How would 5,682,450,003 be written in expanded form?

Answer3rd one and 1st

Step-by-step explanation:

The value of exterior angle is 108°.

What are exterior angles ?
An exterior angle is an angle which is formed by one of the sides of any closed shape structure such as polygon and the extension of its adjacent side.

Given:

Interior angles : (a+10)° and 44°

Thus , we know that

Exterior angle  = sum of interior opposite angles

Therefore , Exterior angle  = (a+10)° + 44°

or

2a° = (a+10)° + 44°

or

a = 54°

Therefore , exterior angle = 2a = 2*54° = 108°

Thus , the value of exterior angle is 108°.

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Answer:

Slope: y= 4/5x+21/8

The distance is 4 units up and 5 units to the right.

Step-by-step explanation:

The correlation between the two variables in the data set for 13 colonies of sparrowhawks is 0.5602.

This means that there is a moderate positive correlation between the two variables, indicating that when one variable increases, the other variable is likely to increase as well.

To calculate the correlation coefficient, we can use Pearson’s correlation coefficient equation:

r = (n * Σxiyi - Σxi * Σyi) / √[(n * Σxi2 - (Σxi)2) * (n * Σyi2 - (Σyi)2)]

Where: n = the number of observations Σxi = the sum of all x-values Σyi = the sum of all y-values Σxiyi = the sum of the products of each x-value and y-value Σxi2 = the sum of the squares of each x-value Σyi2 = the sum of the squares of each y-value

Plugging in the values for our data set, we get:

r = (13 * 0.5602 - (13 * 0.5602)) / √[(13 * 0.2532 - (13)2) * (13 * 0.2532 - (13)2)]

r = 0.5602

This means that there is a moderate positive correlation between the two variables in the data set, indicating that when one variable increases, the other variable is likely to increase as well.

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2.40.π is the  expression can be used to find the circumference of the skating rink.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that a circular skating rink has a radius of 40 feet.

Radius = 40 ft.

We need to find the  expression can be used to find the circumference of the skating rink.

The formula for circumference of circle is 2πr.

Circumference=2.40.π.

Hence, 2.40.π is the  expression which can be used to find the circumference of the skating rink.

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Answer: 2 x 40 x pie

Step-by-step explanation:

The solution to the given inequality  [tex]-5f + 6 > 10f - 10[/tex] is [tex]f < 16/15[/tex].

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

[tex]-5f + 6 > 10f - 10[/tex]

To solve the inequality [tex]-5f + 6 > 10f - 10[/tex], we need to isolate the variable [tex]f[/tex] on one side of the inequality.

We will first subtract 6 from both sides to isolate the [tex]-5f[/tex] term:

[tex]-5f + 6 - 6 > 10f - 10 - 6[/tex]

Simplifying the left side:

[tex]-5f > 10f - 16[/tex]

Next, we will subtract [tex]4f[/tex] from both sides to isolate the [tex]-5f[/tex] term on the left side:

[tex]-5f - 10f > 10f - 10f - 16\\-15f > -16[/tex]

Finally, we will divide both sides by -9,

[tex]-( 15 f )/9 > -16/15[/tex]

Dividing both sides by -15:

[tex]f < 16/15[/tex]

This is the required solution to the given inequality.

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Answer:

96

Step-by-step explanation:

large rectangle area = 7* (4+3+5) =7*12 =84

top & bottom 2 little triangles:

look at the bottom one:

triangle area formula = 1/2 base * height

so it's a right angle triangle, so the height is 4, base is 3

so area = 1/2 * 3* 4 =6

you have another one on the top

so 12

total = 84+12 =96

The decimal number that corresponds to the binary number 11111111 is 255.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. A decimal number is made up of two parts: a whole number and a fractional component separated by a decimal point. The decimal point is the dot between the whole number and the fractions. 25.5, for example, is a decimal number.

Here,

In binary, each digit represents a power of 2, starting with the rightmost digit. The rightmost digit in 11111111 represents 2^0, the second digit from the right represents 2^1, and so on. To convert a binary number to decimal, you add up the value of each digit times the corresponding power of 2.

For 11111111, the calculation would be:

=1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1

=255

The decimal equivalent of the binary number 11111111 is 255.

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Answer:

A=2

B=2+3÷2=2.5

C=10+15÷2=12.5

D=20

The variable b in terms of the variables a and c is b = ac/(a - c)

From the given formula expressed as

1/a + 1/b = 1/c

We want to express variable b in terms of the variables a and c. We would make variable b the subject of the formula.

Subtracting 1/a from the left hand side of the equation and the right hand side of the equation, it becomes

1/a - 1/a + 1/b = 1/c - 1/a

1/b = 1/c - 1/a

1/b = (a - c)/ac

Taking the reciprocal of the left hand side of the equation and the right hand side of the equation, it becomes

b = ac/(a - c)

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12suitcase

Answer:

B.

Step-by-step explanation:

i think 99.9% sure!

Answer:

he representation that is most appropriate to show the relationship between the number of chapters and the total pages of a book is given by:

Graph 3

How to choose the correct graph?

Before choosing the correct graph, we must classify the function as discrete or continuous, as follows:

Discrete function: the input values of the function are only certain values on an interval.

Continuous function: the input values of the function are all the real values in the interval.

Then the graph of each type of function is given as follows:

Discrete function: dots.

Continuous function: solid line.

The input and output variables in this problem are given as follows:

Input variable: number of chapters.

Output variable: number of pages.

The number of chapters assumes only integer values, hence the function has a discrete domain, meaning that the graph is composed by dots.

However, the first graph is correct, as the third graph has a range of input and output values that is not present on the table, while the range in the first graph is according to the table.

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Step-by-step explanation:

Answer:

6.00

Step-by-step explanation:

4r + g = 24

4r + 2g = 30       Subtract equation 2 from equation 1

     -g = -6

so g = cost of gravity = 6 dollars

The length of the diagonal is 12.6 feet.

"Information available from the question"

The perimeter of a rectangle is 32 feet.

The length is three times as long as the width.

We have to find the length of the diagonal.

Let w = width

then

3w = length.

Because we know the perimeter:

Perimeter of the rectangle is : 2(l + w)

32 = 2(w + 3w)

32 = 2(4w)

16 = 4w

4 feet = w (width)

Length:

3w = 3(4) = 12 feet

Diagonal, we use the Pythagorean theorem:

Let d = diagonal

then,

[tex]d^2 = 4^2 + 12^2[/tex]

[tex]d^2[/tex] = 16 + 144

[tex]d^2[/tex] = 160

d = 12.6 feet

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The table that represents a linear relationship that is also proportional is; Table B

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and as such it can be modeled or represented by the following mathematical expression:

y = kx

Where:

x and y represents the variables.

k represents the constant of proportionality.

For us to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) using table B as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = -2/-1 = 2 or 2/1 = 2

Constant of proportionality (k) = 2

Thus, table B is correct.

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Answer:

the second one....

x −1 0 1

y −2 −1 0

Step-by-step explanation:

Answer:

assuming that it can be solved, then yes

Step-by-step explanation:

So, approximately 2.28% of the observations are less than 140.

To find the percentage of observations that are less than 140, we need to find the standard score (z-score) that corresponds to 140, and then use a standard normal table to find the proportion of data that is less than that z-score.

The standard score is calculated as follows:

z = (140 - 130) / 5 = 2

Using a standard normal table, we can find the proportion of data that is less than 2 standard deviations from the mean. This proportion is approximately 0.0228 or 2.28%.

Mean is nothing but the average of data.

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The simplification steps are as follows:

(2³)(7.2³) = 2³+3 = 128

(5³)³ = 125

(1 + 3) = 4

72² = 5184

125 - 7 = 118

So, the simplified expression is:

118 (5xy³) (5184³) 2y

Properties of rational exponents are rules that dictate how to simplify expressions with fractional exponents. Some of the key properties are:

Fractional Exponent: a^(m/n) = (a^m)^(1/n)

These properties are used to simplify expressions with rational exponents, which are exponents that are in the form of a fraction.

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In order to score at least 76 for the full course, you have to score a total of 70 marks on the third test.

Average is calculated by first adding all the values of the total number of terms in a problem by the total number of terms.

Suppose there are five terms in a given problem, the formula will stand as:

Average of five terms = (n1 + n2 + n3 + n4 + n5)/5.

In this problem, the score of the first two tests are provided and the average of the three final tests is provided.

Marks scored in 1st test = 70

Marks scored in 2nd test = 88

Average marks = 76

Let the score of the third test be [tex]x[/tex]

Therefore, (70 + 88 + [tex]x[/tex])/3 = 76

(158 + [tex]x[/tex])/3 = 76

158 + [tex]x[/tex]= 228

[tex]x[/tex]= 228-158 = 70

Hence, the test score of the third test has to be 70 in order to get an average of 76 in the final marks.

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Answer:

(-2,2)

Step-by-step explanation:

First, let's look at the 2 inequalities:

y ≤ -x + 1

y > x

Just by looking at the second inequality, we can remove any ordered pairs where x is greater than or equal to y. This eliminated the ordered pairs (-1,-3) and (0,-1). Now, the answer has to be (-3,5) or (-2,2). Knowing this, we can plug x and y into the equation and see if either of the answers are true.

(-3,5):

x = -3

y = 5

y ≤ -x + 1

5 ≤ -(-3) + 1

5 ≤ 3 + 1

5 ≤ 4

NOT TRUE

(-2,2)

x = -2

y = 2

2 ≤ -(-2) + 1

2 ≤ 2 + 1

2 ≤ 3

TRUE

So, since plugging in the ordered pair (-2,2) into the inequality gives us a true answer while (-3,5) doesn't, the order pair (-2,2) must be out answer.

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The inequality that represents the graph is y ≤ -x - 2.

In mathematics, inequality is a declaration of an order connection between two numbers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).

In the graph, we have

1. the line is going down (negative slope) so that's why u have the negative

2. it translated 2 units Downwards on the y-axis so that's why there is - 2

3. the line is Solid so it's going to have the equal sign under it, if the line was dashed it would just be a regular sign fr example (<)

4. the shading is below the line so that means it's going to be Less than or Equal to.

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The gross pay of the worker when using the given parameters is; $1,129.46

Gross pay is defined as the total amount of money you get before taxes or any other deductions are subtracted from your salary.

Net pay is defined as the amount of pay remaining for issuance to an employee after deductions have been taken from individual's gross pay.

Thus;

Gross pay = Net pay + deductions

Net pay = Gross pay - deductions

The parameters are;

Regular salary: $984 per month

Overtime rate: $10.39 per hour (14 hours overtime to be paid)

Gross Pay = 984 + 14(10.39)

Gross Pay = $1,129.46

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12 ounces of cherries did Ms Winn buy.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Ms. Winn bought = 3/5 lb of grapes

Ms Winn bought = 5/8 lb of cherries.

As, there are 16 ounces in a pound then

= 3 pounds/4 x 16 ounces/pound

= 3 x 4

= 12 ounces

Hence, She buy 12 ounce of cherries.

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If a man has a garden and he divide them equally into minimum number of square plots , then length of each square plot is 28m  .

the length of the garden is = 84m  ;

the width of garden is = 56m ;

the man is dividing the garden into equally minimum number of square plots ,

then , Factors of Width = 2×2×2×2×7 = 2×28  ;

the Factors of Length is = 2×2×2×3×7 = 3×28  ;

So , we will notice with a side of 28 m each , we can make 2 squares along the width of the garden ;

Similarly , with the side = 28m each, we can make 3 squares along the length of the garden ;

That means , we can make 6 squares of 28m side.

Therefore , the minimum length of each square plot = 28 m.

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Here are the simplified expressions for each equation:

(x⁵) * (x⁸) * (2x³)² * (x⁻³) * (x⁵) = (x⁵) * (x⁸) * (2x⁶) * (x⁻³) * (x⁵) =

2x⁽⁵⁺⁸⁺⁶⁻³⁺⁵⁾ = 2x²¹

(y⁶) * (y⁹) = y⁽⁶⁺⁹⁾ = y¹⁵

(3x)³ = 27x³

(y⁷) * (y⁻³) = y⁽⁷⁻³⁾= y⁴

(z⁻⁸) * (z³) = z⁽⁻⁸⁺³⁾ = z⁻⁵

(x⁻²) * (x^⁻⁶) * (x⁴) = x⁽⁻²⁻⁶⁺⁴⁾ = x⁻⁴

(x¹⁵) * (x¹⁰) = x⁽¹⁵⁺¹⁰⁾ = x²⁵

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

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the simplified expressions for each equation is:

a) 2x²¹            b)  y¹⁵

c) 27x³           d)  y⁴

e) z⁻⁵              f)   x⁻⁴

g)  x²⁵

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation.

Addition, subtraction, multiplication, or division are all examples of math operations. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided.

An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

Here are the simplified expressions for each equation:

(x⁵) * (x⁸) * (2x³)² * (x⁻³) * (x⁵) = (x⁵) * (x⁸) * (2x⁶) * (x⁻³) * (x⁵) =

2x⁽⁵⁺⁸⁺⁶⁻³⁺⁵⁾ = 2x²¹

(y⁶) * (y⁹) = y⁽⁶⁺⁹⁾ = y¹⁵

(3x)³ = 27x³

(y⁷) * (y⁻³) = y⁽⁷⁻³⁾= y⁴

(z⁻⁸) * (z³) = z⁽⁻⁸⁺³⁾ = z⁻⁵

(x⁻²) * (x^⁻⁶) * (x⁴) = x⁽⁻²⁻⁶⁺⁴⁾ = x⁻⁴

(x¹⁵) * (x¹⁰) = x⁽¹⁵⁺¹⁰⁾ = x²⁵

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The linear equation that represents this situation will be y = 4x + 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

To ride go-carts at Rick's Play Zone costs $4 per ride plus $3 to rent a helmet.

Let 'y' be the total cost in dollars and 'x' be the number of times you ride the go-carts. Then the equation is given as,

y = 4x + 3

The equation that represents this situation will be y = 4x + 3.

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