Which statement is true about the function f(x)=8^3

Answer:

380

Step-by-step explanation:

This is an airthmatic sequence

we can use the following equation to find the nth term

a₁+(n-1)d

where the common difference (d) is 5

and the first term (a₁) is 10

and n is 75

we have

10+(75-1)*5

10+370

380

Answer:

they want you to find the error in the problem

Step-by-step explanation:

they want you to go through and find what they did wrong. You just have to correct the error they did, that is the question.

Answer:

(a) \(x\³ - 6x - 6\)

(b) Proved

Step-by-step explanation:

Given

\(r = $\sqrt[3]{2} + \sqrt[3]{4}$\) --- the root

Solving (a): The polynomial

A cubic function is represented as:

\(f = (a + b)^3\)

Expand

\(f = a^3 + 3a^2b + 3ab^2 + b^3\)

Rewrite as:

\(f = a^3 + 3ab(a + b) + b^3\)

The root is represented as:

\(r=a+b\)

By comparison:

\(a = $\sqrt[3]{2}\)

\(b = \sqrt[3]{4}$\)

So, we have:

\(f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3\)

Expand

\(f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

Evaluate like terms

\(f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)\)

Recall that: \(r = $\sqrt[3]{2} + \sqrt[3]{4}$\)

So, we have:

\(f = 6 + 6r\)

Equate to 0

\(f - 6 - 6r = 0\)

Rewrite as:

\(f - 6r - 6 = 0\)

Express as a cubic function

\(x^3 - 6x - 6 = 0\)

Hence, the cubic polynomial is:

\(f(x) = x^3 - 6x - 6\)

Solving (b): Prove that r is irrational

The constant term of \(x^3 - 6x - 6 = 0\) is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

\(f(-6) = (-6)^3 - 6*-6 - 6 = -186\)

\(f(-3) = (-3)^3 - 6*-3 - 6 = -15\)

\(f(-2) = (-2)^3 - 6*-2 - 6 = -2\)

\(f(-1) = (-1)^3 - 6*-1 - 6 = -1\)

\(f(1) = (1)^3 - 6*1 - 6 = -11\)

\(f(2) = (2)^3 - 6*2 - 6 = -10\)

\(f(3) = (3)^3 - 6*3 - 6 = 3\)

\(f(6) = (6)^3 - 6*6 - 6 = 174\)

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

Since none equals 0, then r is irrational

Answer:

C

Step-by-step explanation:

The test-statistic (z-score) is 1.19984.

To find the test statistic (z-score) using the p-value, you will need to use the inverse of the standard normal cumulative distribution function (CDF), also known as the inverse normal function or the "normal inverse function." This function can be found using a calculator or a spreadsheet program with built-in functions, or you can use a table of standard normal probabilities to find the corresponding z-score for a given p-value.

For example, if the p-value is 0.05, you would look up the corresponding z-score in a table of standard normal probabilities and find that it is approximately 1.645. This means that the test statistic (z-score) for a p-value of 0.05 is 1.645.

It's important to note that this method only works for a one-tailed test, for a two-tailed test you need to divide your p-value by 2 and then use the inverse normal function.

so, the p-value is 0.1151, you would look up the corresponding z-score in a table of standard normal probabilities and find that it is approximately 1.19984.

Therefore, the test-statistic (z-score) is 1.19984.

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In order to determine if the process of claims processing in the medical insurance company is in control, we need to use statistical process control (SPC). One commonly used tool for this is the control chart.

A control chart is a graph of the data collected over time, with control limits representing the range of variation that is considered acceptable. To create a control chart for this situation, we need to calculate the proportion of claims mailed late for each sample and plot them over time. We can then calculate the average proportion and the control limits, which are typically set at three standard deviations above and below the average. If the data falls within the control limits and there are no other patterns or trends, then we can conclude that the process is in control. Using the data provided, we can calculate the average proportion of claims mailed late to be 0.1536, and the control limits to be 0.0427 and 0.2644. Plotting the data on a control chart shows that the data points mostly fall within the control limits, with some variation but no major trends or patterns. Therefore, we can conclude that the process of claims processing in the medical insurance company is in control, meaning that the claims department is meeting its policy of processing all claims received within five days.

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The amount that Blake should have invested is $28875.38

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

Given here: Interest rate=5.7% compounded daily

Let p be the principal that Blake needs to invest

76000=P(1+5.7%/365)³⁶⁵ ˣ ¹⁷

76000=P(1.000156)⁶²⁰⁵

P=$28875.38

Thus Blake should have invested $28875.38

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Answer:

2 Right Angled Triangles

Step-by-step explanation:

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

If there is a low supply and a high demand, there is an increase in price and vice versa.

Last 2012, there was a virus which infected millions of chicken. It was known as Avian influenza or bird flu. It resulted to scarcity of eggs.

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

For example we can use water. If a product becomes scarce its price would increase due to supply in demand.

If drinkable water became scarce its price would be greatly increased to its need and being in extreme demand.

In short,  if there is a low supply and a high demand, there is an increase in price and vice versa.

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Answertank cu

Step-by-step explanation:

Answer:

The expected value of weekly demand is 1.3 units, the variance is 0.81, and the standard deviation is 0.9 units.

To find the expected value, variance, and standard deviation of the weekly demand, we can follow these steps:

1. Calculate the expected value (E[X]):
\(E[X] = \sum(x \times f(x))\)
= (0 * 0.2) + (1 * 0.4) + (2 * 0.3) + (3 * 0.1)
= 0 + 0.4 + 0.6 + 0.3
= 1.3

2. Calculate E[X²]:
\(E[X^2] = \sum(x^2 \times f(x))\)
= (0² * 0.2) + (1² * 0.4) + (2² * 0.3) + (3² * 0.1)
= 0 + 0.4 + 1.2 + 0.9
= 2.5

3. Calculate the variance (Var[X]):
Var[X] = E[X²] - (E[X])²
= 2.5 - (1.3)²
= 2.5 - 1.69
= 0.81

4. Calculate the standard deviation (SD[X]):
SD[X] = √(Var[X])
= √(0.81)
= 0.9

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Answer:

We are given : A scale factor of 1/3 and center of dilation (0, 0).

For the given image, the coordinates of the vertices of the triangle are

(0,9), (0,0) and (-6,0).

We can apply formula for finding new coordinates:

Scale factor * [Vertex coordinates of the given image - Coordinate of Center of dilation] +Coordinate of Center of dilation.

Applying same formula to each coordinates we are given.

(0,9) --> 1/3 [ (0,9) - (0,0) ] + (0,0) ]  = 1/3 [ (0,9)] +(0,0) = (0,3).

(0,0) --> 1/3 [ (0,0) - (0,0) ] + (0,0) ]  = 1/3 [ (0,0] +(0,0) = (0,0).

(0,9) --> 1/3 [ (-6,0) - (0,0) ] + (0,0) ]  = 1/3 [ (-6,0)] +(0,0) = (-2,0).

Now, we can plot those resulting coordinates on the graph and form a triangle.

Step-by-step explanation:

The image of the dilated polygon is attached below

Transformation is the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.

Dilation is the increase or reduce in size of a figure by a factor k. If a point A(x, y) is dilated by a factor k about the origin, the new point is A'(kx, ky).

Let us assume that the polygon has vertices at A(0,0), B(3, 3) and C(-3, 3). If the polygon is dilated by a scale factor of 1/3 and center of dilation at ​(0, 0)​, the new vertices is at:

A'(0,0), B'(1, 1) and C'(-1, 1)

The graph of the polygon is attached.

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Rational numbers are indeed closed under the operations of addition, subtraction, and multiplication is true.

We have,

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero.

The set of rational numbers is closed under the operations of addition, subtraction, and multiplication.

This means that if we take any two rational numbers and add them, subtract them, or multiply them together, the result will always be another rational number.

To see why this is true,

Consider two rational numbers a/b and c/d, where a, b, c, and d are integers and b and d are not equal to zero.

To show that rational numbers are closed under addition, we can add the two rational numbers as follows:

a/b + c/d = (ad + bc) / bd

Since a, b, c, and d are all integers, ad + bc is also an integer.

Also, since b and d are not equal to zero, bd is also not equal to zero.

And,

(ad + bc) / bd is a ratio of two integers, where the denominator is not equal to zero.

This means that it is a rational number.

To show that rational numbers are closed under subtraction, we can subtract the two rational numbers as follows:

a/b - c/d = (ad - bc) / bd

Again, since a, b, c, and d are all integers, ad - bc is also an integer, and bd is not equal to zero.

Therefore, (ad - bc) / bd is a rational number.

Finally, to show that rational numbers are closed under multiplication, we can multiply the two rational numbers as follows:

(a/b) x (c/d) = (ac) / (bd)

Once again, ac and bd are integers, and since b and d are not equal to zero, bd is also not equal to zero.

Therefore, (ac) / (bd) is a rational number.

Thus,

Rational numbers are indeed closed under the operations of addition, subtraction, and multiplication.

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Answer:

zero

Step-by-step explanation:

for example,

2 x 0 = 0

124 x 0 = 0

its some number zero times so when you multiply by zero, its zero

Answer: The answer is F

Step-by-step explanation:

Answer:

do I need to answer the questions in every pic?

Answer:

open the ones in bracket first

(_6)2 = _ 36

Step-by-step explanation:

so there fore 26.08 + (- 36) + 3.4 - 8.9 ÷ 9

open bracket by multiplying the signs

which implies

26.08 - 36 + (3.4 - 8.9) ÷ 9

- 9 .92 + (- 5.5) ÷ 9

open brackets by multiplying the signs

-9.92 - 5.5 ÷ 9

- 15.42 ÷ 9

which will give -1.713 approximately

Answer:

I believe your answer is 9

Step-by-step explanation:

The way I found this answer was by assuming that triangle CDE was expanded to get triangle FGH. So I divided 18/4 and got the answer 4.5, which means that the triangle was expanded by a factor of 4.5. So I then multiplied the similar side to HG by 4.5 which was side ED. This got me with 4.5 x 2 and I got the answer 9.

Hope this helps! :)

The economic impact of fishing for nearly all great lakes states varies, but according to a report by the U.S. Fish and Wildlife Service, it falls within the range of $1 to $8 billion (in millions of dollars).

This impact includes the economic contributions of recreational fishing, commercial fishing, and related industries such as tourism and boat manufacturing. The exact amount varies from state to state and from year to year depending on factors such as weather, fish populations, and fishing regulations.

The Great Lakes region of the United States is home to some of the largest freshwater bodies in the world and boasts a rich variety of fish species. Fishing is an important economic activity in the region, contributing billions of dollars to the local and national economy. The economic impact of fishing in the Great Lakes region includes not only the direct revenue generated by commercial and recreational fishing, but also the indirect and induced effects of fishing-related industries such as tourism and boat manufacturing.

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The required answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

Subtraction is mathematical terminology that helps and elaborates the decrease in the original value by some value.

Here,
To perform the subtraction, you line up the decimal points and subtract the digits in each place value starting from the right. In this case, you subtract 8 from 6, which requires borrowing 1 from the digit to the left, giving you 16 - 8 = 8 in the one's place. You then subtract 2 from 5, giving you 3 in the tenth place. Continuing this process, you get the result of 82,727.12.

Thus, the answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

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The solution of the DTDS is xn = (0.63)^n * 41 grams, where n represents time in hours.

a) The updating function f(x) for the discrete time dynamical system (DTDS) can be derived from the given information that the body eliminates 37% of the alcohol present in the body per hour.

Since 37% of the alcohol is eliminated, the amount remaining after one hour can be calculated by subtracting 37% of the current amount from the current amount. This can be expressed as:

f(x) = x - 0.37x

Simplifying the equation:

f(x) = 0.63x

b) The initial condition for the DTDS is given as Peter having 41 grams of alcohol in his body after consuming three alcoholic drinks. Therefore, the initial condition is:

x0 = 41 grams

c) To find the solution of the DTDS with the given initial condition, we can use the updating function f(x) and iterate it over time.

For n hours, the solution is given by:

xn = f^n(x0)

Applying the updating function f(x) repeatedly for n times:

xn = f(f(f(...f(x0))))

In this case, since the function f(x) is f(x) = 0.63x, the solution can be written as:

xn = (0.63)^n * x0

Substituting the initial condition x0 = 41 grams, the solution becomes:

xn = (0.63)^n * 41 grams

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Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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1) The volume of the solid obtained by rotating the region bounded by y² = x and x = 2y about the y-axis is 8π cubic units. 2) The volume generated by rotating the region bounded by y = 4(x - 2)² and y = x² - 4x + 7 about the y-axis is 4π cubic units.

1) To find the volume of the solid obtained by rotating the region bounded by the equations y² = x and x = 2y about the y-axis, we can use the method of cylindrical shells.

First, let's sketch the region bounded by the given equations which is attached as Figure1

We have y² = x, which represents a rightward-opening parabola with the vertex at the origin and the axis of symmetry along the y-axis.

x = 2y represents a line passing through the points (0, 0) and (2, 1).

To find the points of intersection between these curves, we can solve the equations y²  = x and x = 2y simultaneously:

Substituting x = 2y into y² = x, we get y²  = 2y.

Rearranging this equation, we have y²  - 2y = 0.

Factoring out y, we get y(y - 2) = 0.

So, y = 0 or y = 2.

Therefore, the region bounded by y² = x and x = 2y is bounded by the curves y = 0, y = 2, and x = 2y.

Now, let's find the volume of the solid using cylindrical shells

Consider a small vertical strip of width Δy at height y within the region. When this strip is rotated about the y-axis, it forms a cylindrical shell with radius x = 2y and height Δy.

The volume of this cylindrical shell is given by V = 2π(2y)(Δy), where 2π(2y) is the circumference of the shell and Δy is its height.

To find the total volume of the solid, we integrate the volumes of all such cylindrical shells over the range y = 0 to y = 2

V = ∫[0,2] 2π(2y)(Δy)

Integrating this expression, we get

V = ∫[0,2] 4πy(Δy)

= 4π ∫[0,2] y(Δy)

= 4π ∫[0,2] y dy

Evaluating this integral, we get

V = 4π [(y² /2)] [0,2]

= 4π (2² /2 - 0²/2)

= 4π (2)

= 8π

2) To find the volume generated by rotating the region bounded by the equations y = 4(x - 2)² and y = x² - 4x + 7 about the y-axis, we can again use the method of cylindrical shells.

First, let's sketch the region bounded by the given equations which is attached as Figure2

The equation y = 4(x - 2)² represents a parabola that opens upward and is centered at (2, 0). The equation y = x² - 4x + 7 represents a parabola that opens upward and intersects the first parabola at two points.

To find the points of intersection, we can set the two equations equal to each other

4(x - 2)² = x² - 4x + 7

Expanding and rearranging the equation, we get

4x² - 16x + 16 = x² - 4x + 7

Simplifying further

3x² - 12x + 9 = 0

Factoring the equation, we have

(x - 1)(3x - 9) = 0

So, x = 1 or x = 3.

Therefore, the region bounded by y = 4(x - 2)² and y = x² - 4x + 7 is bounded by the curves x = 1, x = 3, and the two parabolas.

Now, let's find the volume of the solid using cylindrical shells

Consider a small vertical strip of width Δx at position x within the region. When this strip is rotated about the y-axis, it forms a cylindrical shell with radius r = x and height Δx.

The volume of this cylindrical shell is given by V = 2πx(Δx), where 2πx is the circumference of the shell and Δx is its height.

To find the total volume of the solid, we integrate the volumes of all such cylindrical shells over the range x = 1 to x = 3

V = ∫[1,3] 2πx(Δx)

Integrating this expression, we get

V = 2π ∫[1,3] x(Δx)

= 2π ∫[1,3] x dx

Evaluating this integral, we get

V = 2π [(x²/2)] [1,3]

= 2π (9/2 - 1/2)

= 4π

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-- The given question is incomplete, the complete question is

1) Find the volume of the solid obtained by rotating the region bounded by y^2= x,x=2y; about the y-axis. Sketch the region, the solid and the cross section. 2) Find the volume generated by rotating the region bounded by y=4(x−2)^2,y= x^2−4x+7 about the y-axis. Sketch the region and the solid." --

Answer:

I think this is the correct solution

The quotient after division is (2t+1) and the remainder is 9.

In maths, a division is a process of splitting a specific amount into equal parts.

Given is an expression, (2t²+13t+15)÷(t+6)

Firstly take 2t,

2t(t+6) = 2t²+12

(2t²+13t+15) - 2t²+12 = t+15

Now take 1,

(t+6)X1 = t+6

t+15 - t-6 = 9

Hence, The quotient after division is (2t+1) and the remainder is 9.

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The antiderivative of f(x) with f′(x) = f(x) = 7/21x^2 + 18x^5 and f(1) = 0 is:
f(x) = (1/3)x^3 + (3/2)x^6 - 5/6

To find an antiderivative of f(x) with f′(x) = f(x) = 7/21x^2 + 18x^5 and f(1) = 0, we can use the formula for finding antiderivatives of power functions.

The antiderivative of x^n is (1/(n+1))x^(n+1) + C, where C is the constant of integration.

Using this formula, we can find the antiderivative of each term in f(x):

∫(7/21)x^2 dx = (1/3)x^3 + C1

∫18x^5 dx = (3/2)x^6 + C2

To find the antiderivative of f(x), we add the antiderivatives of each term:

f(x) = (1/3)x^3 + (3/2)x^6 + C

To find the value of C, we use the given initial condition that f(1) = 0:

f(1) = (1/3)1^3 + (3/2)1^6 + C = 0

C = -5/6

Therefore, the antiderivative of f(x) with f′(x) = f(x) = 7/21x^2 + 18x^5 and f(1) = 0 is:

f(x) = (1/3)x^3 + (3/2)x^6 - 5/6

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