Determine lim x→ 4 f(x) given the definition of f(x) below. (If the limit does not exist, enter DNE.) if= -2x² + 3x - 1 if x-4
-1 if -4 < x < 1
-2x² + x if x ≥ 1

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.

Check the picture below.

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 segment drawn from the apex to the edge of the circular base is 24.2 units.

A right triangle's hypotenuse, or side opposite the right angle, has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean Theorem can be used to determine the slant height of a right cone. The circular base's radius is equal to its diameter times half, or 6/2 = 3 units.

The volume of the cone can be found using the formula:

V = (π/3)r²h

Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:

72π = (π/3)r²h

72π = (π/3)3²h

72π = (π/3)9h

72π = 3πh

24 = h

Using the Pythagorean Theorem, we can find the slant height as follows:

c² = a² + b²

Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:

c² = 24² + 3²

c² = 576 + 9

c² = 585

c = 24.2

Hence, the segment drawn from the apex to the edge of the circular base is 24.2 units.

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Answer:  3:10

Step-by-step explanation:

Answer:

6:20 or 3/10

Step-by-step explanation:

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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The cost of a 32-ounce container is 2.92 and the cost of 6 8-ounce containers is $4.18.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let's call the unit price of 8-ounce yogurt x.

32-ounce unit price = x + 0.002

32-ounce container cost = 32 * (x + 0.002) =0.064 + 32x

6 * 8-ounce container cost = 6 * 8 * x = 48x

Given, 32-ounce container cost = 6 * 8-ounce container cost - $1.33

Substituting the costs,

0.064 + 32x = 48x - 1.33

Solving for x,

48x - 32x = 0.064 + 1.33

16x = 1.394

x = $0.087125

So, the unit price of 8-ounce container is $0.087125

Cost of 32-ounce container = $0.064 + 32 * (0.087125 + 0.002) = $2.92

Cost of 6 8-ounce containers = 6 * 8 * 0.087125 = $4.18.

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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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Answer:

135°

Step-by-step explanation:

The standard form of the equation of the circle with the given characteristics is  (x - 6)² + (y - 1)² = 65.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Given, center:  (6, 1) and solution Point: (5,9)

By solution point, it means that the circle passes through that point. Hence, the radius of the circle is the distance between  (6, 1) and  (5,9)

Distance formula is given by

D = √[(x2 - x1)² + (y2 - y1)²]

D=  √[(5 - 6)² + (9 - 1)²] = 8.062

r= 8.062  or r²=65

We have, equation of the circle centered ant (h, k) and radius ‘r’ as

(x - h)² + (y - k)² = r².

=>  (x - 6)² + (y - 1)² = 65.

The standard form of the equation of the circle with the given characteristics is  (x - 6)² + (y - 1)² = 65.

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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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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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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 equation is z = (-2/3)*xy with of x , y and z are jointly varied.

Joint variation describes a situation in which, while the other variables are held constant, the value of one variable relies on the values of two or more additional variables.

Joint variation is used to describe when more than two variables are directly correlated or when one variable changes as a result of the change product of more than two variables. X can be symbolically expressed as X YZ if it is in joint variation with Y and Z. If Y is also constant, then X and Z directly depend on one another.

Joint variation is a type of variation where a quantity changes when two or more other numbers are multiplied together. For instance, when a rectangle's length or breadth changes, so does its area. Where A is the area, l is the length, and w is the width, we say that A = lw.

Joint Variation of x,y and z

z = kxy

k is the cofficient

for x = 7, y = 3 and z = -14

-14 = k*3*7

⇒k = -2/3

for x= 3 and z = -8

-8 = (-2/3)*3*y

y = 4

The equation is z = (-2/3)*xy with of x , y and z are jointly varied.

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The postulate theorem used to prove the congruence of triangles MNQ and PXN is given as follows:

B. SAS.

The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.

The congruent sides are given as follows:

The angle between these two sides is a vertical angle, having the same measure in each of the triangles, hence the SAS theorem can be applied and the correct option is given by option B.

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The scatter plot shows [negative linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values decreases

This represents a negative linear] association.

Hence, the association is a negative linear] association.

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The length of AL, BK and CH are 12, 9 and 6 respectively.

Similar triangles are those triangles which has the same shape but different size.

The length of sides are proportional in similar triangles.

Given a figure of a big triangle.

We can clearly see that angles made by each of the triangles ALE, BKE, CHE and DGE are equal and thus they are similar triangles.

The sides of similar triangles are proportional.

DG / GE = CH / HE = BK / KE = AL / LE

We have DG = 3, GE = 5,HG = 5, KH = 5, LK = 5

HE = 5 + 5 = 10

KE = 5 + 5 + 5 = 15

LE = 5 + 5 + 5 + 5 = 20

Substituting,

Consider DG / GE = CH / HE

3 / 5 = CH / 10

CH = (3/5) × 10 = 6

Consider DG / GE = BK / KE

3 / 5 = BK / 15

BK = (3/5) × 15 = 9

Consider DG / GE = AL / LE

3 / 5 = AL / 20

AL = (3/5) × 20 =  12

Hence the length of AL is 12, length of BK is 9 and length of CH is 6.

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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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0.947 g/ml is the cube density the volume was 9.01.

The term "density" refers to the ratio between the volume (the amount of space taken up by an item or substance) and the amount of matter contained inside (its mass). The quantity of mass per unit of volume is another method to define density.

We are know that items float in liquids when their density is less than that of the liquid.

Objects floating in a liquid are those whose density is equal to that of the liquid.

So, in this case, the cube is solely suspended in the first liquid combination. Therefore, the first liquid mixture's density is the same as a cube. The other mixes have densities that are higher than that of the cube.

Density of methanol = 0.7913 g/ml

Density of water = 1 g/ml

Density of the 6th liquid mixture:

= {(2 × 0.7913 ) + (1 × 6)}/8 g/ml

= 0.947 g/ml

Therefore density of cube = 0.947 g/ml

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The complete question is as follows:

What Is The Cube Density The Volume Was 9.01? The Cube Floated Up To 8.1 Ml

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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The polynomials is divided using synthetic division and the remainder theorem to 3x³ -6x² - 20x - 77/x + 4

Synthetic division is described as one of the methods that is used to manually perform the Euclidean division of polynomials.

The steps taken in a synthetic division include;

Given the polynomial;

f(x) = 3x³ + 6x² + 4x +3 by x + 4

We have;

        3          6        4         3

-4     _____-12__24___80__

        3          -6       -20      -77

Then, we have;

3x³ -6x² - 20x - 77/x + 4

Hence, the expression is 3x³ -6x² - 20x - 77/x + 4

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The equation of the plane that passes through (1, 3, 6) and is parallel to x = 11 is x = 1.

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations (such as addition, subtraction, multiplication, and division). It represents a value that can be determined if the values of the variables are known. An algebraic expression does not contain an equal sign and cannot be solved like an equation, but it can be simplified or manipulated using algebraic rules. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.

A plane can be represented by a normal vector (a,b,c) and a point (x⁰,y⁰,z⁰) that lies on the plane. If a plane is parallel to the plane x = 11, the normal vector must be in the direction of the x-axis, meaning (a,b,c) = (1,0,0).

The equation of the plane can then be found using the point-normal form, which is given by:

ax + by + cz = d, where d = ax⁰ + by⁰ + cz⁰

Plugging in the values for (1,3,6) and (a,b,c) = (1,0,0), we get:

a(1) + b(3) + c(6) = d

1 + 0 + 0 = d

d = 1

So the equation of the plane that passes through (1,3,6) and is parallel to x = 11 is: x = 1

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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 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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Answer:

12. m = 1/3

14. m = 5/6

16. m = -5/2

Step-by-step explanation:

m = y2-y1/x2-x1

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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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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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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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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