QUICK Give me a long version of Pi!!!

\((5x - 6) (x + 9)\)

How to Solve:

STEP 1:

Use the sum-product pattern:

\(5x^{2} + 39x - 54\)

\(5x^{2} + 45x - 6x - 54\)

STEP 2:

Common factor from the two pairs:

\(5x^{2} + 45x - 6x - 54\)

\(5x( x+ 9) - 6(x + 9)\)

STEP 3:

Rewrite in factor form:

\(5x(x + 9) - 6(x + 9)\)

AND NOW YOUR ANSWER IS:

\((5x - 6)(x + 9)\)

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a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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If \(y=x^m\) is a solution to the ODE

\(x^2 y'' - 7xy' + 15y = 0\)

then substituting \(y\) and its derivatives

\(y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}\)

gives

\(m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0\)

\(m(m-1)x^{m} - 7mx^{m} + 15x^m = 0\)

\((m(m-1) - 7m + 15)x^{m} = 0\)

We ignore the trivial case of \(y=x^m=0\). Solve for \(m\).

\(m(m-1) - 7m + 15 = 0\)

\(m^2 - 8m + 15 = 0\)

\((m - 3) (m - 5) = 0\)

\(\implies \boxed{m=3} \text{ or } \boxed{m=5}\)

Confidence intervals of treatment effects estimation in panel data models with interactive fixed effects A confidence interval (CI) is an interval estimate for an unknown parameter.

The most commonly used level of confidence is 95 percent, although other levels of confidence can also be used. The range is calculated from a given set of sample data using a statistical method. In this case, we are looking at confidence intervals of treatment effects estimation in panel data models with interactive fixed effects.

Panel data models with interactive fixed effects are commonly used in economics to analyze the effects of treatments on outcomes over time. These models account for both individual-level and time-level variation, and they can be used to estimate treatment effects more accurately than other types of models.

In addition, panel data models with interactive fixed effects allow for the estimation of fixed effects that vary by individual and time, which can provide important insights into the dynamics of treatment effects over time.

However, several methods have been developed to estimate confidence intervals for treatment effects in panel data models with interactive fixed effects. These methods typically involve bootstrapping or simulation techniques that account for the correlation structure of the data.

Overall, the estimation of confidence intervals for treatment effects in panel data models with interactive fixed effects is an important area of research that has the potential to improve the accuracy of treatment effect estimates in economics and other social sciences.

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The correctanswer is-the percentage of the pieces that will meet the length specs is 98.78%.

The given data may be a random variable that takes after the normal distribution with mean μ=64 and standard deviation σ=0.1

The required value is to discover the rate of the pieces that will meet the length specs which is between 63.76 and 64.24 inches.

To find the required percentage, standardize the given limits as follows: Lower Limit: (63.76 - μ) / σ= (63.76 - 64) / 0.1 = -2.4

Upper Limit: (64.24 - μ) / σ= (64.24 - 64) / 0.1 = 2.4

Using the Standard Normal Distribution Table, the probability that the value will fall between -2.4 and 2.4 is found to be 0.9878.

The required percentage is then found by multiplying the probability by 100, which is: Percentage = 0.9878 x 100% = 98.78%

Therefore, the percentage of the pieces that will meet the length specs is 98.78%.

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Answer:

38%

Step-by-step explanation:

Answer:

C. 38%

Step-by-step explanation:

3 ÷ 8 = 0.375

Make it a percent

0.375 x 10 = 37.5

Since it isn't an option, round up. A good rounding rule is:  Four or less, let is rest. Five or more, let it soar.

Since this number ends in 5, round up.

37.5 is now 38

38%

The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².

To find the area of the original square, we can use the following formula:

Area of the original square = x²

where x is the original length of the square field.

Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².

Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:

(x + 5)² = 245 + x²

Expanding the left-hand side of the equation and simplifying, we get:

x² + 10x + 25 = 245 + x²

Solving for x, we get:

10x + 25 = 245

x = 22

Plugging x = 22 into the formula, we can find the area of the original square:

Area of the original square = x² = 22² = 484 ft²

Therefore, the area of the original square is 484 ft².

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Answer:

0.25

Step-by-step explanation:

0.25 x 24 = 6

The data which is given by the historian is used to find the population, variable, parameter, sample, data, and statistic. He estimated the mean number of children per household in New York City in 1900.

Population - all of the households in New York City in 1900.

Variable - a quantity equivalent to the number of children in a randomly selected household

Parameter -  the mean number of children per household in New York City in 1900

Sample - the 200 households selected by the historian

Data - the 200 records collected by the historian

Statistic -  the mean number of children per household in the historian's sample.

Complete question:

Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households. Classify each description as one of a parameter, variable, population, sample, data, or statistic.

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Answer:

x>2

Step-by-step explanation:

Step 1: Subtract 60x from both sides.

100x−200−60x>60x−120−60x

40x−200>−120

Step 2: Add 200 to both sides.

40x−200+200>−120+200

40x>80

Step 3: Divide both sides by 40.

40x/40> 80/40

x>2

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Answer:

7 and 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first step is to find the √58.

The answer is 7.61577310586.

Since this is between 7 and 8, the correct answer is 7 and 8.

Answer:

The mode is 78, which appears the most times (3).

The mode of the given data 62, 78, 84, 62, 72, 78, 54, 60, 78, 80 is 78.

The mode is the data that occurs most frequently, in the data set listed below 62, 78, 84, 62, 72, 78, 54, 60, 78, 80. We can see that the number 78 appears three times, which is more than any other value in the set when we look at the data.

Note: If multiple values occur with the same highest frequency, but in this case, 78 is the only mode, the data set may have multiple modes.

Thus, the mode of 62, 78, 84, 62, 72, 78, 54, 60, 78, and 80 data set is 78.

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Answer:

the answer and explanation are In the picture

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Answer:

4900mm^2 or 24010000mm

Step-by-step explanation:

Answer:

The mapping diagram above is a function since there are no two values (integers) in the range (Set B) where there is only one value (integer) in the domain (Set A) mapped unto them

Step-by-step explanation:

By definition a function is an association between the individual elements within two sets such that all element in one set is mapped to precisely one element of the other set

In the given example, all the elements in Set A are mapped to exactly one element of the Set B

That is the function from A to B is the set C (-1, -4), (9, 5), (1, 4), whereby the first component of the ordered pair in the set C are the elements of the set A.

The mapping diagram above is a function since there are no two values in set B where there is only one value in Set A mapped to them.

Therefore, since the mapping diagram illustrates a 1 input to 1 output relationship, then it is a function.

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Answer:

y = 6.7

x = 8

Step-by-step explanation:

3^2 + 6*2 = y

√9 + 36 = y

6.7 = y

10^2 = 6^2 + x

100 = 36 + x

100 (-36) = 36 (-36) +x

√64 = x

8 = x

Answer:

\(\frac{2}{7}\)

Step-by-step explanation:

Plug in points to equation \(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1}\)

\(m = \frac{ -3 - -1}{-2 - 5}\)

Subtract to get \(\frac{2}{7}\)

The radius of convergence is 1, as the power series for ln(y) converges for |y-1| < 1, or |x^2 - 1| < 1.

(a) For the power series expression centered at 0, we have:

f(x) = Σ (c_n * x^n), where n=0 to infinity.

As 2002 is a constant, the power series expression is:

f(x) = 2002, which is a constant function.

The radius of convergence is infinite, as a constant function converges everywhere.

(b) Given f(x) = Σ (x^n / (n! * (n+1))), where n=0 to infinity.

To compute S₅f(x), sum the first six terms of the series:

S₅f(x) = x^0 / (0! * 1) + x^1 / (1! * 2) + x^2 / (2! * 3) + x^3 / (3! * 4) + x^4 / (4! * 5) + x^5 / (5! * 6).

(c) To write a power series expression for ln(x^2) centered at 1, we can use the following substitution:

Let y = x^2. Then, ln(y) centered at y=1.

The power series for ln(y) is:

ln(y) = Σ [(-1)^(n-1) * (y-1)^n / n], where n=1 to infinity.

Replace y with x^2:

ln(x^2) = Σ [(-1)^(n-1) * (x^2 - 1)^n / n], where n=1 to infinity.

The radius of convergence is 1, as the power series for ln(y) converges for |y-1| < 1, or |x^2 - 1| < 1.

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Answer:

The answer is a

Step-by-step explanation:

every y value is just the x value doubled

Answer and step-by-step explanation:

The answer is A because:

When you plug in a value for x, the result (y) is twice that number, which correlates with this equation.

For example, if we plug in 5 for x, we will get 10.

2 times 5 is equal to 10. This is also shown on the table given.

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Answer:

the second option

Step-by-step explanation:

one thing i recommend is when you get asked to solve for the equation of a problem and they give you points, plug them in all of options you're given.  that is literally the only reason i've been getting a's on all of my math classes and even the psat  

5 rules of scientific notation which helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent.

The exponent is either positive or negative depending on how big or little the number is. Learn about power and exponents to have a deeper understanding. The five golden rules of the scientific notation:

Hence there are the rules of the the scientific notation.

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Answer:

\(150( {1.01}^{12} ) - 150 = 19.02\)

The account will earn $19.02 interest in 12 months.

Answer:

Step-by-step explanation:

To determine the future value of the savings account after 12 months, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the account

P = the principal or initial value of the account (in this case, $150)

r = the annual interest rate (1% per month or 0.01)

n = the number of times the interest is compounded per year (12)

t = the time period in years (1)

Plugging in these values, we get:

A = 150(1 + 0.01/12)^(12*1)

A = 150(1.0075)^12

A = $162.89

Therefore, the savings account will be worth approximately $162.89 after 12 months with 1% monthly interest. It is important to note that this is only an estimate, as the actual amount could vary depending on any additional deposits or withdrawals made during the year, and the interest rate could also change.

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Answer:

-4(v+1)

(-4 X v ) + -4 X 1

-4v + -4

it is your polynomial equation....

meiosis results in four haploid genetically unique daughter cells, each with half the DNA of the parent cell . In human cells, the parent cell has 46 chromosomes (23 pairs), so the cells produced by meiosis have 23 chromosomes.

Chromosomes

Chromosomes are threadlike structures made of protein and a single molecule of DNA that serve to carry the genomic information from cell to cell. In plants and animals, chromosomes reside in the nucleus of cells.

DNA

DNA, or deoxyribonucleic acid, is the hereditary material in humans and almost all other organisms. Nearly every cell in a person's body has the same DNA.

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Answer:

A 500 grain arrow moving at 260 fps has a kinetic energy of 75.04 ft-lbs and a momentum of . 577 slugs*. A 700 grain arrow moving at 175 fps has a kinetic energy of 47.59 ft-lbs and a momentum of . 544 slugs*.

The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g which is false.

A statement, opinion, or rule that forms a linking of two variables is characterized as a function. Mathematics has functions, which are necessary for the design of meaningful relationships.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

The denominator of the rational function shouldn't be 0. The function is not defined if the denominator is 0.

Thus, the given statement is false.

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