The following chart shows a store?s records of sales of stuffed toys for two months. 2 circle graphs. A circle graph titled September. Teddy bears is 346, rabbits is 297, cats is 199, horses is 245, other is 225. A circle graph titled October. Teddy bears is 308, rabbits is 260, cats is 285, horses is 186, 275 is other. Which of the following are accurate assessments of trends displayed in this graph? I. Sales of teddy bears decreased by about 2.9% between September and October. II. The change in sales of rabbits is roughly equal to the change in sales of all toys. III. Roughly 24.1% fewer horses were sold in October than in September. a. I and II b. II only c. I and III d. III only

The radius of convergence is 5/7. The interval of convergence is (-5/7, 5/7) in interval notation.

To express the function f(x) = 7x² - 3x - 10 as the sum of a power series, we can start by factoring the quadratic term in the numerator:

f(x) = (7x² - 3x - 10)

The quadratic expression can be factored as follows:

f(x) = (7x + 5)(x - 2)

Now we can write the function f(x) as a sum of partial fractions:

f(x) = A/(7x + 5) + B/(x - 2)

To find the values of A and B, we can multiply both sides of the equation by the denominators and equate the coefficients of corresponding powers of x:

(7x + 5)(x - 2) = A(x - 2) + B(7x + 5)

Expanding both sides of the equation:

7x² - 14x + 5x - 10 = Ax - 2A + 7Bx + 5B

Grouping the terms with the same power of x:

(7x² + (5 - 14)x - 10) = (A + 7B)x + (-2A + 5B)

Equating the coefficients of corresponding powers of x:

7x² + (5 - 14)x - 10 = (A + 7B)x + (-2A + 5B)

Comparing the coefficients:

7 = A + 7B

5 - 14 = -2A + 5B

-10 = -2A

From the first equation, we can solve for A:

A = 7 - 7B

Substituting this value of A into the second equation:

-10 = -2(7 - 7B)

Simplifying:

-10 = -14 + 14B

14B = -10 + 14

B = 4/14

B = 2/7

Now we have the values of A and B:

A = 7 - 7B = 7 - 7(2/7) = 7 - 2 = 5

Therefore, the function f(x) can be expressed as:

f(x) = 5/(7x + 5) + 2/(x - 2)

Now, to find the interval of convergence for the power series representation of f(x), we need to determine the radius of convergence. The power series representation will converge within the interval (-r, r), where r is the radius of convergence.

In this case, since we have a rational function, the interval of convergence will be determined by the denominator with the smallest radius of convergence.

The denominators in the partial fractions are (7x + 5) and (x - 2). The radius of convergence for a power series centered at a point c is the distance from c to the nearest singularity.

For (7x + 5), the singularity occurs when 7x + 5 = 0, which gives x = -5/7.

For (x - 2), the singularity occurs when x - 2 = 0, which gives x = 2.

The distance from the center (c = 0) to the nearest singularity is the minimum of the absolute values of the two singularities: min(|-5/7|, |2|) = 5/7.

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The number of all partitions of a set of 6 rudiments into 3 disjoint sets is 69( S( 6, 3) = 69).

To calculate the number of all partitions of a set of 6 rudiments into 3 disjoint sets, we've to apply knowledge of Stirling numbers of the alternate kind. The Stirling figures of the alternate kind, denoted by S( n, k), represent the number of ways to partition a set of n rudiments into  k non-empty subsets.

Then, we want to calculate S( 6, 3), which defines the number of ways to partition a set of 6 rudiments into 3 disjoint sets.

Using the conception of Stirling figures of the alternate kind

S(n, k) = k * S(n-1, k) + S(n-1, k-1)

we can calculate S(6, 3) as given below-

S(6, 3) = 3 * S(5, 3) + S(5, 2)

S(5, 3) = 3 * S(4, 3) + S(4, 2)

S(4, 3) = 3 * S(3, 3) + S(3, 2)

S(3, 3) = 1

S(3, 2) = 3

S(4, 3) = 3 * 1 + 3 = 6

S(5, 3) = 3 * 6 + 3 = 21

S(6, 3) = 3 * 21 + 6 = 69

Therefore, the number of all partitions of a set of 6 elements into 3 disjoint sets is 69 (S(6, 3) = 69).

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The correct question is given below -

Calculate S(6,3) , the number of all partitions of a set of 6 elements into 3 disjoint sets.

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:

(-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:

$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

answer of this question:

8

Step-by-step explanation:

$20÷$2.50

=8

:)

Answer:

4

Step-by-step explanation:

Answer:

64 %

Step-by-step explanation:

( 16 / 25 ) x 100

= ( 16 x 100 ) / 25

= 16 x 4

= 64 %

Answer:

Step-by-step explanation:

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:

It is 7

Step-by-step explanation:

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:

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

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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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:

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

Answer:

y=45u

Step-by-step explanation:

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

Answer:

4.5826

Step-by-step explanation:

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:

46 + W = 231

Step-by-step explanation:

Answer:

231-W=amount of brown eggs (185)

Step-by-step explanation:

Answer:

number of females =16

Step-by-step explanation:

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

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:

x = 2

Step-by-step explanation:

distribute -2 first

-2 + 8x = 3x + 8

-2 + 5x = 8

5x = 10

x = 2

Answer:

(-2,3)

Step-by-step explanation:

Answer:

C. (-2,3)

Step-by-step explanation:

(-2,3)

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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Hypothesis testing is a statistical method used to determine if a hypothesis regarding a population parameter is correct or not.

It is a decision-making process that aids in making decisions about population parameters when only a sample statistic is available. It has the following steps: State the null and alternative hypotheses. Choose the significance level. Determine the critical value or p-value. Calculate the test statistic. Make a decision and state the conclusion. The formula for the test statistic is given, where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size. The null and alternative hypotheses for this problem are:H0: μ = R+ (the sample mean is equal to the block population's mean)Ha: μ ≠ R+ (the sample mean is not equal to the block population's mean)We will use a two-tailed test since we are testing whether the sample mean is not equal to the block population's mean.

The significance level is given as 99%. This means that α = 1 - 0.99 = 0.01.The critical value for a two-tailed test with α = 0.01 and degrees of freedom (df) = n - 1 is obtained from a t-distribution table. Since the sample size is not provided, we cannot determine the critical value. The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. The p-value for a two-tailed test is given by:

P-value = P(|t| > |t*|)where t* is the test statistic and |t| is the absolute value of the test statistic. Since we do not have the sample size or the test statistic, we cannot calculate the p-value. Therefore, we cannot make a decision and state a conclusion about the hypothesis test.

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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:

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

Answer:

B

Step-by-step explanation:

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