Figure out the probability below (ONLY REAL ANSWERS PLEASE)

The points of inflection for the function [f(x) = (x⁴ - 6x²)] are (1, -5) and

(-1, -5).

As per the question statement, we are provided with a function

[f(x) = (x⁴ - 6x²)].

We are required to determine the points of inflection for the above mentioned function.

To solve this question, we will have to calculate the second derivative of the given function. Then, we will have to equate the derivative to zero and solve for x. The obtained values for "x" will be our abscissa, and substituting these values of "x" in f(x), we will obtain our respective ordinates [Since, {y = f(x)}].

[tex]f(x)=(x^{4} -6x^{2})\\or,\frac{d[f(x)}{dx} = \frac{d(x^{4} -6x^{2}) }{dx}\\ or, f'(x)=\frac{dx^{4}}{dx}-\frac{d(6x^{2})}{dx}\\ or, f'(x)=\frac{dx^{4}}{dx}-6\frac{d(x^{2})}{dx}\\or, f'(x)=4x^{(4-1)}-(6*2)[x^{(2-1)}]\\ or,f'(x)=4x^{3}-12x\\[/tex]

Therefore, the second derivative of f(x) = [tex]\frac{d^{2}f(x)}{dx^{2} }[/tex]

[tex]or,f"(x)=\frac{d[f'(x)]}{dx}\\or,f"(x)=\frac{d(4x^{3} -12x)}{dx}\\or, f"(x)=\frac{d(4x^{3}) }{dx}-\frac{d(12x)}{dx}\\ or, f"(x)=4\frac{d(x^{3}) }{dx}-12\frac{d(x)}{dx}\\or,f"(x)=(4*3)[x^{(3-1)}]-(12*1)[x^{(1-1)}]\\ or, f"(x)=12x^{2} -12[/tex]

Now, equating (12x² - 12) to Zero, we get,

[tex](12x^{2} -12)=0\\or,12x^{2} =12\\or,x^{2} =1\\or,x=(1, -1)[/tex]

Now, substituting (x = 1) in f(x), we get,

[tex]y=f(1)=[(1)^{4}-6(1)^{2}]\\ or,y=[1-(6*1)]\\or,y=(1-6)\\or,y=(-5)[/tex]
Hence, one point of inflection for the function [f(x) = (x⁴ - 6x²)] is (1, -5).

Again, substituting [x = (-1)] in f(x), we get,

[tex]y=f(-1)=[(-1)^{4}-6(-1)^{2}]\\ or,y=[1-(6*1)]\\or,y=(1-6)\\or,y=(-5)[/tex]

That is, another point of inflection for the function

[f(x) = (x⁴ - 6x²)] is (-1, -5).

To learn more about Points of Inflection, click on the link below.

https://brainly.com/question/14202844

#SPJ9

Answer:

x = 6

Step-by-step explanation: (See picture)

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

Hope this helps!

Have a great day and God bless! :)

Answer:

  (d)  48(0.25^(n-1))

Step-by-step explanation:

The points shown on the graph have y-values that decrease by a factor of 4 as x-values increase by 1. The first couple are (1, 48), (2, 12). You want the formula for the n-th term.

The terms of a geometric sequence have a common ratio (r). If the first term is a1, the general term is ...

  an = a1(r^(n-1))

The given sequence has first term a1 = 48. The common ratio is ...

  r = 12/48 = 1/4 = 0.25

Using these value in the formula for the general term, we find the n-th term to be ...

  an = 48(0.25^(n-1)) . . . . n-th term of the pattern

[tex]\begin{array}{ccccccccc} 1&&2&&3&&4&&5\\\cline{1-9} \\48&,&12&,&3&,&\underset{0.75}{\frac{3}{4}}&&\underset{0.1875}{\frac{3}{16}}\\[2em]\cline{1-9} &&48\left( \frac{1}{4} \right)&&12\left( \frac{1}{4} \right)&&3\left( \frac{1}{4} \right)&&\frac{3}{4} \end{array}~\hfill \begin{array}{llll} a_1=48\\\\ r=\frac{1}{4} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\stackrel{\textit{first term}}{48}\\ r=\stackrel{\textit{common ratio}}{\frac{1}{4}\to 0.25} \end{cases}\implies a_n=48\left( 0.25 \right)^{n-1}[/tex]

Answer:

Mean = 41.588

Standard Deviation = 17.765

Step-by-step explanation:

60 - N/D = 1.03643

75 - M/D

75 - (60 - 1.03643D)/D = 1.88079

15 + 1.03643D = 1.88079D

15 = 0.84436D

17.765 = D

D = 17.765

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

60 - M = 1.03643D

60 - 1.03643D = M

M = 60 - 1.03643(17.765)

M = 41.588

The scores on the test are centered around 66 and vary from 43 to 85.

A stemplot is a type of table where figures are divided into a stem and a leaf. The stem is the first number in the digit while the leaf is the last number. For example in the number 31, 3 would be the stem and 1 would be the leaf.

The range is used to measure variation. The range is the difference between the highest number and the smallest number. The largest number is 85 and the smallest number is 43.

The data would be centered around the median. The median is the number at the center of a dataset. The median is a measure of central tendency.

Median = (sum of numbers + 1) / 2

(26 + 1) / 2

= 27 / 2 = 13.5th number

(66 + 67) / 2 = 66.5

To learn more about stem plots, please check: https://brainly.com/question/12925429

#SPJ1

Answer:

4/12

Step-by-step explanation:

brainest plz

Answer:

b

Step-by-step explanation:

Answer: No solutions

Step-by-step explanation: These equations, when done by substitution, end up not equaling each other.

Answer:

16

Step-by-step explanation:

Answer:

is important because yo understand more with paragraph

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

You notice 8 to 10 is 2. So take 2 divided by 8 to find the percent and add 8 to see if it makes 10.

The monthly repayment of $145.59  is less than expected monthly payment of $150, hence, the individual can afford tp purchase the car on finance

How do we determine affordability in this case?

In order to determine whether the individual can afford to purchase the car on finance, we need to ascertain the monthly payment of the loan based on the terms of deal provided which would be compared to the expected monthly repayment of $150 using a financial calculator as below:

N=60(number of monthly payments in years=5*12)

I/Y=15.9/12(monthly interest rate without the % sign)

PV=-6000(loan principal)

FV=0(after 60 monthly payments, the balance would be nil)

CPT(press compute)

PMT=$145.59

Find out more about monthly repayment on:https://brainly.com/question/24182131

#SPJ1

Answer:

false true true true

Step-by-step explanation:

The equation for x = 6 is true and would be equal to 6x = 12. and the rest are false.

An equation represents the equality of two or more mathematical expressions. When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold for those values). Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

The given equations are;

6x = 12

Substitute x = 6 to check whether the solution satisfies the equation;

6(6)  = 36

Thus, it is False.

5 + x = 11

Substitute x = 6 to check whether the solution satisfies the equation;

5 + x = 11

5+ 6 = 11

Thus, it is True.

x ÷ 2 = 3

Substitute x = 6 to check whether the solution satisfies the equation;

6/2 = 3

Thus, it is True.

17 – x = 11

Substitute x = 6 to check whether the solution satisfies the equation;

17 - 6 = 11

Thus, it is True.

Hence, the equation for x = 6 is true and would be equal to 6x = 12. and the rest are false.

Learn more about solving equations here:

https://brainly.com/question/18015090

#SPJ2

Answer:

23m-18

Step-by-step explanation:

2(7m−5)+(−8+9m)

Remove parenthesis

2(7m-5)-8+9m

expand

14m-10

14m-10-8+9

simplify

23m-18

Ask me for more questions brainliest please.

Answer:

x=75/4

Step-by-step explanation:

4x+3=8x-9

4x+3= -72

4x= -72-3

4x= -75

x=75/4

Answer:

(C) $1.5

Step-by-step explanation:

Profit Percent * Cost Price = Profit

20% * $1.25 =

20/100 = .2 * $1.25 =

$.25

Selling Price = Profit + Cost Price

$.25 + $1.25 = $1.5

Answer: use this link

Step-by-step explanation:

Answer:

35+25

Step-by-step explanation:

Olivia first add 25 and 35 to get the sum 10.

Addition is a technique for merging items and counting them as one big group. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

Given:

Olivia had numbers as 25, 35 and 9.

So, to get the 10 the number should contain 5 at unit place.

then we first add 25 and 35

= 20+ 5 + 30+ 5

= 50+ 10

= 60

Then, 60+ 9= 69

Learn more about Addition here:

https://brainly.com/question/29560851

#SPJ2

Answer:

1) Combine the x tiles to get: [tex]\mathbf{4x}[/tex]

2) Combine integer tiles to get: 3

3) The equivalent function is: [tex]\mathbf{4x+3}[/tex]

4) If we Substitute any value of x both expressions will be equivalent

Step-by-step explanation:

We are given expression: [tex]x+x+x+x++4-1\\[/tex]

We need to complete following statements.

1) Combine the x tiles to get:

[tex]x+x+x+x\\=4x[/tex]

Combine the x tiles to get: [tex]\mathbf{4x}[/tex]

2) Combine integer tiles to get:

[tex]+4-1\\=3[/tex]

Combine integer tiles to get: 3

3) The equivalent function is:

[tex]x+x+x+x++4-1\\\\4x+3[/tex]

The equivalent function is: [tex]\mathbf{4x+3}[/tex]

4) If we Substitute any value of x both expressions will be equivalent

Verifying:

[tex]x+x+x+x+4-1=4x+3\\Let\: x = 1\\1+1+1+1+4-1=4(1)+3\\4+4-1=4+3\\7=7[/tex]

So, Both expressions are equivalent.

The answer is "4x" for the first box

                        "3" for the second box

                        "4x + 3" for the third box

And "Substitution"  for the last box

                                               You're Welcome!

    PS: I want to thank the first person for answering, you are amazing,

                                                       thanks!

Answer:

3.72 ft

Step-by-step explanation:

Height of the wall will be equal to the width of the wall because we are considering over surface area of the wall

Therefore,

Area of the wall = length * height

1534 = 412 * height

Height = 1534/412

Height = 3.72 ft

Answer:

B

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

6+9=15

15/3=5

Answer:

(1, -3)

Step-by-step explanation:

Use Desmos! It's really useful.

Answer: -18

Step-by-step explanation:

if 6-2d=42

just subtract 6 from both sides

-2d=42-6

-2d=36  now divide by 2

-d=18

multiply by -1

d=-18

Answer: d=-18

Step-by-step explanation:

6-2d=42

First subtract 6 from both sides

-2d=36

Now divide both sides by -2 to get d alone

d=-18

Answer:

Step-by-step explanation: log x +log x +log15=2

2log x=2-log 15

log x= 0.823/2

x=antilog (0.411)

x=2.58

Answer:

a

Step-by-step explanation:

The expressions of the range of temperatures would be 2000 - (-120) found in the thermosphere which is the correct answer would be option (D).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

The fourth layer of the Earth's atmosphere is the thermosphere. It begins just above the mesosphere and rises to a height of 600 kilometres above the Earth's surface.

As you go in height, the temperature in this layer rises. The range of temperatures is from -120°C to 2000°C.

The range of temperatures found in the thermosphere would be the difference between the final temperature and the initial temperature.

initial temperature = -120°C

final temperature = 2000°C

The range of temperatures = final temperature - initial temperature

The range of temperatures = 2000 - (-120)

Therefore, the expressions of the range of temperatures would be 2000 - (-120) found in the thermosphere.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ2

Answer:

Top Middle, Top Right, Bottom Left.

Answer:

In 8 minutes, she can jog 4000 feet.

Step-by-step explanation:

Davita jogs 2000 feet in 4 minutes.

Her rate is 2000/4 or 500 feet per minute.

500*8 = 4000

Answer:

2 × 1 +2 × 4= 10

Step-by-step explanation:

because 2×1 is 2 and 2×4 is 8 then you add them and get 10

Answer:

8,2,2,3

d,d,

HOPE THIS HELPS

Answer:

5d²

Step-by-step explanation:

Given

8d² - 3d² ← collect like terms by subtracting the coefficients, that is

(8 - 3)d²

= 5d²