What is 2/3 to the third power\\

In regression analysis, the independent variable is typically plotted on the x-axis.

The x-axis represents the independent variable or predictor variable, which is the variable that is believed to influence or have an impact on the dependent variable. This variable is typically plotted horizontally on the graph.

For example, let's say we are studying the relationship between the amount of study time and exam scores. In this case, the independent variable would be the amount of study time, which could be measured in hours.

By plotting the amount of study time on the x-axis, we can visually analyze how it relates to the dependent variable, which is the exam scores, typically plotted on the y-axis. This helps us understand the nature and strength of the relationship between the two variables.

So, in summary, the independent variable is plotted on the x-axis in regression analysis.

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Given: A = 43.7°, a = 8.7, and b = 10.3We can find the number of possible triangles by using the Law of Sines, which states that a / sin A = b / sin B = c / sin C, where a, b, and c are the side lengths and A, B, and C are the opposite angles. Let's first use the Law of Sines to find the value of sin B: a / sin A = b / sin B => sin B = b sin A / a.

Substituting the given values, we get: sin B = 10.3 sin 43.7° / 8.7≈ 0.641Now we know the value of sin B. We can use the inverse sine function (sin⁻¹) to find the possible values of angle B: B = sin⁻¹ (0.641)≈ 40.4° or B ≈ 139.6°Note that there are two possible angles for B because sine is a periodic function that repeats every 360°.Now that we know the possible values of angle B, we can use the fact that the sum of the angles of a triangle is 180° to find the possible values of angle C: C = 180° - A - B. For B = 40.4°, we get: C = 180° - 43.7° - 40.4° = 95.9°For B = 139.6°, we get: C = 180° - 43.7° - 139.6° = -2.3°Note that we get a negative value for angle C in the second case, which is not possible because all angles of a triangle must be positive. Therefore, the second case is not valid and we only have one possible triangle. Answer: There is only one possible triangle.

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The properties of the quadratic equation y=-3x^2+6x+17 is Axis of symmetry - x=1, Vertex (maximum) - (1,20), Parabola opens downwards and the end behaviour is x→∞,y→-∞, x→-∞, y→-∞.

What is a quadratic equation?

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax^2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

The quadratic equation in the general form can be written as -

y=-3x^2+6x+17

Here, a=-3

b=6

c=17

An imaginary straight line known as the axis of symmetry divides a shape into two identical sections, making one part the mirror image of the other.

Here, the axis of symmetry is x=1.

The vertex of the equation is at the maximum or the lowest point of the parabola.

So, after plotting the graph the maximum point is (1,20).

The leading coefficient of the equation is -3, which is less than zero.

So, the parabola formed by the quadratic equation opens downwards and forms a upside-down U shaped parabola.

According to the equation has an even degree and the graph of  the parabola is leading towards negative infinity.

Therefore, it can be denoted as x→∞,y→-∞, (right end down) and as x→-∞, y→-∞ (left end down).

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There are probability (6 choose 3) = 20 possible ways to select 3 or more students from 6 students, since the order in which the students are selected is not important.

If 3 or more students must be selected from 6 students, and the order in which the students are selected is not important, then this is an example of a combination problem. Combination problems are used to calculate the number of ways a certain number of objects can be selected from a larger group of objects. To calculate this, the formula that is used is (n choose r) = n!/(r!(n-r)!), where n is the total number of objects, and r is the number of objects that must be selected. In this case, n = 6 and r = 3, so the answer is (6 choose 3) = 6!/(3!(6-3)!) = 20. This means that there are 20 possible ways to select 3 or more students from 6 students, since the order in which the students are selected is not important.

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Answer: Each wheel makes 437.5 revolutions in 20 mins

Step-by-step explanation:

Circumference = 2πr

Given that the radius is 40 cm

Circumference = 2π(40) = 80π cm

Find the distance traveled in 20 mins

Speed = 66 km/h

1 hour = 66 km

Rewrite hour into min

60 min = 66 km

1 min = 66 ÷ 60 = 1.1 km

Rewrite km in cm

1.1 km = 1.1 x 10,000 cm = 110,000 cm

Find the number of revolutions in 20 mins:

1 revolution = 80π cm

Number of revolution = 110,000 ÷ 80π = 437.5

Solution,

Let the price of car be X.

Rate(R)=5%

Here,

Commission % of price of car=32500

or,5% of X=32500

or,5/100*X=32500

or,X=32500*20

X=Rs 650000

Hope it helps

Good luck on your assignment........

Answer:

The answers are 2 and 4

Step-by-step explanation:

A=bh for Rectangle

A=1/2 r^2 π for Half circle

The range is the appropriate measure of variability, and its value is 700.

The appropriate measure of variability for the given data set is the range. The range measures the spread of the data by calculating the difference between the maximum and minimum values.

To find the range for the data set [400, 550, 650, 650, 900, 1100], we subtract the minimum value from the maximum value:

Range = Maximum value - Minimum value

= 1100 - 400

= 700

Therefore, the range for the given data set is 700.

To address the statements you provided:

The mean is not the best measure of variability, as it represents the average value of the data, not the spread or variability.

The median is also not the best measure of variability, as it represents the middle value of the data set, not the spread or variability.

The IQR (Interquartile Range) is not applicable in this case since it is used for analyzing data with quartiles and dividing the data into lower and upper halves.

Hence, the correct answer is:

The range is the appropriate measure of variability, and its value is 700.

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Answer:

Step-by-step explanation:

The zero (root) of a function is any value of the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x-axis.

~~~~~~~~~

f(x) = x³ + 3x² - x - 3

f(-3) = ( - 3 )³ + 3( - 3 )² - ( - 3 ) - 3 = 0

f(-1) = ( - 1 )³ + 3( - 1 )² - ( - 1 ) - 3 = 0

f(1) = ( 1 )² + 3( 1 )² - ( 1 ) - 3 = 0

Answer:

The zeroes of the function are x = -3, x = -1, and x = 1.

Step-by-step explanation:

We are given a polynomial and asked to find the zeroes of the polynomial. Our given polynomial is:

\(x^3 + 3x^2 - x - 3\)

The zeroes of a polynomial are the solutions or roots of the function. This is where if the line were graphed, the line would intersect the x-axis at those points (sometimes there will only be one).

This is a cubic polynomial. We can use a factoring technique referred to as grouping, which is most effective when factoring a trinomial with the only satisfaction met is: a > 1.

However, it can also be used when a > 1 is not true.

We can work with an example polynomial first and then work through solving the given polynomial.

An example polynomial would be:

\(10x^2 + 8x - 9 = 0\)

In grouping, our main goal is to factor as quickly as possible. If you examine the polynomial, there is no common factor between 10x², 8x, or -9, so we cannot take out a GCF and need to use another factoring technique.

Since a > 1, we can instantly jump to using the grouping factoring technique.

Please note that the parent function for a quadratic is \(ax^2 + bx + c = 0\).

To group:

Let's use grouping to solve \(x^3 + 3x^2 - x - 3\).

Because we already have four terms, we can skip steps one through three and go straight to step four.

\((x^3 + 3x^2)(-x - 3)\)

Now, we need to take the GCF of both parentheses sets. Let's do this with our first set of terms.

Then, we can also do this with our second set of terms.

Because our remaining terms for both sets match, we have grouped our polynomial correctly. Now, let's combine our GCFs into one term and list our common term as the second term.

\((x^2-1)(x+3)\)

Now, we can break apart x² - 1 into more factors.

This is the difference of two squares. The formula for the difference of two squares is \((a^2-b^2)=(a+b)(a-b)\)

Our perfect squares are every integer in the spectrum of numbers, so 1 is a perfect square. Therefore, x² becomes x and 1 becomes ±1.

Our new terms would therefore be \((x+1)(x-1)(x+3)\).

Finally, to find zeroes of a function, x needs to equal something. Therefore, we can set our terms equal to zero and solve for x.

Term 1 (x + 1)

\(x + 1 = 0\\\\x + 1 - 1 = 0 - 1\\\\\boxed{x = -1}\)

Term 2 (x - 1)

\(x - 1 = 0\\\\x - 1 + 1 = 0 + 1\\\\\boxed{x = 1}\)

Term 3 (x + 3)

\(x + 3 = 0\\\\x + 3 - 3 = 0 - 3\\\\\boxed{x = -3}\)

Therefore, our zeroes are listed above. To finalize our answer, we want to list them in increasing order, so this will be most negative to most positive. Therefore, our final answer is x = -3, -1, 1.

Using the Runge-Kutta method of second order, the approximate value of y when x = 0.02 is is 1.0203045100525125.

To apply the Runge-Kutta method of second order to approximate the value of y when x = 0.02, we can follow these steps:

\(y' = x^2 + y\)

y(0) = 1

h = 0.01 (step size)

x = 0.02 (desired x-value)

The general formula for the second-order Runge-Kutta method is:

y(i+1) = y(i) + (k1 + k2)/2

where

k1 = h * f(x(i), y(i))

k2 = h * f(x(i) + h, y(i) + k1)

Let's calculate the values step by step:

Set x(0) = 0, y(0) = 1.

k1 = h * f(x(0), y(0))

\(= 0.01 * (0^2 + 1)\)

  = 0.01

k2 = h * f(x(0) + h, y(0) + k1)

\(= 0.01 * ((0 + 0.01)^2 + 1 + 0.01)\)

  = 0.01 * (0.0001 + 1.01)

  = 0.010101

y(1) = y(0) + (k1 + k2)/2

    = 1 + (0.01 + 0.010101)/2

    = 1 + 0.020101/2

    = 1.0100505

Let's perform the calculations iteratively:

Iteration 1:

x = 0.01

y = 1.0100505 (from Step 4)

Iteration 2:

Now we need to repeat steps 2-4 with the new x and y values:

k1 = h * f(x(1), y(1))

\(= 0.01 * (0.01^2 + 1.0100505)\)

  = 0.0102010050025

k2 = h * f(x(1) + h, y(1) + k1)

\(= 0.01 * ((0.01 + 0.01)^2 + 1.0100505 + 0.0102010050025)\)

  = 0.010307015102525

y(2) = y(1) + (k1 + k2)/2

    = 1.0100505 + (0.0102010050025 + 0.010307015102525)/2

    = 1.0203045100525125

After the second iteration, when x = 0.02,

we obtain y ≈ 1.0203045100525125.

Therefore, the approximate value of y when x = 0.02 using the Runge-Kutta method of second order is 1.0203045100525125.

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The blanks are filled as follows

Step one

Equation 2x + y = 18 Isolate y,

y = 18 - 2x

Step Two:

Equation 8x - y = 22, Plug in for y

8x - (18 - 2x) = 22

Step Three: Solve for x by isolating it

8x - (18 - 2x) = 22

8x - 18 + 2x = 22

8x + 2x = 22 + 18

10x = 40

x = 4

Step Four: Plug what x equals into your answer for step one and solve

y = 18 - 2x

y = 18 - 2(4)

y = 18 - 8

y = 10

So the solution to the system of equations is x = 40 and y = 10

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Answer:

A. $180

Step-by-step explanation:

18000*5*7/100 =6300

18000*6*6/100=6480

6480-6300=180

The point of intersection between the given plane and the line perpendicular to the plane and passing through (8, 4, 3) is (-4, -14, 9).

To find the point of intersection between a plane and a line, we need to know the equation of the plane and the equation of the line.

Given:

Plane equation: ax + by + cz = d

Line equation: P = P₀ + tV

To find the point of intersection, we can substitute the line equation into the plane equation and solve for the parameter 't'.

Let's assume the plane equation is:

2x + 3y - z = 4

And the line equation passing through (8, 4, 3) and perpendicular to the plane can be represented as:

P = (8, 4, 3) + tV

First, we need to find the normal vector of the plane. From the coefficients of x, y, and z in the plane equation, we can determine the normal vector as (2, 3, -1).

Since the line is perpendicular to the plane, the direction vector 'V' of the line will be the same as the normal vector of the plane. Therefore, V = (2, 3, -1).

Substituting the values into the plane equation:

2(8) + 3(4) - 1(3) + t(2) + t(3) + t(-1) = 4

Simplifying the equation:

16 + 12 - 3 + 2t + 3t - t = 4

28 + 4t = 4

4t = -24

t = -6

Now, substitute the value of 't' back into the line equation to find the point of intersection:

P = (8, 4, 3) + (-6)(2, 3, -1)

P = (8, 4, 3) + (-12, -18, 6)

P = (-4, -14, 9)

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Tthe Fourier series may converge to a value that is different from the left and right limits of f at the point of discontinuity, or it may not converge at all (known as Gibbs phenomenon).

To determine the specific value to which the Fourier series converges at a point of discontinuity, we would need to analyze the specific function f and its Fourier series.

This typically involves calculating the Fourier coefficients, examining the convergence properties of the series, and potentially using techniques such as Cesàro summation to obtain a more accurate estimate of the limit.

Without further information about the specific function and point of discontinuity, we cannot provide a more specific answer.

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Answer:

0.444... or 4/9

Step-by-step explanation:

Answer:there are 21 fish in the tank.

Step-by-step explanation:

Let's assume that the total number of fish in the tank is x.

We know that 6/7 of the fish have a red stripe on them. Therefore:

(6/7)x = number of fish with red stripes

We also know that the number of fish with red stripes is 18. Therefore:

(6/7)x = 18

Multiplying both sides of the equation by (7/6), we get:

x = 21

The length vector is 1. So the sketch vector field f is given below. So the option a is correct.

In the given question, the vector field F by drawing a diagram like this figure.

The given vector field F is:

F(x, y) = (yi + xj)/√(x^2 + y^2)

We can write the vector field as:

F(x, y) = yi/√(x^2 + y^2) + xj/√(x^2 + y^2)

Here

F(x, y) = [y/√(x^2 + y^2)]^2 + [x/√(x^2 + y^2)]^2

F(x, y) = y^2/(x^2 + y^2) + x^2/(x^2 + y^2)

F(x, y) = (y^2+ x^2)/(x^2 + y^2)

F(x, y) = 1

F(0, y) = y/|y| = ±1

F(x, 0) = x/|x| = ±1

So the length vector is 1.

So the sketch vector field f is given below:

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The complete question is:

Sketch the vector field F by drawing a diagram like this figure.

F(x, y) = (yi + xj)/√(x^2 + y^2)

Answer:

h x c

Step-by-step explanation:

For the given standard deviation the minimum value we would assign is 22.the maximum value we would assign is 88.

To calculate the minimum and maximum values based on the given information, we need to consider the standard deviation and the respective interest rates for the 3-year and 10-year periods.

Given:

S = 26.32 (Initial value)

E = 55 (Expected value)

t = 3 (Years)

Standard deviation = 60% (of the expected value)

3-year interest rate = 2.4%

10-year interest rate = 3.1%

To find the minimum value, we will calculate the value at the end of the 3-year period using the lowest possible growth rate.

Minimum value calculation:

Minimum value = E - (Standard deviation * E) = 55 - (0.6 * 55) = 55 - 33 = 22

Therefore, the minimum value we would assign is 22.

To find the maximum value, we will calculate the value at the end of the 10-year period using the highest possible growth rate.

Maximum value calculation:

Maximum value = E + (Standard deviation * E) = 55 + (0.6 * 55) = 55 + 33 = 88

Therefore, the maximum value we would assign is 88.

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The number of servings that can be made with two quarts

It's important to note that word problem in mathematics refers to a question that is written as one sentence or more which requires the students to be able to apply their maths knowledge into a ‘real-life’ scenario.

In such a scenario, the person must be familiar with the vocabulary that is associated with the mathematical symbols in order to make sense of the word problem.

let x represent the number of servings

1 quart = 4 cups

So, 2 quarts = 8 cups

So, 8 cups to make x servings That is, 8 cups = x servings

When 3 cups = 15 servings8 cups will be equal tox = 8 cups × 15 servings/ 3 cupsx = 40 servings

Therefore, 40 servings can be made from 2 quarts.

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The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.

A composite figure is a figure comprising of two or more regular figures.

The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.

Please find attached the cross section of the Cargo Trailer Floor created with MS Word.

The dimensions of the rectangle are; Width = 6 ft, length = 10 ft

The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft

Height of the triangular cross section = √(4² - (6/2)²) = √(7)

The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)

A = 60 + 3·√7

Volume of the trailer, V = Cross sectional area × Height

V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7

Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³

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Answer:

The population in 14 weeks is 232 fishes

Step-by-step explanation:

The equation for exponential growth is f(x) = a·(1 + r)ˣ

Where;

a = The starting population size = 3

r = The rate at which the population of grows

x = The number of periods to of change of the population

Therefore, we have;

f(6) = 31 = 3 × (1 + r)⁶

31/3 = (1 + r)⁶

㏑(31/3) = 6㏑(1 + r)

(㏑(31/3))/6 =㏑(1 + r)

1 + r = e^((㏑(31/3))/6) ≈ 1.476

1 + r ≈ 1.476

Therefore, the population in 14 weeks is given as follows;

f(14) = 3 × (1.467)¹⁴ ≈ 232.574

Given that we the information is with regard of living things, such that there are no fractions, we round down to the nearest whole number as follows;

f(14) ≈ 232

The population in 14 weeks = 232 fishes.

Answer:

Step-by-step explanation:

Sale price of the coat:

Total of three items:

Add tax to get the total:

Answer:

\(The \: inverse \: of \: the \: function \\ y = 2 {x}^{2}  + 2 is  {f - }^{1} (x) = √(x - 2) / √2\)

The speed of the water wave is 2.0 meters per second.

The speed of a wave is calculated by dividing the distance traveled by the time it takes to travel that distance. In this case, the distance traveled by the water wave is 10.0 meters, and the time taken is 5.0 seconds.

To determine the speed, we use the formula:

Speed = Distance / Time

Substituting the given values, we have:

Speed = 10.0 meters / 5.0 seconds = 2.0 meters per second

Therefore, from the given information, we can determine that the speed of the water wave is 2.0 meters per second.

This information about the speed of the water wave is useful for various purposes. It allows us to understand how quickly the wave is propagating through the medium. It also helps in analyzing wave behavior, such as interference, reflection, or refraction, and studying the characteristics of the medium through which the wave is traveling. Additionally, the speed of the wave can be used in calculations involving wave frequencies, wavelengths, and periods.

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Answer:

Points B, C, and D are on line n

Step-by-step explanation:

Answer:

лттьло. ьнеь е екбюедку к е. еккд

Answer: 5?

maybe

Step-by-step explanation:

By calculation, your grade in the class now is 78.7

From the question, we have the following parameters that can be used in our computation:

Score of 47.2 in 60

Represent the score in 100% with x

So, we have the following equation

47.2/60 = x/100

Multiply both sides of the equation by 100

So, we have

100 * 47.2/60 = x/100 * 100

This gives

100 * 47.2/60 = x

So, we have

x = 100 * 47.2/60

Evaluate

x = 78.7

Hence, your grade in the class now is 78.7

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The expression is already in decimal form.

0

3×10^9

NOT CONGREUNT!! There is no axiom to prove congruent.