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The end behavior of a polynomial function can be determined by examining the leading coefficient and degree of the polynomial. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. If the leading coefficient is negative, the graph will decrease without bound as the x-values increase.

The end behavior of a polynomial function depends on the equation of the function. The degree of a polynomial is the highest power of the variable, and the leading coefficient is the coefficient of the term with the highest degree. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. This is because the terms in the equation with positive coefficients will become increasingly larger than the terms with negative coefficients as the x-values increase. On the other hand, if the leading coefficient is negative, the graph will decrease without bound as the x-values increase. This is because the terms in the equation with negative coefficients will become increasingly larger than the terms with positive coefficients as the x-values increase. In addition, the degree of the polynomial can also affect the end behavior of the graph. If the degree is even, the graph will not have an extreme point. However, if the degree is odd, the graph will have an extreme point. The extreme point will be a maximum or a minimum depending on the sign of the leading coefficient.

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The relationship between the volume of a sphere and the volume of a cylinder is said to be that the volume of any sphere is 2/3rd of the volume of any with equal radius and height which is equal to the diameter.

Assuming a cylinder with radius r, height h.

We are aware that the cylinder-volume formula is,

V₁ = π * r² * h

Consider a sphere with radius r₁.

We know that the formula for the volume of sphere is,

V₂ = 4/3 * π * r₁³

If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r₁ = r and h = 2r

V₂ = 4/3 * π * r³

And V₁ = π * r² * (2r)

V₁ = 2 * π * r³

V₁ = 2 * 3/4 * V₂

V₁ = 3/2 * V₂

Volume of cylinder = (3 / 2) *  Volume of sphere

Therefore, the Volume of a sphere = 2/3 * Volume of a cylinder

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95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.

What is proportional limit?

The maximum stress at which stress and strain are directly proportional and the stress-strain graph is a straight line with a gradient equal to the elastic modulus of the material is known as the proportional limit.

To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the following formula:

lower confidence bound = sample mean - (t-value * standard error)

The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:

              [tex]standard\ error = sample\ standard\ deviation / \sqrt{(sample \ size)}\\\\= 0.78 / \sqrt{(20)}\\\\= 0.19[/tex]

To find the t-value, we can consult a t-distribution table or use a t-distribution calculator. At a 95% confidence level with a sample size of 20, the t-value is approximately 1.725.

Substituting these values into the formula for the lower confidence bound, we get:

lower confidence bound = 8.52 - (1.725 * 0.19)

= 8.52 - 0.327

= 8.19

So the 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.19 mpa.

Hence,  95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.

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Answer:

30 inches

Step-by-step explanation:

The longest piece (15 in) is represented as 5 in the ratio, so we can find what one unit is. We can do 15÷5=3, so one unit is 3 inches. We could multiply each of them by 3 and add them up, but there's a simpler way. We can find the total of the ratio, 2+3+5=10. So, we can do 3x10=30 inches. Therefore, the length of the stick is 30 inches.

Therefore , the given expression of this problem of square root

 2√2  not equal to √2.

The value that results from multiplying the square root of an integer by itself is the number.

Example: Since 5* 5 = 25, 5 is the square root of 25. Observe that (5) (5) also equals 25, proving that (5) is a square root of 25.

Here,

In this case, the mathematical symbol for Root 2 is 2.

Root 2 then multiplied by Root 2.

√2 + √2 = 2√2

If we take the estimated value of 2 = 1.4142

Then

=> 2√2 = 1.4142 x 2

=> 2.8284 (approximately)

Please take note that 2 is an irrational number.

Alternatively, root2* root 2

√2 * √2 = 2

Because 2 is just the square root of 2,

Therefore,

what happens when root 2 + root 2 and root2 root 2 are different

2√2 - 2 = 2.8284 - 2 = 0.8284 (approx)

Therefore , the given expression of this problem of square root

 2√2  not equal to √2.'

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Equiangular triangle or Equilateral triangle have  all the sides equal and all the angles are also equal.

A triangle that has equal-length sides is known as an equilateral triangle in geometry. The three angles that lie across the three equal sides are also equal in size since the three sides are also equal.

With each angle measuring 60 degrees, it is also known as an equiangular triangle.

An equilateral triangle has three interior angles that are all equivalent to one another and each measure 60 degrees in the basic Euclidean geometry. The term "regular triangle" is also used to describe this polygon because it is a regular polygon. The exceptional case of an isosceles triangle with three equal sides and angles is an equilateral triangle.

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The option that would not be a lurking variable in the above scenario is c.) the day of the week that stephanie attends service

a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable. Although it is not taken into account in the study, it might affect how the variables are related.

When researching the relationship between two or more variables, we occasionally neglect the influences on the relationship that exist outside of these two variables. These are also known as lurking variables or extraneous variables. These significantly impact the relationship. Lurking variables are those that were not taken into consideration for the study but have an impact on the two studied variables.

The day of the week will not be a lurking variable since we are talking about the number of churches and bars. Hence, Option c is correct.

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Answer:

Step-by-step explanation:

a.) Correct.

A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely street name length is related to the number of bars in a given area.

Answer:

Step-by-step explanation:

We can reduce the margin of error in an interval estimate of p by doing any of the following except using a planning value p* closer to 0.5.

The breadth of the confidence interval is affected by the following features:

Correct Question:

We can reduce the margin of error in an interval estimate of p by doing any of the following except ____.

increasing the sample size

using a planning value p* closer to 0.5

increasing the level of significance

reducing the confidence coefficient

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The measure of the sides 'b' and 'c' will be 5.7 units and 8.2 and angle C will be 55°.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = CA / sin B

The measure of the third angle is given as,

∠A + ∠B + ∠C = 180°

35° + 90° + ∠C = 180°

∠C = 55°

Then the measure of the side c (AB) is calculated as,

AB / sin C = BC / sin A

c / sin 55° = 10 / sin 90°

c = 8.2

Then the measure of the side b (AB) is calculated as,

AC / sin B = BC / sin A

b / sin 35° = 10 / sin 90°

b = 5.7

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An example of continuous data is the temperature of a room over time. It can change gradually, or even rapidly, but the data is always changing.

Continuous data is data that can take on any value within a given range. It can be measured on an infinite scale and can have an infinite number of values. An example of continuous data is the temperature of a room over time. This data can change gradually or rapidly, but it is always changing. Continuous data can be measured directly, such as measuring the temperature of a room with a thermometer, or indirectly, such as measuring the temperature of a room through observation. Continuous data can also be used to describe physical or psychological phenomena, such as measuring a person’s heart rate over time or measuring the concentration of a chemical in a solution. Continuous data is often used in scientific research, as it allows researchers to observe trends and correlations over time.

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Whole Numbers are the numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …}.

Whole Numbers

Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered as whole numbers.

Addition , Subtraction , Division and multiplication are also possible with the whole numbers as they are also numbers . Addition and Multiplication are closed which means the sum and multiplication of two numbers is also a whole number whereas Subtraction and Division are unclosed.

We know that natural numbers refer to a set of counting numbers starting from 1, 2, 3, 4 and so on. In simple words, whole numbers are a set of numbers without fractions, decimals, or even negative integers.

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The value of the following expression is true.

Expressions include operators and can consist of any set of variables and constants that can be evaluated to produce a result. Relational expressions are used in decision-making to compare operands and evaluate to 1 (true) or 0. (false).

If a logical expression is true when it is evaluated by C++, it returns an integer value of 1; if it is false, it returns an integer value of 0. Any value other than zero is treated as true in C++, while a value of zero is considered false.

Correct Question :

Suppose x is 5 and y is 7. Choose the value of the following expression: (x ! = 7) & & (x <= y)

a. false

b. true

c. 0

d. null

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The Median of the following sample 3 4 6 7 8 9 10 12 13 15 is 8.5.

One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.

When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:

sort the data in ascending or descending order.

If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.

The average of the top two observations is the same as the median of the data given (as determined in step 2).

Median = [tex]\frac{1}{2} [(\frac{n}{2} ) + (\frac{n}{2}+1 )][/tex].

Here n = 10, So [(10/2) + (10/2 + 1)]/2.

=> Median = 8.5.

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The function representing the area to paint as a function of time is A(t) = 52 - 8t, where A(t) represents the area left to paint after t hours.

The area to paint, A(t), can be represented as a linear function based on the given information. Initially, Hiro had the entire room to paint, which can be represented as A(0) = A₀, where A₀ is the total area of the room.

Given that Hiro painted at a rate of 8 square meters per hour, after t hours, he would have painted 8t square meters.

Therefore, the remaining area to paint after t hours can be expressed as A(t) = A₀ - 8t.

We are told that after 3 hours, Hiro had 28 square meters left to paint. Substituting t = 3 and A(t) = 28 into the equation, we can solve for A₀:

28 = A₀ - 8 x 3

28 = A₀ - 24

A₀ = 52

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The complete question:

Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?

More than 50 in mathematical expression is written as >50.

Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.

The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 3x - 2 > 50].

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Answer:

1/256

Step-by-step explanation:

-4 times -4 times -4 times -4 = 256

A negative exponent means it's a fraction!

So, the answer is 1/256

answer :

1/256

steps:

negative exponent means it's a fraction

4^-4 =

1/4^4 :

4^4 =

4 * 4 * 4 * 4 =

256

again negative exponent means it's a fraction so

1/256

Answer:

[tex]\frac{2}{15} (3+\sqrt[3]{3})[/tex]

or

[tex]\frac{6+2\sqrt[3]{3} }{15}[/tex]

You can rationalize the denominator to simplify the answer so many different ways.

Step-by-step explanation:

Simplify the radicals.

The formula can be used to find the missing number in an array of 1 100 is N * (N + 1) / 2.

The size of the array is N – 1. So the sum of n elements, that is the sum of numbers from 1 to N can be calculated by using the formula N * (N + 1) / 2. Now find the summation of all elements in the array and subtract it from the summation of first N natural numbers, the value obtained will be the value of the missing element.

The formula can be used to find the missing number in an array of 1 100 is N * (N + 1) / 2.

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The equation of line in slope intercept form passing through (-5,-2) and parallel to  y = -2x+1 is  y = -2x -12 .

The Slope intercept form of the line is written as " y = mx + c " , where c is the y intercept and m is the slope of line .

the required line is parallel to the line with equation ⇒ y = -2x+1 ,

on comparing it with slope intercept form of line ,

we get the slope(m) as "-2"  .

the required line is passing through (-5,-2).

substituting the values , we get ;

-2 = (-2)(-5) + c ,

-2 = 10 + c ,

c = -10 -2

c = -12 .

So , the equation is ⇒ y = -2x -12 .

Therefore , the slope intercept form of the required line is y = -2x -12  .

The given question is incomplete , the complete question is

How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation ?  the point is (-5,-2); and is parallel to y = -2x + 1   .

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The Side-Side-Side (SSS) criterion states that two triangles are similar if "sides of one triangle in two triangles are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and so the two triangles are comparable."

Look at the triangles in the picture below. We can observe that the triangles' three sets of side pairs are all congruent. "SSS" or "side-side-side" are other names for this. Two triangles are congruent if they have three pairs of congruent sides, according to the SSS requirements for triangle congruence.

Congruence Rule Theorem for SSS

Two triangles are said to be congruent if the corresponding three sides of one triangle match the corresponding three sides of the other triangle exactly.

We shall now demonstrate the aforementioned theorem.

Given: [tex]\triangle A B C[/tex] and [tex]\triangle P Q R[/tex] such that AB=PQ, BC=QR and AC=PR.

To prove: [tex]\triangle A B C \cong \triangle PQR[/tex]

Construction: Let BC be the longest side of [tex]\triangle A B C[/tex] and so QR is the longest side of [tex]\triangle P Q R.[/tex]

Draw PS so that [tex]\angle R Q S=\angle C B A[/tex] and [tex]\angle Q R S=\angle B C A[/tex].

Join SQ and SR.

In [tex]\triangle ABC[/tex] and [tex]\triangle SQR[/tex],

BC=QR Given

[tex]\angle C B A=\angle R Q S[/tex] By construction

[tex]\angle B C A=\angle Q R S[/tex] By construction

[tex]\triangle A B C \cong \triangle SQR[/tex] By ASA congruence

[tex]\angle A=\angle S[/tex] By CPCTC

AB=SQ By CPCTC

AC=SR

Now, AB=PQ and AB=SQ => PQ=SQ

Similarly, AC=PR and AC=SR => PR=SR

Hence, [tex]\triangle ABC \cong \triangle PQR,[/tex]

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Answer:

May be minus

Step-by-step explanation:

minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32

The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).

An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way.  By comparing the sizes of two numbers on the number line, it is most frequently utilized. Different types of inequalities are represented by a variety of different notations, including:

The symbol a b indicates that an is less than b.

A bigger value for a than a lesser value for b is indicated by the notation a > b.

A is not equal to b in either situation. These relationships are referred to as stringent inequalities, which means that an is strictly less than or strictly bigger than b. Equivalence is not included.

There are two kinds of inequality relations that are not strict, in contrast to strict inequalities:

When something is written with an an or b, it signifies that.

A is smaller than or equal to b when a notation like a ≤ b is used (or, equivalently, at most b, or not greater than b).

A greater or equal value for a indicates that b is greater than it (or, equivalently, at least b, or not less than b).

The symbol for "greater than" that is divided in half by a slash, "not," can also be used to express the connection not greater than. The same applies to and not less than and a b.

Hence, The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).

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It signifies that the supplied variable or number must have a value that is larger than or equal to the specified limit. It is the opposite of less than or equal to.

The phrase "more than or equal to" denotes that the variable is either greater than or equal to a specific value. When a quantity is bigger than another, the phrase "more than" is used to indicate this. Two quantities are said to be equal when the phrase "is equal to" is used. It is possible for the quantity or amount value limit to be equal to or larger than the stated limit when these phrases are combined to form the new term Greater Than Or Equal To.

The phrase "less than or equal to" denotes that a variable is either less than or equal to another quantity, number, or variable. Other ways to say "less than or equal to" include at most, no more than, a maximum of, and not surpassing.

Inequalities like less than or equal to and greater than or equal to are represented in a different way on a number line. To denote these, we use the closed circle to mark the limit value and point the arrow towards the given condition of inequality.

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Each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

To find the scale factor of the dilation, we can divide the length of each side of the dilated triangle by the length of the corresponding side of the original triangle.

For example, for the side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.

We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.

In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.

This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

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The side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.

We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.

In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.

This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

The coefficient of  y² in the expression 3y²+ 4x is 3.

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6.

Firstly,

The given equation is 3y²+ 4x

To find : The coefficient of y²

The coefficient is nothing but the number beside the variable.

In the equation 3y²+ 4x, the number beside the variable y² is 3 and it is termed as coefficient of y² which is 3.

As we can see that the term that is in multiplication with y² is 3. Similarly, the term that is coefficient of  x is 4.

Hence, the coefficient of y² in the equation is 3.

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Answer:

Bookcase A

Step-by-step explanation:

Bookcase A

1 half = 35 book

4 half = 140 books

So, bookcase A can hold 140 books

Bookcase B

1 half = 26 books

5 half = 130 books

So, bookcase B can hold 130 books

So, Mary should buy bookcase A

Answer:

Bookcase A is the answer

Step-by-step explanation:

Mary has 138 books

Bookcase A = 4 shelves holds 35 books per shelf

= 4 * 35=140

Bookcase B = 5 shelves holds 26 books per shelf

= 5 * 26=130

He should buy Bookcase A, it has enough space for his books

The dimensions of the rectangle is length = 5ft and width = 3ft

Define System of equation

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

Let,

x = length of rectangle

y = width of rectangle

Next, set up system of equation

We have given, the length of a rectangle is 5 ft more than twice its width.

x = 2y + 5    --------(a)

Next,  The area of the rectangle is 33 ft²

xy = 33      ----------(b)

x = 33/y

substitute the value of x in eq(a)

x = 2y + 5

33/y = 2y + 5

33 = 2y² + 5y

2y² + 5y - 33 = 0

Factor it,

2y² + 11y - 6y - 33 = 0

y( 2y + 11) - 3( 2y + 11) = 0

(y - 3) (2y + 11) = 0

Split the values,

y - 3 = 0               and         2y + 11 = 0

y = 3                 and             y = -11/2 (ignore this as width cannot be -ve)

Substitute y = 3 in eq(b)

x * 3 = 33

x = 11

So, we get

length = 11 ft and width = 3 ft

Hence, the dimensions of the rectangle is length = 5ft and width = 3ft

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Answer:

13

Step-by-step explanation:

Divide 500 by 40 to find the amount of buses you need

500 ÷ 40 = 12.5

BUT, you cannot have .5 of a bus! So you need ONE extra bus to hold the remaining people

you'll need 13 buses

Answer:

13 buses

Step-by-step explanation:

12 buses but 20 people left so they need 12 buses, and the 13th bus will be half filed.

(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial. A degree three polynomial might be referred to as a cubic polynomial.

A degree three polynomial might be referred to as a cubic polynomial. In other words, the number three will be the largest exponent of the variable in a cubic polynomial. A cubic polynomial would therefore have the generic form ax3+bx2+cx+d, where a ≠0.

here

Let p(x)=[tex]x^{3}[/tex]−7x+6

From figure, we have p(1)=0

Thus, (x−1) is a factor of p(x)

The other factor is [tex]x^{2}[/tex]+x−6

=(x+3)(x−2)

Therefore, [tex]x^{3}[/tex]−7x+6 =(x−1)(x+3)(x−2)

(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial.

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A dilation is a type of transformation that enlarges or reduces a figure.It is also called pre image.To create new figure is called image.For this purpose we can use scale factor ,r how much bigger or smaller the dilation image will be compared to pre-image.

It is a transformation which is used to resize the image.It is used to make objects smaller or greater.But there is no difference in the size of the shape.The pre -image and image is not congruent.

For this purposes we use scale factor.

When you dilates a image the scale factor find that how much image will be smaller or larger.

.If the scale factor is between o0 and 1 .Then image is smaller than preimage.Dilation with a scale factor between 0 and 1 i called transformation.

.if the scale factor is greater than 1.Then image will be larger than the preimage.

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