how many times greater is 6x10⁹ than 3x10²​

Answer:

the two consecutive integers are 6 and 7.

Step-by-step explanation:

Im %99 sure

Answer:

Lets choose y

Plug in

Answer:

I'll choose 'x' variable first to eliminate because -

Step-by-step explanation:

Eqn.1 → -3x - 8y = -24

Eqn.2 → 3x - 5y = 45

If we'll add both the equations , then '3x' would be getting cancelled first.

⇒ \((-3x - 8y) + (3x - 5y) = (-24) + (45)\)

⇒ \(3x - 3x - 8y - 5y = 45 - 24\)

⇒ \(-13y = 21\)

⇒ \(y = \frac{-21}{13}\)

Putting the value of y in eqn.2 ,

⇒ \(3x - 5(\frac{-21}{13}) = 45\)

⇒ \(3x + \frac{105}{13} = 45\)

⇒ \(3x = 45 - \frac{105}{13}\)

⇒ \(3x = \frac{585 - 105}{13} = \frac{480}{13}\)

⇒ \(x = \frac{480}{13 \times 3} = \frac{480}{39}\)

Reducing the fraction gives ,

⇒ \(x = \frac{160}{13}\)

Answer:

A = 228 tickets

Step-by-step explanation:

We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.

Because the number of adult and student tickets together equals 506, we have A + S = 506.

Because there are 56 more student tickets than adult tickets we have A + 56 = S

And the way the system is already set up allows us to use substitution.

Thus, we have:

\(A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S\)

The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.

Therefore, a point c satisfying the conclusion of the Mean Value Theorem for f(x) = x⁻³ on the interval [1, 8] is approximately x = 2.3608.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function is often represented as an equation or a graph. It is a fundamental concept in mathematics and plays a crucial role in many areas, including calculus, algebra, and geometry. Functions are used to model real-world phenomena and solve problems in various fields, such as physics, engineering, economics, and more.

Here,

By the Mean Value Theorem, there exists a point c in the open interval (1, 8) such that:

f'(c) = [f(8) - f(1)] / (8 - 1)

where f'(x) is the derivative of f(x).

First, let's find the derivative of f(x):

f(x) = x⁻³

f'(x) = -3x⁻⁴

Now, substitute the values into the Mean Value Theorem equation:

-3c⁻⁴ = [8⁻³ - 1⁻³] / (8 - 1)

Simplify the right-hand side:

-3c⁻⁴ = (1/512) - (1/1)

-3c⁻⁴ = -511/512

Solve for c:

c⁻⁴ = (511/512) / 3

c⁻⁴ = 511/1536

c = \((511/1536)^{\frac{1}{4} }\)

c ≈ 2.3608

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Answer:

it is correct or not ? if it is incorrect sorry

the answer is....... x= -4

Answer:

The Answer is option (D)

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

9514 1404 393

Answer:

Step-by-step explanation:

The numbers are shown plotted on a number line in the attachment. The X marks the boundary where the "closest to ..." value changes.

The tenths digit of 0 in 0.0009999 indicates that number is closer to 0 than to 0.5 or 1.0.

The other two numbers are between 0.25 and 0.75, so are closer to 1/2 than to zero or 1.

Answer:

1.) -5/4

2.) 2

3.) 7/3

4.) 4

5.) -6

6.) -1

7.) 5/3

8.) -4

9.) 2

Step-by-step explanation:

this is what i got i hope they are all right

slope formula: (y2 - y1) / (x2 - x1)

9514 1404 393

Answer:

  (x, y) = (-7, 5)

Step-by-step explanation:

I find a graphing calculator to be useful for solving equations by graphing. The graph shows the solution to be ...

  (x, y) = (-7, 5)

__

In these equations, the y-coefficients are the same, so we can eliminate y by subtracting the first equation from the second.

  (4x -6y) -(-2x -6y) = (-58) -(-16)

  6x = -42 . . . . . . . . . simplify

  x = -7 . . . . . . . . divide by 6

Substituting into the first equation gives ...

  -2(-7) -6y = -16

  6y = 30 . . . . . . . . . . add 16+6y to both sides

  y = 5 . . . . . . . . .divide by 6

The solution is (x, y) = (-7, 5).

During halftime of a basketball game, a slingshot launches T-shirts at the crowd.

What is the maximum height?

Generally, To find the time it takes the T-shirt to reach its maximum height, we need to find the time when the height of the T-shirt stops increasing and starts decreasing. At this point, the velocity of the T-shirt will be 0, since it is not moving up or down.

The velocity of the T-shirt at any time t can be found by taking the derivative of the equation for height:

v(t) = dh/dt = -32t + 72

Setting the velocity to 0 and solving for t, we get:

0 = -32t + 72 32t = 72 t = 72/32 t = 9/4

So it takes the T-shirt 9/4 seconds, or approximately 2.25 seconds, to reach its maximum height.

To find the maximum height, we plug this value back into the equation for height:

h(t) = -16(9/4)^2 + 72(9/4) + 4 h(t) = -81 + 162 + 4 h(t) = 77

The maximum height of the T-shirt is 77 feet.

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To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

Answer:

Step-by-step explanation:

Ap classroom

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

for every x value you can pick, there is exactly one y value associated with it.

and for every y value you can pick, there is exactly one x value that leads to this y value (is associated with it).

Answer:

30

Step-by-step explanation:

30 because 15/20=30/40

NUMBER 5:

INFORMATION:

We have a trapeze and, we need to find the probability that a randomly chosen point is the figure lies in the shaded region

STEP BY STEP EXPLANATION:

To find the probability, we must divide the area of the shaded region by the total area of the trapeze

- Total area:

To calculate the total area, we must use the formula for the area of a trapeze

Where, b1 and b2 are the bases and h is the height

Then, analyzing the trapeze we can see that b1 = 20, b2 = 14 and h = 12

So, the total area is 204 square units

- Shaded area:

To find the shaded area, we must subtract the no shaded area from the total area.

We can see that the no shaded area is a rectangle with width = 14 and height = 12

Now, using the formula for the area of a rectangle

Then, subtracting the area of the rectangle from the total area

So, the no shaded are is 36 square units.

Finally, the probability would be

ANSWER:

the probability that a randomly chosen point is the figure lies in the shaded region is

Answer:

t = 1.2, -1.2

Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

we have the function

Complete the table

Substitute each value of x in the given function to obtain the value of f(x0

so

For x=10^0=1

For x=10^1=10

For x=10^2=100

For x=10^3=1,000

For x=10^4=10,000

For x=10^5=100,000

For x=10^6=1,000,000

therefore

see the attached figure below

as the value of x increases -----> the value of f(x) decreases

as x ----> ∞ f(x) ---> 0

Answer:

(3, –6)

Step-by-step explanation:

A function is a relation where one input is assigned to exactly one output.

This means that no inputs must be repeated in the relation.

(0, 2), (3, 8), (–4, –2), (3, –6), (–1, 8), (8, 3)

The input of '3' repeats in the relation.

By removing (3, -6), we can make the relation given a function.

Hope this helps.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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Answer:

Step-by-step explanation:

base area=41.57 in²

height=9 in

volume=41.57×9=374.13 in³

Complete question :

Find the standard deviation of the following data. Round your answer to one decimal place.

X: 0 1 2 3 4 5

P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2

Answer:

1.833

Step-by-step explanation:

Given the data :

X: 0 1 2 3 4 5

P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2

Standard deviation (s) = Sqrt[Σx²*f(x) - E(x)²]

E(x) = (0*0.2) + (1*0.3)+(2*0.1)+(3*0.1) + (4*0.1) + (5 * 0.2) = 2.2

Sqrt[Σx²*f(x) - E(x)²]: [(0^2 * 0.2)+(1^2 * 0.3)+(2^2 * 0.1)+(3^2 * 0.1) + (4^2 * 0.1) + (5^2 * 0.2)] - 2.2²

Sqrt(8.2 - 4.84) = 1.833

Answer:

B. (-12,-3,4,6)

Step-by-step explanation:

The above question is asking the domain

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

The one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

A one sided limit will not exist when it is outside the domain of the function.

The domain of a function is composed by the set of all the input values of the function, hence on the graph it is given by the values of x.

For this problem, the domain is then given as follows:

-6 ≤ x ≤ 8.

To the left of -6, the function is not defined, hence the one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

Meaning that the correct option is given by the last option.

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