3. One hundred million copper atoms are arranged in a line. Which is a reasonable estimate for the length of this line?
O
1 nanometer
1 kilometer
1 meter
1 centimeter

Answer: To solve for all values of x in the equation x^2 - 2x - 48 = 0 by completing the square, we can follow these steps:

Bring the x term to one side of the equation by adding 2x to both sides: x^2 - 2x = 48

Divide the coefficient of the x^2 term (which is 1) by 2 and square it to find the value to add to both sides of the equation to complete the square: (1/2)^2 = 1/4. Add 1/4 to both sides of the equation: x^2 - 2x + 1/4 = 48 + 1/4

Take the square root of both sides of the equation: (x - 1)^2 = 192 + 1

Solve for x by taking the square root of both sides of the equation: x - 1 = ± √193

Add 1 to both sides of the equation to find the values of x: x = 1 ± √193

So the solutions of the equation are x = 1 + √193 and x = 1 - √193

It is important to notice that these are the solutions in radical form, so they are not exact values of x.

Step-by-step explanation:

The linear function with a slope of 1/3 and intercept of 7 is defined as follows:

y=1/3x+7.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

Considering a slope of 1/3 and intercept of 7, the values of the parameters are given as follows:

m = 1/3, b = 7.

Hence the function is defined as follows:

y = 1/3x + 7.

The problems asks for the linear function with a slope of 1/3 and intercept of 7.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The solution for f(3) in the function is -7772

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

f(x) = 4 − (x + 3)⁵

Also from the question, we have

f(3)

This means that the value of x is 3, and we calculate f(x) when x = 3

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

f(3) = 4 − (3 + 3)⁵

Evaluate

f(3) = −7772

Hence, the solution is −7772

Read more about functions at

brainly.com/question/28277110

#SPJ1

Complete question

Given f ( x ) = 4 − ( x + 3 )^5, find f(3).

To determine the key terms refer to in the following conducted study in a local community will be as follows:

a. voted, didn't vote, voted will be variable.

b. a group of voters in the community who voted, randomly selected will be sample.

c. the number of eligible voters who actually plan to vote will be population.

d. the number of eligible voters in the study who actually plan to vote statistic.

e. the attendance of a single voter will be data

f. all eligible voters in the comunity will be parameter.

Any quantity calculated from sample values and taken into consideration for statistical purposes is referred to as a statistic (singular) or sample statistic. A population parameter estimate, a sample description, or a hypothesis evaluation are examples of statistical purposes. Statistics are expressed as the average (or mean) of sample values.

To learn more about statistics: https://brainly.com/question/15525560

#SPJ4

Strategic planning is an essential process for any organization that wants to succeed and achieve long-term success. It involves identifying long-term organizational goals, strategies, and resources that will help the organization reach its objectives.

This process requires a comprehensive assessment of the organization's current and future needs, including its strengths and weaknesses, opportunities and threats, and the external environment. Once identified, the organization must develop and implement a plan to achieve its goals and objectives. This involves setting objectives, developing and implementing strategies and tactics, and allocating resources in a way that will maximize the organization's chances of success.

Learn more about Strategic planning: https://brainly.com/question/24864915

#SPJ4

The amount to save according to the recommendation of 3/10 of income is $17400.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

Given that the amount made in a year is $58,000.

The recommended savings is 3/10 thus:

(58000) (3/10) = 17400

Hence, according to the recommendation the amount that needs to be saved in one year is, $17400.

Learn more about fractions here:

https://brainly.com/question/10354322

#SPJ1

The length of the base is equal to 13 inches.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

10 5/6 = 4 1/3 × base

65/5 = 13/3b

Length of the base, b = 65/5 ÷ 13/3

Length of the base, b = 65/5 × 3/13

Length of the base, b = 195/65

Length of the base, b = 13 inches.

Read more on area of a rectangle here: brainly.com/question/25292087

#SPJ1

Answer:

f(-2)=14

Step-by-step explanation:

 f(x)=x^2 +2x - 10 and  f=(-2)

f(-2)=-2^2 +2(-2) - 10

4+0+10

14

f(-2)=14

:)

Indicated by a trend line is a linear relationship. Y = mx + b, where x is the independent variable and b is the constant, is the equation for a linear connection.

To learn more about variable refer to:

https://brainly.com/question/82796

#SPJ1

The square root of 6^2 (√6²) is 6.

What is square root?

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.

Suppose x is the square root of y, then it is represented as x=√y, or we can express the same equation as x^2 = y. Here, ‘√’ is the radical symbol used to represent the root of numbers. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.

For example, the square of 3 is 9, 32 = 9 and the square root of 9, √9 = 3. Since 9 is a perfect square, hence it is easy to find the square root. But for an imperfect square like 3, 7, 5, etc., we have to use different methods to find the square root.

Now ,

given expression √6²

=√36

square root value of √6² =6

To know more about square root visit the link

https://brainly.com/question/29286039?referrer=searchResults

#SPJ1

The square root of 6^2 (√6²) is 6.

What is square root?

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.

Suppose x is the square root of y, then it is represented as x=√y, or we can express the same equation as x^2 = y. Here, ‘√’ is the radical symbol used to represent the root of numbers. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.

For example, the square of 3 is 9, 32 = 9 and the square root of 9, √9 = 3. Since 9 is a perfect square, hence it is easy to find the square root. But for an imperfect square like 3, 7, 5, etc., we have to use different methods to find the square root.

Now ,

given expression √6²

=√36

square root value of √6² =6

To know more about square root visit the link

https://brainly.com/question/29286039?referrer=searchResults

#SPJ1

The conditions that are required to validate the use of t for the significance test would be:

D). l and ll only

A response variable, also known as a dependent variable, is a variable that is being studied or measured in an experiment or statistical analysis. It is the outcome or output of the study, and its value is influenced by one or more predictor variables, also known as independent variables.

The goal of a study is often to understand how the response variable is affected by the predictor variables.

For example, in a medical study, the response variable might be the level of a certain protein in the blood, and the predictor variable might be the dosage of a new drug being tested.

In a marketing study, the response variable might be the number of units sold of a product, and the predictor variables might be the price of the product and the advertising budget.

Therefore, The conditions that are required to validate the use of t for the significance test would be:

D). l and ll only

To know more about response variables refer to:

brainly.com/question/14662435

#SPJ4

Answer:

Step-by-step explanation:

5 quart to gallon is 1.25

5 quart to cup is 20

5 Quart to oz is 160

5 Quart to tablespoon is 320

Answer: C

We can only say that X+y=21 is a true statement for any values of X and y that satisfy this equation.

In mathematics, elimination is the process of solving a system of equations by eliminating variables. Elimination involves two steps: first, a variable is chosen to be eliminated and then the coefficients of the variable are used to modify the remaining equations so that they contain only the other variables.

To solve for the unknown variables, we can use the following methods:

Graphing: We can graph the equation on a coordinate plane by plotting the line of the equation. The point of intersection of the line with the x and y-axis represents the solution of the system of equations.

Substitution: We can solve for one variable in terms of the other by isolating one variable and substituting it into the other equation.

Elimination: We can eliminate one variable by adding or subtracting the equations to eliminate one of the variables.

In this case, we don't have any other equation to solve the system, so we can not find a unique solution, we can only say that X+y=21 is a true statement for any values of X and y that satisfy this equation.

To know more about Elimination visit:

https://brainly.com/question/13885360

#SPJ1

Answer:

yes u would be on track.

Step-by-step explanation:

yes; 10 miles in 12 days is equivalent to 10 ÷ 2 = 5 miles in 12 ÷ 2 = 6 days.

:o)

The required number of pieces cut from 22 metal rods each 21 in are 242 pieces.

A mixed fraction is one that is represented by both its quotient and remainder. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

We have,

1(4/5) = 9/5 ,

So,

21/9/5

105/9

11(6/9)

Now,the waste is 6/9

Number of pieces are 11(22)

= 242 pieces

Thus, required number of pieces are 242.

To know more about Mixed fraction visit:

brainly.com/question/29264210

#SPJ1

Jennifier was paid $1.49 for each shirt, $4.99 for each pair of slacks and $7.99 for each sports coat.

Two or more expressions with an Equal sign is called as Equation.

Let x = shirts, y = slacks, z = sports coats.

Set up your systems of equations equations.

3x+2y=$14.45..(1)

6x+2y+z=$26.91...(2)

4x+2z=$21.94...(3)

From equation 2

$14.45+3x+z=$26.91

3x+z=12.46...(4)

Multiply equation 4 with 2

6x+2z=24.92..(5)

6x+2z-4x-2z=24.92-21.94

2x=2.98

Divide both sides by 2

x=$1.49

Now plug in x value in equation 1.

3(1.49)+2y=$14.45

4.47+2y=14.45

2y=9.98

Divide both sides by 2

y=$4.99

4x+2z=$21.94

4(1.49)+2z=21.94

5.96+2z=21.94

2z=21.94-5.96

2z=15.98

Divide both sides by 2

z=$7.99

Hence, Jennifier was paid $1.49 for each shirt, $4.99 for each pair of slacks and $7.99 for each sports coat.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The degree measure of the smaller angle formed by the hands of a clock at 10 O'clock is 60°.

The degree measure of a full circle is 360 degrees. The clock face is divided into 12 equal parts, or 30-degree increments, for the hours. At 10 o'clock, the hour hand would point to the 10 on the clock face, and the minute hand would point to the 12.

This makes them 1/6th of a circle apart, and (1/6) * 360° = 60°.

The angle between the two hands would be formed by the distance between the 10 and the 12, which is 60 degrees.

Read more about Clock:

brainly.com/question/82007

#SPJ4

Total 18 different paths are there from a to b that go through the point circled in the following lattice

In the given question, we have to find how many different paths are there from a to b that go through the point circled in the following lattice.

The diagram of the lattice is given below:

Therefore, we must first go from A to the encircled point.

We must travel 2 horizontally and 2 vertically to do that.

Now, to get to this point, we have ways = [tex]C_{2}^{4}[/tex] ways

Total ways to go from A to the encircled point = [tex]\frac{4!}{2!(4-2)!}[/tex]

Total ways to go from A to the encircled point = 6 ways

Additionally, we must travel 2 horizontal and 1 vertical units to get from the encircling point to B.

As a result, total ways to go from the encircling point to B = [tex]C^{3}_{1}[/tex]

Total ways to go from the encircling point to B = [tex]\frac{3!}{1!(3-1)!}[/tex]

Total ways to go from the encircling point to B = 3 ways

So, different paths are there from a to b = 6×3

Different paths are there from a to b = 18 ways

To learn more about permutation and combination link is here

brainly.com/question/16837159

#SPJ4

The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

Learn more about inequality on:

brainly.com/question/25275758

#SPJ1

m+n is equal to (x+y+z)^2 + n x, y, and z are real numbers.

First, we can rewrite x+y+z as n(x+y+z)^2.

Then, we can substitute x^2+y^2+z^2 into the equation and solve for m^2. We get m^2 = (x+y+z)^3 - 3xyz, which can be simplified to

m^2 = (x+y+z)(x^2+y^2+z^2-xyz).

We can substitute the original equation back in to get

m^2 = (x+y+z)\frac{m^2}{n}.

Then, we can divide both sides of the equation by (x+y+z) to get m^2 = \frac{m^2}{n}. Finally, we can solve for m+n by multiplying both sides of the equation by n, which gives us m+n = m^2.

Learn more about real numbers here:

https://brainly.com/question/551408

#SPJ4

In the expression n + 23 ,23 is a constant because it contains two part and other part is variable.

The concept that will be used here is algebraic equation, The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables. One example is x3 + 1.

We were given n + 23

n is the dependent variables which changes with the input.

23 is the constant that never changes.

Learn more about expression at:

https://brainly.com/question/723406

#SPJ1

The ratio of rubies to diamonds is given as follows:

4.

The ratio between two amounts is obtained applying proportions, as the ratio between the amounts a and b is given by the division of a by b, as follows:

r = a/b.

The amounts in this problem are given as follows:

The number of rubies is four times the number of diamonds, hence:

x = 4y.

Then the ratio between the number of rubies and the number of diamonds is given as follows:

r = 4y/y

r = 4.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

In JMP, open the data in Fit Model and choose scatterplot, and a residual usually looks like the scatterplot but more extended vertically.

(a): Yes, because there is not much of a trend in the data.

(b): The materials cost is a very small percentage of the average cost. It could be true that items that use fewer materials take more labor hours to make ready for the customer.

(c): chose a correct residual plot

In JMP, in the top red triangle, click on save columns, and then click on Residuals. Then go to the data table in JMP and in Graph, press GRAPH BUILDER... put residuals on y and # of labor hours on x

As the number of labor hours​ increases, the residual values from the regression also tend to​ increase, suggesting that the labor input is a lurking variable.

To know more about the manufacturer of custom metal blanks:

https://brainly.com/question/13012170

#SPJ4

Answer: this is a function since there is only one value of y for every value of

Step-by-step explanation:

The values for x at which f has a relative maximum are -3 and 4.

A relative maximum is a point on a function where the function has the highest value within a certain interval or region. It is a local maximum, meaning that it is the highest value within a certain interval, but it may not be the highest value overall.

For example, a function may have multiple relative maxima but only one global maximum.

It's important to note that a relative maximum is not always an actual maximum, it's only a maximum in a specific interval or region of the function.

It's also important to note that for some functions, there might not be any relative maximum in the interval or domain where the function is defined, and for others, it might have a relative maximum at the endpoint of the interval.

On plotting the zeroes of the f(x) on the number line we observe the value of the derivative of f(x) changes from positive to negative indicating points of relative maximum.

Therefore, The values for x at which f has a relative maximum are -3 and 4.

To know more about relative maximum refer to:

brainly.com/question/12717449

#SPJ4

The family spent $2004 per month on groceries and eating out.

The amount spent in five months is given as follows: $10,020.

The amounts are obtained applying the proportions in the context of this problem.

The monthly budget is given as follows:

$6012.

1/3 of that is spent in groceries and eating out, hence the amount is of:

1/3 x 6012 = $2004.

Hence in five months the amount spent is going to be of:

5 x 2004 = $10,020.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

[tex]x = 2 \: and \\ y = 5[/tex]

Step-by-step explanation:

greetings!!!

look at the attachment above

Hope it helps!!!

Note: The row echelon form of a matrix is a way of putting it in a specific form, in which all the leading entry of a non-zero row is to the right of the leading entry of the row above it, and all the entries below a leading entry are zero. A pivot is the leading entry of a non-zero row. In a matrix in row echelon form, the number of pivots is equal to the rank of the matrix, which is the number of linearly independent rows or columns. A matrix with a pivot in every column is said to be in reduced row echelon form, and it is unique for a given matrix.

A linear transformation is a function that maps a vector from one vector space to another vector space. The matrix associated with this transformation is a way of representing the linear transformation using a matrix. The row echelon form of the matrix is a specific way of arranging the matrix, where all the leading entry of a non-zero row is to the right of the leading entry of the row above it, and all the entries below a leading entry are zero. The properties of the transformation can be determined by analyzing the row echelon form of the matrix.

For example, if the row echelon form of the matrix has a pivot in every column, it means that the transformation is one-to-one (meaning that the function assigns a unique output for each input). On the other hand, if the row echelon form of the matrix has a pivot in every row, it means that the transformation is onto(meaning that the function's range is equal to the output vector space). If there are zero rows in the row echelon form of the matrix, it means that the transformation is not one-to-one.

Learn more Linear Transformation Matrix Properties here:

https://brainly.com/question/14351384

#SPJ4

Answer: If Hue can form 2 rows of a given length with 3 chairs left over, we can represent this as:

2x + 3 = chairs in that row length

Also, if she can form 8 rows of that same length if she gets 15 more chairs, we can represent this as:

8x + 15 = chairs in that row length

Since the number of chairs in that row length is the same in both equations, we can set them equal to each other:

2x + 3 = 8x + 15

To solve for x, we can subtract 3 from both sides:

2x = 8x + 12

Then we can subtract 2x from both sides:

6x = 12

Finally, we can divide both sides by 6:

x = 2

So the number of chairs in that row length is 2x + 3 = 2(2) + 3 = 7.

Step-by-step explanation: