Factor the polynomial: 11x− xy +11y−x2

Answers

Answer 1

[tex]11x- xy +11y-x^2=\\-x^2-xy+11x+11y=\\-x(x+y)+11(x+y)=\\-(x-11)(x+y)[/tex]

Answer 2

Answer:

(x - 11)(-x - y)

Step-by-step explanation:

To factor the polynomial 11x - xy + 11y - x² completely, let's group the terms and factor them separately.

Rearranging the terms, we have:

11x - xy + 11y - x²

Let's rearrange the terms again to group similar terms together:

x² + 11x - xy + 11y

Now, we can factor out the common factor from each pair of terms:

x(-x + 11) - y(x - 11)

Simplifying further, we can factor out -1 from the first pair of terms:

-x(x - 11) - y(x - 11)

Now, notice that we have a common factor of (x - 11) in both terms. Factoring out this common factor, we obtain:

(x - 11)(-x - y)

Therefore, the polynomial 11x - xy + 11y - x² can be factored completely as (x - 11)(-x - y).


Related Questions

determine the results of the following operations​

Answers

Answer:

[tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex]

Step-by-step explanation:

Let be [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex], this expression is simplified as follows:

1) [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex] Given

2) [tex]\sqrt[3]{4^{3}}-\sqrt[3]{2^{5}}\times \sqrt[3]{5^{3}}[/tex] Definition of power

3) [tex](4^{3})^{1/3}-(2^{2}\cdot 2^{3})^{1/3}\times (5^{3})^{1/3}[/tex] Definition of n-th root/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a^{b})^{c} = a^{b\cdot c}[/tex]

4) [tex]4 - (2^{2})^{1/3}\times 2\times 5[/tex] [tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]

5) [tex]4 - 10\times 4^{1/3}[/tex] Multiplication/Definition of power

6) [tex]4^{1/3}\cdot (4^{2/3}-10)[/tex] Distributive property/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]

7) [tex]\sqrt[3]{4}\times [(4^{2})^{1/3}-10][/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]/Definition of n-th root

8) [tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex] Definition of power/Result

If f(x) = 2x2 – 3x – 1, then f(-1)=

Answers

ANSWER:
Given:f(x)=2x^2-3x-1
Then,f(-1)=2(-1)^2-3(-1)-1
f(-1)=2(1)+3-1
f(-1)=5-1
f(-1)=4


HOPE IT HELPS!!!!!!
PLEASE MARK BRAINLIEST!!!!!

The value of function at x= -1 is f(-1) = 4.

We have the function as

f(x) = 2x² - 3x -1

To find the value of f(-1) when f(x) = 2x² - 3x -1, we substitute x = -1 into the expression:

f(-1) = 2(-1)² - 3(-1) - 1

      = 2(1) + 3 - 1

      = 2 + 3 - 1

      = 4.

Therefore, the value of function at x= -1 is f(-1) = 4.

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A normal distribution has a mean of 30 and a variance of 5.Find N such that the probability that the mean of N observations exceeds 30.5 is 1%.​

Answers

Answer:

109

Step-by-step explanation:

Use a chart or calculator to find the z-score corresponding to a probability of 1%.

P(Z > z) = 0.01

P(Z < z) = 0.99

z = 2.33

Now find the sample standard deviation.

z = (x − μ) / s

2.33 = (30.5 − 30) / s

s = 0.215

Now find the sample size.

s = σ / √n

s² = σ² / n

0.215² = 5 / n

n = 109

What is 5 feet and 11 inches in inches

Answers

Answer:

60

Step-by-step explanation:

5 is 60 inch

A work shift for an employee at Starbucks consists of 8 hours (whole).
What FRACTION (part) of the employees work shift is represented by 2
hours? *

Answers

Answer:

1/4 of an hour

Step-by-step explanation:

2 divided by 8 = 1/4

Answer:

1/4

Step-by-step explanation:

A whole shift is 8 hours

Part over whole is the fraction

2/8

Divide top and bottom by 2

1/4

What is the value of the product (3 – 2i)(3 + 2i)?

Answers

Answer:

13

Step-by-step explanation:

(3 - 2i)(3 + 2i)

Expand

(9 + 6i - 6i - 4i^2)

Add

(9 - 4i^2)

Convert i^2

i^2 = ([tex]\sqrt{-1}[/tex])^2 = -1

(9 - 4(-1))

Add

(9 + 4)

= 13

Answer:

13.

Step-by-step explanation:

(3 - 2i)(3 + 2i)

= (3 * 3) + (-2i * 3) + (2i * 3) + (-2i * 2i)

= 9 - 6i + 6i - 4[tex]\sqrt{-1} ^{2}[/tex]

= 9 - 4(-1)

= 9 + 4

= 13

Hope this helps!

find the 5th term in the sequence an=n÷n+1

Answers

Answer:

The 5th term of a sequence is defined as the term with n = 5.  So for this sequence, a sub 5 = 5/6

Simplify 6.92 to the exponent of 1000

Answers

Answer:

Whatever is raised to the power of 0 is 1

SO the answer is 1


An apartment building is infested with 6.2 X 10 ratsOn average, each of these rats
produces 5.5 X 10' offspring each year. Assuming no rats leave or die, how many additional
rats will live in this building one year from now? Write your answer in standard form.

Answers

Answer: 3.41x10^3

Step-by-step explanation:

At the beginning of the year, we have:

R = 6.2x10 rats.

And we know that, in one year, each rat produces:

O = 5.5x10 offsprins.

Then each one of the 6.2x10 initial rats will produce 5.5x10 offsprings in one year, then after one year we have a total of:

(6.2x10)*(5.5x10) = (6.2*5.5)x(10*10) = 34.1x10^2

and we can write:

34.1 = 3.41x10

then: 34.1x10^2 = 3.41x10^3

So after one year, the average number of rats is:  3.41x10^3

A soccer player has made 3 of her last 10 field goals, which is a field goal percentage of 30%. How many more consecutive field goals would she need to make to raise her field goal percentage to 50%?

Answers

Answer:

4 consecutive goals

Step-by-step explanation:

If 3 of last 10 field goals = 30%

Which is equivalent to

(Number of goals scored / total games played) * 100%

(3 / 10) * 100% = 30%

Number of consecutive goals one has to score to raise field goal to 50% will be:

Let y = number of consecutive goals

[(3+y) / (10+y)] * 100% = 50%

[(3+y) / (10+y)] * 100/100 = 50/100

[(3+y) / (10+y)] * 1 = 0.5

(3+y) / (10+y) = 0.5

3+y = 0.5(10 + y)

3+y = 5 + 0.5y

y - 0.5y = 5 - 3

0.5y = 2

y = 2 / 0.5

y = 4

Therefore, number of consecutive goals needed to raise field goal to 50% = 4

Find the solution of the inequality 5 > r - 3.
A) r<2
B) r = 2
C) r=8
(D) r < 8​

Answers

Answer:

[tex]\huge\boxed{r<8}[/tex]

Step-by-step explanation:

[tex]5 > r - 3[/tex]

Adding 3 to both sides

[tex]5 + 3 > r[/tex]

[tex]8 > r\\OR \\r < 8[/tex]

Answer: D. r<8

Step-by-step explanation:

[tex]5>r-3[/tex]

add 3 to both sides

[tex]r-3+3<5+3[/tex]

[tex]5+3=8[/tex]

simplify

[tex]r<8[/tex]

Figure out if the figure is volume or surface area.​

(and the cut out cm is 4cm)

Answers

Answer:

Surface area of the box = 168 cm²

Step-by-step explanation:

Amount of cardboard needed = Surface area of the box

Since the given box is in the shape of a triangular prism,

Surface area of the prism = 2(surface area of the triangular bases) + Area of the three rectangular lateral sides

Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]

                                                           = [tex]\frac{1}{2}(6)(4)[/tex]

                                                           = 12 cm²

Surface area of the rectangular side with the dimensions of (6cm × 9cm),

= Length × width

= 6 × 9

= 54 cm²

Area of the rectangle with the dimensions (9cm × 5cm),

= 9 × 5

= 45 cm²

Area of the rectangle with the dimensions (9cm × 5cm),

= 9 × 5

= 45 cm²

Surface area of the prism = 2(12) + 54 + 45 + 45

                                           = 24 + 54 + 90

                                           = 168 cm²

2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)

Answers

Answer:

16/45x-11/12

Step-by-step explanation:

Multiply across

2/15x-30/40-1/6+2/9x=

Get common denominators of like terms

6/45x+10/45x-9/12-2/12=

Combine like terms

16/45x-11/12

The simplified expression is: (16/45)x - (11/12)

To simplify the given expression, we'll follow the steps:

Step 1: Distribute the fractions through the parentheses.

Step 2: Simplify the expression by combining like terms.

Let's proceed with the simplification:

Step 1: Distribute the fractions through the parentheses:

2/5 * (1/3x - 15/8) - 1/3 * (1/2 - 2/3x)

Step 2: Simplify the expression:

To distribute 2/5 through (1/3x - 15/8):

2/5 * 1/3x = 2/15x

2/5 * (-15/8) = -15/20 = -3/4

So, the first part becomes: 2/15x - 3/4

To distribute -1/3 through (1/2 - 2/3x):

-1/3 * 1/2 = -1/6

-1/3 * (-2/3x) = 2/9x

So, the second part becomes: -1/6 + 2/9x

Now, the entire expression becomes:

2/15x - 3/4 - 1/6 + 2/9x

Step 3: Combine like terms:

To combine the terms with "x":

2/15x + 2/9x = (2/15 + 2/9)x

Now, find the common denominator for (2/15) and (2/9), which is 45:

(2/15 + 2/9) = (6/45 + 10/45) = 16/45

So, the combined x term becomes:

(16/45)x

Now, combine the constant terms:

-3/4 - 1/6 = (-18/24 - 4/24) = -22/24

To simplify -22/24, we can divide both numerator and denominator by their greatest common divisor (which is 2):

-22 ÷ 2 = -11

24 ÷ 2 = 12

So, the combined constant term becomes:

(-11/12)

Putting it all together, the simplified expression is:

(16/45)x - (11/12)

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Complete question is:

Simplify the given expression: 2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)

There are four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag. Which expression represents the probability of randomly selecting a blue marble, replacing it, and then randomly selecting a red marble? StartFraction 4 over 10 EndFraction (StartFraction r over 10 EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction 4 over 10 r EndFraction) StartFraction 4 over 10 + r EndFraction (StartFraction r over 10 + r EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction r over 10 r EndFraction)

Answers

Answer:

4/ (10+r) * r/ (10+r)

Step-by-step explanation:

four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag = 4+r+6 = 10+r marbles

P( blue) = blue marbles / total marbles

             = 4/ (10+r)

Then replace

P( r) = red marbles / total marbles

             = r/ (10+r)

P( blue replace ,red) =P ( blue ) * P(red)

                                    =  4/ (10+r) * r/ (10+r)

                                    = 4r / ( 10+r) ^2

Answer:

C. 4/10+r (r/10+r)

Step-by-step explanation:

EDG20

Which of the following is an even function? f(x) = (x – 1)2 f(x) = 8x f(x) = x2 – x f(x) = 7

Answers

Answer:

f(x) = 7

Step-by-step explanation:

f(x) = f(-x) it is even

-f(x)=f(-x) it is odd

f(x) = (x – 1)^2 neither even nor odd

f(x) = 8x   this is a line  odd functions

f(x) = x^2 – x  neither even nor odd

f(x) = 7  constant  this is an even function

Answer:

answer is f(x)= 7

Step-by-step explanation:

just took edge2020 test

Find all values of x on the graph of f(x) = 2x3 + 6x2 + 7 at which there is a horizontal tangent line.

Answers

Answer:

the equation is not correct, u have to write like

ax'3+bx'2+cx+d

Answer:

x=-2 and x=0

Step-by-step explanation:

So I know it isn't x=-3 and x=0. So my guess is that it is x=0 and x=-2 and heres why.

First, I find the derivative of f(x)=2x^3+6x^2+7 which is 6x^2+12x

Then, I plugged in all the values of x's I had and I found out that you get 0 for -2 and 0 when you plug them in

So, in conclusion I believe the answer to be x=-2 and x=0

Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure. Question 9 options:
A) (x, y) → (x, y – 6)
B) (x, y) → (x – 6, y)
C) (x, y) → (x, y + 6)
D) (x, y) → (x + 6, y)

Answers

Answer:

  B) (x, y) → (x – 6, y)

Step-by-step explanation:

Each x-value in the image is 6 less than in the pre-image. Each y-value is the same. That means x gets mapped to x-6, and y gets mapped to y:

  (x, y) → (x – 6, y)

Please answer this correctly without making mistakes

Answers

Answer:

355/12

Step-by-step explanation:

Answer:

355/12mi

Step-by-step explanation:

9 1/2 = 19/2

20 1/12 = 241/12

19/2 + 241/12 = 355/12mi

(a) Five friends are in a netball squad. In each game during the 21-round season, at least 3 of them are picked in the team. Prove that there will be at least 3 matches in which the same three friends are selected to play.
(b) How does the answer change if there are six friends instead of 5?
PLS ANSWER FAST!!!!

Answers

Answer:

  (a) there are 10 sets of 3 friends, so in 21 games, at least one set must show 3 times

  (b) there are 20 sets of 3 friends, so  in 21 games, at least one set must show 2 times.

Step-by-step explanation:

(a) The number of combinations of 5 things taken 3 at a time is ...

  5C3 = 5!/(3!·2!) = 5·4/2 = 10

There can be 10 games in which the same 3 friends do not show up. There can be 10 more games such that the same 3 friends show up exactly twice. In the 21st game, some set of 3 friends must show up 3 times.

__

(b) The number of combinations of 6 things taken 3 at a time is ...

  6C3 = 6!/(3!·3!) = 6·5·4/(3·2) = 20

Hence, there can be 20 games in which the same 3 friends do not show up. In the 21st game, some set of 3 friends will show up a second time.

Take your time! :) Not important, but I would like to know, I'm writing flashcards so I can remember when I start back in school. Can you explain how to get the LCM of two numbers,GCF of two numbers, and what's the difference?

Answers

Answer:

The LCM of two numbers is the least common multiple. You want to find the least possible number that is divisible by the two numbers. So, you can list the factors of the two numbers. If there are factors that are repeated, put the repeated factors to the side. With the remaining factors, multiply the factors by each other and the repeated factors.

For example, let's try to find the least common multiple between 10 and 15.

Factors of 10: 2 * 5

Factors of 15: 3 * 5

The repeated factor is 5.

2 and 3 are left over. 2 * 3 = 6. 6 * 5 = 30. So, that is the least common multiple.

The GCF of two numbers is the greatest common factor. You want to find the greatest factor that is included in both numbers. So, again, you can list the factors of the two numbers and find the greatest factor that is repeated between the two numbers.

For example, let's try to find the greatest common factor between 30 and 45.

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 45: 1, 3, 5, 9, 15, 45

Between the two numbers, shared factors are 1, 3, 5, and 15. So, the greatest common factor is 15.

Hope this helps!

g A random sample of size 16 taken from a normally distributed population revealed a sample mean of 50 and a sample variance of 36. The upper limit of a 95% confidence interval for the population mean would equal:

Answers

Answer:

The  upper limit is    

                   [tex]k = 52.94[/tex]

Step-by-step explanation:

From the question we  told that

     The  sample size is [tex]n = 16[/tex]

      The sample mean is  [tex]\= x = 50[/tex]

      The sample variance is  [tex]\sigma ^2 = 36[/tex]

For  a  95% confidence interval the confidence level is  95%

Given that the confidence level is 95% then the level of significance is  mathematically evaluated  as  

             [tex]\alpha = 100 - 95[/tex]

              [tex]\alpha = 5 \%[/tex]

              [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference- math dot armstrong dot edu), the value is  

              [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

             

Generally the margin of error is mathematically represented as

             [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

 Here  [tex]\sigma[/tex] is the standard deviation which is mathematically evaluated as

                  [tex]\sigma = \sqrt{\sigma^2}[/tex]

substituting values

                  [tex]\sigma = \sqrt{36}[/tex]

=>                [tex]\sigma = 6[/tex]

So

                    [tex]E = 1.96 * \frac{6}{\sqrt{16} }[/tex]

                     [tex]E = 2.94[/tex]

The 95% confidence interval is mathematically represented as

                 [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

                [tex]50 -2.94 < \mu <50 +2.94[/tex]

                [tex]47.06 < \mu <52.94[/tex]

The  upper limit is    

                   [tex]k = 52.94[/tex]

   

                 

find the range of the inequality 2e-3< 3e-1​

Answers

Answer:

[tex]x = { - 1, 0,1 ,2 ...}[/tex]

Step-by-step explanation:

[tex]2e - 3 < 3e - 1 = 2e - 3e < - 1 + 3 = - 1e < 2 = e > - 2[/tex]

Hope this helps ;) ❤❤❤

Let f(x) = x - 1 and g(x) = x^2 - x. Find and simplify the expression. (f + g)(1) (f +g)(1) = ______

Answers

Answer:

The simplified answer of the given expression is 1.

Step-by-step explanation:

When you see (f + g)(x), then it means that you are going to add f(x) and g(x) together. So, we are going to add the terms together that are given in the problem. We are also given the value of x which is 1. So, we are going to combine this information together so we can simplify the expression.

(f + g)(1)

f(x) = x - 1

g(x) = x²

(f + g)(1) = (1 - 1) + (1²)

Simplify the terms in the parentheses.

(f + g)(1) = 0 + 1

Add 0 and 1.

(f + g)(1) = 1

So, (f + g)(1) will have a simplified answer of 1.

A box is 90 cm long. Which of these is closest to the length of this box in feet?{1 inch= 2.54cm} (1 point)

Answers

Answer:

2.952755906 ft

Step-by-step explanation:

We need to convert 90 cm to inches

90 cm * 1 inch / 2.54 cm =35.43307087 inches

Now convert inches to ft

12 inches = 1ft

35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft

anyone can help me with these questions?
please gimme clear explanation :)​

Answers

Step-by-step explanation:

The limit of a function is the value it approaches.

In #37, as x approaches infinity (far to the right), the curve f(x) approaches 1.  As x approaches negative infinity (far to the left), the curve f(x) approaches -1.

lim(x→∞) f(x) = 1

lim(x→-∞) f(x) = -1

In #38, as x approaches infinity (far to the right), the curve f(x) approaches 2.  As x approaches negative infinity (far to the left), the curve f(x) approaches -3.

lim(x→∞) f(x) = 2

lim(x→-∞) f(x) = -3

99 litres of gasoline oil is poured into a cylindrical drum of 60cm in diameter. How deep is the oil in the drum? ​

Answers

Answer:

  35 cm

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr²h

We want to find h for the given volume and diameter. First, we must convert the given values to compatible units.

  1 L = 1000 cm³, so 99 L = 99,000 cm³

  60 cm diameter = 2 × 30 cm radius

So, we have ...

  99,000 cm³ = π(30 cm)²h

  99,000/(900π) cm = h ≈ 35.01 cm

The oil is 35 cm deep in the drum.

For a certain instant lottery game, the odds in favor of a win are given as 81 to 19. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

Answers

Answer: 0.81

Step-by-step explanation:

[tex]81:19\ \text{can be written as the fraction}\ \dfrac{81}{81+19}=\dfrac{81}{100}=\large\boxed{0.81}[/tex]

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the males​ surveyed, responded that they had at least one tattoo. Of the females​ surveyed, responded that they had at least one tattoo. Construct a ​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  95% interval for [tex]p_1 - p_2[/tex] is  [tex]-0.0171 ,0.0411[/tex]

Option A is correct

Step-by-step explanation:

From the question we are told that

   The sample size of male  is [tex]n_1 = 1211[/tex]

    The number of males that  said they have at least one tattoo is [tex]r = 182[/tex]

   The sample size of female is [tex]n_2 = 1041[/tex]

     The number of females that  said they have at least one tattoo is [tex]k = 144[/tex]

Generally the sample proportion of male is  

            [tex]\r p_1 = \frac{r}{ n_1}[/tex]

substituting values

            [tex]\r p_1 = \frac{ 182}{1211}[/tex]

             [tex]\r p_1 = 0.1503[/tex]

Generally the sample proportion of female is  

            [tex]\r p_2 = \frac{k}{ n_2}[/tex]

substituting values

           [tex]\r p_2 = \frac{ 144}{1041}[/tex]

           [tex]\r p_2 = 0.1383[/tex]

Given that the confidence level is  95% then the level of  significance is mathematically represented as

          [tex]\alpha =100-95[/tex]

          [tex]\alpha =5\%[/tex]

          [tex]\alpha =0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is

          [tex]Z_\frac{\alpha }{2} = 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }[/tex]

substituting values

       [tex]E = 1.96 * \sqrt{\frac{ 0.1503 (1- 0.1503)}{1211} + \frac{0.1383 (1- 0.1383)}{1041} }[/tex]

       [tex]E = 0.0291[/tex]

The 95% confidence interval is mathematically represented as

        [tex](\r p_1 - \r p_2 ) - E < p_1-p_2 < (\r p_1 - \r p_2 ) + E[/tex]

substituting values

         [tex](0.1503- 0.1383 ) - 0.0291 < p_1-p_2 < (0.1503- 0.1383 ) + 0.0291[/tex]

          [tex]-0.0171 < p_1-p_2 < 0.0411[/tex]

So the interpretation is that there is 95% confidence that the difference of the proportion is in the interval .So conclude that there is insufficient evidence of a significant difference in the proportion of male and female that have at least one tattoo

This because the difference in proportion is less than [tex]\alpha[/tex]

Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario

Answers

Answer:

The test statistic is [tex]t = 2.79[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is [tex]\mu = 59.3[/tex]

    The sample size is  [tex]n = 79[/tex]

    The  sample mean is  [tex]\= x = 62.4[/tex]

    The  standard deviation is  [tex]\sigma = 9.86[/tex]

Generally the test statistics is mathematically represented as

            [tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]

substituting values

          [tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]

          [tex]t = 2.79[/tex]

Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.) ∫4x2 lnx dx ; u= lnx , dv=4x 2dx

Answers

Take

[tex]u=\ln x\implies\mathrm du=\dfrac{\mathrm dx}x[/tex]

[tex]\mathrm dv=4x^2\,\mathrm dx\implies v=\dfrac43x^3[/tex]

Then

[tex]\displaystyle\int4x^2\ln x\,\mathrm dx=\frac43x^3\ln x-\frac43\int x^2\,\mathrm dx=\frac43x^3\ln x-\frac49x^3+C[/tex]

[tex]=\boxed{\dfrac49x^3(3\ln x-1)+C}[/tex]

The required integration is,

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C

The given integral is,

∫4x² lnx dx

Using integration by parts, choose u and dv.

In this case, we choose u = lnx and dv = 4x²dx.

Using the formula for integration by parts, we have:

∫ u dv = uv - ∫ v du

Substituting the values of u and dv, we get:

∫4x² lnx dx = (lnx) (∫ 4x² dx) - ∫ [(d/dx)lnx] (∫4x² dx) dx

Simplifying the first term using the power rule of integration, we get:

∫ 4x² dx = (4/3)x³ + C₁

For the second term, we need to evaluate (d/dx)lnx,

Which is simply 1/x. Substituting this value, we get:

∫ [(d/dx)lnx] (∫4x² dx) dx = ∫ [(1/x) ((4/3)x³ + C₁)] dx

Simplifying this expression, we get:

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - ∫ [(4/3)x³/x] dx

Using the power rule of integration again, we get:

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C

Where C is the constant of integration.

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