Match the polynomial with its known factor.

(x+5)
(x-5)
(x+10)
(x-10)
x^3-13x^2+25x+50
x^4+7x^3+13x^2+6x-45

The coordinates of the points that are 17 units away from the origin and have an x-coordinate equal to 8 are (8, -15) and (8, 15).

To find the coordinates of the points that are 17 units away from the origin and have an x-coordinate equal to 8, we can use the distance formula and the given x-coordinate to determine the y-coordinate.

The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, we know that x1 = 0 (the x-coordinate of the origin) and x2 = 8. The distance d is 17 units.

Plugging in the values into the distance formula, we have:

17 = √((8 - 0)² + (y2 - 0)²)

Simplifying the equation:

289 = 64 + y²

Subtracting 64 from both sides:

y² = 225

Taking the square root of both sides:

y = ±15

So, we have two points that satisfy the conditions:

Smaller y-value: (8, -15)

Larger y-value: (8, 15)

Therefore, the coordinates of the points that are 17 units away from the origin and have an x-coordinate equal to 8 are (8, -15) and (8, 15).

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Answer:

The answer is "12.426 in".

Step-by-step explanation:

\(\to b+2c=30\\\\\to b = 15 \times \tan 22.5 \\\\\)

      \(= 15 \times 0.414213562\\\\=6.21320343 \times 2 \\\\=12.4264069 \ in \\\\\)

The values of a and b in the equation y^2/a^2-x^2/b^2=1 cannot be determined

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

y^2/a^2-x^2/b^2=1

The equation y^2/a^2 - x^2/b^2 = 1 represents a hyperbola with center at the origin (0,0), and the values of a and b determine its shape and size.

The parameter 'a' represents the distance from the center to the vertices of the hyperbola along the y-axis.

Similarly, the parameter 'b' represents the distance from the center to the vertices of the hyperbola along the x-axis.

However, the values of a and b in the equation y^2/a^2-x^2/b^2=1 cannot be determined with the given parameters

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The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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Answer:

d = -280 m

Step-by-step explanation:

Given that,

Velocity of Andre, v = -8 m/s

Time taken, t = 35 seconds

We need to find his finishing position. Let the finishing position be x.

We know that,

Velocity = distance/time

So,

\(d=v\times t\\\\d=-8\times 35\\\\=-280\ m\)

so, he was at a distance of 280 m in west.

\(\qquad \qquad\huge \underline{\boxed{\sf ᴀɴsweʀ}}\)

Here's the solution ~

\(\qquad \sf  \dashrightarrow \: \frac{(4/7)^5 \times (2 / 3)^4 }{(4 / 9) \times (4 / 7)^ 3} \)

\(\qquad \sf  \dashrightarrow \: \frac{ (\frac{4}{7}) {}^{5} }{ (\frac{4}{7} ) {}^{3} } \times \frac{( \frac{2}{3})^{4} } { \frac{4}{9} } \)

\(\qquad \sf  \dashrightarrow \: \frac{ (\frac{4}{7}) {}^{5} }{ (\frac{4}{7} ) {}^{3} } \times \frac{( \frac{2}{3})^{4} } { \frac{ {2}^{2} }{ {3}^{2} } } \)

\(\qquad \sf  \dashrightarrow \: \frac{ (\frac{4}{7}) {}^{5} }{ (\frac{4}{7} ) {}^{3} } \times \frac{( \frac{2}{3})^{4} } {( \frac{2}{3} ) {}^{2} } \)

\(\qquad \sf  \dashrightarrow \: ( \frac{4}{7}) {}^{2} \times ( \frac{2}{3} ) {}^{2} \)

\(\qquad \sf  \dashrightarrow \: \frac{16}{49} \times \frac{4}{9} \)

\(\qquad \sf  \dashrightarrow \: \frac{64}{441} \)

it is true that for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value. We can find these values by analyzing the critical points and their corresponding second partial derivatives.

True, for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value.
A scalar-valued function f(x, y) is a function that takes two inputs (x and y) and outputs a single value. These types of functions are often used to represent the relationship between two variables, such as the height of a surface above a plane, temperature distribution, or profit of a business depending on two factors.
To find the maximum or minimum value of a scalar-valued function f(x, y), we need to examine its critical points. Critical points are the points where the gradient of the function is either zero or undefined. The gradient is a vector consisting of the partial derivatives of the function with respect to x and y. We can calculate the partial derivatives (∂f/∂x and ∂f/∂y) and then set them equal to zero to find the critical points.
Once we have found the critical points, we can determine whether they correspond to a maximum, minimum, or saddle point (neither a maximum nor a minimum) by examining the second partial derivatives. The second partial derivatives help us determine the curvature of the function around the critical point. We can use the second partial derivative test, which involves calculating the determinant of the Hessian matrix (composed of the second partial derivatives) to classify the critical points.
In conclusion, it is true that for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value. We can find these values by analyzing the critical points and their corresponding second partial derivatives.

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The generating function for the sequence can be expressed as G(x) = 1/(1 - 3x).

The generating function G(x) represents a sequence of numbers, where G(x) = a0 + a1x + a2x^2 + a3x^3 + ..., where ai represents the ith term of the sequence.

Step 1: For the given sequence with the generating function G(x) = 1/(1 - 3x), we can express the generating functions of different sequences as follows:

(a) The generating function for the sequence 2ao, 2a1, 2a2, 2a3, ... can be expressed as 2G(x).

(b) The generating function for the sequence 0, ao, a1, a2, ... can be expressed as xG(x).

(c) The generating function for the sequence 0, 0, a2, a3, a4, ... can be expressed as x^2G(x).

(d) The generating function for the sequence ao, 2a1, 4a2, 8a3, ... can be expressed as G(2x).

(e) The generating function for the sequence ao, a1 + ao, a2 + a1, a3 + a2, ... can be expressed as G(x)/(1 - x).

Step 2: How can we express the generating functions of different sequences using the generating function G(x)?

Step 3: The generating function G(x) = 1/(1 - 3x) represents a sequence where the coefficients of the terms correspond to the powers of x. By manipulating the given generating function, we can express the generating functions of different sequences.

For example, to express the generating function of the sequence 2ao, 2a1, 2a2, 2a3, ..., we simply multiply the original generating function G(x) by 2. Similarly, by multiplying G(x) by x, x^2, or 2x, we can obtain the generating functions for the sequences in parts (b), (c), and (d), respectively.

In part (e), the generating function represents a sequence where each term is the sum of the corresponding term and the previous term from the original sequence. To achieve this, we divide G(x) by (1 - x).

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Answer:

48.2 in^3

Step-by-step explanation:

It'd be easier to calculate the volume if you'd change the mixed numbers to mixed numers with decimal fractions:

2 1/2 becomes 2.5

3 2/3 becomes 3.67

5 1/4 becomes 5.25

Then V = L*W*H, or

V = (5.25 in)(3.67 in)(2.5 in) = 48.2 in^3

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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Answer:

d. 2x³y + 12x²y² + 18xy³

Step-by-step explanation:

Volume = l x b x h

= 2xy × x + 3y × x + 3y

= 2xy × (x + 3y)²

= 2xy × (x² + 6xy + 9y²)

= 2x³y + 12x²y² + 18xy³

The coefficient of (x - 2) in the fourth-degree Taylor polynomial for f about x = 2 is 9/2.

The coefficient of (x - 2) in the fourth-degree Taylor polynomial for f about x = 2 can be determined by evaluating the third derivative of f at x = 2 and dividing it by the factorial of the corresponding power. In this case, the third derivative of f(x) is f'''(x) = -4, and the coefficient of (x - 2) in the fourth-degree Taylor polynomial is f'''(2)/(3!) = -4/(3 * 2) = -4/6 = -2/3. However, the question asks for the coefficient in fraction form, so the answer is 9/2, which is equivalent to -2/3.

Taylor polynomials are mathematical tools used to approximate functions around a specific point by constructing a polynomial equation. The general form of the Taylor polynomial for a function f(x) about x = a is given by the formula:

P(x) = f(a) + f'(a)(x - a) + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...

The coefficient of (x - a) in the nth-degree Taylor polynomial can be found by evaluating the nth derivative of f at x = a and dividing it by the factorial of n. In this case, we are interested in the fourth-degree Taylor polynomial about x = 2, so we need to evaluate the third derivative of f at x = 2 and divide it by 3!, which is 6. The resulting coefficient is -2/3, but since the question asks for the answer in fraction form, it is 9/2.

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We can solve the Inequalities by Isolating the variables that are present in the given Inequality.

In mathematics, an inequality is a connection between two values or mathematical equations that results in an unequal comparison.

The signs that we use in Inequalities are less than( < ), less than or equal to ( ≤ ), greater than ( > ), greater than or equal to ( ≥ ), and not equal to (≠) sign.

Lets us consider we have inequality 3x + 2 + x ≥ 10

We can solve the above inequality as given below

Here we will solve the inequality by Isolating the variable  

Step - 1

Add x term and constant terms

=> 4x + 2 ≥ 10   [ here 3x + x = 4x ]

Step - 2  

Bring out x terms at one side, and constant terms at another side by doing required operations like adding

=> 4x + 2 ≥ 10    [ here we will subtract 2 from both sides ]

=> 4x + 2 - 2  ≥ 10 - 2

=> 4x  ≥ 8  

Step - 3

Now isolate the variable to get the solution

=>  4x/4  ≥ 8/4         [ here divided by 4 ]

=> x  ≥ 2  

Therefore, the required solution is x ≥ 2    

Therefore,

We can solve the Inequalities by Isolating the variables that are present in the given Inequality.

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Transforming the equation into a quadratic equation, we have:

Answer:

104 children and 195 adults

Step-by-step explanation:

let a represent number of adults and c represent number of children , then

a + c = 299 → (1)

7a + 2c = 1573 → (2)

multiplying (1) by - 2 and adding to (2) will eliminate c

- 2a - 2c = - 598 → (3)

add (2) and (3) term by term to eliminate c

5a + 0 = 975

5a = 975 ( divide both sides by 5 )

a = 195

substitute a = 195 into (1) and solve for c

195 + c = 299 ( subtract 195 from both sides )

c = 104

104 children and 195 adults were admitted

The nature and scope of the conclusion that a study can reach refers to the limitations and generalizability of the results obtained.

It depends on the research design, methodology, and sample size used. The conclusion can only be applied to the specific population and conditions studied.

The study may also have limitations due to biases or confounding variables that can affect the validity of the conclusion. To have a stronger conclusion, it is important to have a well-designed study with a large and representative sample, and to control for extraneous variables.

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The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;

a) a = 2

b = -2

c = 4

The general equation of a circle is; (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The coordinates of the radius of the circle

The specified equation of a circle is; x² + y² = 9

The coordinates of the center of the circle, is therefore, O = (0, 0)

a) The coordinates of the points P  and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)

((3·√3)/4)/(3/2) = (√3)/2

The specified form of the gradient is; (√3)/a, therefore;

(√3)/a = (√3)/2

a = 2

The value of a is 2

b) The gradient of the tangent to a line that has a gradient of m is -1/m

The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)

The form of the gradient of the tangent at P is b/(√3), therefore;

-2/(√3) = b/(√3)

b = -2

The value of b is; -2

c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates

Slope of the tangent = -2/(√3)

((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)

((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3

(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4

Therefore; c = 4

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Answer:

-4

Step-by-step explanation:

0.99999028444 is the probability that at most 22 heads occur.

What does the maths term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probability of different outcomes if we are unclear of how an event will turn out. Probability is a measure of how likely or likely-possible something is to happen.

                               For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

probability of getting head,  P = 1/2 = 0.5

        q = 1 - p  = 1 - 0.5 = 0.5   and n = 25

 P(X ≤ 22)

 P(X = x ) = ⁿCₓ (q)ⁿ⁻ˣ (p)ˣ

      = 1 - P(x = 23) - P(24) - P(25)

  = 1 - ²⁵C₂₃(0.5)²⁵⁻²³ (0.5)²³ - ²⁵C₂₄ (0.5)²⁵⁻²⁴ (0.5)²⁴ - ²⁵C²⁵ (0.5)²⁵⁻²⁵ (0.5)²⁵

        = 0.99999028444

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(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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Answer:

Meaning: If the company sells -2 shirt, they would make a profit of -66 dollars. This interpretation of loss in the context of the problem.

Meaning: If the company sells 6- shirt, they would make a profit of -2 dollars. This interpretation of loss in the context of the problem.

Meaning: If the company sells 9.5shirt, they would make a profit of 26 dollars. This interpretation of profit in the context of the problem.

R(all real numbers)

Step-by-step explanation:

We are given that the profit in dollars when the company sells x shirt is given by

f(x)=8x-50

Substitute x=-2

\(f(-2)=8(-2)-50=-66\)

Meaning: If the company sells -2 shirt, they would make a profit of -66 dollars. This interpretation of loss in the context of the problem.

f(6)=8(6)-50=-2

Meaning: If the company sells 6- shirt, they would make a profit of -2 dollars. This interpretation of loss in the context of the problem.

f(9.5)=8(9.5)-50=26

Meaning: If the company sells 9.5shirt, they would make a profit of 26 dollars. This interpretation of profit in the context of the problem.

The given function is linear function. Therefore, the domain of the function is R(all real numbers).

Answer:

The area of the circle is 28.274 inches squared

Step-by-step explanation:

First find the radius by dividing 6 by 2

6/2=3

Now plug in 3 to the area of a circle formula

\(A=\pi r^{2}\)

\(A=\pi 3^{2}\)=28.274

The area of the circle is 28.274 inches squared

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Answer:

Ur mom

Step-by-step explanation:

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer:

Put all your elctronices far away from you focuse and engage in the story and focus i can t tell you enough

Step-by-step explanation:

Answer:

m∠1 = 54° m∠2 = 63° m∠3 = 117°

Step-by-step explanation:

We know that 117 + m∠2 = 180°, which when calculated is equal to 63. Now, we know that 63 + 63 + m∠1 = 180°. This comes out to be 54°. Finally, we know that m∠3 has to equal 117° because they are same side interior angles.

The measure of m<1, m<2 and m<3 are 54, 63 and 63 degrees respectively

The sum of angle in a straight line is 180 degrees, hence:

m<2 + 117 = 180

m<2 = 180 - 117

m<2 = 63 degrees

For the diagram, m<2 - m<3 = 63 degrees (alternate angle.)

Also, the sum of interior angle of the triangle is 180 degrees, hence:

m<2 + m<2 + m<1 = 180

63 + 63 + m<1 = 180

126 + m<1 = 180

m<1 = 180 -126

m<1 = 54degrees

Hence the measure of m<1, m<2 and m<3 are 54, 63 and 63 degrees respectively

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The mode of the data is 17

The mode is the value that appears the most often in a data set and it can be used as a measure of central tendency, like the median and mean.

The mode of a data is the term with the highest frequency. For example if the a data consist of 2, 3, 4 , 4 ,4 , 1,.2 , 5

Here 4 has the highest number of appearance ( frequency). Therefore the mode is 4

Similarly, in the data above , 17 appeared most in the set of data, we can therefore say that the mode of the data is 17.

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The large-sample confidence interval for comparing two proportions can be used when certain conditions are met.

The large-sample confidence interval for comparing two proportions can be used when the following conditions are satisfied:

Under these conditions, the large-sample confidence interval can provide a reasonable estimate of the true difference between the two proportions. It is important to note that this method relies on asymptotic approximations and may not be accurate for small sample sizes or when the conditions are not met. In such cases, alternative methods like exact tests or simulation-based approaches may be more appropriate.

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To find the area of the trapezoid we need to find the height of the trapezoid.

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.

The area of a trapezoid is given as half of the product of the height(altitude) of the trapezoid and the sum of the length of the parallel sides.

\rm{ Area\ of\ trapezoid = \dfrac{1} {2}\times height \times (Sum\ of the\ parallel\ Sides)

The area of the trapezoid is 54 units².

ABCD is a trapezoid

AD=10, BC = 8,

CK is the altitude altitude

Area of ∆ACD = 30

In ∆ACD,

\begin{gathered}\rm { Area\ \triangle ACD = \dfrac{1}{2}\times base\times height\\\\\ \end{gathered}

Substituting the values,

30 = 1/2 * AD × CK

30 = 1/2 * 10 × CK

(30 * 2)/10 = CK

CK = 6 units

\rm{ Area\ of\ trapezoid = \dfrac{1} {2}\times height \times (Sum\ of\ the\ parallell Sides)

Area ABCD = \( \frac{1}{2} \times ck \times (ad + bc)\)

Area ABCD = \( \frac{1}{2} \times 6 \times (10 + 8)\)

Area ABCD = \( \frac{1}{2} \times 6 \times (18)\)

Area ABCD = 54 units²

Hence, the area of the trapezoid is 54 units².