Situation:
Find the age of the spear head to the nearest
year.
An archaelogist in Turkey discovers a
spear head that contains 32% of its
original amount of C-14.
Enter the correct answer.
DONE
N = Noekt
No - inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years

According to the calculation used to compute it, [tex]3\frac{1}{3}[/tex] liters of water are required to water all the indoor plants.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. An expression in mathematics is a combination of digits and operations. A mathematical expression that performs an operation has the following components: Operations and Operands

The amount of water needed to water all the indoor plants is 1/3 liter, according to the calculation used to determine this.

[tex]= 4/3 / 2/5\\ = 4/3 X 5/2\\ = 3\frac{1}{3}[/tex]

Consequently, 3 1/3 liters are needed.

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The x-coordinate of the solution to this system of equations is x = -6.

The x-coordinate of the solution to the following system of equations can be determined by solving the system of equations using the substitution method. The substitution method involves replacing the value of one of the variables with the other. This can be done by solving one of the equations for one of the variables and then substituting it into the other equation.  

In this case, we will solve the first equation for y:

2x = -4y

y = -2x

Substituting this expression for y into the second equation, we get:

5x - 6(-2x) = -6

5x + 12x = -6

17x = -6

x = -6/17

Therefore, the x-coordinate of the solution to this system of equations is x = -6.

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No, your cousin is not correct. 5,953 should be rounded up to 6,000 when rounded to the nearest hundred.

When you round a number to the nearest hundred, you look at the tens place to determine which hundred to round to. In this case, the tens place is 9, which means that 5,953 should be rounded up to 6,000 when rounded to the nearest hundred.

To round to the nearest hundred, you can follow these steps:

Look at the tens place (the digit in the ones place).

If the tens place is 0, 1, 2, 3, or 4, round down.

If the tens place is 5, 6, 7, 8, or 9, round up.

For example, if you want to round 4,567 to the nearest hundred, you would look at the tens place, which is 6. Since the tens place is greater than 5, you would round up to 4,600. Similarly, if you want to round 5,432 to the nearest hundred, you would look at the tens place, which is 3. Since the tens place is less than 5, you would round down to 5,400.

∴5,953 should be rounded up to 6,000 when rounded to the nearest hundred.

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To round to the nearest hundred, you can follow these steps:

Look at the tens place (the digit in the ones place).

If the tens place is 0, 1, 2, 3, or 4, round down.

If the tens place is 5, 6, 7, 8, or 9, round up.

For example, if you want to round 4,567 to the nearest hundred, you would look at the tens place, which is 6. Since the tens place is greater than 5, you would round up to 4,600. Similarly, if you want to round 5,432 to the nearest hundred, you would look at the tens place, which is 3. Since the tens place is less than 5, you would round down to 5,400.

5,953 should be rounded up to 6,000 when rounded to the nearest hundred.

Answer:

3x + 2y = 6

Step-by-step explanation:

When you solve for y in this equation, it is in the same format as the slope-intercept equation.

3x + 2y = 6

2y = -3x + 6

y = -3/2 x + 3  

The slope intercept equation is ...

y = mx + b

(m can be any number)

The slope-intercept equation is for linear functions!

Answer:

2[tex]\sqrt{10}[/tex]

Step-by-step explanation:

[tex]\sqrt{5}[/tex] * [tex]\sqrt{8}[/tex] =

[tex]\sqrt{5*8}[/tex] =

[tex]\sqrt{40}[/tex] =

[tex]\sqrt{4*10}[/tex] =  ==> 4 has a square root: [tex]\sqrt{4}[/tex] = 2

2 * [tex]\sqrt{10}[/tex] = 2[tex]\sqrt{10}[/tex].

The closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number.

What is Property of Closure ?

A set has the closure property only under a particular operation which is if the result of the operation is always an element in the set.  When a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”

a)The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.

b) The set of integers is not closed under the operation of division because when you divide one integer by another, you don’t always get another integer as the answer.  For example, 4 and 9 are both integers, but 4 ÷ 9 = 4/9.  4/9 is not an integer, so it is not in the set of integers!

Hence , the closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number.

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Answer:

x = 90 degree

y = 43 degree

Step-by-step explanation:

x is at the right angle, so it must be 90 degrees.

A triangle has a total of 180 degrees.

We know two angles, one is 90 degrees and one is 47 degrees

90 + 47 = 137 degrees

180 - 137 = 43 degrees

So, y = 43 degrees

Answer:

Your answer is B

Step-by-step explanation:

Answer in image.

The level of a line's slope indicates its steepness, for the line y = 3x + 1 the graph is looks like:

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

Now, given that,  

Y = 3x + 1 ........ (1)

slope intercept form equation is: y = mx+c ........... (2)

next, if we compare (1) and (2)

it comes out to be

m = 3 representing slope

and c = 1 representing y-intercept.

now, slope angle: tan θ = m (slope)

tan θ = 3              [putting the value of m]

θ = [tex]tan^{-1/3}[/tex]

The graph is shown as:

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The complete question is as follows:

What does y = 3x + 1 look like on a graph?

Answer:

Option C

1 and 5

Step-by-step explanation:

So,

as you can see here,

are the vertical angles.

Constant, variable, operator and terms are four types of expression.

A constant term in mathematics is a term in an algebraic expression whose value is fixed or cannot change since it lacks any variables that may be changed. As the component is not yet included in the new term, a constant term that has a constant applied as a multiplicative coefficient likewise indicates a constant term. The term identify themselves as constants because the phrase has been modified. 5 is a constant term, in the quadratic polynomial 2x^2 + 5.

Is -4 a constant?

Yes, negative sign have nothing to do with the definition of constant. -4 is still a constant.

There are four types of expression in mathematics:

1. Constant: any numeric value e.g. 6

2. Variable: any alphabetic/unknow value e.g. x,y etc.

3. Operators: +,-, *, / (addition, subtraction, division, multiplication)

4. Term: it can be constant, variable, constant multiplied by variable. It is separated by an operator.

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The number of students that failed the examination in the class is 64

information from the problem

there are 160 students in a class

60% of students passed in examination

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

if 60% of the students passed the examination then the percentage that failed is solved by subtraction from 100. This is done by

= 100 - 60

= 40%

The number of failed students is solved by converting the 40% to a factor by diving by 100 such that 40% = 40 / 100 = 0.04

= 0.4 * 160

= 64

The total number of failed students is 64

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The chi-squared statistic can be used to determine whether there is a significant association between the two variables.

What is chi-squared statistic?

When the sample sizes are large, a chi-squared test is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine whether two category factors have independent effects on the test statistic.

To test whether people who kiss more than ten times a day wear brighter colors to work than those who do not, the appropriate test statistic to use would be the chi-squared statistic.

The chi-squared statistic is a measure of the difference between observed and expected frequencies in a contingency table.

Once we have the contingency table, we can calculate the chi-squared statistic using the following formula:

     [tex]chi-squared = ((observed - expected)^2 / expected)[/tex]

In this case, the null hypothesis is that there is no association between kissing more than ten times a day and wearing bright colors to work. To calculate the expected frequency of each cell, we need to use the formula:

    expected = (row total * column total) / sample size)

Plugging in the values from our contingency table, we can calculate the chi-squared statistic as follows:

     [tex]chi-squared = (10 - 15)^2 / 15 + (20 - 15)^2 / 15\\\\= 25 / 15 + 25 / 15\\\\= 2[/tex]

The chi-squared statistic can be used to determine whether there is a significant association between the two variables.

Refer following diagram.

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The two formulas for area of a triangle of sides a, b, c and height h for base b are

A = √(s×(s - a)×(s - b)×(s - c)) and

A = 1/2 × b × h

By Heron's formula area of a triangle of sides a, b, c and perimeter s = (a + b + c), the area of the triangle is

A = √(s×(s - a)×(s - b)×(s - c))

Also we know area of a triangle of base b and height h is given by the formula

A = 1/2 × b × h

So there are the two formulas for area of a triangle.

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

"What are the 2 formulas for area of triangle?"

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A vertical straight line is not a function. It is a relation, but not a function as it does not follow the condition to be a function.

A condition for a function is that a unique input gives a unique output, that is a unique output can trace back to only one unique input.

In the case of a vertical straight line, it is of the form x = a, where a is a constant. That is for x = a, there is infinitely many values for y, therefore it does not follow the condition of a function and hence a vertical straight line is not a function.

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Step-by-step explanation:

that means we need to transform the equation, so that it is in the form of

b = ...

b - c + d/8 = a | add c to both sides

b + d/8 = a + c | subtract d/8 from both sides

b = a + c - d/8

that's it.

Answer:

-2

Step-by-step explanation:

plug both equations in desmos graphing calculator website

and you can see that the solution (where both equations intersect)

is (-2,6)

solutions are (x,y)

so the x coordinate of the solution is -2

The roots of the quadratic equation 3x² - 10x + 8 = 0 are x = 4/3  and x = 2  .

The Roots of the quadratic equation are defined as the numerical values that satisfy the equation .

The quadratic equations is 3x² - 10x + 8 = 0  ;

⇒ 3x² - 6x -4x + 8 = 0   ...by using split the middle term method ;

⇒ 3x(x - 2) -4(x - 2) [tex]=[/tex] 0

⇒ (3x-4)(x-2) = 0 ;

⇒ 3x - 4 = 0   and   x - 2 = 0 ;

On solving further , we get

x = 4/3 and x = 2  .

Therefore , the required roots are 4/3 and 2 .

The given question is incomplete , the complete question is

What is the roots of the quadratic equation 3x² - 10x + 8 = 0 ?

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Equation of the line that passes through (2, 0) and is parallel and perpendicular to the line shown is y = - x + 5

What is perpendicular?

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular symbol,, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x - 3 ← is in slope intercept form

with slope m = 1

Given a line with slope m then the slope of a line perpendicular to it is

= -  = -  = - 1, thus

y = - x + c ← is the partial equation of line j

To find c substitute (2, 0) into the partial equation

0 = - 2 + c ⇒ c = 0 + 2 = 2

y = - x + 2 ← equation of line j

Parallel lines have equal slopes, thus

y = - x + c ← is the partial equation of line k

To find c substitute (- 1, 6) into the partial equation

6 = 1 + c ⇒ c = 6 - 1 = 5

y = - x + 5 ← equation of line k

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1. 4y

2. 2b

3. 3r

4. -1c

5. 5/3d+3b

6. 3x+2y^3 -4y

7. -2x+3y

8. 1/3

9. 27

10. 4

11. 12

To achieve the goal you have to make the annual sales of home entertainment equipment $3. 45 million

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

The annual sales of home entertainment equipment in your area are $23 million.

You want to capture 15% of the market.

let x be the $x million sales to capture 15% of the market.

So,

$23 million  ----- 100%

$x million  ------- 15%

by doing cross multiplication we get,

x = (23 * 15) /100

x =  $3. 45 million

hence, to achieve the goal you have to make the annual sales of home entertainment equipment $3. 45 million.

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Answer:

2.) the answer is D, because 12 hours is the closest number between 10 and 15

Following are the steps to solve multi-step equations:

1. Paraphrase

2. Constituents

3. Division and/or addition

4. Subtraction and addition

Therefore,

Following are the steps to solve multi-step equations:

1. Paraphrase

2. Constituents

3. Division and/or addition

4. Subtraction and addition

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To find the slope from a table, you need to find the difference in the y-values (the dependent variable) between two points and divide it by the difference in the x-values (the independent variable) between those same two points.

This is known as the slope formula:

Here is an example of finding the slope from a table:

Suppose we have the following table:

x y

3 7

4 9

To find the slope between these two points, we can use the slope formula as follows:

slope = (9 - 7)/(4 - 3) = 2/1 = 2

So the slope between these two points is 2.

It's important to note that the slope is a measure of the slope of the line that passes through the two points. If you want to find the slope of the line that is the best fit for a larger set of data, you will need to use a different method, such as linear regression.

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Domain is the input of a function and range is the output of a function, for f(x) = sin(x), domain will be (-inf, +inf) and range will be [0,1].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

Domain is the input of a function and range is the output of a function.

Examples:

f(x) = sin(x), domain =  (-inf, +inf) and range = [0,1].

f(x) = cos(x), domain =  (-inf, +inf) and range = [0,1].

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Answer:

x=5/6

Step-by-step explanation:

5/6+1/6=1

Answer: x= 5/6

Step-by-step explanation:

x + 1/6 = 1

Change 1 to an improper fraction = 6/6

x + 1/6 = 6/6

1/6 - 1/6 = 0

6/6 - 1/6 =5/6

 x = 5/6

Answer:

Step-by-step explanation:

HE SPENDS 1/3 on food and saves.

Answer: He spends more on food

Step-by-step explanation:

First you have to make the denominator in each fraction equivalent

3/4 to 1/8      so you have to multiply 4 by 2 to get eight so you do the same to the numerator 3x2=6 so 6/8>1/8

The roots of the quadratic equation 2x² + 5√3x - 6 = 0 are imaginary.

To solve this equation, we can use the Quadratic Formula. The Quadratic Formula is:

x = [ -b ± Â√(b2 - 4ac) ] / 2a

In this equation, a = 2, b = 5√3, and c = -6.

Plugging these values into the formula, we get:

x = [ -(5√3) ± Â√((5√3)2 - 4(2)(-6)) ] / (2(2))

Simplifying, we get:

x = [ -(5√3) ± Â√(25*3 + 24) ] / 4

Simplifying further, we get:

x = [ -(5√3) ± Â√(75) ] / 4

Since √75 is an irrational number, the roots of the equation are imaginary.

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14-bit strings that contain exactly six 1's is 3003. the number of 14-bit strings that contain at least eleven 1's is 16384 - 16382 = 2. The number of 14-bit strings that contain at least one 1 is equal to the total number of 14-bit strings minus the number of 14-bit.

The number of 14-bit strings that contain exactly six 1's is equal to the number of ways to choose the positions for the 1's in the string. There are 14 positions in the string, and we need to choose 6 of them to be occupied by 1's. This can be done in 14 choose 6 ways, which is equal to 3003. The number of 14-bit strings that contain at least eleven 1's is equal to the total number of 14-bit strings minus the number of 14-bit strings that contain ten 1's or fewer. The total number of 14-bit strings is 2^14 = 16384, and the number of 14-bit strings that contain ten 1's or fewer is equal to the sum of the number of 14-bit strings that contain 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 1's. This sum is equal to 14 choose 0 + 14 choose 1 + 14 choose 2 + ... + 14 choose 10 = 1 + 14 + 91 + 364 + 1001 + 2002 + 3003 + 3432 + 3003 + 2002 + 1001 + 364 + 91 + 14 + 1 = 16382. Therefore, the number of 14-bit strings that contain at least eleven 1's is 16384 - 16382 = 2. The number of 14-bit strings that contain at least one 1 is equal to the total number of 14-bit strings minus the number of 14-bit

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As per the given 4 x 5 matrix, the reduced row echelon form of A is [tex]\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right][/tex]

The term matrix in math refers a set of numbers arranged in rows and columns so as to form a rectangular array.

Here we have the 4 x 5 matrix.

And here we also know that a1,a2,a4 are linearly independent and the value of a3=a1+2a² and a5=2a1-a²+3a⁴.

Now, we have to apply the value of

a1 = 1, a2 = 0, a3 = 0, a4 = 0, a5 = 1, a6 = 0, a7 = 0, a8 = 0, and a9 = 1.

Then we get the matrix of 3 x 3 looks like the following,

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

Now, we have to do the following steps in order to get the reduced row echelon form of A,

The first and foremost steps is to take the non-zero number in the first row is the number 1.

Then we have to place any non-zero rows are placed at the bottom of the matrix.

This steps are repeated until the final row becomes zero.

Then we get the resulting matrix as [tex]\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right][/tex]

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