A candy company can sell fruit gums in rectangular boxes or in cylindrical tubes. Each box is 8 cm by 3 cm by 7 cm. Each cylinder has radius 3 cm and height 6 cm. The company wants the packaging that uses less material. Which packaging should the company choose? Justify your choice.

The factors of x³ 2x² 5x 6 are two binomials. The first binomial is x² + 2, and the second binomial is x + 3. These two binomials can be multiplied together to get the original equation, x³ 2x² 5x 6.

To find the factors of x³ 2x² 5x 6, we need to use the factorization process. This involves breaking down the equation into its prime factors. First, we need to factor out the greatest common factor (GCF) from the equation. The greatest common factor of x³ 2x² 5x 6 is x, so we can factor out x to get x² 2x 5 6. Now, we can use the difference of squares formula to factor out the remaining terms. The difference of squares is (a + b)(a - b). We can use this formula with 2x and 5 to get (2x + 5)(2x - 5). This leaves us with the two binomials (x² + 2)(x + 3). These two binomials can be multiplied together to get the original equation, x³ 2x² 5x 6.

x³ 2x² 5x 6 = (x)(x² 2x 5 6)

= (x)(2x + 5)(2x - 5)

= (x)(x² + 2)(x + 3)

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A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.

For a triangle the circumcentre is a point equidistant from each of the three vertices. Every non-degenerate triangle has such a point. This result can be generalised to cyclic polygons: the circumcentre is equidistant from each of the vertices. Likewise, the incentre of a triangle or any other tangential polygon is equidistant from the points of tangency of the polygon's sides with the circle.

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Answer:

h = 1.25m

Step-by-step explanation:

a=20m, b= 30m

Area = (½) (a+b) (h)

375= ½ (20+30) h

375= 300h

300h = 375

h= 375÷300

= 1.25m

IQ scores follow a normal distribution, with a mean of 100 and a standard deviation of 15. Approximately 68% of people have IQ scores in the range [85,115].

In mathematics and statistics, the mean is the average of a set of variables. The simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean are all ways for calculating the mean. The mean (average) of a data set is computed by adding all of the numbers in the set and dividing by the number of values in the set. When arranging data from smallest to greatest, the median is the value in the middle. The mode is the most commonly occurring number in a data set.

Here,

In this example, the population mean is 100 and the standard deviation is 15. Based on the 68-95-99.7 Rule, approximately 68% of the individuals in the population have an IQ between 85 and 115. Values in this particular interval are the most frequent.

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. About 68% of individuals have IQ scores in the interval [85,115] .

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Answer:

a)perpendicular

b) parallel

c) none

d) parallel

e) none

Step-by-step explanation:

The value of "i" squared results in:

(-1) = i²

Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.

Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.

In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:

(-1) = i²

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The common denominator needed to subtract the given fractions is 42.

Given that,

5/6 - 2/7

The denominator is the number that is placed below the horizontal line of a fraction. It is the bottom number of a fraction that shows the total number of equal parts an object is divided into.

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators the same first and then subtract them.

Here, the LCM of denominators 6 and 7 is 42.

Now, 35/42 - 12/42

= 23/42

So, the common denominator is 42.

Hence, the common denominator needed to subtract the given fractions is 42.

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The quantity written below a fraction's horizontal line is known as the denominator. The total number of equally spaced sections into which an object is divided is indicated by the bottom number of a fraction.

When subtracting fractions, it's possible to use either the same or distinct denominators for two or more of the fractions. While unlike fractions must first have their denominators made the same before being subtracted, like fractions can be done so immediately.

The LCM of denominators 6 and 7 in this case is 42.

Now, 35/42 - 12/42

= 23/42

Therefore, 42 is the common denominator.

Consequently, 42 is the common denominator required to remove the provided fractions.

The coefficient of the variable x squared is number 5.

The coefficients are the numbers on the left side or before each variable.

Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In this problem we have an expression given by:

5x²y

And we want to know what is the coefficient of x²

5 is the coefficient

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Two triangles are congruent because the sides of two triangles and angles are congruent and the transformation applied to map triangle EBD onto triangle CBA is rotation of 90 degrees.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

There are two triangles in the coordinate plane.

Triangle ABC and triangle EBD are in plane.

We need to find the transformation applied to EBD onto triangle CBA.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

The triangle EBD undergoes a rotation of 90 degrees in clockwise direction to get triangle CBA.

The two triangles are congruent because the sides of two triangles and angles are congruent. So we conclude that the two triangles are congruent.

Hence, rotation of 90 degrees is the transformation (s) could be applied to map triangle EBD onto triangle CBA.

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The perimeter of the triangle is 35.0 inches

We should know that perimeter of an object is the distance round the very object.  the triangle has three sides, then the perimeter of the trianggle is the sum of the three sides.

Hence the altitude forms a right angled triangle, there are two right angled triangles.

Using  the Pythagoras theorem, let the two sides of the triangle be x and y

X²=13²+4²    (the altitude divided the base into 2)

x²=169+16

x²=185

Taking the square root of both sides

x=[tex]\sqrt{185}[/tex]

x=13.6 inches

For the length y

Use the same Pythagoras theorem

X²=13²+4²

x²=169+16

x²=185

x=13.6 inches

The perimeter is 8+13.6+13.6 = 35.2 inches

Therefore, the  perimeter of the triangle to the nearest tenth is 35.0 inches

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As per the solenoid turn the measure of the current is written as 23.45

Here we have given that the inductor in is a 9.0-cm-long, 2.0-cm-diameter solenoid wrapped with 300 turns.

And we need to find the measure of the current flow.

While we looking into the given question, here we have given that  

Here the

R refers resistance of resistor = 30 Ω

V refers voltage of battery = 6.0 V

s refers length of solenoid = 9.0 cm = 0.09 m

d refers diameter of solenoid = 2.0 cm = 0.02 m

N refers number of turns of wire = 300

μ0 refers permeability of free space = 12.56 x 10⁻⁷ H/m

Then the flow of the current is calculated as,

=> [4π x 10⁻⁷ x 300  x 12.56 x 10⁻⁷] / 2 x 10⁻²

When we simplify this one then we get the result as,

=> 23.45

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We need 6 cans of paint are needed to cover an area of 2 200 square units.

In this question we need to find the number of cans of paint needed to cover an area of 2 200 square units.

We have been given one can of paint covers an area of 400 square units.

Let x cans of paint are needed to cover an area of 2200 square units..

1 can = 400 square units

x cans = 2200 square units

Bu Unitary method,

x = 2200/400

x = 22/4

x = 11/2

x = 5.5

x ≈ 6

Therefore, six cans of paint are needed to cover an area of 2 200 square units.

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A complete question is:

How many cans of paint are needed to cover an area of 2 200 square units if one can of paint covers an area of 400 square units?

Answer:

D. 16y – 20

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

16y^2-16y-4(-4y+5+4y^2)

16y^2-16y+16y-20-16y^2

16y^2-20-16y^2

16y^2-16y^2-20

-20

Answer:

c.)    a = (2(x-b-vy))/t^2

Step-by-step explanation:

Manipulate the given equation to isolate a on the left side:

x=b+vy+(1/2)at^2

x=b+vy+(1/2)at^2

(1/2)at^2 = x-b-vy

at^2 = 2(x-b-vy)

a = (2(x-b-vy))/t^2

For a contour map as shown in the figure attached, for a function f on the square r = [0, 2] ⨯ [0, 2], estimated value of ∫∫f(x,y)dA using midpoint rule where m = n = 2 is 91 and the average value of f is 22.75.

Using the midpoint rule, the total volume

V ≈ ∑(i=1 to m) ∑(j = 1 to n) f(xij*⁻, yij*⁻)ΔA

where Δx = (b - a)/ m,

Δy = (c - d)/ n and

ΔA = ΔxΔy

Here r = [0, 2] ⨯ [0, 2] and m = n = 2

Therefore a = d = 0 and b = c = 2

Δx = (2 - 0)/ 2 = 1

Δy = (2 - 0)/ 2 = 1

ΔA = 1×1 = 1

∫∫f(x,y)dA ≈ ∑(i=1 to m) ∑(j = 1 to n) f(xij*⁻, yij*⁻)ΔA

= ΔA(f(0.5, 0.5) + f(0.5, 1.5) + f(1.5, 1.5) + f(1.5, 0.5))

= ΔA( 37 + 4 + 27 + 23)

= 1 × 91

= 91

The average value of f

f avg = 1/ A(r) × (∫∫f(x,y)dA)

f avg = 91/ (2×2)

f avg = 22.75

-- The question is incomplete, complete question is given below--

"A contour map is shown for a function f on the square r = [0, 2] ⨯ [0, 2].

a) Use the Midpoint Rule with m=n=2 to estimate the value of ∫∫f(x,y)dA.

b) Estimate the average value of f."

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A group of clearly defined objects or elements make up a set. A collection of numbers is known to as an element and forms up a set.

A collection of numbers is known to as an element and forms up a set. The set of numbers can either be an endless or a limited collection. Using "{" and "}" with the elements separated by commas is one way to represent a set in roster notation; for example, the set {5,29} has the elements 5 and 29.

A group of clearly defined objects or elements make up a set. The cardinal number of a set is shown in a curly bracket next to the capital letter symbol for a set, which denotes the number of elements in a finite set.

Sets of integers are among the most frequent types of sets in mathematics. Numbers come in a wide variety of forms. We have natural numbers, whole numbers, integer numbers, rational numbers and real numbers.

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Answer:

Step-by-step explanation:

Answer:

4/25

Step-by-step explanation:

There are a total of 25 books at the library, of which 4 are nonfiction biographies. Therefore, 4 out of the 25 books are nonfiction biographies, which can be expressed as the fraction 4/25.

As per the unitary method,  the best estimate of the number of passengers is 9 x 10⁸

the term unitary method in math is defined as the quantity of one object when the quantity of another object and the ratio between two are given.

Here we have given that in 2015, about 895. 5 million passengers traveled by plane in the united states.

And we need to find  the best estimate of the number of passengers

While we looking into the given question, we know that the about 895. 5 million passengers traveled by plane in the united states.

So, it can be written as,

=> x = 895.5 million

Here we know that 1 million = 1 x 10⁶

So, it can be rewritten as the number of passengers as,

=> x = 895.5 x 10⁶

Here we have to round off the values, then we get

=> x = 900 x 10⁶

When we further simplify this then we get

=> x = 9 x 10⁸

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To find the probability of an event, you will need to use the probability formula

which is expressed as P(Event) = Favorable Outcomes/Total Outcomes = x/n. You can calculate the probability by dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1, as the favorable number of outcomes can never cross the total number of outcomes, and the favorable number of outcomes cannot be negative.

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Answer:

Step-by-step explanation:

jjj

The snapshot of the graph of the function d(x, t=0s) of the wave is illustrated below.

The term function in math referred as a relation between a set of inputs having one output each.

Here we have given that d(x,t=0s) of this wave at t=0s.

And we need to find graph of the function

While we looking into the given question we have identified that the history graph of the wave is given at distance is written as,

=> x=2m

Then the velocity of the wave is given as v= 1 m/.sec

Here we have identified the wave is traveling to the right.

Then snapshot graph shows the displacement of the wave with respect to the position at a given time whereas a history graph shows the displacement of the wave with respect to the time at a given position.

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The equation y= 2x-15 can be used to estimate how many minutes will pass after 4:00 pm until she reaches her destination.

The following equation can be used to estimate how many minutes after 4:00 p.m. the pilot will reach her destination:

y = 2x - 15

This equation represents the number of minutes after 4:00 p.m. the pilot will arrive at her destination. The variable x represents the time, in minutes, of her original flight, and y represents the number of minutes after 4:00 p.m. she will arrive at her destination. The expression "2x" represents the time the pilot will arrive at her destination if she had traveled at twice her original speed, and the "-15" represents the delay caused by air traffic.

To solve this equation, you would substitute the value of x into the equation and solve for y. For example, if the pilot's original flight time was 60 minutes, the equation would be:

y = 2(60) - 15

= 120 - 15

= 105

This means that the pilot will arrive 105 minutes after 4:00 p.m., or at 5:45 p.m.

The complete question is:-

A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 15 minutes. Air traffic control approved a new flight plan that

will allow her to arrive two times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation

that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.

y = 2x + 15

©y=-*x+15

y = x-15

y = 2x - 15

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When population grows exponentially with a proportionality constant, k , this population will take 4.620 time to double.

If the population is growing exponentially, the rate of population change is directly proportional to its current size. So assume that the total population at some point in time t is y.

Next, write the differential equation subject to the condition that it increases in proportion to its magnitude. We can get rid of the proportional sign by introducing a constant of proportionality. We then isolate and integrate the variables of the differential equation thus formed and use the initial values to find the value of the constant of proportionality. We have , a population grows exponentially.

The proportionality constant, k = 15% = 0.15

The exponential growth function is y = y₀ eᵏᵗ

where y₀ --> initial population or at t = 0

k --> proportionality constant

t --> time

y --> is value of y at any t

let there be population y₀ at t = 0 . Then, we have to calculate how much time take the population to double.

2 yo = yo e⁰·¹⁵ᵗ

=> 2 = e⁰·¹⁵ᵗ

Introducing natural logarithms on both sides of above equation,

=> ln (2) = ln ( e⁰·¹⁵ᵗ )

=> ln (2) = 0.15t ( since ln e = 1)

=> t = ln(2)/1.5 = 4.620

Hence, required time is 4.620.

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Pure maths can be quite challenging. It requires the ability to think logically and to understand complex concepts.

What is pure math?

Pure mathematics is the branch of mathematics that deals with abstract concepts, such as numbers and equations, that are not related to any physical objects or phenomena. It is the study of abstract concepts and properties, including number theory, geometry, algebra, and analysis. Pure mathematics is used in many areas of mathematics, such as applied mathematics, which is the use of mathematical techniques for solving real world problems.

It also requires knowledge of calculus, geometry and trigonometry, as well as problem-solving and analytical skills. Pure maths is often used in physics, engineering and computing, making it a valuable tool for anyone in these disciplines. However, mastering pure math takes practice and dedication, as it can be difficult.

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I.

The measure of the angle that is complementary to the angle 20° is 70°, 67° is 23°, 14° is 76°, 81° is 9° and 45° is 45°.

The sum of the complementary angles is 90°

Thus,

The complement of the angle 20° is 90°-20°=70°

The complement of the angle 67° is 90°-67°=23°

The complement of the angle 14° is 90°-14°=76°

The complement of the angle 81° is 90°-81°=9°

The complement of the angle 45° is 90°-45°=45°

II.

The measure of the angle that is supplementary to the angle 120° is 60°, 56° is 124°, 29° is 151°, 162° is 18° and 83° is 97°.

The sum of the supplementary angles is 180°

Thus,

The supplement of the angle 120° is 180°-120°=60°

The supplement of the angle 56° is 180°-56°=124°

The supplement of the angle 29° is 180°-29°=151°

The supplement of the angle 162° is 180°-162°=18°

The supplement of the angle 83° is 180°-83°=97°

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