pq²(p² - 3pq - 4q²) answer fast pls

Answer:

(i) 458000 (ii) 10486

Step-by-step explanation:

(i) (729)²-(271)²

The identity is : \(a^2-b^2=(a-b)(a+b)\)

(729)²-(271)² = (729-271) × (729+271)

= 458 × 1000

= 458000

(ii) 98x107 = (100-2) (100+7)

Idenity : \((x-a)(x-b) = x^2+(a+b)x+ab\)

\((100-2) (100+7)=100^2+(-2+7)100+(-2)(7)\\\\=10000+500-14\\\\=10486\)

Hence, this is the required solution.

Answer:

3, 3, 6,9,12 if that's wrong try 3, 3, 6, 12, 36, 144

Step-by-step explanation:

you just multiply the numbers together to get your answer

Answer:

200 in²

Step-by-step explanation:

To find the area, you need to split it into two squares. The upper square would be 10 inches times 10 inches which would give you 100 inches squared. Since both are the same size, you can add both square areas together to give you 200 inches squared.

Answer:

B

Step-by-step explanation:

Do you have to show any work?

Answer:

(-7, -2)

Step-by-step explanation:

Answer:

Sale price of a sweat shirt is $15.30 and a soccer ball is $21.08.

Step-by-step explanation:

A). Usual price of a sweat shirt is = $18

Sale price of the sweat-shirt is 85% of the usual price.

Therefore, Sale price = 85% of $18

=

= $15.30

B). Usual price of a soccer ball is = $24.80

Sale price of the soccer ball is 85% of its usual price.

Therefore, Sale price = 85% of $24.80

=

= $21.08

Therefore, sale price of a sweat shirt is $15.30 and a soccer ball is $21.08.

heres the real answer hope it helps :)

There is no definitive answer to the proportion of early-twenty-first-century men who finished school, left home, become financially independent, married, and had a child by age 30.

In terms of finishing school, in 2016, the U.S. Census Bureau estimated that 88.6% of males aged 25 and older were high school graduates, while 33.4% had attained a bachelor's degree or higher. As for financial independence, a 2019 report by the St. Louis Federal Reserve Bank found that the percentage of 25-year-olds who earned more than their parents did at the same age has declined since 1970.

In terms of marriage, a 2017 report by the Pew Research Center found that the median age for men getting married for the first time was 29, up from 23 in 1960. Finally, regarding fatherhood, a 2018 report by the National Center for Health Statistics found that the mean age of first-time fathers in the United States was 31.1. However, it is important to note that these statistics and studies do not provide a complete picture of the proportion of men who have accomplished all these factors by age 30.

Learn more about proportion here:

https://brainly.com/question/29774220

#SPJ11

Given the vertices of triangle ABC:

A(2, 5), B(-3, 3), C(2, -1)

Let's dilate the triangle ABC by a scale factor of 2 with a center of dilation of (2, 3)

Here, since we have a scale factor, k, of 2 and center of dilation (2, 3), apply the formula:

(x', y') = k(x - a)+a, k(y - b)+ b

Where:

(a, b) is the center of dilation: (2, 3)

(x, y) is the coordinate

(x' y') is the new coordinate

k is the sale factor = 2

Thus, we have the following:

A(2, 5) ==> 2(2 - 2)+2, 2(5 - 3)+3 ==> 2(0)+2, 2(2)+3 ==> (2, 9)

B(-3, 3) ==> 2(-3 - 2)+2, 2(3 - 3)+3 ==> 2(-5)+2, 2(0)+3 ==> (-8, 3)

C(2, -1) ==> 2(2 - 2)+2, 2(-1 - 3)+3 ==> 2(0)+2, 2(-4)+3 ==> (2, -5)

Therefore, the vertices of triangle ABC after the dilation are:

A'(2, 9), B'(-8, 3), C'(2, -5)

ANSWER:

A'(2, 9), B'(-8, 3), C'(2, -5)

The extent of the sampling error might be affected by all of the following factors like the variability of the population except the "number of previous samples taken".

Sampling error refers to the difference between the sample statistic and the population parameter that it represents, caused by the fact that a sample of the population is being used to estimate the characteristics of the entire population. It is the error that arises from the process of selecting a sample from a population, rather than using the entire population. Sampling error can be reduced by increasing the sample size, using appropriate sampling methods, and minimizing measurement errors.

The variability of the population refers to the degree to which individuals in a population differ from each other. In statistical terms, it is a measure of the spread or dispersion of the data in a population. A population with high variability will have a wide range of values, while a population with low variability will have values that are closer together. The variability of the population can have an impact on the precision of statistical estimates, such as the mean or standard deviation, and can influence the sampling error.

To know more about Sampling errors visit:

brainly.com/question/23842153

#SPJ1

The extent of the sampling error might be affected by all of the following factors like the variability of the population except the "number of previous samples taken".

Sampling error refers to the difference between the sample statistic and the population parameter that it represents, caused by the fact that a sample of the population is being used to estimate the characteristics of the entire population. It is the error that arises from the process of selecting a sample from a population, rather than using the entire population. Sampling error can be reduced by increasing the sample size, using appropriate sampling methods, and minimizing measurement errors.

The variability of the population refers to the degree to which individuals in a population differ from each other. In statistical terms, it is a measure of the spread or dispersion of the data in a population. A population with high variability will have a wide range of values, while a population with low variability will have values that are closer together. The variability of the population can have an impact on the precision of statistical estimates, such as the mean or standard deviation, and can influence the sampling error.

To know more about Sampling errors visit:

brainly.com/question/23842153

#SPJ1

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

Learn more about  balance from

https://brainly.com/question/28767731

#SPJ11

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

To learn more about the system of equations from the given link

https://brainly.com/question/25976025

#SPJ1

Answer: -4

There are rules, just follow the rules

The statement ' if this model suffers from heteroskedasticity, then the usual OLS t statistics no longer have a t distribution and the f statistics no longer have an f distribution' is true because a model suffering from heteroskedasticity will not be accurate.

If a model suffers from heteroskedasticity, which is the condition where the variance of the errors is not constant across observations, then the usual OLS t statistics and F statistics no longer have t or F distributions, respectively. In other words, the standard errors of the coefficients and the overall fit of the model cannot be accurately estimated using the usual assumptions of OLS regression.

Specifically, when heteroskedasticity exists, the OLS estimator remains unbiased, consistent, and asymptotically normal, but its estimated standard errors are biased and inconsistent, leading to invalid inference. This means that t-tests for individual coefficients and F-tests for overall model significance based on these standard errors may be unreliable.

Instead, alternative methods such as robust standard errors or weighted least squares should be used to correct for heteroskedasticity.

To learn more about heteroskedasticity, click here:

https://brainly.com/question/18403256

#SPJ11

Answer:

45%

Step-by-step explanation:

18 divided 40 =

18/40 =

9/20 = .45

.45 <- move the decimal to 2 spaces to the right =

45%

it is two i think. hope i could help

Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.

Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:

Isolation and Cleavage of DNA:

The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.

Insertion of DNA Fragments into the Vector:

Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.

Transformation of Host Cells:

The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.

Introduction of rDNA into Cells:

Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:

Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.

Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.

Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.

Clinical Applications of rDNA:

Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:

Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.

Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.

Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.

Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.

for such more question on isolating

https://brainly.com/question/27746495

#SPJ8

The exponential growth equation is x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶ , where x ( t ) is the population in the year 2015 = 40,115,896

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units'

Given data ,

Let the exponential growth equation be represented as x ( t )

Now , the average percentage change from the year 2000 - 2009 is calculated by

The total percentage = ( 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93 )

The total number of years = 9 years

So , the average percentage change = total percentage / number of years

On simplifying , we get

The average percentage change = 12.21 / 9 = 1.35667 %

b)

The population in 2009 was 37,000,000

So , the population growth rate r = 1.35667 %

And , the population in the years 2015 is given by

The number of years n = 6 years

x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶

On simplifying , we get

x ( t ) = 37,000,000 ( 1.013567 )⁶

x ( t ) = 40,115,896

Hence , the population in the year 2015 is 40,115,896

To learn more about exponential growth factor click :

https://brainly.com/question/13674608

#SPJ1

Answer:

Step-by-step explanation:

the Lincoln-Douglas debates propelled Lincoln's political career into the national spotlight, while simultaneously stifling Douglas' career, and foreshadowing the 1860 Election. By 1858, Stephen A. Douglas was the most prominent politician in the West. Lincoln-Douglas debates, series of seven debates between the Democratic senator Stephen A. Douglas and Republican challenger Abraham Lincoln during the 1858 Illinois senatorial campaign, largely concerning the issue of slavery extension into the territories. The result of the debates was inconclusive. Senators were then chosen by state legislatures, and in the 1858 legislative election, Illinois Republican candidates slightly outpolled their Democratic rivals. Southerners believed that Abraham Lincoln was an abolitionist and also felt betrayed by Stephen Douglas's suggestion that territories could refuse to grant slavery legal protection. In 1860, Lincoln won the Republican Party's presidential nomination.In that election, he faced Douglas (again), who represented the Northern faction of a heavily divided Democratic Party, as well as Southern Democrat John C. Breckinridge and Constitutional Union candidate John Bell.

The correct value of r is 2.

What is the power inverse variation?

Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.

The equation for a power inverse variation is y = kx^r,

where k is a constant, x is the independent variable, y is the dependent variable, and r is the power.

We have given the set of ordered pairs,

we can find the value of r by substituting in the known values of x and y and solving for r.

(1/2,20) => 20 = 5 * (1/2)^r => r = log(20)/log(1/2) = -2

So the answer is:

r = 2

Hence, the correct value of r is 2.

To learn more about the power inverse variation visit,

https://brainly.com/question/14978895

#SPJ4

8 a) The fifth term in the expansion is 8,960.

b) The sixth term in the expansion is -11,264.

c) The seventh term in the expansion is approximately 28.6152.

9) The expansion of 2/(1-3x^2) up to the term in x^8 is 2 + 24x^2 + 162x^4 + 972x^6 + 1458x^8.

8) a) To find the fifth term in the expansion of (1 + 4x)^7, we use the binomial theorem formula:

(1 + 4x)^7 = C(7,0) + C(7,1)(4x) + C(7,2)(4x)^2 + C(7,3)(4x)^3 + C(7,4)(4x)^4 + C(7,5)(4x)^5 + ...

The fifth term corresponds to the coefficient of (4x)^4, which is given by:

C(7,4)(4)^4 = 35 x 256 = 8,960

b) To find the sixth term in the expansion of (2 - x)^11, we use the same formula as above:

(2 - x)^11 = C(11,0) + C(11,1)(-x) + C(11,2)(-x)^2 + C(11,3)(-x)^3 + C(11,4)(-x)^4 + C(11,5)(-x)^5 + ...

The sixth term corresponds to the coefficient of (-x)^5, which is given by:

C(11,5)(-1)^5(2)^6 = -11 x 32 x 32 = -11,264

c) To find the seventh term in the expansion of (3 - (2/3x))^12, we again use the same formula:

(3 - (2/3x))^12 = C(12,0) + C(12,1)(-2/3x) + C(12,2)(-2/3x)^2 + C(12,3)(-2/3x)^3 + ...

The seventh term corresponds to the coefficient of (-2/3x)^6, which is given by:

C(12,6)(-2/3)^6 = 924 x (2/3)^6 = 28.6152

9) To obtain the expansion of 2/(1-3x^2) up to the term in x^8, we can use the formula for the geometric series:

2/(1-3x^2) = 2(1 + (3x^2) + (3x^2)^2 + (3x^2)^3 + ...)

To find the term in x^8, we need to find the coefficient of (3x^2)^4:

C(n,r) = n!/[r!(n-r)!]

C(4,0) = 1, C(4,1) = 4, C(4,2) = 6, C(4,3) = 4, C(4,4) = 1

The term in x^8 is then given by:

2C(4,0) + 2C(4,1)(3x^2) + 2C(4,2)(3x^2)^2 + 2C(4,3)(3x^2)^3 + 2C(4,4)(3x^2)^4

= 2 + 24x^2 + 162x^4 + 972x^6 + 1458x^8

To learn more about expansion click on,

https://brainly.com/question/13689068

#SPJ4

Answer:

your answer should be 8 according to the bearing given

Correlation is the measurement of the association between two variables. The following statements are true about correlation:1) It describes the strength of any relation between two variables:This statement is correct since correlation tells us about the degree of the relationship between two variables.2) It always takes on values between 0 and 1:

This statement is incorrect. Correlation coefficients can range from -1 to +1, not just 0 to 1.3) It quantifies the strength of the linear relationship between two variables:This statement is correct. Correlation measures the degree to which two variables are linearly related.4) It always takes on values between −1 and 1:This statement is correct. Correlation coefficients can range from -1 to +1.5) Both c and d: This statement is correct since both statements C and D are correct.

Correlation coefficients measure the strength of the linear relationship between two variables, with values ranging from -1 to +1, where negative correlations indicate a negative association between two variables, positive correlations indicate a positive association between two variables and the value of zero represents no association between two variables.

To know more about relationship visit :

https://brainly.com/question/23752761

#SPJ11

The given problem states that the number of rushing yards in game 16 is an outlier in the x-direction. Hence, we can say that game 16 has a significant effect on the equation of the least-squares regression line.

We need to find out the effects that this game has on the correlation and on the equation of the least-squares regression line. We also need to calculate the correlation and equation of the least-squares regression line with and without this game to confirm our answers.

Effect on Correlation:

An outlier in the x-direction has no effect on the correlation coefficient(r). The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is not influenced by the presence of an outlier in the independent variable. So, the correlation coefficient with or without this game will remain the same.

Effect on Equation of the Least-Squares Regression Line:

An outlier in the x-direction has a significant effect on the equation of the least-squares regression line. The least-squares regression line is a straight line that summarizes the relationship between the independent and dependent variables. This line is constructed by minimizing the sum of squared deviations between the observed and predicted values. If an outlier is present, it will pull the regression line closer to it. So, the equation of the least-squares regression line will be different with or without this game.

Calculation of Correlation and Equation of Least-Squares Regression Line:

Without game 16,

the correlation coefficient and equation of the least-squares regression line are:

Correlation Coefficient(r) = 0.94

The equation of the least-squares regression line:

y = 2.25x + 10.5 With game 16,

the correlation coefficient and equation of the least-squares regression line are:

Correlation Coefficient(r) = 0.93

The equation of the least-squares regression line:

y = 1.92x + 22.8

From the above calculations, we can see that the correlation coefficient has a negligible change with or without game 16. However, the equation of the least-squares regression line is quite different with and without game 16.

for such more question on least-squares

https://brainly.com/question/23305357

#SPJ11

Answer:

V=160.22114

Step-by-step explanation:

Volume of cone = 47.12389

Volume of cylinder = 113.09734

By using the line segment formula, we conclude that the coordinates of point E are E(x, y) = (- 11, 9).

In this problem we find a line segment of which the coordinates of an endpoint and a point within the segment and in accordance with a segment ratio are known. The coordinates of the other endpoint must be found in accordance with the following expression:

E(x, y) = A(x, y) + k · [P(x, y) - A(x, y)]          (1)

Where E(x, y) is the missing endpoint.

If we know that A(x, y) = (- 1, - 1), P(x, y) = (- 7, 5) and k = 5 / 3, then the coordinates of point E are:

E(x, y) = (- 1, - 1) + (5 / 3) · [(- 7, 5) - (- 1, - 1)]

E(x, y) = (- 1, - 1) + (5 / 3) · (- 6, 6)

E(x, y) = (- 1, - 1) + (- 10, 10)

E(x, y) = (- 11, 9)

To learn more on partioning line segments: https://brainly.com/question/3148758

#SPJ1

Answer: 9x-15

Step-by-step explanation:

Given

34x-(25x-3)-18

Expand parenthesis

34x-25x+3-18

Put like terms together

(34x-25x)+(3-18)

Combine like terms

9x-15

Hope this helps!! :)

Please let me know if you have any questions

Answer:

45

Step-by-step explanation:

To find area, it's length * width. the length is 5 and the width is 9, so you would do 5*9=45

The given function f(t)= 4400(0.992)^t/365 represents the change in quantity over t days. In this function, the constant 0.992 reveals the rate of change quantity.

The correct answer is:The constant 0.992 reveals the rate of change quantity.Explanation:The given function f(t)= 4400(0.992)^t/365 represents the change in quantity over t days. It can be observed that the given function is an exponential function, where 0.992 is the base of thel exponentia function and t/365 is the exponent. The constant 0.992 reveals the rate of change quantity. We can analyze it as follows:When the base is between 0 and 1, the function will decrease as the value of t increases.When the base is greater than 1, the function will increase as the value of t increases.The absolute value of the base is less than 1, and so it will decay exponentially.The absolute value of the base is greater than 1, and so it will grow exponentially.Therefore, the constant 0.992 is the base of the exponential function, which is less than 1. Thus, it decays exponentially, which implies that the quantity is decreasing at a certain rate, where 0.992 is the rate of change quantity.

To know more about function,visit:

https://brainly.com/question/30721594

#SPJ11

Answer:the dots -2 and 2

Step-by-step explanation:

The constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream

The proportional relationship between the number of scoops of ice cream and the amount of milk can be expressed as:

1 scoop of ice cream = 1/2 cup of milk

we evaluate for k the constant of proportion as follows:

1 = k × 1/2

k = 2 {cross multiplication}

if we represent a scoop of ice cream with y and a cup of milk with x, then we can write the equation that represent the relation as:

y = 2x.

In the graph of y = 2x, for every value of x on the x–axis, there are 2 units of x for y on the y–axis, that is when x = 1, y = 2 or x = 3 then y = 6.

For 18 scoops of ice cream, we will evaluate for the amount of cup of milk as follows:

18 = 2x

x = 18/2 {divide through by 2}

x = 9.

In conclusion, he constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream

Know more about proportion here:https://brainly.com/question/1266676

#SPJ1