Determine if (x-1) is a factor of g(x)=-2x^4+4x^3-x+9

If numbers is a two-dimensional array, which of the following would give the length of row r is d. numbers[r].length

A two-dimensional array is a data structure used to store data in a tabular format, consisting of rows and columns. Each element in the array is accessed by two indices, one for the row and one for the column. The length of a row in a two-dimensional array can be determined by accessing the array at the specified row and then returning the length of that row. To do this, the expression numbers[r].length can be used, where 'numbers' is the name of the two-dimensional array, and 'r' is the index of the row whose length is being determined.

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The population of the country in 2003 is, 368.3 million.

What is population?

The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.

Given:

The exponential model a = 368.3e^0.002t describes the population,

'a' is the population of a country in millions,

t years after 2003.

We have to find the population of country in 2003.

At 2003, t = 0.

So plug t = 0 in above exponential model.

a = 368.3e^0.002(0)

a = 368.3e^0

a = 368.3

Hence, the population of the country in 2003 is, 368.3 million.

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Of the following, the option which is not a polynomial is 1/x+2. (Option D)

In mathematics, a polynomial refers to an expression consisting of indeterminates and coefficients, that only includes basic arithmetic operations of addition, subtraction, multiplication, and positive-integer powers of variables. In other words, it is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power. The general form of a polynomial is a + bx + cx^2. Hence, it is identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The non-polynomial expressions will be the expressions which contain other operations such as 1/x+2.

Note: The question is incomplete. The complete question probably is: Which of the following is not a polynomial (a) 3x+5 (b) 3y³-4y² +2y (c)x³-3 d) 1/x+2

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For the given matrix A ,(a) the eigen values are 0 and -3 . and the eigen vectors corresponding to the given eigen vectors are   [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex]  and  [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .

In the question ,

it is given that ,

the matrix A is = [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex]

Part(a)

the eigen values of the matrix A can be found by the characteristic equation ,

|A - λI | = [tex]\left|\begin{array}{ccc}-6-\lambda &6\\-3&3-\lambda\\\end{array}\right|[/tex] = 0 ;

= -(6 + λ)(3 - λ) + 18

= λ² - 3λ + 6λ = 0

= λ² + 3λ = 0

So , λ = 0 and λ = -3 .

the eigen values are 0 and -3 .

Part(b)

for finding the eigen vectors ,

For eigen value λ = 0  , [A - λI]*X = 0

on solving [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}x_{1} \\x_{2} \\\end{array}\right][/tex] = 0 ,

we get x₁ = 1 and x₂ = 1 ,

the eigen vector corresponding to eigen value 0 is [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex] .

Similarly solving for eigen value λ = -3 ,

[tex]\left[\begin{array}{ccc}-3&6\\-3&6\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}x_{1} \\x_{2} \\\end{array}\right][/tex] = 0 ,

Solving further ,

we get , x₁ = 2 and x₂ = 1 ,

the eigen vector corresponding to eigen value -3 is [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .

Therefore , (a) the eigen values are 0 and -3 .

(b) the eigen vectors are  [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex]  and  [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .

The given question is incomplete , the complete question is

The matrix is A = [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex] ,

(a) Find the eigenvalues of Matrix A .

(b) Find corresponding eigenvector for each of eigenvalues found in (a).

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The probability to choose a group of four tiles with each tile worth one point is 0.200.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let there are total 25 tiles.

From this 20 tiles having one point each and 5 tiles having more than one point.

We have to choose a group of four tiles with each tile worth one point.

So,

probability = 4/20 = 0.200

Hence, the probability to choose a group of four tiles with each tile worth one point is 0.200.

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Therefore option a) 5x+4 is the simplified form of the equation.

Equations in mathematics are logical statements with two algebraic expressions on either side of the equals (=) symbol. The equality of the expressions on the left and right in relation to one another is shown. LHS = RHS (left hand side = right hand side) is the first step in any mathematical equation. You can solve equations to determine a variable's or quantity's value. It is not an equation if the statement lacks the "equal to" sign. It will be thought of as a phrase. Later on in this essay, there will be an explanation of the distinctions between an expression and an equation.

Here,

Given:

=>(−3x − 12) + (16 + 8x)

=> -3x-12+16+8x

=> 5x+4

So 5x+4 is the simplified form of the equation

Therefore option a) 5x+4 is the simplified form of the equation

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Answer:

44

Step-by-step explanation:

For given data of ten professional athletes:

A) A scatter plot of the data is as shown below.

B) An equation of the line of best fit is:

y = 1.7946x + 2.1956

C) The line of best fit on the scatter plot is as shown below.

D) The y-intercept of the line of best fit is: a = 2.1956

The y-intercept represents, on average players with no endorsements earn million dollars each year.

In this question we have been given a random sample of ten professional athletes. In data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

A) A scatter plot of the data is as shown below.

B) For given scatter plot we can obsere that the variables show a linear regression.

And the equation of the line of best fit is:

y = 1.7946x + 2.1956

And the coefficient of regression is: R² = 0.9657

C) The line of best fit on the scatter plot is as shown below.

D) The y-intercept of the line of best fit is:

a = 2.1956

The y-intercept means that on average, players with no endorsements earn million dollars each year.

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The complete question is:

A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

x  y  x  y

0  2  5  11

3  8  4  9

2  6  3  8

1  3  0  3

6  14  5  10

A) Draw a scatter plot of the data.

B) Use regression to find the equation for the line of best fit. (Round your answers to three decimal places.)

ŷ = ____ + ____ x

C) Draw the line of best fit on the scatter plot.

D) What is the y-intercept, a, of the line of best fit? (Round your answer to three decimal places.)

a =

What does it represent? (Round your answer to three decimal places.)

Answer:

  C  2.35 x 10¹¹

Step-by-step explanation:

You want the number 235,000,000,000 written in scientific notation.

The exponent of 10 when a number is written in scientific notation is the same as the exponent of 10 for the most significant digit when the number is written in expanded form using exponents.

  235,000,000,000 = 2×10¹¹ +3×10¹⁰ +5×10⁹ +0×10⁸ +... +0

The place value multiplier for the most-significant digit is 10¹¹, so this is the multiplier when the number is written in scientific notation.

  2.35×10¹¹

The given trigonometric equations have the value tan x, -cot x.

Since the given trigonometric equations  are: cos2x-cos4x/sin2x+sin4x   and  cos2x+cos4x/sin2x-sin4x. The problem is related to trigonometric Ratios, which are the ratios of the side of a right-angled triangle.Now for the equation (cos 2x - cos 4x )/(sin2x +sin4x)

since we know the formulas  :

cos A + cos B = - sin (A+B)/2 sin(A-B)/2

sin A - sin B = sin( A+B)/2 cos (A-B)/2

so for the equation, we can

= (-sin 3x) sin ( -2x)/2)/( cos 3x cos x)

= sin 3x sin x/ (sin 3x) cos x

= tan x

for the second equation    cos2x+cos4x/sin2x-sin4x

= cos 3x cosx/ cos3x sin(- x)

= - cot x

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The equations are given whose graphs enclose a region. when the area of the region is 301.5

The given function is f(x) and g(x), we need to calculate the area.

A = ₐ∫ᵇ (f(x) + g(x)) dx

A = ₀∫³ (x² + 15(x + 5)) dx

A = ₀∫³ (x²dx  + ₀∫³15(x + 5)) dx

A =  (x³/3) + 15x²/2 + 75x

A = ₀[x³/3]³ + ₀[15x²/2 + 75x]³

A = [(3 - 0)³/3] + [15(3 - 0)²/2 + 75(3 - 0)]

A = 27/3 + 15(9/2) + 75(3)

A = 9 + 15(4.5) + 7

A = 76.5 + 225

A = 301.5

Therefore, the equations are given whose graphs enclose a region. when the area of the region is 301.5

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Using direct variation, the value of j when f equals 9 is 3

A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

In the question given, we have f varying directly with j

f ∝ j

f = k j

k = f / j

f₁ / j₁ = f₂ / j₂

Substituting the values into the equation;

27 / 9 = 9 / j₂

j₂ = 9 * 9 / 27

j₂ = 81 / 27

j₂ = 3

The value of j₂ = 3

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Translation: We have that f varies directly with j, if f = 27 when j = 9. Calculate the value of j when f = 9

The correct options are;

a. The variables x and y also have a correlation close to 1 .

b. A scatterplot of the variables log x and y shows a strong nonlinear pattern .

The correlation is a measurement of a dependence between 2 variables. If the logarithm of the correlation function shows a linear tendency, it because the correlation between x and y shows a exponential tendency.

This mean that x and y are non linear correlated, but them are correlated.

For this type of data is used a non linear correlation technique know it as logarithm correlation.

Option c is incorrect because random patterns have a correlation value close to 0, which is not the case.

So ,

The correct options are;

a. The variables x and y also have a correlation close to 1

b. A scatterplot of the variables log x andy shows a strong nonlinear pattern

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On solving the provided question, we got to know that  -Pythagoras' Theorem -  [tex]a^2 + b^2 = c^2 =[/tex][tex]5^2 + 8^2 = c^2[/tex]

The square of the hypotenuse of a right triangle (90 degrees) is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC below. where BC is the hypotenuse, AB is the base, and AC is the height (height). Keep in mind that the hypotenuse of a right triangle is its longest side.

Pythagoras' Theorem -

[tex]a^2 + b^2 = c^2[/tex]

where the other two sides' lengths are a and b, and c is the length of the hypotenuse.

so

[tex]5^2 + 8^2 = c^2\\c^2 = 25 + 64\\c^2 = 89\\c = \sqrt{89}[/tex]

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The dimensions of the rectangle are:

Length = 10 m

Width = 6.5 m

Recall that the area of aa rectangle is given as, length × width.

Given the following:

Area of the rectangle = 65 m²

Let the width of the rectangle be represented as w.

Length of the rectangle = 2w - 3 m

Therefore:

(2w - 3)(w) = 65

Expand:]

2w² - 3w = 65

2w² - 3w - 65 = 0

Factorize:

w = 6.5 or w = -5

The width cannot be negative, therefore, the width = 6.5 m.

Length of the rectangle = 2w - 3 = 2(6.5) - 3 = 10 m

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The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

As per the given graph of a function,

The time period is the time interval after curves repeat their behavior.

The given graph repeats after 1 + 1 + 1 + 1 = 4 thus period will be 4.

Hence "The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4".

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Answer: 8/-9

Step-by-step explanation:

If h(7), plug in 7 into all the x-values.

=[tex]\frac{7^{2}-5(7)-6}{7^{2}-6(7)-16 }[/tex]

=[tex]\frac{49-35-6}{49-42-16}[/tex]

=[tex]\frac{8}{-9}[/tex]

After solving, the surface integral S is [tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14.

In the given question, we have to evaluate the surface integral.

(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6.

Now the surface integral is:

[tex]\int\int_{S}(x + y + z) dS[/tex]

x = u+v, y = u−v, z = 1+2u+v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6

The parametric curve is

r(u,v) = <u+v, u−v, 1+2u+v>

Then surface integral is calculated as

[tex]\int\int_{S}(x + y + z) dS=\int\int_{A}f(x(u,v), y(u,v), z(u,v))|r_{u}\times r_{v}| dudv[/tex]

Now find partial derivatives of parametric curve with respect to u and v

[tex]r_{u}[/tex](u,v) = <1, 1, 2>

[tex]r_{v}[/tex](u,v) = <1, -1, 1>

Now find cross product

[tex]r_{u}\times r_{u}[/tex] = <1, 1, 2> × <1, -1, 1>

[tex]r_{u}\times r_{u}[/tex] = <1+2, 2-1, -1-1>

[tex]r_{u}\times r_{u}[/tex] = <3, 1, -2>

Now parametric function is

x+y+z = u+v+u-v+1+2u+v

x+y+z = 4u+v+1

Then the surface integral is:

[tex]\int\int_{S}(x + y + z) dS=\int^{6}_{0}\int^{8}_{0}(4u+v+1)\sqrt{14}dudv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(4\frac{u^2}{2}+uv+u)^{8}_{0}dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}[(4\frac{(8)^2}{2}+8v+8)-(4\frac{(0)^2}{2}+0\cdotv+0)]dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(128+8v+8)dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(136+8v)dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}(136v+8\frac{v^2}{2})^{6}_{0}[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}[(136\times6+8\frac{6^2}{2})-(136\times0+8\frac{0^2}{2})][/tex]

[tex]\int\int_{S}(x + y + z) dS[/tex] = √14×(816+144)

[tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14

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(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph thus option (B) will be correct.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane.

As per the given coordinates,

The coordinate is the representation of horizontal and vertical distinctions.

The (3,1) is the point that is 3 grid right or horizontal and 1 unit up or vertical from the origin.

Hence "(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph".

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Congruent triangles are triangles having corresponding sides and angles to be equal.

Congruent triangles are triangles that have both the same size and the same shape and they have the same perimeter and the same area. Congruence is denoted by “≅”.  For example, we can write ABC ≅ DEF. They have the same area and the same perimeter.

Congruent triangles have the same angle measures and the same side lengths.

On the other hand, the similar triangle is the term used for triangles that have the same shape, but not necessarily the same size.

Two triangles are considered to be congruent if they meet one of the following criteria.

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At 9 AM Bob could declare the pool was full of water, using given information about fill rate, discharge rate and time.

What is fill rate and discharge rate ?

The definition of fill rate is the percentage of customers orders you are able to meet without running out of stock at any given time.

The discharge rate is the amount of fluid that is passing through a given cross sectional area per unit time.

We need to divide it in 3 parts:

Part 1: When only 1 hose is filling the pool at 3 gal per hr.

Part 2 : When after 10 hours animals started drinking water .

Part 3: When 2nd hose also started at the rate 2 gal per hr.

Part 1:

For 10 hours it get started . So, pool get filled is 30gal.

Part 2:

After 10 hours, rate decreased by animals at 1 gal/hour.

So, rate = 3-1 = 2 gal/hour.

So, water filled for 5 hour = 10 gal.

So, total pool is filled = 10 + 30 = 40 gal.

Remaining = 60 - 40 = 20 gal.

Part 3:

2nd hose is added at the rate 2gal/hour.

Now, rate = 2+2 = 4 gal/hour.

Time taken for 20 gal = 5 hours.

So, total time taken = 10 + 5 +5

                                 = 20 hours.

We need to find the time ,

Time at which water is started = 1pm

1PM + 11hours = 12AM

For remaining , 9 hours

12AM + 9hours = 9AM.

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The values are 5, 6, 8, 9 for the given function y=∛x+7.

So, option D is correct.

In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y.

The earliest known concept of a function was created by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. [4] At first, functions were envisioned as the perfect representation of the relationship between two variables. In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output. Each function has a codomain or range.

Given,

y=∛x+7

Let x=-8,

y=∛8+7

y=-2+7

y=5

x=-1, y=∛(-1)+7

y=-1+7

y=6

x=1, y=∛1+7

y=1+7

y=8

x=8, y=∛8+7

y=2+7

y=9

Therefore, the values are 5, 6, 8, 9

So, option D is correct

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The complete question is:

"Complete the table for the function y = ∛x+7

OA) -5, -6, -8, -9

OB) -9, -8, -6, -5

Oc9,8. 6. 5

OD) 5,6, 8, 9".

The time required for the total amount in Harrison's account to reach $410 is 4.49 years.

The simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

A/P = 1 + rt

A/P - 1 =  rt

t = ( A/P - 1 ) / r

t = ( $410/$345 - 1 ) / 0.042

t = ( 13/69 ) / 0.042

t = 4.49 years

Therefore, the time needed to reach accrued amount is 4.49 years.

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a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.

b. ∅ = (Rx/Ry)

Vectors are used to represent physical quantities in terms of magnitude and direction. Vectors can be added using the parallelogram method or the triangle addition method. The magnitude and direction of the resulting vector are generally proportional to the magnitude and direction of the component vectors.

I have every vector in 2D that has both vertical and horizontal components.

There are vectors say:  A = xi + yj

                              and, B =zi + wj

For example, adding two vectors gives the result

R = (x +z)i + (y + w) j.

The - component has y +w as z and the y component as w. The sum has the horizontal component as x + z and the vertical component as y + w. So we get the y component of the resulting vector R = A+ y component of B

The direction of the angle is found as

tan∅ = Rx/Ry

     ∅ = (Rx/Ry)

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42 pounds has a weight of clothing to weight to dye different from the other ratios

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another

The ratio weight of clothing to the weight of dye will be:

For 21 and 3:

21:3 = 7: 1

For 42 and 9:

42:9 = 14: 3

For 84 and 12:

84:12 = 7: 1

For 105 and 15:

105:15 = 7: 1

Thus, 42 pounds is different from the other ratios

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Answer:

The answer is 2.9

Step-by-step explanations are not quite accurate

Answer:

Step-by-step explanation:

1. Multiply 9 times 4t in parentheses

2. Once you get the answer you add it to 3t and that gives you 39t

Is this question any helpful enough for?

Answer:

1.14x = 19.38

$17

Step-by-step explanation:

Let the price before delivery charge = x.

The charge is 14%, so it is 14% of x, or 0.14x.

The original price plus charge is x + 0.14x, or 1.14x.

1.14x = 19.38

x = 19.38/1.14

x = 17

The price is $17

There are 3 more days will it take her to plant all the trees.

What is rate?

The numerator of a ratio in mathematics represents the rate of change in the other (dependent) variable if the denominator of the ratio is expressed as a single unit of one of the related quantities and it is assumed that this quantity can be changed systematically (i.e., is an independent variable).

Given:

Tamika must plant 432 trees.

In the past 6 days Tamika planted 288 trees.

She continues the planting tree at the same rate.

As she planted 288 trees in 6 days.

That means she plant 288 / 6 = 48 trees in a day.

The remaining trees are 432 - 288 = 144.

So, 144 trees will be planted in 144 / 48 = 3 days.

Hence, there are 3 more days will it take her to plant all the trees.

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Answer:

Step-by-step explanation: