Which statement correct

On solving the provided question, we can say that  fraction of her apple cider will she put in each bottle x = 1/48

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Let's refer to the quantity of apple cider she will add to each bottle as:

She divides her apple cider across six bottles since, as you know, she wants to bottle 1/8 of it.

As a result, you can compose the following sentence while keeping the facts above in mind:

6x = 1/8

x = 1/6*8

x = 1/48

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The numbers that are potential roots of the function given above are:
Option B-D. That is -  ±1, ±2, and ±12.

It is correct to state that in mathematics, a root of an equation is a value that, when substituted into the equation, makes the equation true.

To obtain the potential roots of the expression p(x) = x⁴ + 22x² - 16x - 12:

Note that from the rational root theorem, all the possible roots of the function are in the form of a rational number.

x =  ± p/q

x = ± (Factors of the constant term)/ (Factors of leading coefficient)

Thus, according to the polynomial above,  we know that

Factors of 1 are ±1.

Thus, according to the theorem of rational root, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

Therefore, the potential roots of the function from the options listed are: are ±1, ±2, and ±12.

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Full Question:

Which of the number(s) below are potential roots of the function? p(x) = x⁴ + 22x² - 16x - 12?

± 5
±1

±2

±12

±17

Th area of parallelogram with vertices (-3, 0), b(-1, 7), c(9, 6), and d(7, -1) is 46.5 square units.

The vertices of a parallelogram are a (-3, 0), b(-1, 7), c(9, 6), and d(7, -1).

Area of triangle abc= [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}-3&0&1\\-1&7&1\\9&6&1\end{array}\right][/tex]

=1/2[-3(7-6)-1(-6-63)]

= 1/2[-3(1)-1(-66)]

=1/2[63]

=63/2 sq. units

Area of triangle acd= [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}-3&0&1\\9&6&1\\7&-1&1\end{array}\right][/tex]

=1/2[-3(6+1)-1(-9-42)]

= 1/2[-3(7)-1(-51)]

=1/2[-21 + 51]

=1/2[30]

=15

Area of parallelogram abcd = Area of triangle abc + Area of triangle acd

= 63/2 + 15

= (63 + 30)/2

= 46.5 sq units.

Therefore, the area of the parallelogram is 46.5 sq. units.

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Answer:

correct answer is 72

Step-by-step explanation:

The distance between base of ladder and the building should be

4.4 meter.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AC² = AB² + BC²

Given,

Height of the window from the ground AB = 9 meter

Length of the ladder AC = 10 meter

Distance between base of ladder and building BC = ?

By Pythagorean theorem,

In the right ΔABC

AC² = AB² + BC²

10² = 9² + BC²

BC² = 10² - 9²

BC² = 100 - 81

BC² = 19

BC = √19

BC = 4.359 meter

BC = 4.4 meter

Hence, base of ladder should be 4.4 meter away from the building.

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The value of the expression [tex]\frac{999999999\times 999999999}{1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1}[/tex] , which involves the division of a large number is obtained by making use of a scientific calculator is; 12345678987654321

Depending on the processor of the calculator, and the number of digits the calculator can handle, the exact value following the operations with very large numbers can be obtained. Graphing calculators can also be made to increase the number of digits of precession, up to 9999 digits.

The expression in the question can be presented as follows;

999999999 × 999999999 ÷ (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1)

The value can be computed using a calculator;

999999999 × 999999999 = 999999998000000001

(1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 81

999999999 × 999999999 ÷ (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 999999998000000001 ÷ 81 = 12345678987654321

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Answer:

11. Slope = 1, y-int = (0, -3)

Step-by-step explanation:

Move the numbers so that they math the formula y=mx+b, m being the slope, and b being the y intercept. If for example its 2y, divide the entire equation by 2. Basically you separate "y" on one side, and whatever is next to the x is your slope.

Two examples below:

The expression shows the differences of cubes is (5x⁷)³-(4y)³. Therefore, option C is the correct answer.

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y³.

A) 27x¹⁵-9y³

= 3³x¹⁵-3²y³

= (3x⁵)³-3²y³

B) 3x⁹-64y³

= 3x⁹-4³y³

= 3x⁹-(4y)³

C) 125x²¹-64y³

= 5³x²¹-4³y³

= (5x⁷)³-(4y)³

D) x⁶+27y⁹

= (x²)³+(3y)³

Therefore, option C is the correct answer.

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The initial weight of the toy before removing the spare parts was found to be 440gm since the weight after 25% removal was given as 330gm

The final weight of the toy after removal of spare parts is given as 330g

Percentage weight removed in the form of spare parts from the toy= 25%

Let us consider the initial weight to be x

The equation becomes,

x – 0.25x = 330, since 25% is removed from the original weight of the toy to give us the final weight of 330gm

0.75x= 330

x = 330/0.75

x = (330*100)/75

x = 440

Therefore, initial weight of the toy was found to be 440g

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When two line segments are of equal length then both the line segments are congruent to each other.

As given in the question,

Therefore, the two line segments with equal lengths they both are congruent to each other.

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There are a total of 9 women and 6 men on the council, for a total of 15 council members.

If we randomly choose 2 of them to co-chair a committee, the number of ways to choose 2 people of the same gender is:

So the total number of ways to choose 2 people of the same gender is 3+15 = 18.

The total number of ways to choose 2 people without considering their gender is 15 choose 2 = 105

So the probability of choosing 2 people of the same gender is 18/105 = 6/35

So, the probability that these chairpersons are the same gender is 6/35.

Answer:

so the square root is x so when you point the square root at the rwaterfall you waill have your

Step-by-step explanation:

the drone would need to be 1.4 miles away from your to be the opposite value. pou pou pou pou pou pou pou pou pou pou pou pou ufo p

Step-by-step explanation:

The value of x in the simplest radical form is 6.633

What is value ?

Value in mathematics can refer to a number of concepts that are closely related. Any specific mathematical object can be a mathematical value in general. In elementary mathematics, this is typically a number, such as a real number like or an integer like 42.

The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. For illustration, let's look at the number 45.

The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important." Examples include valor, integrity, freedom, and creativity, among others.

cos Ф = adjacent / hypotenuse

cos 45° = √22 / x

x = √22 / cos 45°

  = (√22* √2 )

  = √44

  = 6.633

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The simples radical form in which the line divides quadilateral is 4 + √ 5

Congruent quadrilaterals are quadrilaterals that have the same size and shape. They have corresponding sides and angles that are equal in measure. In other words, if one quadrilateral can be superimposed on another, they are congruent.

y  =  x/2

This line will  intersect the square at x values  -a  and a

So....the associated y values are:

y =  (-a)/2  =  -a/2     and   (a)/2  

So....the perimeter of one of the quadrilaterals is

=> 2a  +  [(a) -  (-a/2)] + [(a) - a/2 ]  + √  [ ( a - (-a)) ^2 + ( a/2 - (-a/2)^2]  =

=> 2a  + 3a/2  + a/2  + √  [ 4a^2  + a^2 ]  

4a  +  a√ 5  

dividing the above equation by a  produces  = 4  + √ 5

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Complete question:

The square with vertices (-a, -a), (a, -a), (-a, a), (a, a) is cut by the line y = x/2 into congruent quadrilaterals. The perimeter of one of these congruent quadrilaterals divided by a equals what? Express your answer in simplified radical form.

Therefore , the value of the given problem of trigonometry comes out to be  x = 2 √3.

Trigonometry is the branch of mathematics that studies the relationship between triangle side length The field was first developed in the Classical era, most likely in the third century BC, as a product of the fusion of geometry and astronomy research. Certain geometric equations and potential applications to calculations are covered in precise methods to mathematics. In trigonometry, there are six typical trigonometric operations. Sine, quadrature, tangent, secant, etc. are some of the names and acronyms that they go by (csc). Trigonometry is the study of triangle properties, particularly those of right triangles. However, understanding about the properties of all polygons is a necessary part of mastering geometry.

Here,

Given : Let x be the given

2 is the base

Using trigonometric ratio comes out to be :

=> Tan 30 = 2/x

=> 1/√3 = 2/x

=> x = 2 √3

Therefore , the value of the given problem of trigonometric comes out to be  x = 2 √3.

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The time estimates for units 2, 3, 4, and 5, rounded to 2 decimal places, are 4.8 hours, 34.56 minutes, 4.14 minutes, and 0.48 minutes respectively.

A learning percentage is the percentage by which the time required to complete a task decreases as the number of units produced increases. In this case, the learning percentage is 88%.

To develop the time estimates for units 2, 3, 4, and 5, we can use the formula:

Time for unit n = Time for unit 1 (1 - learning percentage)⁽ⁿ⁻¹⁾

Where n is the unit number, and the learning percentage is expressed as a decimal.

For example, to find the time estimate for unit 2:

Time for unit 2 = Time for unit 1 (1 - 0.88)⁽²⁻¹⁾

= 40 (1 - 0.88)

= 40 × 0.12 = 4.8 hours

To find the time estimate for unit 3:

Time for unit 3 = Time for unit 1 (1 - 0.88)²

= 40 (1 - 0.88)²

= 40 × 0.12²

= 0.576 hours

= 34.56 minutes

To find the time estimate for unit 4:

Time for unit 4 = Time for unit 1 * (1 - 0.88)^(4-1)

= 40 * (1 - 0.88)^3

= 40 * 0.12^3

= 0.069 hours

= 4.14 minutes

To find the time estimate for unit 5:

Time for unit 5 = Time for unit 1 * (1 - 0.88)^(5-1)

= 40 * (1 - 0.88)^4

= 40 * 0.12^4

= 0.008 hours

= 0.48 minutes

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The given system of equations  intersect in quadrant II at (-6,2)

What is linear equation ?

linear equation can be defined as the equation in which highest power is one.

Given system of equations,

y = (-1/3) x -4

y = (2/3) x + 2

In the first equation ,

y = (-1/3)x- 4

the 1st line slopes up with y intercept = -4

y = (2/3) x + 2

the 2nd line slopes down with y intercept = 2  

By equating the equations , we get

(-1/3) x -4 =  (2/3) x + 2

-4-2 = (2/3) x + (1/3) x

-6 = x

x = -6

By putting x = -6 in y = (-1/3) x -4

we get ,

y= (-1/3 ) -6 - 4

y = 2-4

y = -2

Hence, The given system of equations  intersect in quadrant II at (-6,2).

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Square pyramid has triangles and square, pentagonal prism has two pentagons and five rectangles,  triangular prism has nine triangles and  triangular pyramid has triangles

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Net of a square pyramid consist of triangles and square.

The net of a pentagonal prism consists of two pentagons and five rectangles.

The net of a triangular prism consists of nine triangles

The net of a triangular pyramid consists of four triangles

Hence, square pyramid has triangles and square, pentagonal prism has two pentagons and five rectangles,  triangular prism has nine triangles and  triangular pyramid has triangles

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The experimental probability of a cube tossed 60 times, landing on a number greater than 4 is the option;

18 over 60

A probability is the fraction or proportion of the times an event will occur when an experiment or task is repeated. It is the measure of the liklyhood an event will occur

Probability compares the number of times an event occurs to the number of times all possible event outcomes occurs.

The formula for the experimental probability is presented as follows;

[tex]Probability = \frac{The \ sum \ of \ the \ times \ the \ event \ takes \ place}{The \ sum \ of \ the \ trials}[/tex]

The number of times the outcome from tossing the coin is greater than 4 obtained by adding the frequencies when for the outcomes of 5 and 6 are;

Number of outcomes greater than 4 = 10 + 8 = 18

The sum of all trials = 12 + 13 + 11 + 6 + 10 + 8 = 80

Therefore, the experimental probability = 18/60

The correct option is; 18 over 60

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Answer: B: 18/60 (18 over 60)

Step-by-step explanation:

There are two ways to fence the garden in 3 areas with some equal sections.

2/5, 2/5, 1/5 and 3/5, 1/5, 1/5.

Fraction definition

A fraction depicts a segment or component of the whole. It represents the equal parts that make up the whole. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that are taken.

Given The garden is divided into 5 equal pieces, each of which is 1/5 of the total garden size.

By arranging some equal parts together, she will fence the garden into three sections. There are two ways to do this.

(1/5 +1/5) = 2/5

(1/5 +1/5) = 2/5

1/5

these are the 3 areas 2/5, 2/5, 1/5.

and

(1/5 +1/5 + 1/5) = 3/5

1/5, 1/5

these are 3 areas =  3/5, 1/5, 1/5.

Hence there are only two ways to fence the garden into three areas by grouping some equal sections.

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There are 33 short-answer questions on the test and 33 * 4 = 132 points are from short-answer questions.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include operations such as addition, subtraction, multiplication, and division.

We know that the test has 75 questions and it is worth 216 points total.

We know that multiple-choice questions worth 2 points each and short answer questions worth 4 points each.

To calculate the number of points from short-answer questions, we need to find out how many questions are short-answer and multiply that by 4 (points per question).

Let x be the number of short-answer questions.

We know that x + 75 - x = 75, which is the total number of questions on the test.

Also, we know that x * 4 + (75-x) * 2 = 216, which is the total number of points on the test.

Solving for x, we get:

x * 4 + 150 - 2x = 216

2x = 66

x = 33

So there are 33 short-answer questions on the test and 33 * 4 = 132 points are from short-answer questions.

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The probability of the sum of the two recorded numbers being less than 4 is $\frac{3}{4}$.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.
This is because there are three possible scenarios in which the sum of the two numbers can be less than 4:

1) both numbers are 1 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$)

2) one number is 1 and the other is 2 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$).

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The probability of the sum of the two recorded numbers being less than 4 is [tex]\frac{3}{4}[/tex].

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.

This is because there are three possible scenarios in which the sum of the two numbers can be less than 4.

1) both numbers are 1 (probability of [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{4} = \frac{1}{16}[/tex])

2) one number is 1 and the other is 2 (probability of [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{4} =[/tex] [tex]\frac{1}{16}[/tex])

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Answer:

480ft.it does not matter how much east or west they are.it asks how much"they are apart"

so it should be 480.

The principal stresses are the maximum normal stresses in the x, y, and z directions.

These are typically determined using Mohr's circle. The absolute maximum shear stress is the maximum shear stress that can act on a given material, which is equal to one-half the difference between the two principal stresses.

The principal stresses are determined using Mohr's circle and the absolute maximum shear stress is equal to one-half the difference between the two principal stresses.

The principal stresses are the maximum normal stresses in the x, y, and z directions.

These are typically determined using Mohr's circle. The absolute maximum shear stress is the maximum shear stress that can act on a given material, which is equal to one-half the difference between the two principal stresses.

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So, it would take 36 days for all 24 gallons of water to leak out of the pool at this rate

To find out how many days it takes for all 24 gallons of water to leak out of the pool, we need to determine the rate at which the water is leaking and use that to calculate the total time it takes for the pool to empty.

We know that the pool initially has 24 gallons of water and that it is leaking out at a rate of 2 gallons every 3 days. This means that the pool loses 2/3 of a gallon of water per day.

To find out how many days it will take for the pool to empty, we can divide the total amount of water in the pool by the rate at which it's leaking out.

24 gallons / (2/3 gallons/day) = 24*3/2 = 36 days

Therefore, it would take 36 days for all 24 gallons of water to leak out of the pool at this rate.

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A zero solution, also known as the trivial solution, refers to a solution of a system of equations in which all variables are equal to zero.

This type of solution occurs when the coefficients in the system of equations are set up in such a way that the only solution to the system is for all the variables to be equal to zero.

A zero solution is the answer to a system of equations where all the variables are equal to zero. This happens when the coefficients in the equations are set up such that the only solution is for all the variables to be equal to zero. This type of solution is also known as the trivial solution. A trivial solution can be thought of as a “placeholder” for when there is no other meaningful solution to a system of equations.

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On solving the provided question, we can say that the probability of both = 4/9*1/3 or 4/27

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

18 marbles  = 8 are blue and 6 are red .

probability  a blue marble = 8/18 = 4/9.

probability of getting a red marble i=6/18 = 1/3.

probability of both = 4/9*1/3 or 4/27

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In the given time interval [0,7]:

(a) the maximum speed is 1096.63 units at t = 7 and

(b) the minimum speed is 0.91 units at time t = ln2/4.

Parametric equations of the curve

x(t) = [tex]e^t + e^{-t}[/tex]

y(t) = [tex]e^{-t}[/tex]

so, dx/dt = [tex]e^t - e^{-t}[/tex]

dy/dt = [tex]-e^{-t}[/tex]

So, speed: v(t) = [tex]\sqrt{(dx/dt)^2 + (dy/dt)^2}[/tex] = [tex]\sqrt{(e^t-e^{-t})^2 + (-e^{-t})^2}[/tex]

When v(t) is maximized or minimized, evidently v² is also maximized or minimized because speed is a positive quantity.

or (speed)² = v² = [tex](e^t-e^{-t})^2 + (-e^{-t})^2[/tex] = [tex](e^{2t} + 2e^{-2t} -2)[/tex]

Now, to get the maxima or minima of a curve we have to derivate function

d/dt(v²) = 0 or d/dt[tex](e^{2t} + 2 e^{-2t} -2)[/tex]

or [tex]2e^{2t} -4 e^{-2t} = 0[/tex] or [tex]e^{2t} = 2 e^{-2t}[/tex]

taking logs on both sides

4t lne = ln2 or 4t = ln2 or t = ln2/4

so, the only critical point is t = ln2/4 ∈ [0,7]

To calculate the maxima/minima of v, we will find functional values at the critical point and boundary values of the given interval [0,7].

At t = 0 : v(0) = [tex]\sqrt{e^0 + 2e^0 - 2} = \sqrt{1+2-2}[/tex] = 1

At t = ln2/4: v(ln2/4) = [tex]\sqrt{e^{2ln2/4} + 2e^{-2ln2/4} - 2} = \sqrt{2\sqrt{2} -2 }[/tex] = 0.91

At t = 7: v(7) = [tex]\sqrt{e^{14} + 2e^{-14} - 2}[/tex] = 1096.63

Therefore, in the given time interval [0,7]: (a) the maximum speed is 1096.63 units at t = 7 and (b) the minimum speed is 0.91 units at time t = ln2/4.

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Answer:

Step-by-step explanation:

We are given that,

The surveyor is located 340 meters from one entrance at an angle of 58°.

The surveyor is located 193 meters from one entrance at an angle of 21°.

Let the length of the tunnel = x meters

Using the Law of Cosines,

[tex]x^{2} =(340)^{2}+(193)^{2}-(2)(340)(193)cos(21+58)\\x^{2} =115600+37249-131240cos(79)\\x^{2} =115600+37249-25041.77255\\x^{2} =127807.2274\\x=\sqrt{127807.2274} \\x=357.50 meters\\[/tex]

If the dimensions of the box were all doubled, then the surface area of the box be 640 square units.

Use the concept of prism defined as:

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat sides, and identical bases.

Without bases, the prism's faces are parallelograms or rectangles. And any n-sided polygon, whether a triangle, square, rectangle, or other, might serve as the prism's basis.

Given that,

The dimension of the rectangular prism = 2yd x 10yd x 5yd

Since we know that,

Dimension of prism = length x breadth x height

length x breadth x height =  2yd x 10yd x 5yd

Therefore,

Length = 2 yd

Breadth = 10 yd

Height = 5 yd

Now if dimension doubled the,

The dimension of the new prism = 4yd x 20yd x 10yd

Then,

Length 'l' = 4 yd

Breadth 'b'= 20 yd

Height 'h' = 10 yd

Since we know that,

The surface area of a rectangular prism is,

A=2(bl+hl+hb)

Substitute the values,

A = 2(20x4 +10x4 + 10x20)

A = 640 square units.

Hence the surface area is 640 square units.

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No , it is not possible to draw a triangle with the given side length of 4cm , 3cm , and 7cm as sum of two sides ( 4cm + 3cm ) is not greater than the third side ( 7cm).

As given in the question,

Measure of the required triangle are given as follow:

Measure of Side length 1 = 4cm

Measure of Side length 2= 3cm

Measure of Side length 3 = 7cm

To draw a triangle following condition need to be satisfied:

Sum of the measure of two side length is always greater than the measure of the third side length.

Here for a given triangle ,

4cm + 3cm

= 7cm

= measure of the side length 3

It does not satisfied the required property to draw a triangle.

Therefore, it is not possible to draw a triangle with given measurements as ( 4cm + 3cm ) is not greater than the third side.

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