Which graph do you create if you plot the function on a coordinate plane?

Hence the formula of [tex]a ^2 + b^ 2 + c^ 2[/tex] is [tex]( a + b + c )^ 2 - 2 ( ab + bc + ca ) .[/tex]

Formulas are equations that compute values from your spreadsheet. A formula always starts with the equal sign (=).

Using a calculating operator and a constant, you can make a straightforward formula.

For instance, the equation =5+2*3 multiplies two numbers before adding one more to the outcome.

A formula is a rule or relationship in mathematics that utilizes letters to indicate amounts that might change; these amounts are known as variables. For instance, the triangular area calculation formula.

The word "formula" is pluralized to "formulas." A list of elements that are employed in various concoctions and potions is referred to as a formula, which can also refer to a specific mathematical calculation.

Because English might be erratic at times, newborns can also be fed formula.

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The function f(x,y) is defined for all (x,y) pairs that lie within the region d, which is bounded by the parabolas y= 2x2 and y= 1 x2. It returns the product of x and 2 to the power of y.

The function f(x,y) is a two-variable function defined on the region d, which is bounded by the parabolas y= 2x2 and y= 1 x2. In order to calculate the output of this function, we must first identify the values of x and y that lie within the region d. We can do this by graphing both parabolas and finding the intersection point, which is when x=1 and y=2. This tells us that any (x,y) pairs with x<1 and y<2 will be within the region d. Now that we have identified the region, we can calculate the output of the function by multiplying x and 2 to the power of y. For example, if x=0.5 and y=1, then f(x,y)= 0.52 = 0.25.

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Given the following information, we can calculate the requested probabilities:

Probability that the customer is at least 20 but no older than 60:

Number of customers in the specified age range: 72 + 52 + 100 + 71 + 69 = 364

Total number of customers: 364 + 1 = 365

So, the probability is 364/365 = 0.997

Probability that the customer is either older than 40 or younger than 20:

Number of customers in the specified age range: 72 + 52 = 124

Total number of customers: 365

So, the probability is 124/365 = 0.338

Note: The chart doesn't provide information about customers who are older than 60 or younger than 20, so we can't calculate the probability for those ranges.

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Answer:  3:10

Step-by-step explanation:

Answer:

6:20 or 3/10

Step-by-step explanation:

The minimum degree of a Taylor polynomial required to calculate to 3 decimal places depends on the complexity of the function being approximated.

A Taylor polynomial is a way of approximating a function with a polynomial. The polynomial is built based on the function's value and its derivatives at a specific point.

To calculate a Taylor polynomial to 3 decimal places, the degree of the polynomial required depends on the complexity of the function and the desired accuracy.

If the function is smooth, with no sudden changes, a lower degree polynomial may be sufficient to approximate the function to 3 decimal places.

A general rule is to use a polynomial of degree at least two times the number of decimal places desired. So, for 3 decimal places, a polynomial of degree 6 or higher is required.

However, it is important to note that the minimum degree required can be determined by experimenting with different degrees of polynomials and checking the accuracy of the approximation.

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The recursive formula for the arithmetic sequence in this problem is given as follows:

c(1) = -16.

c(n) = c(n - 1) - 17.

Arithmetic sequences are collections of numbers that share a consistent difference between them; that is, there is a constant amount of subtraction between any two entries in an arithmetic sequence.

The recursive formula for an arithmetic sequence is defined as follows:

c(n) = c(n - 1) + d.

In which d is the common difference of the arithmetic sequence.

The sequence in this problem is given as follows:

-16, -33, -50, -67,...

Then the common difference is obtained as follows:

d = -33 - (-16) = -33 + 16 = -17.

So, c(n) = c(n - 1) - 17.

c(1) = -16.

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1) The area of the board shown on the scale drawing is; 1800 cm².

2) The way that Adam can use the scale factor to find the area of the actual electronics board is; The scale factor 5:1 means that 1 cm in the drawing is 0.2 cm in reality. Thus, he would multiply both 36 and 50 and by 0.2 cm then add them to get 17.2.

3)  The area of the actual electronics board is; 17.2 cm².

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size maybe bigger or smaller.

1) The formula for area of a rectangle is;

Area = Length * Width

Thus;

Area of board = 36 * 50

Area = 1800 cm².

2) He can figure out that the scale factor 5:1 means that 1 cm in the drawing is 0.2 cm in reality. Thus, he would take 36 and 50 and multiply them both by 0.2 cm then add them to get 17.2, which is the actual area of the rectangle.

3) Actual area is 17.2 cm²

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If the Circle has Center: (6, 1); and solution point: (5, 9) , then the standard form of Equation is (x - 6)² + (y - 1)² = 65 .

The standard form of a circle is given by ⇒ (x - h)² + (y - k)² = r²,

where (h, k) is the center of the circle and r is the radius.

To find the standard form of the circle that has center (6, 1) and a solution point (5, 9), we need to find the radius "r" first.

The distance(r)  between the center and the solution point is given by the Pythagorean theorem:

⇒ r = √((5 - 6)² + (9 - 1)²)

⇒ r = √((-1)² + (8)²)

⇒ r = √65

Now substituting  radius(r = √65) in  the standard form of the circle:

we get ;

⇒ (x - 6)² + (y - 1)² = √65²

⇒ (x - 6)² + (y - 1)² = 65

Therefore , the standard form of circle is (x - 6)² + (y - 1)² = 65  .

The given question is incomplete , the complete question is

Write the standard form of the circle that has Center: (6, 1); and solution point: (5, 9) .

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Her sales are at least $1000 during that week.

Let x stand in for her sales.

The equation to determine her sales is as follows, based on the data in the question:

Hillary works at a video store. She earns $8. 50 per hour plus a 12% commission on all the weekly sales she makes.

he works 24 hours a week if she earns at least $324 during that week

(8.50 × 24) + (12% × x) ≥ 324

204 + (0.12 × x) ≥ 324

204 + 0.12x ≥ 324

0.12x ≥ 324 - 204

0.12x ≥ 120

x ≥ 120/0.12

x ≥ 1000

Her sales are at least $1000

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Answer:

135°

Step-by-step explanation:

Ponyboy shivered as he recalled the Socs jumping him and asking if he was a greaser.

The statement is referencing a scene from the novel "The Outsiders" by S.E. Hinton. In the novel, Ponyboy is a member of a poor, lower-class gang called the "greasers." The Socs are the wealthier, more privileged gang in town. The scene described in the statement is likely one in which Ponyboy is confronted and beaten up by members of the Socs gang, who are asking him if he is a member of the greaser gang.

The scene highlights the tensions and conflicts between the two gangs and their different experiences growing up in different social classes.

"The Outsiders" is considered a young adult novel, so it can be read by kids who are at or near the target age range for that genre, typically around 12 to 18 years old. However, the themes and content of the novel may be mature for some younger readers, so it is always a good idea for parents or guardians to read the book first and determine if it is appropriate for their child.

Additionally, individual reading levels can vary greatly, so it is always best to assess a child's individual abilities and interests when determining if a particular book is suitable for them to read.

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The value of the operation sec theta plus cot theta using trigonometric ratios is; 2.465

The primary trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

sec x = 1/cos x

cosec x = 1/sin x

cot x = cos x/sin x

The parameters are;

sin θ = 0.6224

cos θ = 0.8820

Thus;

sec θ = 1/cos θ = 1/0.8820

cot θ = cos θ/sin θ = 0.8820/0.6624

Thus

sec θ  + cot θ = (1/0.8820) + (0.8820/0.6624)

= 2.465

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Answer: 12

Step-by-step explanation:

you would first add up all of the numbers togeather, and it would give you 60. You then need to divide 60 by the amount of numbers which is 5. So you would do 60 divided by 5 to get 12.

The mean/standard error of the sampling distribution of the proportion is 0.0111.

Its root-mean The square root of the mean of the squares of all the values in a series calculated from the arithmetic mean is the square deviation, also referred to as the standard deviation and denoted by the symbol.

The standard deviation reveals the degree of data dispersion. It expresses how far away from the mean each observed value is.

Almost 95% of the values in any distribution will be within two standard deviations of the mean. The degree of data dispersion from the mean is described by the term "standard deviation" (or " σ").

The data tend to cluster around the mean when the standard deviation is low; when it is high, the data are more dispersed.

The formula to calculate the standard error of sampling distribution of sample proportion is:

[tex]$ SE(p) =\sqrt{\frac{p(1-p)}{n} }[/tex]

It is given that the bank believes that 8% of people who receive loans will not make payments on time. That is,

Population proportion, p =0.08

Sample size, n= 800

Using the formula defined :

[tex]$ SE(p) =\sqrt{\frac{0.08(1-0.08)}{600} }[/tex]

[tex]$ SE(p) =\sqrt{0.000123}[/tex]

SE(p) = 0.0111

Thus, the mean/standard error of sampling distribution of the proportion is 0.0111.

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According to the histogram, the expected mean exam score is approximately 6.5. This value is centered on the majority of scores, indicating that it is most likely the exam's average.

A histogram is a graph that shows data points arranged in user-defined ranges. By grouping a large number of data points into logical ranges or bins, the histogram, which looks like a bar graph, makes a data series easier to understand.

Histograms and bar charts both use columns to present a visual display, and the terms are frequently used interchangeably. However, technically speaking, a histogram depicts the frequency distribution of a data set's variables.

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For the given coordinates, the equation of line is y = 1, The coordinates of foot of perpendicular will be (0, 5)

Assume that ax + by + c = 0. is a continuous line. If a perpendicular line is drawn from any point on the plane to the provided straight line, the intersection of the two lines is referred to as the foot of the matching perpendicular.

Because a perpendicular line is created from point P to the y-axis, the distance between its intersection with the x-z plane remains constant.

Given,

the points of line are - (1, 1) and (5, 5).

equation of line = (y - yo) = m (x - xo)

⇒ y - 1 = [tex]\frac{5 - 1}{5 - 1}[/tex] (x - 1)

⇒ y = 1. is the equation of the line,

Let us consider the point (a,b) such that it is the foot of the perpendicular,

Now, as the line line joining the points (1,5) and (a,b) will be perpendicular to each other,

⇒ y - 1 = b - 5 / a - 1 (x - 1)

The slope of one line is the negative inverse of other line,

⇒ b - 5 / a -1 = 0

⇒ b = 5

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Answer:

Step-by-step explanation:

this is a case of linear pair...

52° + 90° (of the right angled triangle) + x° = 180°

52° + x° = 180° - 90°

x° = 90° - 52°

x° = 38°

The values of a and b such that y∼n(0,1) are a = ± (1/σ) and b = ± (μ/σ)

of a gaussian distribution.

Gaussian distribution (also known as normal distribution) is a bell-shaped curve, and it is assumed that during any measurement values will follow a normal distribution with an equal number of measurements above and below the mean value.

E(X) = μ, Var(X) = σ^2

Y = aX + b

We want E(Y) = 0 and Var(Y) = 1

E(Y) = a E(X) + b

0 = a μ + b

b = -a μ  --- (1)

Var(Y) = (a^2) Var(X)

1 = (a^2) σ^2

a^2 = 1/σ^2

a = ± 1/σ  --- (2)

From (1) and (2)

b = (± 1/σ) μ

So, a = ± (1/σ) and b = ± (μ/σ)

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The complete question is :

A random variable X ∼ N (µ, σ2 ) is Gaussian distributed with mean µ and variance σ 2 . Given that for any a, b ∈ R, we have that Y = aX + b is also Gaussian, find a, b such that Y ∼ N (0, 1)

The equation is unchanged when you replace x with --x AND y with -y.

Hence, according to the above hypothesis, our equation is origin symmetry.

Equation graphs may be symmetric with regard to the origin or with respect to one of the coordinate axes.

If the Cartesian plane were folded along the -axis, the area of the graph above the x-axis and the area below the x-axis would coincide. This is known as symmetry with regard to the -axis.

Similar concepts apply to symmetry with regard to the y-axis or the origin.

x-axis, not symmetry, the equation will be changed when we replace the y with -y.

y-axis, not symmetry,  the equation will be changed when we replace the x with -x.

origin symmetry , the equation is unchanged when you replace x with --x AND y with -y.

hence, according to the above hypothesis, our equation is origin symmetry.

The complete question is-

Use the algebraic tests to check for symmetry with respect to both axes and the origin. (Select all that apply.)

y=x3

x-axis symmetry

y-axis symmetry

origin symmetry

no symmetry

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"The function is increasing in the interval (-2.5,∞)".

To determine whether the function is increasing or decreasing we are going to use the derivative test.

f(x) = x² + 5x + 6

f'(x) = 0

2x + 5 = 0

x = -5/2

Intervals associated with this point are  (-∞,-2.5) and (-2.5,∞)

Now by checking in the interval  (-∞,-2.5)  at a point, let's say -3

Then,

f'(-3) = -1 so function is decreasing over this interval.

Now by checking in the interval  (-2.5,∞)  at a point, let's say 2

Then,

f'(2) = 1 so function is increasing over this interval.

Hence "The function is increasing in the interval (-2.5,∞)".

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The sign of the second derivative of a function can determine whether the function is increasing or decreasing. If the second derivative is positive, the function is concave up and therefore increasing.

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The sum or difference matched with its simplified form;

(7x³ -12x + 4) - (6x²- 8x - 3)

open parenthesis

= 7x³ -12x + 4 - 6x² + 8x + 3

= 7x³ - 6x² - 4x + 7

(5x³ - 3x + 7) - (2x³ + 6x² - x)

= 5x³ - 3x + 7 - 2x³ - 6x² + x

= 3x³ - 6x² - 2x + 7

(3x³ - 10x² + 2x) - (10x² + 7x - 10)

= 3x³ + 10x² + 2x - 10x² - 7x + 10

= 3x³ - 5x + 10

(5x³- 3x + 7) + (2x³ + 6x² - x)

= 5x³- 3x + 7 + 2x³ + 6x² - x

= 3x³ + 6x² - 4x + 7

Therefore, a given expression can be written Ina simplified form.

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The slope of the equation c=450+28g represents the increase in cost per additional guest.

Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2). The letter "m" is frequently used to signify slope.

We can see that the preceding equation is in the slope-intercept format, where m denotes the line's slope and b is its y-intercept or starting point.

In this case, the slope is 28 dollars per additional guest. This means that for every additional guest, the cost of the banquet increases by $28.

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The value of x for the expression is 168 = 18x + 12.2x.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

168 = 18x + 12.2x

Add like terms.

168 = 30.2x

Divide both sides by 30.2

168/30.2 = x

x = 5.56

Thus,

The value of x is 5.56.

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-3)}}} \implies \cfrac{4 +1}{-5 +3} \implies \cfrac{ 5 }{ -2 } \implies - \cfrac{ 5 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- \cfrac{ 5 }{ 2 }}(x-\stackrel{x_1}{(-3)}) \implies y +1 = - \cfrac{ 5 }{ 2 } ( x +3) \\\\\\ y+1=- \cfrac{ 5 }{ 2 }x-\cfrac{15}{2}\implies y=- \cfrac{ 5 }{ 2 }x-\cfrac{15}{2}-1\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 2 }x-\cfrac{17}{2} \end{array}}[/tex]

The formula of standard deviation method is

[tex]P=\sqrt{\frac{ \sum(X-\mu)^2}{N}}[/tex]

[tex]S=\sqrt{\frac{ \sum(X-\bar{x})^2}{n-1}}[/tex]

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

population mean:

[tex]P=\sqrt{\frac{ \sum(X-\mu)^2}{N}}[/tex]

X- the value in the data distribution

[tex]\mu[/tex]  - the population mean

N- total number of observations

[tex]S=\sqrt{\frac{ \sum(X-\bar{x})^2}{n-1}}[/tex]

[tex]\bar{x}[/tex]  - the sample mean

n- total number of observations

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Using the details given, the exponential growth at rate of 10% over 14 years is 26582.5

An exponential function is a mathematical function in which the variable appears as an exponent. It can be written in the form of y = ab^x, where a is the base, b is a constant, and x is the variable. This function has the property that y grows or decays at an exponential rate as x increases or decreases.

y = a(1 + r)^t

In the given problem, we have the data given as;

Substituting the values into the formula;

y = 7000(1 + 0.1)^14

y = 26582.5

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Answer:

600,000 is greater than 11,733.83. Or

600,000>11,733.83

Step-by-step explanation:

To compare the values of 600,000 and 11,733.83, we can simply look at the magnitude of the numbers.

600,000 is much larger than 11,733.83. This means that 600,000 is greater than 11,733.83

The greatest common factor of 5x⁷, 30x⁴, 10x³ is 5x³

The Greatest Common Factor is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The greatest common factor between 5, 10 and 30 is 5. This means out all of the common factors between 5,10 and 30 , 5 is the greatest

The greatest common factor between x⁷ and x⁴ and x³ is x³.

Therefore the greatest common factor between 5x⁷, 30x⁴, 10x³ is 5× x³ = 5x³

This means 5x³ is the highest factor that can go through 5x⁷, 30x⁴, 10x³

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The equation for the volume of a cylindrical shell is:

V = πr² * h * w, where r is the radius of the semicircle base, h is the height of the shell, and w is the width of the shell.

The volume of the solid can be found using the method of cylindrical shells. The volume of each cylindrical shell is equal to the product of the area of the base (a semicircle), the height of the shell, and the width of the shell (which is equal to the difference in the x-coordinates of the two vertices that define the height).

To find the total volume, we would sum up the volumes of all the cylindrical shells, from the top to the bottom of the solid.

The equation for the volume of a cylindrical shell is:

V = πr² * h * w, where r is the radius of the semicircle base, h is the height of the shell, and w is the width of the shell.

The height of the shell is given by the difference in the y-coordinates of the two points that define the height, and the width of the shell is given by the difference in the x-coordinates of these two points.

To find the total volume, we would integrate the volume of the cylindrical shell over the height of the solid. The limits of integration would be the y-coordinates of the bottom and top of the solid.

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