How hard is pure maths?

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

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:

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

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:

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

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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The statement is true that is root 2 over 2 is equal to 1 over root 2 is true we can write as √2/2=1/√2.

Given that,

We have to find is root 2 over 2 is equal to 1 over root 2.

We know that,

A number can be squared, but it can also be divided into its square root. The value we get from multiplying a number by itself yields its square value, whereas the value we get from finding a number that, when squared, yields the original value of the number yields its square root value.

Now,

Root 2 over 2 is equal to 1 over root 2 can write as

√2/2=1/√2

Taking multiplying √2 on both side.

√2/2×√2=1/√2×√2

(√2×√2)/2=(1×√2)/√2

2/2=√2/√2

1=1

Therefore, The statement is true that is root 2 over 2 is equal to 1 over root 2 is true we can write as √2/2=1/√2.

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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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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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Epidemiological process is used to determine the who had contacted with the measles and to identify those with immunity and assesses the probability of containing the measles .

The term "Epidemiology" is the study of the determinants, occurrence, and distribution of health and disease in a defined population. Infection is the replication of organisms in host tissue, which may cause disease. A carrier is an individual with no overt disease who harbors infectious organisms. Dissemination is the spread of the organism in the environment. Epidemiology process utilizes an organized approach to problem solving by:

(1) confirming the existence of an epidemic and verifying the diagnosis.

(2) developing a case definition and collating data on cases.

(3) analyzing data by time, place, and person.

(4) developing a hypothesis.

(5) conducting further studies if necessary.

(6) developing and implementing control and prevention measures.

(7) preparing and distributing a public report.

(8) evaluating control and preventive measures.

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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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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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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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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].

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

Answer:

Bonjour

h(x) = x² - 6x + 5 définie sur [0 ; 5 ]

1)

L' oiseau a commencé son vol à

h(0) =(0)² - 6(0) + 5 = 5 donc 5 mètres

3)

h(x) atteint son maximum pour x = -b/2a = 6 / 2 = 3

h(3) = 9 - 18 + 5 = -4 mètres

4)

(x-1)(x-5) = x² - 5x - x + 5 = h(x) ce qu'il fallait démontrer

5)

h(x) = 0 revient à

(x-1)(x-5) = 0 pour x = 1 et pour x = 5

L' oiseau est entré dans l'eau à 1 mètre et en est ressorti à 5 mètres

Bonne fin de journée

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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The required average of Will's bowling average after 8 games is 126.

Given the information, Willis’s bowling average after 5 games was 120. In his next 3 games, Willis scored 118,124, and 142.

The average of the values is the ratio of the total sum of values to the number of values.

here,
An average of 8 games is given as,
As an average of 5 games is 120, taking this average as 1 term
Now,
Average = 120 + 118 + 124 + 142 / 4 = 504 / 4
Average = 126

Thus, Will's required bowling average after eight games is 126.

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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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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:

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

The distance between Katie and Helicopter will be 5.774 miles approximately.

We will solve this problem with the help of Trignometry. So, what is Trignometry?

A branch of mathematics called trigonometry examines correlations between triangles' side lengths and angles. Three crucial trigonometric functions—sine, cosine, and tangent—are represented by the abbreviations sin, cos, and tan.

In this problem, it is given that Katie is watching a helicopter flying at an altitude of 5 miles and the angle of elevation is π/3.

From Sin Cos Tan, you know that:

Sin = opposite/Hypotenuse

sin(π/3) = (5 miles)/Hypotenuse

Hypotenuse = (5 miles) / Sin(π/3) = 5/ ([tex]\sqrt[]{3}[/tex]/2) miles = 5.774 miles.

So, the distance between Katie to the Helicopter is about 5.774 miles.

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In this problem, it is given that Katie is watching a helicopter flying at an altitude of 5 miles and the angle of elevation is π/3.

From Sin Cos Tan, you know that:

Sin = opposite/Hypotenuse

sin(π/3) = (5 miles)/Hypotenuse

Hypotenuse = (5 miles) / Sin(π/3) = 5/ (/2) miles = 5.774 miles.

So, the distance between Katie to the Helicopter is about 5.774 miles.

The equilateral triangle theorem states that in an equilateral triangle, all sides are equal in length and all angles are equal in measure (60 degrees).

The equilateral triangle theorem states that in an equilateral triangle, all sides are equal in length and all angles are equal in measure (60 degrees).

To prove this theorem, we can use the following steps:

1. Draw an equilateral triangle and label the sides as a, b, and c.

2. Use the definition of an equilateral triangle to state that all sides are equal in length, which means a = b = c.

3. Use the definition of an equilateral triangle to state that all angles are equal in measure, which means all angles are equal to 60 degrees.

4. Use the properties of a triangle to show that the sum of the interior angles of a triangle is 180 degrees.

5. Substitute the values for the sides and angles of the equilateral triangle into the formula for the sum of the interior angles of a triangle:

a + b + c = 180 degrees.

6. Simplify the equation by substituting the equal values of a, b, and c:

3a = 180 degrees.

7. Divide both sides of the equation by 3 to find the value of a:

a = 60 degrees.

8. Since a represents the measure of each angle in the equilateral triangle, this proves that the measure of each angle in an equilateral triangle is 60 degrees.

This proof demonstrates that the equilateral triangle theorem is true for all equilateral triangles.

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Answer:

Your answer is B

Step-by-step explanation:

Answer in image.

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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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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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?

The binomial factors of x²-16 is (x+4) and (x-4).

Binomial refers to an algebraic expression that only has two terms. A polynomial with two terms, it. It is referred to as a sum or difference between two or more monomials as well. It is a polynomial's most straightforward form.

Having two terms makes a polynomial a binomial. Binomials include, for instance, x 2 x -2 x2 and x 6 x -6 x6. This article will go over multiplying these binomials.

An integer that may be derived by evaluating a homogeneous polynomial with two terms is known as a binomial number in mathematics, more specifically in number theory.

Here, x²-16=0

Rewrite 16 as 42, and the expression will be equal to 0 if any of the factors on the left side of the equation are equal to 0.

x+4=0 and locate x.

Once x=-4 x-4=0 and x=4 are found.

As a result, the final solution is x = 4, 4 and all choices that lead to (x + 4) (x 4) = 0 are true.

Hence, The binomial factors of x²-16 is (x+4) and (x-4).

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