Find a particular solution yp of
(x−1)y′′−xy′+y=(x−1)2 (1)

given that y1=x and y2=ex are solutions of the complementary equation

(x−1)y′′−xy′+y=0. Then find the general solution of (1).

The following can cause OLS estimators to be biased: Omitting an important independent variable.

Multicollinearity. Heteroskedasticity, Including an irrelevant variable.

The following does not cause the usual OLS t statistics to be invalid (that is, to have t distributions under H0): The error term non-normally distributed

OLS (ordinary least squares) estimates are typically unbiased when calculated.

However, the following problems may cause OLS estimates to be biased:

Omitting an important independent variable: When an important independent variable is omitted from the regression equation, the OLS estimate of the effect of one variable on the dependent variable is biased.

In particular, the estimate of the effect of the variable that is omitted is influenced by the remaining variables' presence in the equation.

Multicollinearity: When the independent variables in a multiple regression model are strongly related, multicollinearity exists.

When there is multicollinearity in a model, the estimated slope coefficients are frequently biased, making them difficult to interpret.

In this scenario, small changes in the data may cause substantial changes in the estimated coefficients.

As a result, the usual tests of hypothesis may fail to produce reliable inferences.

Heteroskedasticity: In the population, heteroskedasticity exists when the variance of the error term is not constant across observations.

Heteroskedasticity can induce OLS estimates' variance to be biased, even if the estimates are unbiased themselves.

When there is heteroskedasticity, the OLS estimates are no longer BLUE (best linear unbiased estimator).

Including irrelevant variable: When an irrelevant variable is included in a regression equation, the OLS estimates of the other variables' effects are biased, and the estimates' standard errors are larger than necessary.

The error term non-normally distributed: When the error term in a regression equation is non-normally distributed, the distribution of the OLS estimates is also non-normal.

However, this does not affect the distribution of the t statistics under H0.

The reason for this is that, even if the error term is non-normally distributed, the sample mean converges to the population mean, according to the central limit theorem.

Furthermore, the standard error of the mean is unaffected by the distribution of the error term, as long as the sample size is large enough.

As a result, the t statistics can be trusted to be asymptotically normally distributed under H0.

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Answer:

The experimental probability of rolling anumber less than 3 is 3/20

Step-by-step explanation:

16+14=30

30/200

=3/20

Answer:

7/50

Step-by-step explanation:

Answer:

Step-by-step explanation:

h

[tex]\frac{-3 - (-4)}{1 - (-5)}[/tex]

= [tex]\frac{-3 + 4}{1 + 5}[/tex]

= 1/6

Answer:

not a complete question..

Step-by-step explanation:

To find the second derivative of F(x) = [tex]\int\limits^0_x {e^t}^{2} } } \, dx[/tex] dt for x ∈ (0, 1), we can use the fundamental theorem of calculus and apply the chain rule twice. The second derivative is given by F''(x) = [tex]2e^{x^{2} } (1+2x^{2} )[/tex]

To find F''(x), we differentiate F'(x) first. Using the fundamental theorem of calculus, we have F'(x) = [tex]e^{x^{2} }[/tex]. Applying the chain rule, we obtain d/dx([tex]e^{x^{2} }[/tex]) = [tex]2xe^{x^{2} }[/tex].

Now, to find F''(x), we differentiate F'(x) with respect to x. Applying the chain rule again, we have d/dx([tex]2xe^{x^{2} }[/tex]) = [tex]2e^{x^{2} }[/tex] + [tex]4x^{2} e^{x^{2} }[/tex]. Simplifying this expression, we get F''(x) = 2[tex]e^{x^{2} }[/tex](1 + [tex]2e^{x^{2} }[/tex]).

Therefore, the second derivative of F(x) is given by F''(x) = 2[tex]e^{x^{2} }[/tex](1 + 2[tex]{x^{2} }[/tex]) for x ∈ (0, 1). This result shows that the second derivative is always positive for x ∈ (0, 1), indicating that the function is concave up within that interval.

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Answer:

42cm3

Step-by-step explanation:

v = 0.5× b × h × l

= 0.5 × 4 × 3 × 7

= 42cm3

Answer:

267/500

Step-by-step explanation:

0.534 = 534 / 1000

Simplify to 267/500

Step-by-step explanation:

537/1000

this is the correct answer

[tex]\Large\boxed{\tt Answer:~A:~y=-3x+5}[/tex]

All we have to do in order to find the equation that is equivalent to 6x + 2y = 10 is to solve for y.

Step 1: Keep y on one side of the equation and move the rest to the other.

[tex]\tt 6x + 2y = 10\\2y = -6x + 10[/tex]

Step 2: Divide all terms by 2 to isolate y.

[tex]\tt 2y \div 2=y\\-6x \div 2 = -3x\\10 \div 2 =5\\\\y=-3x+5[/tex]

Answer:

B. 525 L

Step-by-step explanation:

The exponential model for the data on Hispanic-owned businesses is N(t) =[tex]1.16 e^{(0.084t)[/tex], where t represents the number of years since 1999 and N(t) is the number of businesses in millions.

To find an exponential model for the data, we need to fit it into the general form of an exponential function: N(t) = ae^(kt).

Let's assign t = 0 to correspond to the year 1999 and N(t) represents the number of businesses in millions. We are given two data points: (t=0, N=1.16) and (t=4, N=1.53).

Plugging in the first data point, we have:

1.16 = ae^(k*0) => 1.16 = a.

Next, plugging in the second data point, we get:

1.53 = ae^(4k).

Now, we can substitute a = 1.16 into the second equation:

1.53 = 1.16  e^(4k).

Dividing both sides of the equation by 1.16:

1.32 = e^(4k).

Taking the natural logarithm (ln) of both sides:

ln(1.32) = 4k.

Solving for k:

k = ln(1.32)/4.

Now, we have the values of a = 1.16 and k = ln(1.32)/4. Therefore, the exponential model for the data is:

N(t) = 1.16 * e^((ln(1.32)/4) * t), where t represents the number of years since 1999, and N(t) is the number of businesses in millions.

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Answer:

The neighborhood the home is located in

The factors which does not affect the mortgage payment is the neighborhood the home is located in.

The correct option is D.

We are aware of this;

A mortgage is a loan when the borrower's property is used as security. The mortgage payment is determined by the cost of the property, the interest rate, the down payment, the length of the loan, taxes, and various insurances like homeowners insurance, among other factors.

Hence, It's not depend on ''The neighborhood the home is located in.''

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Answer:

38 ft ^2

Step-by-step explanation:

8x 3 = 24

1/2(4)(3) = 6

1/2(4)(4) = 8

24+6+8 = 38ft^2

Answer:

18 times  a green bead is drawn

Step-by-step explanation:

There are 20 beads in the basket.  The probability of picking a green bead is 6/20 = 3/10.  That means that a green bead would be picked 3/10 of the time.

So, 3/10(60) = 18 times  a green bead is drawn

Answer:

x axis

Step-by-step explanation:

Similar: If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

____________________________________________________________

Congruent: SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

Answer:

-10x+30

Step-by-step explanation:

just got it right on edg 2021 :)

None of these are correct

Answer: January 1, 2025

Step-by-step explanation:

The debt is due to be paid back in 10 years.

If the first payment was in 2016, the last payment should therefore be:

= 2016 + 9 years

= 2025

We used 9 years because 2016 was the first year of payment so the remaining years would be 9 years.

As the first payment was on January 1, 2016, the last payment would have to be on the same date in 2025 which is:

= January 1, 2025

Answer:

B 136.8 cm²

Step-by-step explanation:

Add the diameters of the three smaller circles to find the diameter of the largest circle.

D = 3 cm + 2.5 cm + 1.1 cm = 6.6 cm

area = πr²

area = 3.14 × (6.6 cm)²

area = 136.8 cm²

The point that is NOT 5 units away from the point (1,4) is (4,0).

Answer:

50.37

Step-by-step explanation:

Answer: 50.37

Step-by-step explanation:

Answer:

41.7feet

Step-by-step explanation:

From the question we are given the following

angle of depression = 50°

Distance of the pole from the base of the feet = 35feet (Adjacent)

Required

height of the school (opposite)

Using the SOH CAH TOA identity

Tan theta = opp/adj

Tan 50 = H/35

H = 35tan 50

H = 35(1.1918)

H = 41.7feet

Hence the height of the school is 41.7feet

Answer:the answer is solid B

Step-by-step explanation:

Oh your on edmentum I hate it there is so much work but I can help I'm a math master I'm top 3 smartest at math in my whole school.

Answer:

51 and 261

Step-by-step explanation:

Let the numbers be x and y

x + y =312

x - y =210

2y=102

y=51

x=312-51=261

Solution: Any value for a variable that makes the equation true.

Reciprocal: Focuses on the use of multiplication and division

Coefficient: A number that is multiplied by a variable in an algebraic expression is a coefficient

Term: A term of an algebraic expression is a number, variable, or product of numbers and variables

Base: The base of a power is the factor that is multiplied repeatedly in the power.

Hope this helps, and have a great day!

Answer:

Solution: any value for a variable that makes an equation true

Reciprocal: focuses on use of multiplication and division

Coefficient: A number being multiplied by a variable in an algebraic expression

Base: the base of a power is a factor that is multiplied repeatedly in power

u got the term definition right

Step-by-step explanation:

Answer:

37.36 meters are equal to 3,736 centimeters.

Step-by-step explanation:

We have that 1 meter is equal to 100 centimeters, so if we want to convert 3,736 cm to m we need to divide by 100:

[tex] x = 3,736 cm*\frac{1 m}{100 cm} = 3,736 cm*\frac{1 m}{10^{2} cm} [/tex]          

When we divide a number by a power of 10, we move the decimal point to the left as many places as the power indicates.      

Since we are dividing by 10², we need to move the decimal point two places to the left, as follows:            

[tex] x = 3,736 cm*\frac{1 m}{10^{2} cm} = 37.36 m [/tex]      

Hence, 37.36 meters are equal to 3,736 centimeters.

I hope it helps you!                  

Answer:

models

Step-by-step explanation:

Answer: B.) Models

Edge

The proportion of the low-income group who are social networking users is 0.6514.

The proportion of the high-income group who are social networking users is 0.6144.

We have the following information from the question:

A research organization found that 228 of the 350 respondents who reported earning less than $30,000 per year said they were social networking users.

Another income scale, 290 of the 472 respondents reporting earnings of $75,000 or more were social networking users.

We have to find proportions of each income group who are social networking users.

Low-income group:

228 users / 350 respondents = 0.6514

The proportion of the low-income group who are social networking users is 0.6514.

High-income group:

290 users / 472 respondents = 0.6144

The proportion of the high-income group who are social networking users is 0.6144.

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Mathematical induction can be used to prove that for every non-negative odd integer n, the expression [tex]24 / (2^{(3n+1)}+1+1) * (n^2+1)[/tex] holds true.

To prove the statement using mathematical induction, we need to follow two steps: the base case and the induction step.

First, we verify if the statement holds true for the base case, which is typically the smallest value of n. In this case, let's consider n = 0. Plugging in n = 0 into the expression, we get [tex]24 / (2^{(3*0+1)}+1+1) * (0^2+1)[/tex]. Simplifying, we have 24 / (2+1+1) * 1, which equals 24 / 4 * 1, resulting in 6. Therefore, the statement holds true for n = 0.

Next, we assume that the statement is true for some arbitrary odd integer k, and we will prove that it holds true for k+2. Assume that [tex]24 / (2^{(3k+1)}+1+1) * (k^2+1)[/tex] holds true.

Now, we substitute k+2 into the expression and aim to show that it holds true for k+2 as well. We have [tex]24 / (2^{(3(k+2)+1)}+1+1) * ((k+2)^2+1)[/tex]. Simplifying the expression, we get [tex]24 / (2^{(3k+7)}+1+1) * (k^2 + 4k + 5)[/tex].

We can manipulate the equation further to demonstrate that it is equal to the assumed expression for k. By performing algebraic manipulations and simplifications, we can equate the expressions and conclude that the statement holds true for k+2.

Since we have verified the base case and shown that the statement holds true for k+2 when it holds true for k, we can conclude that the statement is true for every non-negative odd integer n.

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Shape a = 6 x 4 x 3 = 72

Shape b = 4 x 4 x 4 = 64

72 + 64 = 136

A

Answer:

A

Step-by-step explanation: