Mathematics High School

## Answers

**Answer 1**

**Answer: k < 2 or k > 6.**

**Step-by-step explanation: **

**2x - k = xˆ2 + kx - 2**

**xˆ2 + (k - 2)x + (2 - k) = 0**

**For the line to meet the curve at two distinct points, this quadratic equation must have two distinct real roots. In other words, the discriminant (bˆ2 - 4ac) must be greater than zero:**

**(k - 2)ˆ2 - 4(2 - k) > 0**

**kˆ2 - 8k + 12 > 0**

**(k - 6)(k - 2) > 0**

**This inequality is satisfied when k < 2 or k > 6. Therefore, the set of values of k for which the line y= 2x-k meets the curve y= xˆ2+kx-2 at two distinct points is k < 2 or k > 6.**

## Related Questions

What is square root of 12 simplified?

### Answers

The simplified form of the **square root** of 12 is indeed 2 times the square root of 3.

The square root of 12 can be simplified to 2 times the square root of 3. To see why, we can factor 12 into its **prime factors**, which are 2 and 3, as follows:

12 = 2 × 2 × 3

Next, we can group the **two 2's together** and take their square root, which gives us 2. Then, we can take the square root of the **remaining 3,** which gives us the square root of 3. So, the simplified form of the square root of 12 is:

√12 = √(2 × 2 × 3) = 2√3

To verify this **mathematically**, we can use a calculator or long division to approximate the square root of 12, which is approximately 3.464. Then, we can simplify 2 times the square root of 3, which is approximately 3.464 as well. This confirms that the simplified form of the **square root** of 12 is indeed 2 times the square root of 3.

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how many 905 ounces are in a quart?

### Answers

There are approximately 28.28 **quarts** in 905 **ounces**.

A **quart** is a unit of volume measurement commonly used in the United States. One quart is equal to 32 fluid ounces.

To find out how many 905 **ounces** are in a quart, we need to divide 905 by 32.

905 oz ÷ 32 oz/qt = 28.28 qt

Therefore, there are approximately 28.28 quarts in 905 ounces.

Overall, it's important to understand the different units of measurement and how they relate to each other in order to perform accurate **conversions** between them. In this case, we used the conversion factor of 32 fluid ounces per quart to convert from ounces to quarts.

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find the surface area with the area of the box shown

### Answers

The **Surface area **of Cuboidal box is 320 inch².

What is Surface Area?

A 3D object's **surface area **is the entire area that all of its **faces **cover. For **instance**, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.

Given:

length = 10 inch

width = 4 inch

height = 8 inch

So, **Surface Area** of **Cuboid **= l x w x h

= 10 x 4 x 8

= 40 x 8

= 320 inch²

Thus, the Surface area is 320 inch².

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When rotated about its center, a regular pentagon has __ rotational symmetries. In addition to rotational symmetry, a regular pentagon has __ lines of reflectional symmetry.

### Answers

A regular pentagon has five **rotational** symmetries when it is turned around its centre. A regular pentagon has five bands of reflectional symmetry in addition to rotational symmetry.

What are the Pentagon's 5 sides?

Any five-sided shape or 5-gon is referred to as a pentagon in mathematics. In a **straightforward** hexagon, the interior angles add up to 540°. A hexagon could be straightforward or self-intersect.

What role does the Pentagon play?

The Potus and the Defense Secretary have exerted global command and control over the nation's military forces from the Pentagon. Since its construction, the Pentagon has served as a national and international emblem. It is, above all, a **metaphor** for American strength and influence, with all the positive and negative connotations that entails.

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Write 64 ×1 /16^2x

as a power of 4 in terms of x.

### Answers

**Answer: We can simplify the expression 64 ×1 /16^2x as follows:**

**64 ×1 /16^2x = 4^3 × 4^(-2x) [since 64 = 4^3 and 16 = 4^2]**

**Using the law of exponents which states that when we multiply two powers with the same base, we add the exponents, we get:**

**4^3 × 4^(-2x) = 4^(3 - 2x)**

**Therefore, 64 ×1 /16^2x can be expressed as a power of 4 in terms of x as:**

**4^(3 - 2x)**

**Step-by-step explanation:**

Jamil and Vicki have one child, age 3. How much will a tax credit reduce their tax liability? a. $3,000 b. $2,500 c. $500 d. $1,000 e. $2,000

### Answers

If Jamil and Vicki have **one child** , age 3 , then the **tax credit** will reduce their tax liability by $2000 , the correct answer is (e) .

Based on the **current tax laws** in the United States, Jamil and Vicki may be eligible for a** tax credit** of up to $2,000 for their child who is age 3. This tax credit is known as the Child Tax Credit (CTC).

The CTC is a **non-refundable tax credit**, which means it can only be used to reduce the **amount of taxes **owed.

If Jamil and Vicki's tax liability is less than $2,000, the CTC will only reduce their tax liability to zero.

If their **tax liability** is more than $2,000, the CTC will reduce their tax liability by $2,000.

Therefore, the correct answer is Option(e) $2000.

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What Should be Added to Roman Numerals LIV to Get MMMCMLXXXVII?

### Answers

MMMCMXXXIII should be **added** to 54** roman numerals** to get MMMCMLXXXVII.

LIV Roman Numerals:

LIV Roman Numerals can be written as numbers by combining the transformed roman numerals i.e. **LIV = **L + V - I = 50 + 5 - 1 = 54. The higher roman numerals **precede** the lower numerals resulting in the correct translation of LIV Roman Numerals. In this article, we will explain how to convert LIV** Roman numerals **in the correct number **translation**.

LIV = L + IV

LIV = 50 + 4

LIV = 54

We will write **MMMCMLXXXVII** and LIV in numbers, i.e. LIV = 54 and MMMCMLXXXVII = 3987. Now, 3987 - 54 = 3933. And, 3933 = MMMCMXXXIII. Therefore, MMMCMXXXIII should be **added** to 54 roman numerals to get MMMCMLXXXVII.

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scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. what is the minimum score you would need to be in the top 2%?

### Answers

The **minimum** score needed to be in the top 2% of the exam is 90.5, which is two standard deviations above the **mean**.

To calculate the **minimum **score needed to be in the top 2%, we need to find the value of two standard deviations above the mean. This can be done using the **formula** x = μ + (2σ), where μ represents the **mean** and σ represents the standard deviation. In this case, μ = 76.4 and σ = 6.1. We substitute these values into the **formula** to get x = 76.4 + (2*6.1), which equals 90.5. Therefore, the minimum score needed to be in the top 2% is 90.5. To further understand this calculation, it is important to note that the normal distribution curve is symmetrical. This means that the area under the curve that is two standard deviations above the mean is 2%, which is the same as the area under the curve that is two standard deviations below the mean. Therefore, the score that is two standard deviations above the mean is the minimum score needed to be in the top 2%.

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14= x- 13 PLEWASEEEEEEEEEEEEEEE

### Answers

**Answer:**

**x=27**

**Step-by-step explanation:**

14=x-13

14+13=x

27=x

**Answer:**

x=27

**Step-by-step explanation:**

In order to solve this problem you must isolate your variables onto one side which in this case is x. And in order to isolate it you must get rid of the -13 this can be done by adding 13 to both sides which would leave x on one side and 27 on the other resulting in x being 27.

Hope this helps! :)

Help please help please nkwwwww

### Answers

1) The **reaction **is **single replacement**

2) KI and Cl2

3) KCl and I2

4) Cl2 + 2KI → 2KCl + I2

What is a single replacement reaction?

A single replacement reaction, also known as a single displacement reaction, is a type of chemical reaction in which one element or ion in a compound is replaced by another element. The general form of a single replacement reaction is:

A + BC → B + AC

**Single replacement **reactions can also occur with non-metals, in which case the non-metal replaces another non-metal in a compound. For example, when chlorine gas (Cl2) is added to a solution of potassium iodide (KI), a single replacement reaction occurs:

Cl2 + 2KI → 2KCl + I2

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You bike 3 miles the first day of your training, 3.5 miles the

second day, 4.5 miles the third day, and 6.5 miles the fourth day.

If you continue this pattern, how many miles do you bike the

seventh day?

### Answers

**Answer: 15.6 miles !**

**Step-by-step explanation:**

determine the coordinates of the point of intersection for each of the following linear systems by graphing

a) y = 2x - 3 and y = -3x + 2

b) y = - 5/3x + 1 and y = - 1/3x - 3

c) 5x + y - 4 = 0 and x - y - 2 = 0

### Answers

The coordinates of the point of intersection are **(1, -1).** The solution is obtained by **graphing the equations**.

**What is graphing of an equation?**

The method of **graphing** an **equation** involves creating the **graph** of a **relevant equation**. Straightforward equations like direct, quadratic, etc., are very simple to graph, but complex equations require a deeper understanding of a few key concepts. If the curve accurately depicts the equation, then every point on the curve will satisfy the equation.

We are given two equations as y = 2x - 3 and y = -3x + 2

The** graph** for the **equations** has been plotted and attached below.

In the graph, **red** line represents **y = 2x - 3** and **blue** line represents

**y = -3x + 2.**

We can see from the graph that the two lines intersect at **(1, -1)**.

Hence, the coordinates of the point of intersection are **(1, -1).**

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Since, there are multiple questions so, the question answered above is as follows

Question: Determine the coordinates of the point of intersection for the following linear system by graphing

y = 2x - 3 and y = -3x + 2

How do you find the minimum a quadratic function?

### Answers

A **quadratic function** f(x) = ax² + bx + c is **minimum **when the leading coefficient 'a' > 0 and the minimum point is (-b/2a, 0)

We know that the** general form **of** quadratic function **is f(x) = ax² + bx + c

Also, the **graph **of the quadratic function is a **parabola**.

A quadratic function f(x) is **minimum **when the** leading coefficient** 'a' > 0 (the parabola opens upward) and f(x) is **maximum **when a < 0 (the parabola opens downward)

When **parabola **opens upward then the vertex of the parabola is nothing but the minimum of quadratic function.

And when parabola opens downward then the minimum of parabola cannot be determined.

Thus, if parabola opens up then the vertex of parabola tis the the minimum value of the quadratic function.

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What is slope intercept form and point slope form

### Answers

**Answer:**

**Step-by-step explanation:**

Slope-intercept form and point-slope form are two different ways to express the equation of a straight line.

Slope-intercept form is written in the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept, the point where the line crosses the y-axis. This form is useful for graphing and making calculations based on the slope and y-intercept. For example, given the equation y = 2x + 1, we know that the slope of the line is 2 and the y-intercept is 1.

Point-slope form is written in the form y - y1 = m(x - x1), where "m" is the slope of the line and (x1, y1) is a point on the line. This form is useful for finding the equation of a line when given a point on the line and the slope of the line. For example, given a line with slope 3 passing through the point (2, 5), the equation in point-slope form would be y - 5 = 3(x - 2).

**Answer:**

y = mx + b

y - y1 = m(x - x1)

**Step-by-step explanation:**

Kayla uses fancy beads which she purchases online to make bangle bracelets. The chart shows the number of different designer beads in one bag, and only full bags are sold. If Kayla chooses the BEST DEAL, how much will 1200 beads cost?

### Answers

If Kayla **decides** to choose the **best** deal, then, 1200 beads will cost $48.

How to get the best deal

In order to get the best deal, **Kayla **should find the unit cost of the beads in all categories listed. The unit costs are as follows:

For 100 beads sold for $6, the unit cost is $0.06.

For 200 beads sold for $10, the unit cost will be $0.05.

For 400 beads sold for $16, the unit cost will be $0.04.

For 600 beads sold for $30, the unit cost will be $0.05.

For 1000 beads sold for $55, the unit cost will be $0.055.

When we multiply 1200 beads for the given **unit costs**, we will have; $72, $60, $48, $60, and $66. The cheapest of all these is $48 and this is Kayla's best **deal**.

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your classroom has triangular shaped tables. three students can sit around one table. two tables can be pushed together so that two sides are adjacent. how many students can sit around the tables in this arrangement? explain your thinking

### Answers

**Answer:**

6

**Step-by-step explanation:**

If you push two triangle tables together you just multiply 3*2

Find F’(x) and show all applicable work.

### Answers

the integration can be simplified to

∫ t⁻³ with the limits cosx and 0 (sorry it's difficult to type it >.<)

you then integrate the value to get:

∫ -1/2t⁻² with the limits cosx and 0

then sub in your limits to get;

( -1/2(cosx)⁻² ) - ( -1/2(0)⁻² )

= - cosx⁻² / 2

i hope this helps, if you're struggling to understand i can try get a written working out instead :D (not sure if i got this right too...)

brad and sally made a total of 27 cakes for the school bake sale. brad made 5 more cakes than sally. find the numbers of cakes that sally made

### Answers

**Answer: Sally baked 11 cakes**

**Step-by-step explanation:**

Alright, so you should go about solving this by setting up two equations. We will use b to represent Brad and s to represent Sally:

b+s=27

b=s+5 (because Brad made 5 more cakes than sally)

Solve using systems of equations. I will show the substitution method because it is faster in this scenario:

(s+5)+s=27

Solve for s:

s+5+s=27

2s=22

s=11

**So Sally baked 11 cakes, which makes sense because that means that Brad baked 16**

please helppp!!!!!!!!!!!!!!

### Answers

The** rate of change** of the proportional relationship is given as follows:

k = 8/3.

Hence **Nadia **is correct.

What is a proportional relationship?

A proportional relationship is **defined **as follows:

y = kx.

In which k is the constant of proportionality.

The **constant **represents the rate of change, and is obtained as follows:

k = y/x.

From the graph, when x = 3, y = 8, hence the **rate of change** of the proportional relationship is given as follows:

k = 8/3.

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Given m∥n, find the value of x and y.

### Answers

**Answer:**

x = 23

y = 137

**Step-by-step explanation:**

Alternate interior angles have the same measurement (congruent)

3x - 20 = 2x + 3 Subtract 2x from both sides

3x - 2x - 20 = 2x - 2x + 3

x - 20 = 3 Add 20 to both sides

**x = 23**

Adjacent angles add to 180

3x - 20 + y - 6 = 180 Substitute 23 for x

3(23) -20 + y -6 = 180

69 - 20 + y -6 = 180 Combine like terms

43 + y = 180 Subtract 43 from both sides

**y = 137**

Each of the following letters has a line of symmetry: A E M T V In which letter is the direction of the line of symmetry different from that of the others?

### Answers

E letter is the **direction** of the line of symmetry different from that of the others.

A line of symmetry is what?

A form or item is divided into two **equally** and symmetrical portions by a line of symmetry. So it separates the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.

What are the three symmetry lines?

A **triangular** equilateral shape has three symmetry lines. An equilateral triangle has the most lines of symmetry, as opposed to other types of triangles like scalene, isosceles, or right-angled triangles.

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Consider the function of f(x)=2/7-x

a. What is f(7)?

b.what is the domain of f(x)?

c.if g(x) =2x+5 , what is g(3)?

d.now use the output of g(3) as the input for f to calculate f(g(3))

### Answers

Considering the **function **f(x) = 2 / (7 - x). The following can be deduced

a. f(7) = ∞

b. (-∞ 7)] ∪ [7 ∞)

c. g(3) = 11

d. f(g(3)) = -1/2

How to find the f(7)

Using the **function **f(x) = 2 / (7 - x), f(7) is solved as follows

f(7) = = 2 / (7 - 7)

= 2/0

= ∞

The **domain **of the function is

(-∞ 7)] ∪ [7 ∞)

Using g(x) = 2x + 5 , then g(3)

g(3) = 2(3) + 5

g(3) = 11

f(g(3))

f(g(3)) = 2 / (7 - 11)

f(g(3)) = 2 / -4

f(g(3)) = -1/2

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PLEASE HELP SOSOSOS WILL MAKE BRAINLIEST

### Answers

We can see that the **vertex** of Fountain B is higher than that of Fountain A.The Fountain B's water flows to a greater height.

What is vertex?

The vertex of a function is the point on the graph where the function reaches either its maximum or minimum value.

For example, in a quadratic function of the form y = ax^2 + bx + c, the vertex is the point at which the parabola changes direction and reaches either its highest or lowest point.

The vertex is an important point on the graph because it provides information about the shape of the function and its behavior. It is also useful for finding the axis of symmetry, which is a **line** that divides the graph into two symmetric halves.

The vertex can be calculated using a variety of methods, such as completing the square or using the formula d = -b/2a.

The vertex of Fountain A can be found by using the formula:

d = -b/2a, where a = -1 and b = 2

Substituting the values, we get:

d = -2/2(-1) = 1

So, the vertex of Fountain A is (1, 6)

For Fountain B, we can see that the maximum **height** reached is 11 feet, which occurs at x = -3.

So, the vertex of Fountain B is (-3, 11).

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Identify the graph and describe the solution set of this system of inequalities. Y<-3x-2 y>-3x+8

### Answers

There is no **solution **to the given **system **of inequalities.

What are systems of inequalities?

At least two linear **inequalities **in the same variables make up a **system **of a **linear inequality **in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the **solution **of a linear inequality is the ordered pair that resolves all inequalities in the system.

We have a **system **of **inequalities**,

y < -3x - 2

And y > -3x + 8.

The **graph **of the **inequalities **is given below.

And the lines are parallel.

That means there is no **solution **to the **system**.

Therefore, there is no solution to the **system**.

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A pizza shop has available toppings of mushrooms, onions, olives, pepperoni,

bacon, sausage, peppers, and anchovies. How many different ways can a pizza

be made with 4 toppings?

### Answers

**Answer:**

28 Pizza

**Step-by-step explanation:**

how many toppings8x4pizzas 4 with 8 toppings=28

Which of the following ordered pairs IS a solution to the equation 2x+5y=20

### Answers

The only **ordered** pair that is a **solution** to the equation 2x+5y=20 is (5,2), which is option C.

**What is linear equation ?**

Linear can be defined as **equation** in which highest degree is **one**.

To check which of the following ordered pairs is a solution to the equation 2x+5y=20, we can **substitute** the values of x and y from each ordered pair into the equation and see if the equation is true.

The **ordered** pairs are:

A. (2,3)

B. (3,2)

C. (5,2)

D. (4,3)

Let's check each one:

A. (2,3)

2(2) + 5(3) = 4 + 15 = 19

This is not equal to 20, so (2,3) is **not** a solution.

B. (3,2)

2(3) + 5(2) = 6 + 10 = 16

This is not equal to 20, so (3,2) is not a solution.

C. (5,2)

2(5) + 5(2) = 10 + 10 = 20

This is equal to 20, so (5,2) is a **solution**.

D. (4,3)

2(4) + 5(3) = 8 + 15 = 23

This is not equal to 20, so (4,3) is **not** a solution.

Therefore, the only ordered pair that is a solution to the equation **2x+5y=20 is (5,2), **which is option C.

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The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t) = -42t^2 +252t . Re-write h(t) in the form h (t) = a(t- h)^2 + k and determine the maximum height of the projectile. Show all work.

### Answers

The **maximum height** of the **projectile** is 3.72 units.

What is maximum height of projectile?

When a particle is hurled obliquely near the surface of the earth, it travels along a curved path while accelerating continuously in the direction of the planet's center (we assume the particle stays close to the surface of the globe). Such a particle's motion is known as projectile motion, and its route is referred to as a projectile.

The highest **vertical position** along the object's trajectory is considered to be its maximum height. The range of the bullet is defined as its horizontal displacement. The initial **velocity** of the object affects the projectile's range.

The projectile on a planet is given as:

[tex]h(t) = -42t^2 + 25t[/tex]

The maximum height is determined by using the differentiation and equating the differentiation to zero.

[tex]\frac{d}{dt} [ -42t^2 + 25t] = -84t + 25[/tex]

Substituting the value to 0 we have:

-84t + 25 = 0

t = -25/-84

t = 0.29

Thus, we get the maximum height at t=0.29.

Substituting the value of t = 0.29 we have:

h(0.29) = -42(0.29)² + 25(0.29)

h(0.29) = 3.72

Hence, the maximum height of the projectile is 3.72 units.

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A manufacturer of tools, selling rechargeable drills to a chain of home improvement stores, charges $4 more per drill than its manufacturing cost, m. The chain then sells each drill for 120% of the price that it paid the manufacturer. Find a function P(m) for the price at the home improvement stores

### Answers

The **price **of the rechargeable drill in the home improvement stores is P(m) = 1.2m + 4, where m is the manufacturing **total cost**.

P(m) = 1.2m + 4

P(m) = 1.2(manufacturing cost) + 4

P(m) = 1.2m + 4

The manufacturer of tools charges $4 more than its manufacturing cost for a rechargeable drill to a chain of home improvement stores. Following that, the chain sells each drill for 120 **percent **of what it paid the manufacturer.. Therefore, the price of the rechargeable drill in the home improvement stores can be represented by the function P(m), where m is the **manufacturing **cost of the drill. The equation P(m) = 1.2m + 4 shows that the price of the rechargeable drill in the home improvement **stores **is equal to 1.2 times the manufacturing cost plus $4. This equation indicates that the manufacturer of tools charges $4 more than its manufacturing cost and the home improvement stores then increase the price of the drill by 20% of the price they paid to the manufacturer. Therefore, the total cost of the rechargeable drill in the home improvement stores is 1.2m + 4, where m is the manufacturing **cost **of the drill.

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1. Write the following ratios in simplest form and use colon (:). a. Ratio of 50 footballs to 65 basketballs: b. Ratio of 200 motorcycles to 150 bicycles: c. Ratio of 675 girls to 550 boys: d. Ratio of 40 mangoes to 60 apples: e. Ratio of 180 tables to 240 chairs:

### Answers

**Answer:**

a. 50:65

b. 200:150

c. 675:550

d. 40:60

e. 180:240

(10:13)

(4:3)

(27:22)

(2:3)

(3:4)

How much 4 GB is a GiB?

### Answers

The **amount **of 4 GiB is equal to 4,096 **Megabytes **(MB), or 4,194,304 Kilobytes (KB), or 4,294,967,296 Bytes (B). Therefore, 4 GB is equal to 3.8 GiB.

4 GB stands for 4 **Gigabytes**, while GiB stands for Gibibytes. A Gigabyte is a unit of digital information storage, while a Gibibyte is a unit of computer memory or data storage equal to 1024 mebibytes. One Gigabyte is equal to 1,073,741,824 **bytes**, while one **Gibibyte **is equal to 1,073,741,824 bytes. Therefore, 4 Gigabytes is equal to 3.8 Gibibytes.

In more detail, 4 Gigabytes is equal to 4,096 Megabytes (MB), or 4,194,304 Kilobytes (KB), or 4,294,967,296 Bytes (B). It is important to note that these values can vary slightly depending on the system of measurement and the type of **computer memory** being used. For example, a computer system may use a different method to calculate the storage of data and may report larger or smaller values than the standard.

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