+n)² + 5(r+n) + 1] = 0.

Setting the coefficient to zero, we have:

(r+n)² + 5(r+n) + 1 = 0.

Solving this quadratic equation, we obtain the values of r:

r₁ = -3, r₂ = -2.

Therefore, the general solution of the differential equation is:

y(x) = c₁x^(-3) + c₂x^(-2),

where c₁ and c₂ are constants.

2. For the equation 4xy'' + (1/2)y' + y = 0:

Following the same steps as above, we obtain the recurrence relation:

aₙ[(r+n)(r+n-1) + (1/2)(r+n) + 1] = 0.

Simplifying, we find:

aₙ[(r+n)² + (3/2)(r+n) + 1] = 0.

Setting the coefficient to zero, we have:

(r+n)² + (3/2)(r+n) + 1 = 0.

Solving this quadratic equation, we find the value of r:

r = -1.

Therefore, the general solution of the differential equation is:

y(x) = c₀x^(-1)ln(x) + c₁x^(-1),

where c₀ and c₁ are constants.

These are the solutions obtained using the Frobenius method for the given differential equations.

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Answer:

118ft

Step-by-step explanation:

dont ask how i got it i just got the answer from my teacher but they didnt show me the work. ur welcome

Answer:

≈ 56°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{34}{41}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{34}{41}[/tex] ) ≈ 56° ( to the nearest degree )

Answer:

area = (14 x 16) - (0.5 x 16 x 6) = 176 ft²

Step-by-step explanation:

Answer:

A = 176 ft²

Step-by-step explanation:

2 shapes: one rectangle and 1 triangle:

Rectangle:

A = bh

A = 16(14)

A = 224

Triangle:

A = 1/2bh

A = 1/2(16)(6)

A = 48

Combined:

224 - 48

176

Answer:

17 feet

Step-by-step explanation:

L² = 15² + 8² = 225 + 64 = 289

L = √289 = 17 feet

Answer:

do you need the area or the perimiter?

Answer:(1,0)

Step-by-step explanation:

Answer:

66ft

Step-by-step explanation:

I took the quiz

Answer:

the last one

Step-by-step explanation: