Consider the function
f(x) = x² ln(x)
Find the second derivative and use it to calculate f''(1). Type your answer in the space below.

Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

Answer: 107,000

Step-by-step explanation:

the exponent is a positive 5, so move the decimal point 5 places right.

if exponent is negative, go the other direction

Step-by-step explanation:

Let imagine a circle with a center 5,3.

Let our circle have a radius, that passes through 1,2.

We need to find the length of r or distance from 5,3 to 1,2.

\(d = \sqrt{(3 - 2) {}^{2} + (5 - 1) {}^{2} } \)

\(d = \sqrt{1 {}^{2} + {4}^{2} } \)

\(d = \sqrt{17} \)

So the radius is sqr root of 17.

So now we have a circle that has a radius of sqr root of 17 and a center 5,3. Let have a line passing through 5,3 and 1,2 as well.

The slope is 1/4 so

\(y = \frac{1}{4} x + \frac{7}{4} \)

Look at first photo

Now,we are rotating 90 degrees So we need to find a line that is perpendicular to our orginal line and that pass through the center (5,3)

Negative reciprocal slope of 1/4 is -4 and our point is 5,3 so

\(y - 3 = - 4(x - 5)\)

\(y = - 4x + 23\)

The point that intersects the circle will be the new image after we rotate (1,2) 90 degrees, which is the 2nd photo.

To find the next rotated point of (2,3), the distance of the preimage (2,3) and new image (5,3) is 3 so that leaves

(5,0)

So our new rotated points are

(6,-1)

(5,0)

The fraction that is equal to 6 can be some of the following:

\(\mathbf{\dfrac{6}{1} \ ; \dfrac{12}{2} \ ; \dfrac{18}{3} \ ; \ \dfrac{24}{4}\ ; \ \dfrac{36}{6} }\)

A fraction usually comprises a numerator and a denominator separated by a division line.

The factors of a given number are the numbers that can be divided in such a given number without a remainder.

From the given example, we are to determine the factors of 6, so we will think about a number that can be divided by 6 without leaving any remainder.

These numbers are:

From these numbers, we can pick two factors that when divided together, we get 6 as our result and without any remainder.

i.e.

The fraction that is equal to 6 are:

\(\mathbf{\dfrac{6}{1} \ ; \dfrac{12}{2} \ ; \dfrac{18}{3} \ ; \ \dfrac{24}{4}\ ; \ \dfrac{36}{6} }\)

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The powers, (index) and coefficients of the polynomial indicates;

(A) The standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

(B) 4

(C) Positive zeroes; 2 or 0, negative zeroes; 0 or 2, complex zeroes; 0 or 2 or 4

(D) ±1/2, ±1, ±3/2, ±2, ±3, ±6

(E) Please find attached the graph of the polynomial created with MS Excel

(F) Four complex roots

A polynomial is a mathematical expression that consists of variables and coefficients joined together by addition, subtraction and multiplication, with the exponents of the variables consisting of positive integer values.

Part A) The polynomial in standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

Part B) The degree of the polynomial is 4, as the highest power of the polynomial is 4

Part C) The use of the Rule of Signs, to determine the options for the number of positive zeroes, negative zeroes and complex zeroes, can be presented as follows;

Positive zeroes options; The number of time the signs coefficients of the expression; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6, changes are two as follows;

+6 to -12, and from -12 to +9, therefore, the number of possible positive zeroes are 2 or 0, positive zeroes

The negative zeroes options; The negative zeroes options can be found by changing the sign of all the coefficients as follows; -2·x⁴ - 3·x³ - 9·x² + 12·x - 6, therefore, the number of times the sign of the coefficients change are again from -6 to +12, and from +12 to -9, which is 2 times, therefore;

The possible number of negative zeros are 2 or 0, negative zeroes

Whereby there are possibly 0 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 4

Whereby there are 2 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Whereby there are possibly 0 negative zeros and 2 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Part D) The rational roots theorem indicates that for a polynomial the rational roots are in the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.

The constant term is 6, and the leading coefficient is 2. The factors of 6 are ±1, ±2, ±3, and ±6 and the factors of 2 are; ±1, ±2 therefore;

p/q = ±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±2/2, ±3/2, ±6/2, which can be summarized as; ±1/2, ±1, ±3/2, ±2, ±3, ±6

Part E) Please find attached a screenshot of the graph of the polynomial created with MS Excel

Part F) The attached graph of the polynomial, created with MS Excel, indicates that there are no real zeros of the polynomial, therefore, there are four complex zeroes of the polynomial

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Answer: 9 shirts I think

Step-by-step explanation: 54/6=9

Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693

If 58% = 58÷100 of the people have been vaccinated, then;

1 - (58/100) = 42% = 42÷100 of the people who have not been vaccinated.

Now:

Probability, P( > 1 ), that at least one of the selected four has been vaccinated is given by;

P( > 1 ) = 1 - P(0)                 -----------(1)

Where;

P(0) = probability that all of the four have not been vaccinated.

P(0) = P(1) x P(2) x P(3) x P(4)×p(5)

Where;

P(1) = Probability that the first out of the four has not been vaccinated

P(2) = Probability that the second out of the four has not been vaccinated

P(3) = Probability that the third out of the four has not been vaccinated

P(4) = Probability that the fourth out of the four has not been vaccinated

P(5)=Probability that the fifth out of the five has not been vaccinated

Remember that 42÷100 of the population has not been vaccinated. Therefore,

P(1) = 42÷100    

P(2) = 42÷100

P(3) = 42÷100

P(4) = 42÷100

P(5)=42÷100

P(0) = (42÷100) x (42÷100) x (42÷100) x (42÷100)×(42÷100)

P(0) = (42÷100)⁵

P(0) = (0.42)⁵

P(0) = 0.013067

Therefore, from equation (1);

P( > 1 ) = 1 -0.013067

P( > 1 ) = 0.98693

Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693

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Answer:

The answer is "6.635776".

Step-by-step explanation:

If the proportion estimation is not given, then the approximate is true. So, it is in the top condition, which referring its overall error margin that is equal to 0.5.  

Therefore the margin of error=0.05   With z=2.576  

\(\to 0.05=2.576 \times \sqrt{(0.05 \times \frac{0.05}{N})}\\\\\to 0.05=2.576 \times \sqrt{( \frac{0.0025}{N})}\\\\\to \sqrt{N}= \frac{2.576 \times 0.05}{0.05}\\\\\to \sqrt{N}= 2.576\)

square the above equation:

\(\to (N)^2= (2.576)^2\\\\\to N^2= 6.635776\\\\\)

So the number of required residents=6.635776

Answer:

B. y + 7 = -6/5 (x+3)

Step-by-step explanation:

Use the given slope and point to substitute into the point-slope formula  y − y 1 = m ( x − x 1 ) .

Slope-intercept form:  y = − 6 /5 x − 53 /5

Point-slope form:  y + 7 = − 6 /5 ⋅ ( x + 3 )

Draw the graph of x-axis which is lesser than 5 .

What is  Graph inequality ?

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Answer:

3x + 1

Step-by-step explanation:

1/5/2023

7:25PM

answer........................

3x +1

Answer: C

Step-by-step explanation: The layers of rocks implies superposition and changes in species implies evolution

The value of the determinants are

D=13

Dx =26

Dy =52

Dz =26

The determinant of a matrix is ​​a scalar value calculated for a given square matrix. Linear algebra deals with the determinant, it is calculated using the elements of a square matrix. It can be thought of as a scaling factor for the matrix transformation. Useful for solving a system of linear equations, calculating the inverse of a matrix, and numerical operations.

Given system is

x+ y-z= 4

3x+4y-3z=16

9x- 3y+4z=14

from the system the determinants become,

D=  1   1  -1

      3  4  -3

      9   -3  4

D= 1(16-9)-1(12+27)-1(-9-36)

   =7-39+45

   13

Dx=4   1  -1

      16  4  -3

      14   -3  4

   =26

Dy=1  4  -1

      3  16  -3

      9   14  4

   =52

Dz=1  1  4

      3  4  16

      9   -3  14

 =26

Hence, D=13, Dx=26, Dy=52, Dz=26

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Using the triangular inequality we will get that:

A) 2 < x < 34.

B) 0 < x < 130

For a triangle with sides A, B, and C, the triangular inequality says that:

A + B > C

A + C > B

B + C > A

A) two lengths are 18 yards and 16 yards, and the missing length is x, so we can write:

18 + x > 16    →   x > 16 - 18 = -2

16 + x  > 18   →   x > 18 - 16 = 2

16 + 18 > x     →  34 > x

Taking the two more restrictive ones, we can see that 2 < x < 34.

B) Same thing:

x + 65 > 65

x + 65 > 65

65 + 65 >  x

If we simplify that, we will get:

0 < x < 130

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Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment;

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively);

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%;

Given:

Hannah makes 5 out of 8 attempted free-throws.

Now,

The average waiting time of hannah to make her first basket is 5/8

The probability of hannah making basket at her last attempt is 1/8

The probability of hannah making basket before her last attempt is 2/8

Hence, the probabilty will be 1/8 and 2/8;

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Answer:

What you´re going to do, is 0.25 x 20, and that is about 5.00. Then you do 15 + 5 and you get 20 dollars for 20 miles. M = $20

Step-by-step explanation:

Answer:

The answer is $1,175.34

The equation required is C = $120 + $55h

In order to write the required equation, the hourly fee has to be determined first

The total cost Michelle charges is the sum of the initial fee and the hourly rate

Total cost = initial fee + hourly rate

Initial fee = $120

Hourly rate = hourly fee x hours

= 4a

Where a represents hourly fee

$400 = $120 + 4a

Combine similar terms

$400 - $120 = 4a

$220 = 4a

Divide both sides of the equation by 4

a = $55

C = $120 + $55h

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The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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Answer:

x = 3500

Step-by-step explanation:

2580 + 2920 + x

------------------------ = 3000

           3

      5500 + x

------------------------ = 3000(3)

           3(3)

5500 + x = 9000

-5500         -5500

------------------------------

x = 3500

I hope this helps!

D) it is difficult to administer.

Step-by-step explanation:

Answer:

3ax+10x+6a-6

Step-by-step explanation:

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

The missing piece of information is ∠C ≅ ∠C′

From the figure,  we have:

AB ≅ A'B'

<B ≅ <B'

The above means that:

The congruence theorem is given as:

AAS --- Angle Angle Theorem

i.e.

Two corresponding angles and one corresponding side are congruent

Since a congruent side and a congruent angle have been given;

We need a congruent angle to complete the piece

In this case, we have:

∠C ≅ ∠C′

Hence, the missing piece of information is ∠C ≅ ∠C′

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Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

32

Step-by-step explanation:

we substitute the values first

5 * (the absolute value of )-5) + 7

absolute value means neither the positive or negative value, so no signs before that number (the one your taking the absolute value of)

5*5+7

5*5 = 25

25+7 = 32

done!