45 pts i need helppp Select the correct row in the table.
Which row of the table reveals the y-intercept of function
х: -1, 0, 1, 2,3 f(x): 2 2/3, 2, 0, -6, -24

This is known as the Collatz Conjecture, and it remains an unsolved problem in mathematics. Despite extensive computational evidence suggesting that the conjecture is true, a proof or counterexample has yet to be found.

The conjecture states that no matter what positive integer you start with, applying the "3n+1" rule (multiply by 3 and add 1 if n is odd) or "n/2" rule (divide by 2 if n is even) repeatedly will eventually lead to the sequence 4, 2, 1, and then it will loop endlessly: 4, 2, 1, 4, 2, 1, and so on.

While the conjecture has been checked for all starting values up to at least 10^20, no one has been able to prove that it holds true for all positive integers. It is possible that there exists a starting value that does not eventually fall into the 4, 2, 1 loop, but no such value has been found.

The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.

f(x) 10 3 5 2 Let glx) be a twice differentiable function defined by another differentiable function f(x), such that 9 (2) = 21+ J' f (t) dt: Selected values of f(x) are given in the table above.

We can calculate g'(x) as follows:

g'(x) = 2f'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3

1. Start by taking the derivative of g(x) with respect to x. This is done using the chain rule, since g(x) is defined by another differentiable function f(x):

g'(x) = d/dx[21 + J' f(t) dt] = 2f'(x)

2. Now, substitute the function f(x) into the equation for g'(x):

g'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3

The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.

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Answer:

Step-by-step explanation:

(2/3)x - 4 > 1

(2/3)x  > 5

x is larger or equal 15/2

Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

Answer:

8

Step-by-step explanation:

Because its a 2,2

Answer:

2x^2  y^3

Step-by-step explanation:

so its 2x then squared by 2 then y and squared by 3 all together making 2x^2y^3

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

the percent error in the student's measurement is 4.65%.

Step-by-step explanation:

The percent error can be calculated using the formula:

| (measured value - actual value) / actual value | * 100%

In this case, the measured value is 2.7 grams and the actual value is 2.58 grams. Substituting these values into the formula, we get:

| (2.7 - 2.58) / 2.58 | * 100% = 4.65%

Rounding this to the nearest hundredth of a percent, we get a percent error of 4.65%.

Therefore, the percent error in the student's measurement is 4.65%.

Answer: 5

Step-by-step explanation:

x+3x−2=18

x+3x+−2=18

(x+3x)+(−2)=18(Combine Like Terms)

4x+−2=18

4x−2=18

Step 2: Add 2 to both sides.

4x−2+2=18+2

4x=20

Step 3: Divide both sides by 4.  

x=5

The function cannot exist for the values of x = 8, -3.

The domain of a function is the complete set of possible values of the independent variable.

Given is the function -

(x + 4)/(x² - 5x - 24)

We have the function -

(x + 4)/(x² - 5x - 24)

Let -

x² - 5x - 24 = 0

x + 3x - 8x - 24 = 0

x(x + 3) - 8(x + 3) = 0

(x - 8)(x + 3) = 0

x - 8 = 0     or     x + 3 = 0

x = 8   or   x = - 3

So, [x] cannot be equal to 8 and -3.

Therefore, the restrictions on the domain of the function is of the form -

x ≠ 8, -3.

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Answer:

the answer is 6

hope this helps:)

Answer:

6

Step-by-step explanation:

3-2 = 1

6-1= 5

5+1= 6 this is the answer hope it is help for u

Answer:

The answer is number 2

Answer:

Given number = 0.44

Find how many times the value of the hundredths place digit to the value of the tenths place digit.

=> Since this is a decimal number, I believe, the value you mean is tenths and hundredths, not tens and hundreds.

Now, how many times is the value of each digit differs from each other:

The answer is 10 times

=> 4 hundredths x 10 = 4 tenths

=> 0.04 x 10 = 0.4, which is correct

Step-by-step explanation:

The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Step-by-step explanation:

The field lines go out of Earth near Antarctica, enter Earth in northern Canada, and are not aligned with the geographic poles.

From the constraint, we have

\(x+y+z=9 \implies z = 9-x-y\)

so that \(s\) depends only on \(x,y\).

\(s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy\)

Find the critical points of \(g\).

\(\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9\)

\(\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0\)

Using the given constraint again, we have the condition

\(x+y+z = 2x+y \implies x=z\)

so that

\(x = 9 - x - y \implies y = 9 - 2x\)

and \(s\) depends only on \(x\).

\(s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2\)

Find the critical points of \(h\).

\(\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3\)

It follows that \(y = 9-2\cdot3 = 3\) and \(z=3\), so the only critical point of \(s\) is at (3, 3, 3).

Differentiate \(h\) again and check the sign of the second derivative at the critical point.

\(\dfrac{d^2h}{dx^2} = -6 < 0\)

for all \(x\), which indicates a maximum.

We find that

\(\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)\)

The second derivative at the critical point exists

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\) for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

\($&\frac{\partial g}{\partial x}\) = 9 - 2x - y = 0

\($&\frac{\partial g}{\partial y}\) = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

\($\frac{d h}{d x}=18-6 x=0\)

⇒ x = 3

It pursues that y = 9 - 2 \(*\) 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\)

for all x, which suggests a maximum.

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Answer:

11.75

Step-by-step explanation:

Using the exponential decay equation, we can see that after 1000 years we will have  178.43 mg  of Ra₂₂₆

The decay of a radioactive substance, such as Radium-226, can be modeled by the exponential decay equation:

N(t) = N₀ * (1/2)^(t / T)

where:

N(t) is the amount of the substance remaining after time t

N₀ is the initial amount of the substance

t is the time elapsed

T is the half-life of the substance

Given that the half-life of Radium-226 is 1590 years and the initial amount is 500 mg, we can plug in these values into the equation and solve for N(1000), which represents the amount remaining after 1000 years.

N(1000) = 500 * (1/2)^(1000 / 1590)

N(1000) ≈ 178.43 mg

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Answer:

area of a circle = pi*r^2

3 = pi*r^2

r^2 = 3/pi

r = √(3/pi)

diameter = 2*r = 2*√(3/pi)

Answer:

2 only

Step-by-step explanation:

x³ = 8

x = ∛8

x = 2

2 * 2 * 2 = 8

Answer:

(h + k) (2) = 5

Step-by-step explanation:

\(h(x) = x{^2} + 1 \space\ \space\ \space\ \space\ \space\ \space\ \space\ k(x) = x -2\\\\\)

(h + k) (x) = h(x) + k(x)

               = x² + 1  +  x - 2

               = x² + x -1

∴ (h + k) (2) = (2)² + 2 -1

                  = 5

a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer: hii :)

Step-by-step explanation:

The probability of a red marble being drawn in both turns = 9/16, and the probability of a white marble being drawn in both turns = 1/16. So, the total probability = (9/16) + (1/16) = 10/16 = 5/8.

Hopefully this helps you

- Matthew

Answer:

\(\sf \dfrac58\)

Step-by-step explanation:

Given:

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

\(\implies \sf \textsf{P(red marble)}=\dfrac{3}{4}\)

\(\implies \sf \textsf{P(blue marble)}=\dfrac{1}{4}\)

As the marbles are replaced:

\(\implies \sf \textsf{P(red marble) and P(red marble)}=\dfrac{3}{4} \times \dfrac{3}{4}=\dfrac{9}{16}\)

\(\implies \sf \textsf{P(blue marble) and P(blue marble)}=\dfrac{1}{4} \times \dfrac{1}{4}=\dfrac{1}{16}\)

Therefore:

\(\implies \sf \textsf{P(red and red) or P(blue and blue)}=\dfrac{9}{16}+\dfrac{1}{16}=\dfrac{10}{16}=\dfrac58\)

9514 1404 393

Answer:

Step-by-step explanation:

(a) Maria's straight time pay is ...

  (38 h)×($18.40 /h) = $699.20

__

(b) Maria's overtime pay is ...

  (6 h)×(1.5×$18.40 /h) = $165.60

__

(c) Her total pay is the sum of her straight time pay and her overtime pay:

  $699.20 +165.60 = $864.80

Answer:

11/56 i think

Step-by-step explanation:

The slope of the line is m = - 11/7

And the y-intercept is b = 8

Find the slope and the y-intercept.

Step 1 – Transform the equation.

-11x - 7y = -56

To get a slope-intercept form, we need to isolate the variable y on the left-hand side of the equation.

First, we need to eliminate variable x from the left-hand side.

To eliminate the term with x, we'll add it to both sides of the equation. Remember to always perform the same operation on both sides to keep the equality true!

-11x – 7y + 11x = -56 + 11x

Now, let's add terms on the left-hand side. Keep in mind that two opposites add up to zero, so we can just remove it.

-7y = -56 + 11x

Since the variable x should be the firs on the righ-hand side in slope-intercept form, let's make it that way. Use the commutative property to reorder the terms.

-7y = 11x – 56

We're almost there! We just have to eliminate -7 from the left-hand side. To do that, let's divide both sides of the equation by -7.

(-7y)/(-7) = (11x - 56)/(-7)

Simplify the left-hand side. Each number divided by itself equals 1, so we are left with y.

y = (11x - 56)/(-7)

Next, separate the fraction on the righ-hand side into two fractions.

y = 11x/(-7) - 56/(-7)

Simplify the fraction on the right-hand side of the equation.

y = - 11x/7 + 56/7

y = - 11x/7 + 8

Finally, write the expression with x as a product.

y = - 11/7 x + 8

That's it! We've got the slope-intercept form of the equation.

Step 2 – Identify the slope.

Since the equation is written in slope-intercept form, y = m x + b, identify the slope of the lines as the coefficient next to the variable x.

y = - 11/7 x + 8

m = - 11/7

Step 3 – Identify the y-intercept.

Identify the y-intercept of the line as the constant term.

y = - 11/7 x + 8

m = - 11/7

b = 8

The slope of the line is m = - 11/7

And the y-intercept is b = 8

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Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

Answer: x = √-6 - 4

Step-by-step explanation:

x^2+8x+22=0

(x+4)^2 - 16 + 22 = 0

(x+4)^2 + 6 = 0

(x+4)^2 = -6

√(x+4)^2 = √-6

x = √-6 - 4            

√6 = 2.449

Answer:

7350

Explanation:

3763.2/0.512 can be determined by simply dividing.