Find an order pair (x,y)that is a solution to the equation
2x+y=3

The sides of the triangle having length as  5 units , 12 units and 13 units make a Right Triangle because the condition to form a right triangle is satisfied by the given sides .

The Pythagoras Theorem is used to check whether the sides form a right triangle or not , it  states that square of the lonest side (hypotnuse) of the triangle is equal to  sum of  square of other two sides ( perpendicular and Base) ,

The side lengths of  triangle = 5 units , 12 units and 13 units ,

By  Pythagoras theorem , we have  [tex]13^{2} = 12^{2} + 5^{2}[/tex]

On simplifying ;

we get ;

[tex]169 = 144 + 25[/tex] ;

[tex]169 = 169 ;[/tex]

the condition of Pythagoras theorem is satisfied ,

that means the sides form a right triangle .

Therefore , the side 5 units , 12 units and 13 units  make a right triangle .

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x² + y² + 6x - 6y - 207 = 0 is the equation for the circle whose circumference has endpoints at (12, 3), and (-18, 3).

We are aware that a circle's general equation is (x - h)2 + (y - k)2 = r2, where (h, k) is its center and r is its radius.

Therefore, to bring the constant term to the righthand side of the equation, add 21 to both sides.

So, the midpoints of the diameter are determined by the coordinates of the circle's center since the endpoints of the diameter are (x1, y1) = (12,3) and (x2, y2) = (-18,3).

The midpoints are so:

x = (x₁ + x₂)/2 = (12 + (-18))/2 = (12 - 18)/2 = -6/2 = -3 and

y = (y₁ + y₂)/2 = (3 + 3)/2 = 6/2 = 3.

Consequently, the circle's center's coordinates are (-3, 3)

The circle's diameter:

The circle's radius is [(x1 - h)2 + (y1 - k)2], where:

(x₁, y₁) = coordinates of end of diameter = (12, 3) and

(h, k) = coordinates of center of circle = (-3, 3)

As a result, when we enter the values of the variables into r, we get:

r = √[(x₁ - h)² + (y₁ - k)²]

r = √[(12 - (-3))² + (3 - 3)²]

r = √[(12 + 3)² + 0²]

r = √[15² + 0²]

r = √15²

r = 15

The formula for the circle:

The formula for a circle with a center (h,k) is: (x - h)² + (y - k)² = r²

By changing the variables' values in the equation, we arrive at:

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - 3)² = 15²

(x + 3)² + (y - 3)² = 15²

x² + 6x + 9 + y² - 6y + 9 = 225

x² + 6x + y² - 6y + 9 + 9 - 225 = 0

x² + y² + 6x - 6y - 207 = 0

Therefore, x² + y² + 6x - 6y - 207 = 0 is the equation for the circle whose circumference has endpoints at (12, 3), and (-18, 3).

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The surface area of a regular square pyramid is 332.64 square cm

We know that the surface area of pyramid is nothing but the sum of the areas of its lateral faces and its base.

surface area of pyramid

= areas of lateral faces of pyramid + area of base of pyramid

We know that the formula for the lateral surface area of regular pyramid is:

A = ½ × P × l

where P is the perimeter of the base and l is slant height

Here, a base of regular square pyramid with has sides of 13. 2 cm

a = 13.2 cm and slant height of 6 cm i.e., l = 6 cm

Using the formula of area of square, the base area of pyramid would be,

B = (13.2)²

B = 174.24 sq.cm.

the perimeter of base is:

P = 4 × 13.2

P = 52.8 cm

So, using the above formula of lateral surface area of pyramid the lateral surface area would be

A1 = 1/2 ×  52.8 × 6

A1 = 158.4 sq. cm.

So, the surface area of the pyramid is:

A = A1 + B

A =  158.4 + 174.24

A = 332.64 square cm

Therefore, the surface area of the pyramid = 332.64 square cm

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An expression which is equivalent to given [tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex] is 5 / (z + 5)

The correct answer is an option (B)

Consider given quotient.

[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex]

Consider expression 5z + 15

We can write this expression as 5(z + 3) by  taking out the common factor 5.

So given quotient would be,

[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5(z+3)} }[/tex]

As we know a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.

For fraction [tex]\frac{z+3}{5(z+3)}[/tex] , the common term is z + 3.

So, [tex]\frac{z+3}{5(z+3)} = \frac{1}{5}[/tex]

We know that for fractions a/b and c/d where b ≠ 0, d ≠ 0, if we take quotient of these fraction then that would be,

(a/b) / (c/d) = (a/b) × (d/c)

So, given quotient would be,

[tex]\frac{\frac{1}{z+5} }{\frac{1}{5} }\\\\\\=\frac{1}{z+5} \times \frac{5}{1} \\\\\\=\frac{1\times 5}{(z + 5)\times 1}[/tex]

= 5 / (z + 5)

Therefore, an equivalent expression is: 5 / (z + 5)

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The Correct answer is 5.50 p.m

Time between Monday 0445h and Friday 1845h

= 4 x 24 + 14 = 110h

Time lost = 0.5 x 110

= 55min

Time shown in 12 hour system

1845 – 55 = 1750 h

= 5.50 p.m

On an analogue clock, the 12-hour clock is most frequently displayed as the digits 1 through 12; on a digital clock, it is typically followed by either a.m. (ante meridiem, Latin for "before noon") or p.m. (post meridiem, Latin for "after noon").

Digital clocks are more frequently used to display the 24-hour clock, which is printed in a 4-digit format with the first two numbers denoting the hour and the final two denoting the minutes.

No need for a.m. or p.m. is necessary because each time represents one of the 24 hours in a day. For instance, 0300 is the third hour of the day, or 3am; 1400 is the fourteenth hour of the day, or 2pm; and 1830 is the thirty-minute mark after the eighteenth hour of the day, or 6.30pm.

Children can be taught to add 12 to the hours after noon in order to change a 12-hour clock to a 24-hour one. For instance, 3pm becomes 15:00 since 3 + 12 = 15.

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The time shown on 19:45h Fridays is 06: 55 pm Friday.

A collection of synchronized clocks that can communicate with one another and display the exact same time every single time is known as a clock network or clock system. A constant pulse known as a system clock or system timer aids the computer clock in maintaining accurate time. It keeps track of how many seconds have passed since the epoch and utilizes that information to determine the current date and time.

A piece of electronic equipment inside a computer that continuously emits a high-frequency signal to keep everything in sync. electrical gadget type. a piece of equipment that operates electronically. a computerized time-of-day clock.

Given: Watch loses = 1/2 minute every hour

Time difference = 19: 45 h Friday - US:45 h Monday

=4 days 14 hours

=24 × 4+14 hours

=96+14

=110 hours

Time lost [tex]$= & 144^{55} \times \frac{1}{2} \mathrm{~min} \\[/tex]

= 55 min

Time shown on 19:45h Fridays

= 19: 45 - 0: 55

= 18: 55 h Friday

= 06: 55 pm Friday

Hence, 06: 55 pm Friday

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A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman. sophomore. junior, and senior classes to complete the survey.  This plan is an example of Stratified random  type of sampling .

What does "stratified random sampling" mean?

A population is divided into smaller subgroups known as strata as part of a sampling technique called stratified random sampling.

           During stratified random sampling, also known as stratification, groups of people are divided into groups based on shared traits or characteristics, such as level of education or income.

What is a good illustration of a stratified sampling technique?

A stratified sample is one that guarantees that the various strata (subgroups) of a given population are fairly represented in the sample population as a whole.

                                   One could, for instance, divide a sample of persons into age-related subgroups, such as 18–29, 30-39, 40–49, 50–59, and 60 and above.

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Store C offers the best deal

Based on the lowest cost per minute, Store C has the best deal. It charges $45 for a 1.5 hour lesson, which works out to $0.30 per minute. The other stores charge more per minute: Store A charges $0.56 per minute, Store B charges $0.50 per minute, and Store D charges $0.40 per minute for each of the three 1 hour lessons.

Store A has the highest cost that is $0.56 per minute

Next Store B comes in the 2nd place which costs around $0.50 per minute.

After that Store D charges at the rate of $0.40 per minute.

Store C offers the best deal which is $0.30 per minute.

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Answer:

A

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

140° is an exterior angle of the triangle , then

∠ B + 90° = 140° ( subtract 90° from both sides )

∠ B = 50°

∠ ACB and ∠ DCB are a linear pair and sum to 180° , that is

∠ ACB + 140° = 180° ( subtract 140° from both sides )

∠ ACB = 40°

Answer:

5.4

Step-by-step explanation:

"The 'Angle Bisector' Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle."

thus,

DB/AB = DC/AC

2.8/AB = 3/5.8

multiply both sides by AB to make it a numerator

2.8 = 3*AB/5.8

multiply both sides by 5.8/3 to isolate AB

2.8 * 5.8/3 = AB = 5.413 ≈ 5.4

Therefore , the solution of the given problem of triangle comes out to be

AB length = 5.4 units.

In a plane, any three points can be joined to form triangles, which have three sides and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.

Here,

According to the "Angle Bisector Theorem," a triangle's opposing side will be divided into two segments that are proportional to the other two sides.

thus,

DC/AC = DB/AB.

2.8/AB = 3/5.8

By multiplying both sides by AB, the numerator is created.

2.8 = 3*AB/5.8

To distinguish AB, multiply both sides by 5.8/3.

2.8 * 5.8/3 = AB = 5.413 ≈ 5.4

Therefore , the solution of the given problem of triangle comes out to be

AB length = 5.4 units.

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The number of calories Jina is burning per minute is 0.1 and the slope is 0.1

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

Points, (x, y) = (0, 0) and (150, 15)

The burning rate per minute can then be calculated as

Burning rate per minute = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

Burning rate per minute = (15 - 0)/(150 - 0)

Evaluate the quotient

Burning rate per minute = 0.1

In (a), we have

Burning rate per minute = 0.1

This rate is the same as the slope

Hence, the slope is 0.1

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Isosceles triangle has three sides, three angles, a base, a height, and an area in which two sides are equal to each other .

What is an isosceles triangle simple definition?

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length. . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles

the sum of triangle is 180, sum of all the interior angles is equal to 180.

so if you know two angles then apply sum of triangles and find out the value of the third triangle.

isosceles triangle

An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.

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The tasks that Keith can delegate to the assistant are List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet, Add the Debit and Credit columns of the trial balance and Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet.

List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet: Keith should delegate this task to his assistant. This is a relatively straightforward task that does not require a deep understanding of accounting principles. The assistant can be provided with clear instructions on how to pull the account balances from the general ledger and list them in the trial balance columns of the spreadsheet.

Add the Debit and Credit columns of the trial balance: Keith should delegate this task to his assistant. This is a simple arithmetic task that the assistant can perform with clear instructions.

Make the adjusting entries on the spreadsheet: Keith should retain this task. Adjusting entries involve more complex accounting knowledge and require a deeper understanding of accounting principles. It would be difficult for the assistant to complete this task without proper training.

Complete the spreadsheet: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet: Keith should delegate this task to his assistant. The assistant can be provided with clear instructions on how to organize the data from the spreadsheet into formal financial statements. It does not require a deep understanding of accounting principles.

Journalize and post the adjusting entries: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

--The question is incomplete, answering to the question below--

"Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith's assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities could be delegated to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn't have the time to teach the assistant to be an accountant.

For each task listed, state whether Keith should continue to do the work or delegate the task to his assistant. Explain each answer.

1. List the account balances from the general ledger in the Trial Balance columns of the work sheet.

2. Add the Debit and Credit columns of the trial balance.

3. Make the adjusting entries on the work sheet.

4. Complete the work sheet.

5. Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the work sheet.

6. Journalize and post the adjusting entries."

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The graph of the function g(x) is added as an attachment

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

f(x) equals log2 x

Express the equation properly

So, we have

f(x) = log₂(x)

Also, we have

g(x) = -log₂(x - 3)

The transformation from f(x) to g(x) is that:

This means that

g(x) = -f(x - 3)

So, we apply the above transformations on the graph of f(x) to form g(x)

See attachment for graph of g(x)

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Answer:

x - 4y = -4

Step-by-step explanation:

Equation of line in x-intercept and y-intercept form:

         [tex]\sf \boxed{\dfrac{x}{a}+\dfrac{y}{b}=1}[/tex]

Here a is x-intercept and b is y-intercept.

           a = -4 & b = 1

[tex]\sf \dfrac{x}{-4}+\dfrac{y}{1}=1\\\\\text{Mutiply the entire equation by (-4)},\\\\(-4)*\dfrac{x}{-4} + (-4)*\dfrac{y}{1}=1*(-4)\\\\\\x - 4y = -4[/tex]

Equation of line in standard form:

        x - 4y = -4

A large rectangular box has a volume of 15. 75 cubic feet the box is 2. 5 feet long and 1. 5 feet wide. So the height of the box is 4.2 feet.

The formula to find the volume of a rectangular box is

V = lwh

where l is the length, w is the width, and h is the height.

Given that the volume of the box is 15.75 cubic feet, the length is 2.5 feet and the width is 1.5 feet, we can use the formula to find the height.

V = lwh

15.75 = 2.5 × 1.5 × h

h = 15.75/ (2.5 × 1.5)

h = 4.2

Therefore, the height of the box is h = 4.2 feet

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Step-by-step explanation:

(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!

Step-by-step explanation:

Given the system of equation, \left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.{

2x−3y=−19

x+6y=28

, solve by elimination.

\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.{

2x−3y=−19

−2(x+6y=28)

, multiply the top equation by -2.

We get, \left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.{

2x−3y=−19

−2x−12y=−56

+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right. , add the equations together.

We get, -15y=75−15y=75 , we just eliminated the variable, x, we can now solve this equation for y.

-15y=-75 = > y=\frac{-75}{-15}−15y=−75=>y=

−15

−75

, y=\frac{75}{15} = > y=5y=

15

75

=>y=5

We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...

x+6y=28 = > x+6(5)=28 = > x+30=28x+6y=28=>x+6(5)=28=>x+30=28 , subtract the value, 30, from both sides. We get, x=-2x=−2 .

We found the value x, x=-2.

Thus the solution to the given system of equations is (-2,5).

Answer:

Comparing given eqn of line i.e.y=4x + 1 with

y=mx+c,we get,

m=4

We know that parallel lines have same value for m and the line parallel to y=4x+1 passes through the point (-2,-5) i.e (x1,y1)

Now,using point slope formula,we get

y-(-5)=4{x-(-2)}

or,y+5=4(X+2)

or,y+5=4x+8

or,y=4x+8-5

:.y=4x+3 is the req eqn for line parallel to y=4x+1

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The requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol

here,
Given expression,
[tex]F(x) = \int\limits^{x^2}_x {e^{t^7}} \, dx[/tex]

Following the Leibniz rule
[tex]F'(x) = \frac{d}{dx}[ \int\limits^{x^2}_x {e^{t^7}} \, dx]\\F'(x) = \int\limits^{x^2}_x \delta/\delta x (e^{t^7}) + (e^{(x^2)^7}) d/dx (x^2) - e^{x^7}d/dx [x] \\F'(x) = 0 + 2xe^{x^{14}} - e^{x^7}\\F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex]

Thus, the requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].

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The three type of solubility are highly soluble, sparingly soluble or insoluble.

The term solubility is defined as the maximum amount of a substance that will dissolve in a given amount of solvent at a specified temperature

Here we have to major three types of solubility are defined below.

As we all know that Temperature, pressure and the type of bond and forces between the particles are few among them, that are the 3 factors solubility depends on.

According to the concentration of solute dissolves in a solvent, the solutes are categorized into highly soluble, sparingly soluble or insoluble.

Here we have to know that if a concentration of 0.1 g or more of a solute can be dissolved in a 100ml solvent, then it is said to be soluble.

Where as the concentration below 0.1 g is dissolved in the solvent it is said to be sparingly soluble.  

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9 hours will it take to clean the 15 pools.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Dave can clean pools at a constant rate of 3/5 pools per hour.

This also means that he cleans 3 pools in 5 hours

So, the time taken to clean 15 pools is

= 15×3/5

= 9 hours.

Hence, the time taken is 9 hours.

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Answer:

To find the simplest form is to find a number than can evenly go into both numbers. 7/14=1/2. 1/2 as you can divide 7 into 7 one time and 7 into 14 twice. A half (1/2). Because 7 is the half of 14, so the simplest form is 1/2. At first look you think it's already in its simplest form, but

explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{7}{14}}\\\\\\\mathsf{= \dfrac{7\div7}{14\div7}}\\\\\\\mathsf{= \dfrac{1}{2}}\\\\\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{\dfrac{1}{2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

x = 16±2√94 over 3

Step-by-step explanation:

Move terms to the left side.

0 = -6x² + 64x + 80

- ( -6x²+64+80) = 0

Distribute

- ( - 6x²+64x+80) = 0

6x² - 64x - 80 = 0

Common factor

6x² - 64x - 80 = 0

2 (3x²-32x--40) = 0

Divide both sides by the same factor

2 (3x²-32x--40) = 0

3x² - 32x - 40 = 0

Use the quadratic formula (Not explainin this, I forgot this one.)

Simplify

1.Evaluate the exponet

2.Mulitply the numbers

3.Add the numbers

4.Evaluate the sqaure root

5.Mulitply the numbers(Do this 2 more times.)

x = 32±4√94 over 6

Separate the equations

to solve for the unknown varible, separate into two eqautions: one with a plus and another with a minus.

Solve

Rearrange and isolate the varible to find each solution.

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent.

[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]

The coordinates of the intersection of the diagonals of the parallelogram QRST is (0, 1/2)

The coordinates of the parallelogram QRST are:

Q = (-1, 3)

R = (5, 2)

S = (1, -2)

T = (-5, -1)

The diagonals of  parallelogram QRST are QS and RT.

Let M be the point of the intersection of the diagonals of the parallelogram QRST

The diagonals of a parallelogram bisect each other.

This means, M is midpoint of diagonals QS and RT.

Consider diagonal QS.

Let (x1, y1) = (-1, 3) and (x2, y2) = (1, -2)

Using midpoint formula the coordinates of M would be,

M =  ((x1 + x2)/2, (y1 + y2)/2)

M = ((-1 + 1)/2, (3 - 2)/2)

M = (0/2 ,  1/2)

M = (0, 1/2)

Therefore, the point of intersecton of QS and RT is (0, 1/2)

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Answer:

y = -x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise / run or (y2 - y1) / (x2 - x1)

Let's pick 2 points ( -6, 0) (-5, -1)

We see the y decrease by 1 and the x increase by 1, so the slope is

m = -1

The y-intercept is located at (0,-6)

So, our equation is

y = -x - 6

If Punit had 12 tomatoes. He cut each into 6 lice. He used 4 lice of the 16 sandwiches he made then 68 slices were remaining.

There were 12 tomatoes and each was cut into 6 slices, giving a total of 72 slices. Here we have to multiply 6 with 12

12×6=72

Of these, 4 slices were used to make sandwiches, leaving 68 slices remaining. Here we have to subtract 4 from 72

72-4=68

Therefore, Punit had 68 slices left, or 11.33 tomatoes, after making the sandwiches. This means that Punit had 68 lice of tomato remaining after making the sandwiches.

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How likely something is to occur is known as its probability.Probability when die rolled 1st time is 6C1 i.e. (1,2,3,4,5,6).

How likely something is to occur is known as its probability.We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.

Probability when die rolled 1st time=6C1 i.e. (1,2,3,4,5,6) suppose 1 comes, then 2nd time it should not be .as it is given that no 2 people will roll same number.

so 2nd time probability=5C1 i.e. (2,3,4,5,6). same way 3rd and 4th time probability=4C1 and 3C1 respectively.Probability that no one rolls the same no. = 6*5*4*3and total possibility =6^4 

p(same number)= 6*5*4*3/ 6^4

= 5/18

p(no same number will roll)=1-5/18

=13/18

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The correct answer is option A: the optimal corner point won't change.

The optimal corner point is the point where the objective function reaches its maximum value, with the constraints of the problem being satisfied. If the slope of the objective function stays between the slopes of the binding constraints, it means that the current optimal corner point will remain unchanged.

This is because if the objective function's slope is within the slopes of the binding constraints, then the set of points where the objective function reaches its maximum value will be the same. Therefore, the optimal corner point will not change.

Learn more about Slopes here:

https://brainly.com/question/3493733

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