commom difference of an AP -4 , -4 , -4 ,............is...​

Answers

Answer 1

Answer:

0

Step-by-step explanation:

Common Difference = Difference between any two consecutive terms

= - 4 - (-4)

= - 4 + 4

= 0


Related Questions

convert the equation f(x)=1/2x^2+3x-2 to vertex form

Answers

Answer:

Step-by-step explanation:

Hello, please consider the following.

The "vertex form" is as below.

[tex]y=a(x-h)^2+k\\\\\text{Where (h, k) is the vertex of the parabola.}\\[/tex]

Let's do it!

[tex]f(x)=\dfrac{1}{2}x^2+3x-2\\\\f(x)=\dfrac{1}{2}\left(x^2+3*2*x\right) -2\\\\f(x)=\dfrac{1}{2}\left( (x+3)^2-3^2\right)-2\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9}{2}-\dfrac{4}{2}\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9+4}{2}\\\\\large \boxed{\sf \bf \ \ f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{13}{2} \ \ }[/tex]

Thank you.

PLEASE HELP f(x)=x^2 and g(x)=(x-3)^2+2 Describe how the graph of g(x) relates to the graph of its parent function, f(x). (HINT: Think about how f(x) was shifted to get g(x))

Answers

Answer:

The graph f(x) was shifted 3 units to the right and shifted 2 units up to get the graph of g(x).

Step-by-step explanation:

From the original graph to the transformed one, we can see that the transformations (x - 3) and + 2 were added to the equation.

The (x - 3) means that the x-value of the vertex will increase by 3, meaning that the graph will shift 3 units to the right.

The +2 will increase the y-value of the vertex by 2, meaning that the graph will move up 2 units.

So, the graph of g(x) relates to f(x) as it is a transformation 3 units to the right and 2 units upwards.

Two angles are adjacent and form an angle of 160. Their difference is 34. Find the angles​

Answers

Answer:

The angles are 63 , 97

Step-by-step explanation:

Let one angle be x

As sum of two angles is 160, the other angle = 160 - x

Their difference  = 34

x - [160- x] = 34

Use distributive property to remove the brackets

x - 160 + x = 34

Add like terms

x + x - 160 = 34

2x - 160 = 34

Add 160 to both sides

2x  = 34 + 160

2x = 194

Divide both sides by 2

2x/2 = 194/2

x = 97°

One angle = 97°

Other angle = 160 - 97 = 63°

Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.[tex]Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.[/tex]

Answers

Hello, please consider the following.

[tex]x^2 + 10x + 25 = 8\\\\\text{\bf We can notice that } x^2+10x+25=(x+5)^2 \text{ so}\\\\x^2 + 10x + 25 = (x+5)^2=8\\\\\text{\bf We take the root.}\\\\x+5=\pm\sqrt{8}\\\\\text{\bf We subtract 5}\\\\\boxed{x=-5-\sqrt{8}} \ \ or \ \ x=-5+\sqrt{8}[/tex]

In the box, you can find the smallest solution.

Thank you.

A.) pinky bought 1 1/2 kg of apples and 5 1/4 kg of mangoes and 1 1/2 Kg of oranges. Find the total weight of fruits B.) If her family eats 3/4 Kg of apples and 2 1/2 kg of mangoes and 1/2 Kg of oranges. Find the weight of the fruits left (Can any one say the answer please with explanation if who say the answer first I will mark them as the brainliest)

Answers

Answer:

a) The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms, b) The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.

Step-by-step explanation:

a) The total weight of fruits ([tex]m_{T}[/tex]) is calculated by the following formula:

[tex]m_{T} = m_{a} + m_{m}+m_{o}[/tex]

Where:

[tex]m_{a}[/tex] - Total weight of apples, measured in kilograms.

[tex]m_{m}[/tex] - Total weight of mangoes, measured in kilograms.

[tex]m_{o}[/tex] - Total weight of oranges, measured in kilograms.

If [tex]m_{a} = 1\,\frac{1}{2} \,kg[/tex], [tex]m_{m} = 5\,\frac{1}{4}\,kg[/tex] and [tex]m_{o} = 1\,\frac{1}{2}\,kg[/tex], then:

[tex]m_{T} = 1\,\frac{1}{2}\,kg + 5\,\frac{1}{4}\,kg + 1\,\frac{1}{2}\,kg[/tex]

[tex]m_{T} = \frac{6}{4}\,kg + \frac{21}{4}\,kg + \frac{6}{4}\,kg[/tex]

[tex]m_{T} = \frac{33}{4}\,kg[/tex]

[tex]m_{T} = 8\,\frac{1}{4}\,kg[/tex]

The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms.

b) The weight eaten by her family is determined by the following expression:

[tex]m_{E} = m_{a,e} + m_{m,e} + m_{o,e}[/tex]

Where:

[tex]m_{a,e}[/tex] - Eaten weight of apples, measured in kilograms.

[tex]m_{m,e}[/tex] - Eaten weight of mangoes, measured in kilograms.

[tex]m_{o,e}[/tex] - Eaten weight of oranges, measured in kilograms.

Given that [tex]m_{a,e} = \frac{3}{4}\,kg[/tex], [tex]m_{m,e} = 2\,\frac{1}{2}\,kg[/tex] and [tex]m_{o,e} = \frac{1}{2}\,kg[/tex], the weight eaten by her family is:

[tex]m_{E} = \frac{3}{4}\,kg + 2\,\frac{1}{2}\,kg + \frac{1}{2}\,kg[/tex]

[tex]m_{E} = \frac{3}{4}\,kg + \frac{10}{4}\,kg + \frac{2}{4}\,kg[/tex]

[tex]m_{E} = \frac{15}{4}\,kg[/tex]

[tex]m_{E} = 3\,\frac{3}{4}\,kg[/tex]

The weight of the fruits left is found by subtraction:

[tex]m_{R} = m_{T}-m_{E}[/tex]

[tex]m_{R} = 8\,\frac{1}{4} \,kg -3\,\frac{3}{4}\,kg[/tex]

[tex]m_{R} = \frac{33}{4}\,kg-\frac{15}{4}\,kg[/tex]

[tex]m_{R} = \frac{18}{4}\,kg[/tex]

[tex]m_{R} = 4 \,\frac{1}{2}\,kg[/tex]

The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.

What ratio of 25 dextrose and 10% dextrose should be mixed to make a 20% Dextrose? Comments for What Ratio of 25% Dextrose and 10% Dextrose to make 20% Dextrose? 10 parts 25% and 5 parts 10% solution equals 20% mixture.

Answers

Answer:

10:5 OR 2:1

Step-by-step explanation:

Let x be the parts of 25% dextrose and

y be the parts of 10% dextrose are mixed so that

20% dextrose mixture is obtained.

amount of dextrose in the mixture will be 20% of (x+y).

We have to find the value of [tex]\frac{x}y \ OR\ x:y[/tex]

Now, we can apply the concept that sum of amount of dextrose in the two liquids will be equal to the amount of dextrose in the mixture.

[tex]\Rightarrow x \times 25\% + y \times 10\%=(x+y)\times 20\%\\\Rightarrow x \times\dfrac{25}{100} + y \times \dfrac{10}{100}=(x+y)\times \dfrac{20}{100}\\\Rightarrow x \times25 + y \times 10=(x+y)\times 20\\\Rightarrow 25x + 10y=20x+20y\\\Rightarrow 25x -20x =20y-10y\\\Rightarrow 5x=10y\\\Rightarrow \dfrac{x}{y} = \dfrac{10}{5}\\\Rightarrow \bold{x:y=10:5\ OR\ 2:1}[/tex]

So, the answer is 10:5 or 2:1.

Answer:

4.90% is approximately the new Dextrose concentration.

Explanation:

Volume by Volume percent is given by ;

Volume percentage of dextrose solution = 5%

In 100 mL of solution 5 ml of dextrose is present.

Now, volume sterile water added was equal to the 40% of volume of dextrose volume.

So, volume of the sterile water added =  

Total volume of the solution after addition of water = 100 mL + 1 mL = 102 mL

New concentration of dextrose will be;

4.90% is approximately the new Dextrose concentration.

Step-by-step explanation:


5 3/4 - (-3 7/8) = H
What is H ?​

Answers

Answer:

Step-by-step explanation:

convert mixed fraction into improper fraction

[tex]5\frac{3}{4}=\frac{23}{4}\\\\\\3\frac{7}{8}=\frac{31}{8}\\\\5\frac{3}{4}-[-3\frac{7}{8}]=\frac{23}{4}+\frac{31}{8}\\\\=\frac{23*2}{4*2}+\frac{31}{8}\\\\=\frac{46}{8}+\frac{31}{8}\\\\=\frac{46+31}{8}\\\\\\=\frac{77}{8}\\\\=9\frac{5}{8}[/tex]

Answer:

9 5/8.

Step-by-step explanation:

5 3/4 - (-3 7/8)

= 5 3/4 + 3 7/8

= 5 + 3 + 3/4 + 7/8

= 8 + 3/4 + 7/8    

The LCD of 4 and 8 is 8 so we get

8 + 6/8 + 7/8

= 8 + 13/8

= 8 + 1 5/8

= 9 5/8.

ILL GIVE BRAINLIEST!!!! HELP
Two planes have a cruising speed of 750 km/h without wind. The first plane flies for 13 hours against a constant headwind. The second plane flies for 11 hours in the opposite direction with the same wind (a tailwind). The second plane flies for 250 km less than the first plane. Determine two equations that could be used to solve for the wind speed,w, and the distance traveled by the first plane,d.

1. (750+w)(13)=d (750+w)(11)=d+250 2. (750−w)(13)=d (750+w)(11)=d−250 3. (750+w)(13)=d (750−w)(11)=d−250 4. (750−w)(13)=d (750−w)(11)=d+250

Answers

Answer:

The correct option is;

2. (750 - w)(13) = d (750 + w)(11) = d - 250

Step-by-step explanation:

The items with information given are;

The cruising speed of the planes = 750 km/h

The first plane flies against a constant headwind = w

The second plane flies against a constant tailwind  in magnitude to the headwind

The time duration of flight of the first plane = 13 hours

The time duration of flight of the second plane = 11 hours

The distance flown by the second plane = The distance flown by the first plane - 250 km

When we take the headwind magnitude as, w and the distance flown by the first plane as d, we have;

Speed of flight of the first plane = 750 - w

Speed of flight of the second plane = 750 + w

Therefore, the distance flown by the first plane in 13 hours is given as follows;

(750 - w) × (13) = d

Then we have;

The distance flown by the second plane in 11 hours is (750 + w) × (11) = d.

The correct option is (750 - w)(13) = d, (750 + w)(11) = d - 250

Someone pls help . Thank you sm☄️ .

Answers

Answer:

1) 3 is the Coefficient.

2) 10 is the constant.

3) 10.8 is the ans.

Use slope-intercept form, y = mx + b, to find the value for the y-intercept (b) of a line that has a slope of 6 and passes through the point (3, –5)

Answers

Answer:

y=6x-23

Step-by-step explanation:

-5=6(3)+b

-5=18+b

b=-23

If this helps, plz give brainly, I rlly need it!

Answer:

6x-23

Step-by-step explanation:

Which expression is NOT equivalent to 4×38? A. 4×(3×18) B.(4×3)×18 C. (4×18)×3 D. (4×3)×(4×18)

Answers

Answer:

Every choice is not equivalent to 4✖️38.

Step-by-step explanation:

4✖️38=152

A. 54✖️4=216

B. 12✖️18=216

C. 72✖️3=216

D. 12✖️72=864

Every choice is not equivalent to 4✖️38.

The functions q and r are defined as follows
g(x) = -2x-2
r(x) = x² – 2
Find the value of r(q(4)).
r(9 (4)) =

Answers

Answer:

98

Step-by-step explanation:

So we have the two functions:

[tex]g(x)=-2x-2\text{ and } r(x)=x^2-2[/tex]

And we want to find the value of r(g(4)).

To do so, first find the value of g(4):

[tex]g(x)=-2x-2\\g(4)=-2(4)-2\\[/tex]

Multiply:

[tex]g(4)=(-8)-2[/tex]

Subtract:

[tex]g(4)=-10[/tex]

Now, substitute this into r(g(4)):

[tex]r(g(4))\\=r(-10)[/tex]

And substitute this value into r(x):

[tex]r(-10)=(-10)^2-2[/tex]

Square:

[tex]r(-10)=100-2[/tex]

Subtract:

[tex]r(-10)=98[/tex]

Therefore:

[tex]r(-10)=r(g(4))=98[/tex]

Answer:

Step-by-step explanation:

A chocolate company has a new candy bar in the shape of a prism whose base is a 1-inch equilateral triangle and whose sides are rectangles that measure 1 inch by 2 inches. These prisms will be packed in a box that has a regular hexagonal base with 2-inch edges, and rectangular sides that are 6 inches tall. How many candy bars fit in such a box

Answers

BASE AREA OF THE BOX:

Regular hexagon with 2 inch edges contains 180*(6-2) = 180*4 = 720 degrees
That's 120 degrees in each of the corner pockets.
Drawing line segments from the center to each vertex creates 6 congruent isosceles triangles.
Selecting any one of these six triangles and dropping the height from the center to the edge
creates a 30-60-90 right triangle with height equal to the square root of 3 (rad3) and base measure 1.
So the area of each of these triangles is the square root of 3 , or in slang terms "rad 3", which means
the base area is 6*rad3.

The volume of the box is therefore 36*rad3

BASE AREA OF THE CANDY:

Dropping the height from one vertex to the opposite side of this equilateral triangle
creates 2 right triangles with base measure 1/2 and hypotneuse 1. So the height
must be rad3/2. The area of the entire equilateral triangle is rad3/4, which is the base area.

The volume of the candy is rad3/2


36*rad3 divided by rad3/2 =

36 rad3 times 2/rad3 <--- KFC : keep , change, flip

36 * 2 <-- rad3 cancels out

72 candies will fill the box.

It says to find the area of the shaded square, but I not sure how to get the answer. ​

Answers

Answer:

68 square cm

Step-by-step explanation:

Interior square WXYZ is making four right triangles of equal bases (8 cm) and heights (2 cm) inside the square ABCD. Therefore,

Area of shaded Square = Area of square ABCD - 4 times area of one right triangle.

[tex] = {10}^{2} - 4 \times \frac{1}{2} \times 8 \times 2 \\ = 100 - 32 \\ = 68 \: {cm}^{2} [/tex]

complete the square to solve
f(x)=x^2-6x+5​

Answers

Answer: See below

Explanation:

x^2 - 6x + 5 = 0
(x^2 - 6x + 9) + 5 - 9 = 0
(x - 3)(x - 3) - 4 = 0
(x - 3)^2 = 4
x - 3 = +-2 (sqrt both sides)

x - 3 = 2
x = 5

x - 3 = -2
x = 1

Write an expression to represent the product of 6 and the square of a number plus 15.

Answers

Answer:

6x^2 + 15

Step-by-step explanation:

We don't know what the square of a number is, so we represent it as x^2

The first part tells us to find the product of 6 and the square of a number, so

6x^2

The second part tells us to add 15 so,

6x^2 + 15

The expression that should be represented is [tex]6x^2 + 15[/tex]

Given that

The product of 6.The square of number + 15.

Based on the above information,

Let us assume the number should be x

So, from the above information, the expression should be [tex]6x^2 + 15[/tex]

Therefore we can conclude that The expression that should be represented is [tex]6x^2 + 15[/tex]

Learn more about the equation here:brainly.com/question/21105092?

find the value of X in X-X³=17​

Answers

Answer:

Step-by-step explanation:

Step1: find the interval of roots. Consider -3 and -2

[tex]f(-3) = -7 <0[/tex]

[tex]f(-2) = 18 >0[/tex]

Hence, the root must be on [-3,-2]

Step2:  consider the middle point -2.5

[tex]f(-2.5) = 3.875 >0[/tex]

Then, the root must be on [-3, -2.5]

Step 3: Repeat step 2 by finding the value of f at the middle point -2.75

[tex]f(-2.75) = -1.0468 <0[/tex]

Step 3: Repeat step 2 by finding the value of f at the middle point of the interval [-2.75,-2.5] which is -2.625

[tex]f(-2.625) = 1.537 >0[/tex]

Step4: Repeat step 2 on [-2.75, -2.625]

Repeat step 2 until you got the root which is -2.701

HELP! WIll MARK BRAINLIEST! ACME Hardware is introducing a new product called Greener Cleaner. Complete the table by finding the cost per milliliter for each size based on the sales price. One liter is 1,000 milliliters. (Answer the questions too, please!)

Answers

Question 1:

Price per milliliter

Small $4.50 / 250ml

Medium $9.95 / 500 ml

Large $16.95 / 1000 ml

Question 2:

$9.95 / 500 ml > $4.50 / 250ml > $16.95 / 1000 ml

Question 3 - 4:

$4.50 / 250ml = ($4.50 * 6) / (250ml * 6 ) = $27 / 1500ml = 0.018

$9.95 / 500 ml = ($9.95 * 3) / (500 ml * 3) = $29.85 / 1500ml = 0.019

$16.95 / 1000 ml = ($16.95 * 3) / (1000 ml * 3) = $50.85 / 1500ml = 0.0339

( Use the first one for question 3 and the second for question 4)

$4.50 / 250ml would be the cheapest way to get 1500ml.

$9.95 / 500ml would be the most expensive way to get 1500ml.

I hope this helps you! Tell me if I'm wrong!

Please help. Calculate the area of the shaded region in each figure use 3.14 for π and round to the nearest 10th if necessary​

Answers

Answer: See below

Explanation:

Find the area of circle:

A = 3.14 x 5^2
A = 3.14 x 25
A = 78.5 cm^2

Find the area of rectangle:

A = 3 x 4
A = 12

Find area of shaded region:

A(shaded) = A(circle) - A(rectangle)
A = 78.5 - 12 = 66.5 cm^2

Given that p=x^2-y^2/x^2+xy
I. Express p in the simplest form
ii. Find the value of p if x=-4 and y=-6

Answers

Answer:

p = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given

p = [tex]\frac{x^2-y^2}{x^2+xy}[/tex] ( factorise numerator and denominator )

x² - y² ← is a difference of squares and factors as (x - y)(x + y)

x² + xy ← factor out x from each term

= x(x + y) , thus

p = [tex]\frac{(x-y)(x+y)}{x(x+y)}[/tex] ← cancel (x + y) on numerator/ denominator

   = [tex]\frac{x-y}{x}[/tex] ← substitute x = - 4, y = - 6

   = [tex]\frac{-4-(-6)}{-4}[/tex]

   = [tex]\frac{-4+6}{-4}[/tex]

    = [tex]\frac{2}{-4}[/tex] = - [tex]\frac{1}{2}[/tex]

Jeremy drove 180 miles in 3 hours. Find his average rate of change.​

Answers

Answer:

60 miles per hour

Step-by-step explanation:

Total distance= 180 miles

Total time =3 hours

Average rate of change= ?

Distance= Rate × time

Make Time the subject of the formula

Time= Distance / Rate

Make average rate of change the subject of the formula

Average rate of change = Distance / time

= 180 miles / 3 hours

= 60 miles per hour

30 POINTS!! Quadratic function F(x) =2x^2- 4x- 6 is shown below. Which describes the domain of this function.

A. All real numbers greater than or equal to -8

B. All real number less than or equal to -8

C. All real number greater than 10

D. All real numbers


Answers

Answer:

D. All real numbers

Step-by-step explanation:

The domain is the set of values that can be used for x. There is no restriction on x, so the domain is all real numbers.

Answer:

all real numbers

Step-by-step explanation:

The domain is the possible input values

Since x can be any value, the domain is all real numbers

Can someone plz help me ASAP!!!!!!!!

Answers

Answer:

A) The number halfway between -2 and 6 is 2.

B) -10 is halfway between -18 and 8

An octagonal pyramid ... how many faces are there, how many vertices and how many edges? A triangular prism ... how many faces are there, how many vertices and how many edges? a triangular pyramid ... how many faces are there, how many vertices and how many edges?

Answers

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

X-5y=-15x−5y=−15x, minus, 5, y, equals, minus, 15 Complete the missing value in the solution to the equation. (-5,(−5,left parenthesis, minus, 5, comma ))

Answers

Answer:

The missing value is 2. The coordinate will be (-5, 2)

Step-by-step explanation:

The question is not properly written. Find the correct question below.

If x – 5y = -15 . Complete the missing value in the solution to the equation (-5, ____)

Let the coordinate of the variables be (x, y). Comparing the coordinates (x, y) with the given coordinate (-5, __), we will discover that x = -5. To get the y coordinate, we will substitute x = -5 into the given expression as shown;

If x – 5y = -15

-5 - 5y = -15

Adding 5 both sides

-5-5y+5 = -15+5

-5y = -10

Dividing both sides by -5;

-5y/-5 = -10/-5

y = 2

Hence the missing value in the solution of the equation is 2. The coordinate will be (-5, 2)

Answer:

2

Step-by-step explanation:

I did the khan :)

An insurance firm reported that "the typical water-skiing accident occurs near the dock from which they start." Which of the following statistical measurements are they most likely discussing? A. mode B. range C. mean D. median

Answers

Answer:

The correct option is;

B. Range

Step-by-step explanation:

In descriptive statistics which analyses the quantitative summary of the statistical data, the range is the region or area or the statistical interval where the data is obtained from and as such the range (in descriptive statistics) gives a guide to the dispersion of the statistical information.

The range is best suited for the representation of the dispersion when the size of the data set is small.

-2(8 - 1)= complete the following statement

Answers

We simplify the expression by subtracting 1 from 8, resulting in 7. We then multiply 7 by -2 to obtain the final answer of -14.

To simplify the given expression, -2(8 - 1), we can start by evaluating the expression inside the parentheses,

8 - 1 = 7

Now, we substitute this value back into the original expression:

-2(7)

Multiplying -2 by 7, we get:

-2 * 7 = -14

Therefore, -2(8 - 1) simplifies to -14.

In this case, we simplified the expression inside the parentheses first and then applied the multiplication operation. It's important to remember that when there is a negative sign in front of parentheses, it distributes to each term inside the parentheses. So, -2 multiplied by 8 gives -16, and -2 multiplied by -1 gives +2. The sum of -16 and +2 is -14.

In summary, when we evaluate the expression -2(8 - 1), the result is -14. This means that if we follow the order of operations (parentheses first, then multiplication), we simplify the expression by subtracting 1 from 8, resulting in 7. We then multiply 7 by -2 to obtain the final answer of -14.

For more such questions on expression

https://brainly.com/question/29070527

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A coin is tossed. What is the theoretical probability of the coin NOT showing tails?
P(Not tails) =

Answers

Answer:

50%

Step-by-step explanation:

its 50% it will land on head and 50% it will land on tails since there is only two sides on a coin

Answer:

1/2 or .5

p(1/2)

Step-by-step explanation:

its simple, there are 2 sides to a coin, so there are 2 possible outcomes. and the question asks what is the probability of the coin landing on one or in other wrds, its asking what is te probilitity of one of the two heads to be up. SO the probility is 1/2

Someone help me plzz​

Answers

Step-by-step explanation:

distance around the running track means to find the perimeter of whole solid figure

radius(r) = 30/2 =15m

perimeter = 50+ pi× r + 50+ pi × r

= 100 + 2 × pi ×r

= 100 + 2× 22÷7 × 15

= 1360/ 7 m

= 194.285 m

ACME Hardware is introducing a new product called Greener Cleaner. Complete the table by finding the cost per milliliter for each size based on the sales price. One liter is 1,000 milliliters. (Answer the questions too, please!)

Answers

Answer:

Step-by-step explanation:

a). 'Per ml' cost of the small size = [tex]\frac{\text{Sale price of small cane}}{\text{Amount of liquid}}[/tex]

                                                       = [tex]\frac{4.50}{250}[/tex]

                                                       = $0.018

'Per ml' cost of the medium size = [tex]\frac{\text{Sale price of medium cane}}{\text{Amount of liquid}}[/tex]

                                                        = [tex]\frac{9.95}{500}[/tex]

                                                        = $0.0199

     'Per ml' cost of the large size = [tex]\frac{\text{Sale price of large cane}}{\text{Amount of liquid}}[/tex]

                                                      = [tex]\frac{16.95}{1000}[/tex]

                                                      = $0.01695

Therefore, expression to compare per ml cost of three containers will be,

$0.0199 > $0.018 > $0.01695  

b). Least expensive way to buy the cleaner is to choose the container with least per ml cost.

Cost of 1500 ml cleaner = Cost of 1000 ml cleaner + Cost of 500 ml of cleaner

                                        = Cost of 1000 ml cleaner container + Cost of 'n' containers of 250 ml container

Total cost of 1500 ml = $16.95 + $4.50n

                                    = 16.95 + 2(4.5) [For n = 2]

                                    = $25.95

c). Most expensive way to purchase 1500 ml cleaner is to choose the most expensive cleaners

Cost of 1500 ml cleaner = Cost of 'n' containers of medium size containers

                                        = 9.95(n)

                                        = 9.95(3)

                                        = $29.85

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