The histogram represents a data distribution with uniform class widths 1.

Which of the following is the mean of the data distribution?

2
3
4
5
6
7
8
9
10

A. 4.1
B. 4.5
C. 4.7
D. 4.9

The question is a college-level mathematics problem involving taking the third derivative of the function f(x) = 2x/(x^2 - 1). The process requires the application of quotient rule and chain rule of differentiation.

The student question involves calculating the third derivative of the function f(x) = 2x/(x2 - 1). This function is a rational function and can be differentiated using the quotient rule and chain rule of differentiation. Let's proceed with the derivative calculations.

First, we should recall that the function can be rewritten as:

f(x) = 2x/(x2 - 1) = 2x/[(x - 1)(x + 1)]

Now we can calculate the derivatives. For the first derivative f'(x), we use the quotient rule:

f'(x) = [(x2 - 1)(2) - (2x)(2x)]/(x2 - 1)2

For the second derivative f''(x), we differentiate f'(x) again:

f''(x) = Derivative of f'(x) with respect to x

The third derivative f'''(x) is then the derivative of f''(x). Calculations for the second and third derivatives can be a bit complex and lengthy, and it is necessary to apply the quotient rule and product rule carefully.

Through this process, we will arrive at the third derivative, f'''(x), which is what the question asks for.

Answer:

x=0

Step-by-step explanation:

8x=12x

12x-8x=0

4x=0

x=0/4

x=0

Answer:

28.5 inches.

Step-by-step explanation:

Given: Measurement of diagonal= 36 inch.

           Height= 22 inches

Picture attached to show the measurement.

As the screen of televison is measured by diagonal of screen.

∴ Hypotenous= diagonal of screen, which is 36 inches.

Now, using pythagorean theoram to find length of television screen.

[tex]hypotenous^{2} = opposite^{2}+adjacent^{2}[/tex]

∴ [tex]36^{2} = 22^{2} + adjacent^{2}[/tex]

Here adjacent is the length of television.

⇒[tex]1296= 484+ length^{2}[/tex]

Subtracting both side by 484.

⇒[tex]length^{2} = 812[/tex]

Taking square root on both side

remember: [tex]\sqrt{a^{2} } = a[/tex]

∴ [tex]length= \sqrt{812}= 28.495 \approx 28.5[/tex]

Hence, length of televison screen is 28.5 inches.

The width of a television screen can be calculated using the Pythagorean theorem. Given a diagonal of 36 inches and height of 22 inches, the approximate length of the screen is 30 inches.

To solve this problem, we will use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This principle can be written as a^2 + b^2 = c^2 where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

In the case of a television screen, the diagonal (from one corner to the opposite corner) is the hypotenuse. Given the height of the TV screen as 22 inches (one of the sides of the right triangle), and the diagonal as 36 inches (the hypotenuse), the length (the other side of the right triangle) can be found using the formula.

Let's rearrange the formula to solve for the length (b): b = sqrt(c^2 - a^2). Substitute the given measurements into the formula: length = sqrt(36^2 - 22^2), or approximately 30 inches.

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Answer:

The correct answer is C. 15 ¹⁵√x⁵y³

Correct question and statement:

Express 15x^1/3 y^1/5 using a radical, as it is written in the graph attached.

Step-by-step explanation:

15x^1/3 y^1/5

15 * (x^1/3 y^1/5)

For multiplying two fractional exponents with different bases, we need to equal the denominator of the fractional exponents.

Therefore, we have:

1/3 * 5/5 = 5/15 ⇒ 1/5 * 3/3 = 3/15

15 * (x^5/15 y^3/15)

Now we can express the fractional exponents as an only radical, this way:

x^a/b = ᵇ√xᵃ

15 * ¹⁵√x⁵y³

The correct answer is C. 15 ¹⁵√x⁵y³

Answer:

[tex]\large\boxed{y+1=3(x-1)}\\\\\boxed{y=3x-4}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - a point on a line

We have

[tex]m=3,\ (1,\ -1)\to x_1=1,\ y_1=-1[/tex]

Substitute:

[tex]y-(-1)=3(x-1)\\\\\boxed{y+1=3(x-1)}[/tex]

Convert to the slope-intercept form

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]y+1=3(x-1)[/tex]            use the distributive property

[tex]y+1=3x-3[/tex]             subtract 1 from both sides

[tex]\boxed{y=3x-4}[/tex]

Answer:

73

Step-by-step explanation:

Givens

d = 3

Equation 7d^2 + 10 = ?

Solution

7*3*3 + 10                

7*9 + 10

63 + 10 = 73

Answer:

3x-2y^2-2

Step-by-step explanation:

3x-(2y^2+2)=3x-2y^2-2

Answer:

The graph with B(2,-3) i.e) y=[tex]\frac{-3}{2}[/tex] x goes through the point M(-10,15).

Step-by-step explanation:

Consider M(-10,15) and given that equation is y = kx.

Now, substitute M(-10,15) in the equation

⇒ 15 = k × -10

⇒ k = [tex]\frac{15}{-10}[/tex] = [tex]\frac{-3}{2}[/tex]

⇒ y = [tex]\frac{-3}{2}[/tex] x

Now, check with the given points B(2,-3) and B([tex]3\frac{1}{3}[/tex] , -2)

1) B(2,-3)

y = [tex]\frac{-3}{2}[/tex] x

⇒(-3) = [tex]\frac{-3}{2}[/tex] × 2

⇒ -3 = -3 ⇒ LHS = RHS

⇒ B(2,-3) is the required point.

2) for b([tex]3\frac{1}{3}[/tex] , -2)

LHS ≠ RHS.

So,The graph with B(2,-3) i.e) y=[tex]\frac{-3}{2}[/tex] x goes through the point M(-10,15).

Answer:

[tex]3 \leqslant y < 10[/tex]

The inequality that represents the given situation is (3 ≤ y < 10).

So, the inequality will be:

Which means:

So, the inequality will be:

Therefore, the inequality that represents the given situation is (3 ≤ y < 10).

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Answer:

3.75

Step-by-step explanation:

the number you want to turn into apercentage over the total value so you end up with a fraction. Then, turn the fraction into a decimal by dividing the top number by the bottom number. Finally, multiply the decimal by 100 to find the percentage.

Answer:

Graph 3 represents the solution to the system of equations.

Step-by-step explanation:

The given two linear equations of x and y are

y = 3x + 2 ........ (1) and  

10x + 2y = 20 .......... (2)

Now, to solve those two equations let substitute the value of y from equation (1) to the equation (2).

Hence, 10x + 2(3x + 2) = 20

⇒ 16x = 16

⇒ x = 1  

And from equation (1), y = 3x + 2 = 5  

Therefore, the solution of the system of equations (1) and (2) are (1,5).

Therefore, graph 3 represents the solution to the system of equations. (Answer)

Answer:

29,025 is the answer

Step-by-step explanation:

9,675 × 3

The number of people who visited Hank's website last month is found by dividing the total visitors this month (9,675 people) by 3, resulting in 3,225 visitors last month.

The student is faced with a mathematics problem involving division with whole numbers. The problem states that the number of people who visited Hank's website this month is three times the number of visitors from the previous month. Given that we know the number of visitors this month is 9,675, we can find out the number of visitors from the previous month by dividing this number by three.

So, the calculation is:

9675 people (this month) ÷ 3

From this calculation, we can determine that 3,225 people visited Hank's website last month.

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Answer:

Step-by-step explanation:

Sin (π - x ) = Sin x = m

Answer:

The % of the increase in population from 1980 to 2000 will be 72.8%

Step-by-step explanation:

Let the population in the year of 1980 was x.

If the population from 1980 to 1990 has increased by 20%, then the population in the year 1990 will be [tex]x(1 + \frac{20}{100}) = 1.2x[/tex].

Now, from 1990 to 2000, the population has again increased by 20%.

So, the population in the year 2000 will be [tex]1.2x(1 + \frac{20}{100}) = 1.44x[/tex].

Again, from 2000 to 2010, the population has increased by 20%.

Therefore, the population in the year 2010 will be [tex]1.44x(1 + \frac{20}{100}) = 1.728x[/tex].

Now, the population increased from x to 1.728x between the years 1980 to 2010.

Hence, the % of the increase in population from 1980 to 2000 will be [tex](\frac{1.728x - x}{x}) \times 100\% = 72.8\%[/tex] (Answer)

Answer:

[tex]V=200\ yd^3[/tex]

Step-by-step explanation:

we know that

The volume of the prism is equal to

[tex]V=LWH[/tex]

where

L is the length

W is the width

H is the height

we have

[tex]L=10\ yd\\W=5\ yd\\H=4\ yd[/tex]

substitute

[tex]V=(10)(5)(4)=200\ yd^3[/tex]

Answer:

C.) 200 yd3

Step-by-step evaluation:

Step 1.) 4 x 5 = 20

Step 2.) 20 x 10 = 200

Step 3. (Final answer).) C.) 200 yd3

Explanation:

4 times 5 will equal 20 because, 4 + 4 + 4 + 4 + 4, or 5 + 5 + 5 + 5, equals 20.

20 times 10 will equal, the answer, 200 hundred because 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 = 200, and that's our answer.

Final answer:

C.) 200 yd3

Option 4

f(x) = -x is an odd function

Solution:

A function is odd if and only if f(–x) = –f(x)

Option 1

[tex]f(x) = x^3 + 5x^2 + x[/tex]

Substitute x = -x in above equation

[tex]f(-x) = (-x)^3 + 5(-x)^2 + (-x)[/tex]

Cubes always involve multiplying a number by itself three times, so if the number is negative the cube will always be negative

Ans squaring results in positive

[tex]f(-x) = -x^3 + 5x -x[/tex]  --- eqn 1

[tex]-f(x) = -(x^3 + 5x^2 + x)\\\\-f(x) = -x^3 - 5x^2 - x[/tex]  ---- eqn 2

Comparing eqn 1 and eqn 2,

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 2

[tex]f(x) = \sqrt{x}[/tex]

[tex]f(-x) = \sqrt{-x}[/tex]

[tex]-f(x) = - \sqrt{x}[/tex]

Therefore,

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 3

[tex]f(x) = x^2 + x\\\\f(-x) = (-x)^2 + (-x)\\\\f(-x) = x^2 - x[/tex]

[tex]-f(x) = -(x^2 + x) = -x^2 - x[/tex]

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 4

[tex]f(x) = -x\\\\f(-x) = -(-x) = x[/tex]

[tex]-f(x) = -(-x) = x[/tex]

[tex]f(-x) = -f(x)[/tex]

Thus option 4 is correct and it is an odd function

Answer:

D

Step-by-step explanation:

just took test on edge

Answer:

7 kg

Step-by-step explanation:

F=35*2=m*10

70=10m

7=m

The mass of the second object is 7 kg

First, we make the following representations

[tex]F \to[/tex] Force

[tex]a \to[/tex] acceleration

[tex]m \to[/tex] mass

The formula of force is:

[tex]F = m * a[/tex]

Since force is constant, then:

[tex]m_1 =2kg[/tex]    [tex]a_1 = 35m/s^2[/tex] --- subset 1 represents the first object

[tex]m_2 = ??[/tex]       [tex]a_2 = 10m/s^2[/tex] --- subset 2 represents the second object

We are to calculate the mass of the second object

A constant force means:

[tex]m_1 * a_1 = m_2 * a_2[/tex]

Make m2 the subject

[tex]m_2 = \frac{m_1 * a_1}{a_2}[/tex]

Substitute known values

[tex]m_2 = \frac{2kg * 35m/s^2}{10m/s^2}[/tex]

[tex]m_2 = \frac{2kg * 35}{10}[/tex]

[tex]m_2 = \frac{70kg}{10}[/tex]

[tex]m_2 =7kg[/tex]

Hence, the mass of the second object is 7kg

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Answer:

$7.50

Step-by-step explanation:

10 divided by 4 = $2.50

so, $2.50 x 3 = $7.50

Answer:

$7.5 Dollars

Step-by-step explanation:

The cost of 4 bottles is $10. So, 1 bottle is going to be $2.50 (division)

Now, to find the cost of 3 water-bottles, we have to multiply.

$2.50 * 3 = $7.50.

So, the answer to this question is  3 bottles = $7.50

(Hope this helps!)

Answer:

n=(9v-4f)/k

Step-by-step explanation:

kn+4f=9v

kn=9v-4f

n=(9v-4f)/k

Answer:

n = (-4f + 9v) ÷ k

Step-by-step explanation:

All you have to do is... flip the equation

Answer:

The perimeter of crater lake is 17.27 miles.

Step-by-step explanation:

Given as :

The shape of the lake is like a circle

The diameter of lake = d = 5.5 miles

∵ shape pf lake is circle, so the diameter of circle = d = 5.5 miles

Let The perimeter of crater lake = p miles

Now, As we know

The perimeter of circle = [tex]\pi[/tex] × diameter

the value of  [tex]\pi[/tex] = 3.14

Or, p =  [tex]\pi[/tex] × d

Or, p =  [tex]\pi[/tex] × 5.5 miles

Or, p =  3.14 × 5.5 miles

∴ p = 17.27 miles

So, The perimeter of circle = perimeter of lake = p = 17.27 miles

Hence, The perimeter of crater lake is 17.27 miles. Answer

Answer:

The answer is 40

Step-by-step explanation:

First, since roger has 3 times as many grapes as Marissa. do 10 times 3. The answer is 30. Roger has 30 grapes. The question is asking how much they have all together. Add 30 plus 10 and the answer that you will get is 40. The answer is 40

Answer:

yassar

Step-by-step explanation:

Answer:

1/8x___________=7/8 the answer is 6

Answer:

there are 1,440 minutes in 24 hrs a day

Step-by-step explanation:

Now thank me and rate me

Hope your year has been going great !!

The answer is 1440 if im correct

Answer:

Grover has $24, Percy has $31 and Annabeth has $19.

Step-by-step explanation:

Create equations to represent the situation.

let a be Annabeth

let g be Grover

let p be Percy

a + g = 43      Together, Annabeth and Grover have $43

g + p = 55    If Grover and Percy combine their money, they have $55

p = g + 7        Percy has $7 more than Grover

See if any of the equations can be combined. For example, we know p is g+7.

Substitute p for g+7 in an equation that has the variable p.

g + p = 55

g + g + 7 = 55    Combine like terms (g)

2g + 7 = 55   Start isolating g. Subtract 7 from both sides

2g = 55 - 7

2g = 48     Divide both sides by 2

g = 48/2    

g = 24         Money Grover has

Use the equation p = g + 7. Find "p" by substituting g for 24.

p = g + 7

p = 24 + 7   Add

p = 31    Money Percy has

Substitute g for 24 in the last equation, a + g = 43, to find a.

a + g = 43

a + 24 = 43    Subtract 24 from both sides

a = 43 - 24

a = 19     Money Annabeth has

Therefore Grover has $24, Percy has $31 and Annabeth has $19.

Answer:

Grover has $24, Percy has $31 and Annabeth has $19.

Create equations to represent the situation.

let a be Annabeth

let g be Grover

let p be Percy

a + g = 43      Together, Annabeth and Grover have $43

g + p = 55    If Grover and Percy combine their money, they have $55

p = g + 7        Percy has $7 more than Grover

See if any of the equations can be combined. For example, we know p is g+7.

Substitute p for g+7 in an equation that has the variable p.

g + p = 55

g + g + 7 = 55    Combine like terms (g)

2g + 7 = 55   Start isolating g. Subtract 7 from both sides

2g = 55 - 7

2g = 48     Divide both sides by 2

g = 48/2    

g = 24         Money Grover has

Use the equation p = g + 7. Find "p" by substituting g for 24.

p = g + 7

p = 24 + 7   Add

p = 31    Money Percy has

Substitute g for 24 in the last equation, a + g = 43, to find a.

a + g = 43

a + 24 = 43    Subtract 24 from both sides

a = 43 - 24

a = 19     Money Annabeth has

Therefore Grover has $24, Percy has $31 and Annabeth has $19.

Answer:

Step-by-step explanation:

(2,-4)....x1= 2 and y1 = -4

(p,8).....x2 = p and y2 = 8

slope(m) = 1/2

now use the slope formula (y2 - y1) / (x2 - x1) and sub in what we know...

slope(m) = (y2 - y1) / (x2- x1)

1 / 2 = (8 - (-4) / (p - 2)

1 / 2 = (8 + 4) / (p - 2)

1/2 = 12 / (p - 2) .....now multiply both sides by (p - 2)

1/2(p - 2) = 12

1/2p - 1 = 12

1/2p = 12 + 1

1/2p = 13

p = 13 / (1/2)

p = 13 * 2/1

p = 26

so the value of p is 26

2.615

Step-by-step explanation:

22 divided by 8

the average snowfall per hour is 2.75 inch.

Division is the process of splitting a number or an amount into equal parts.

here, given that,

A snowstorm dumped 22 inches of snow in 8 hours.

i.e. per hour = 22/8

                    =2.76

hence,  the average snowfall per hour is 2.75 inch.

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Answer:

[tex]A=65.97\ cm^2[/tex]

Step-by-step explanation:

The complete question is

The shaded region is the area outside the smaller circle and inside the larger circle

we know that

The area of the shaded region is equal to subtract the area of the smaller circle from the area of the larger circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

The area of the shaded region is

[tex]A=\pi [r_1^2-r_2^2][/tex]

where

[tex]r_1=12.5/2=6.25\ cm[/tex] ---> radius of the larger circle (is half the diameter)

[tex]r_2=8.5/2=4.25\ cm[/tex] ---> radius of the smaller circle (is half the diameter)

assume

[tex]\pi =3.1416[/tex]

substitute

[tex]A=3.1416[(6.25)^2-(4.25)^2][/tex]

[tex]A=65.97\ cm^2[/tex]