**Answer:**

most likely the last choice

**Step-by-step explanation:**

Answer: during evaporation

Step-by-step explanation: the sun heats up the water which caused it to evaporate

x557x55 is divisible by 11. find the value of x

**Step-by-step explanation:**

A number is divisible by 11 if and only if the difference between sum of alternate digits is divisible by 11.

Here the number is x557x55. The difference between the sum of alternate digits is,

[tex]\longrightarrow S=(x+5+x+5)-(5+7+5)[/tex]

[tex]\longrightarrow S=2x-7[/tex]

By statement, the number x557x55 is divisible by 11 if and only if [tex]S=2x-7[/tex] is divisible by 11.

Let,

[tex]\longrightarrow 2x-7=11a[/tex]

[tex]\longrightarrow 2x=11a+7\quad\dots(1)[/tex]

We separate the RHS as the following.

[tex]\longrightarrow 2x=10a+a+6+1[/tex]

[tex]\longrightarrow 2x=10a+6+a+1[/tex]

[tex]\longrightarrow 2x=2(5a+3)+(a+1)[/tex]

In this question, the LHS is an even integer since x is a digit, i.e., integer. So RHS should also be an even integer.

Since [tex]2(5a+3)[/tex] is even, [tex]a+1[/tex] must be even. So let,

[tex]\longrightarrow a+1=2k[/tex]

[tex]\longrightarrow a=2k-1[/tex]

Then (1) becomes,

[tex]\longrightarrow 2x=11(2k-1)+7[/tex]

[tex]\longrightarrow 2x=22k-4[/tex]

[tex]\longrightarrow x=11k-2\quad\dots(2)[/tex]

So this is expression for x, for any integer k.

As x is a digit of x557x55, x is a single digit integer, so its value lies in between 1 and 9 [x ≠ 0 because it is also the left most digit of x557x55], i.e.,

[tex]\longrightarrow 1\leq x\leq 9[/tex]

From (2),

[tex]\longrightarrow 1\leq 11k-2\leq 9[/tex]

Adding 2,

[tex]\longrightarrow 3\leq 11k\leq 11[/tex]

Dividing by 11,

[tex]\longrightarrow\dfrac{3}{11}\leq k\leq 1[/tex]

Since k is an integer, we get,

[tex]\longrightarrow k=1[/tex]

Then from (2),

[tex]\longrightarrow x=11(1)-2[/tex]

[tex]\longrightarrow\underline{\underline{x=9}}[/tex]

Hence the value of x is 9.

Is 1 the biggest prime number?

A prime number is a **positive **integer greater than 1 that has no positive integer divisors other than 1 and itself, so 1 is not consider as a prime number.

Therefor 1 is not the biggest prime number.

What is a prime number?A **whole number** higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

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Question In picture

this was an accident how do I delete?

Hi! i need some help:)

**Answer:**

y=1/2x+-2

**Step-by-step explanation:**

What is the mean of 4 6 8 10 12 14 *?

The **mean **of the given observation is 9.

**What are the mean, median, and example?**

The ratio between the total number of observations in a data set and the sum of all observations is known as the mean in statistics. The most frequent number, or the one that happens the most frequently, is known as **the mode.**

Example: Since the number 2 appears three times, more than any other number, it is the mode of** the numbers **4, 2, 4, 3, and 2.

Mean = Sum of all the observations/Number of observations

Mean = 4+6+8+10+12+14/6

Mean = 54/6

Mean = 9

Hence, the mean of the given observation is 9.

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Duncan works at a banquet hall and is setting tables for a wedding reception. He starts with a pile of 144 salad plates, and he places 10 salad plates on every table he sets. Write an equation that shows how the number of salad plates remaining, y, depends on the number of tables Duncan sets, x.

The equation that shows the **number of plates** that is remaining would be = **Y = (Total salad plate/X) - 4.**

A **banquet hall** is a building constructed is a way that various celebrations and functions can be held in such a place such as wedding receptions.

The total number of salad plates available = 144

The number of salad plate per every table set = 10

The number of salad plates remaining = y

The number of tables set by **Duncan** = x.

If 1 table = 10

X tables = 144

make X tables the subject of formula;

X tables = 144/10

X tables = **14 ****tables **(approximately)

But 14 × 10 = 140 salad for the 14 tables

The remaining salad plates is 4 plates.

**Y = (Total salad plate/X) - 4**

Therefore, the number of **salad plates remaining** which is 4 depends on the number of **tables Duncan sets** which is 10.

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What is the correct answer to 2 5 * 4 8 4 ⁄ 5?

The correct answer to the **expression** is 10.

By using BODMAS rule,

BODMAS stands for Brackets, Orders, **Division**, Multiplication, Addition, and Subtraction in its entire form. Therefore, in BODMAS, the orders or exponents are given the second choice here (x n ) A method or sequence called the **BODMAS** rule is used in mathematics to simplify arithmetic expressions with many operators. When there are several operators in an **equation**, we must first determine the correct sequence in which to solve the equation. The BODMAS rule assists in the **solution **of this issue.

Given **expression**,

2+5*4-8/⅘

=2+20- 40/4

= 22-10

= 10

Hence, the correct answer to the **expression** is 10.

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Which of the following is quadratic equation 3x2 5x 9 x2 7x 3?

Yes, the given equation is **quadratic equation**.

Here it has been given that,

3x² - 5x + 9 = x² - 7x + 3

Now, after solving above **equation** further we obtain,

2x² + 2x + 6 = 0

From the above equation the **factor **2 is taken out as it is common and now the equation looks like : x² + x + 3 = 0

The coefficients of the quadratic equation are compared and if it meets the criteria then it is quadratic equation otherwise not.

Now as we can see, the above equation clearly** represents** a quadratic equation of the** form** ax² + bx + c = 0, where a = 1, b = 1 and c = 3.

Hence, the above given equation is a** **algebraic **quadratic equation**.

Which of the following is quadratic equation 3x² - 5x + 9 = x² - 7x + 3 ?

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SV≅SW, WX≅UV, RX≅TU, and RS≅ST. Complete the proof that △RVX≅△TWU.

The **reasons** and **statements** that completes the **two-column** table method used to prove that triangle ΔRVX is congruent to ΔTWU (ΔRVX ≅ ΔTWU) are as follows;

Statement [tex]{}[/tex] Reason

12. UW = VX [tex]{}[/tex] Transitive Property of Equality

13. ΔRVX ≅ ΔTWU [tex]{}[/tex] SSS

What are congruent triangles?Two **triangles** are **congruent** if the **lengths** of the three sides of one triangle are the same as the lengths of the **three** **sides** of the other triangle.

The details and reasons for the statements used to prove the congruency of the ΔRVX and ΔTWU are as follows;

RV = RS + SV; Additive property of length

The **additive property** of **length** states that a point *B* can be located on a segment AC only if, we get; AC = AB + BC

RV = ST + SW Substitution

The **substitution** property states that if *a* = *b* then *a* can substitute *b* in equations and **expressions**, such that the values of the expressions and **equations** remain the same.

RV = TW Transitive Property of Equality

The **transitive **property of equality states that if *a *= *b* and *b* = *c*, then *a* = c

ΔRVX ≅ ΔTWU SSS

The **SSS** (**Side**-**Side**-**Side**) congruency postulate states that two triangles are **congruent** if the lengths of all three sides of one triangle are congruent to the lengths of the sides of the other triangle.

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Is 0 and 1 are prime?

A prime number is a **positive **integer greater than 1 that has no positive integer divisors other than 1 and itself. 0 is not a positive integer and 1 is not greater than 1, so they are not considered a prime number.

A **whole number** higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

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Marvin is playing a solitaire game with marbles. There are n bowls (for some positive integer n), and initially each bowl contains one marble. Each turn, Marvin may eitherremove a marble from a bowl, orchoose a bowl A with at least one marble and a different bowl B with at least as many marbles as bowl A, and move one marble from bowl A to bowl B.The game ends when there are no marbles left, but Marvin wants to make it last as long as possible.Prove that the game must end after at most n(n+1)/2 turns.Prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns.Marisa comes along and asks to join the game. Marvin and Marisa revise the rules: they will alternate taking turns, starting with Marisa. When the game ends, whoever took the last turn is the winner.Prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.

Among any three **consecutive** values of n, there is at least one value for which Marvin has a winning **strategy**.

For the first part of the problem, we can prove that the game must end after at most n(n+1)/2 turns by** induction**. Base case: When there is only one bowl, Marvin can remove the single marble in one turn, so the game ends after one turn.

Inductive step: Suppose the game ends after at most k(k+1)/2 turns when there are k bowls. We will show that the game ends after at most (k+1)(k+2)/2 turns when there are k+1 bowls. If Marvin removes a marble from a bowl, then the number of bowls decreases by one and the game must end after at most k(k+1)/2 turns by the inductive **hypothesis**.

If Marvin moves a marble from bowl A to bowl B, where bowl A has at least one marble and bowl B has at least as many marbles as bowl A, then the number of marbles in bowl A decreases by one and the number of marbles in bowl B increases by one. Since bowl B has at least as many marbles as bowl A, the number of bowls remains unchanged. Thus, the game must still end after at most k(k+1)/2 turns.

In either case, the game ends after at most k(k+1)/2 turns, so the game must end after at most (k+1)(k+2)/2 turns when there are k+1 bowls, as desired.

For the second part of the problem, we can prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns by constructing a strategy.

Suppose Marvin wants to make the n-bowl game last for at least kn turns. He can do this by making sure that there are always at least k marbles in each bowl. To do this, Marvin can start by placing k marbles in the first bowl, k-1 marbles in the second bowl, and so on, down to 1 marble in the nth bowl.

On each turn, Marvin can choose a bowl with at least k marbles and move one marble to a bowl with fewer than k marbles. For example, if there are k+1 marbles in the first bowl and k marbles in the second bowl, Marvin can move one marble from the first bowl to the second bowl. This keeps the number of **marbles** in each bowl at least k. Since Marvin can take at least one turn per bowl, the game will last for at least kn turns.

For the third part of the problem, we can prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.

Let n be a positive integer. We will show that either Marvin has a winning strategy for the n-bowl game or Marisa has a winning strategy for the (n+1)-bowl game.

If Marvin has a winning strategy for the n-bowl game, then he can win the n-bowl game by following his winning strategy.

If Marvin does not have a **winning** strategy for the n-bowl game, then Marisa has a winning strategy for the n-bowl game. In this case, Marvin can adopt Marisa's winning strategy for the n-bowl game as his own winning strategy for the (n+1)-bowl game.

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a 17-tooth spur pinion has a diametral pitch of 8 teeth/in, runs at 1150 rev/min, and drives a gear at a speed of 575 rev/min. find the number of teeth on the gear and the theoretical center-to-center distance.

No. of teeth on the pinion(TP)=17.

Diametral pitch(pd)=8 teeth/in.

**Rotational speed** of the pinion(NP)=1120 rev/min or 1120 rpm.

Rotational speed of the gear(NG)=544 rev/min or **544 rpm.**

To calculate:

No. of teeth on gear(TG) & theoretical centre to centre distance(C).

Solution:

We know that;

**Diametral pitch**(pd)=No. of teeth in the gear/Diameter of the gear

For pinion,

pd=TP/DP

Pittiong the values in above eq.

8 teeth/in =17/DP =>DP=17/8 in.

or DP=2.125 in.

Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)

=>(NP/NG)=(TG/TP)

=>1120/544 =TG/17 =>TG=35

No. of teeth the gear(TG)=35 {Ans}

Also from gear ratio formula,

(NP/NG)=(DG/DP)

=>1120/544=DG/2.125

=>DG=4.375 in.

In the next fig. I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre to centre distance(C)

centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}

**=>C=(DP+DG)/2 **

Diameter =2*radius}

**=>C=(2.125+4.375)/2 in. =3.25 in.**

Theoretical centre to centre distance** (C)=3.25 in. **

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if Z1=(x1,y1) and Z2=(x2,y2) where Z1 and Z2€C then Z1 + Z2=?

**Answer:**

**Step-by-step explanation:**

If Z1 = (x1, y1) and Z2 = (x2, y2) are complex numbers, then their sum is given by:

Z1 + Z2 = (x1 + x2, y1 + y2)

For example, if Z1 = (3, 4) and Z2 = (-2, 5), then their sum is:

Z1 + Z2 = (3 + (-2), 4 + 5) = (1, 9)

In general, to add two complex numbers, we add their real parts and their imaginary parts separately.

The **value **of [tex]z_1[/tex] + [tex]z_2[/tex] = ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])

**Complex Numbers**. Complex numbers are those that are expressed as a+ib, where a and b are **real **numbers and I is a **imaginary **number called a "iota."

Given:

[tex]Z_1=(x_1,y_1)[/tex] and [tex]Z_2=(x_2,y_2)[/tex]

Also, we know by **Complex number**

[tex]z_1[/tex] = [tex]x_1[/tex] + i [tex]y_1[/tex]

and, [tex]z_2[/tex] = [tex]x_2[/tex] + i [tex]y_2[/tex]

Then, [tex]z_1[/tex] + [tex]z_2[/tex]

= ( [tex]x_1[/tex] + i [tex]y_1[/tex]) + ( [tex]x_2[/tex] + i [tex]y_2[/tex])

= ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])

Hence, the **addition **gives ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex]).

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William is a window washer and needs to lean his ladder against the house to reach the windows at the top. he sets the ladder 8 feet from the house which is 14 feet tall. what is the minimum length ladder he needs to use to reach the top of the house?

a² + b² + c²

**Answer:**

**Step-by-step explanation:**

you will need a 10ft tall ladder

i hope that helped

If this net were to be folded into a cube, which number would be opposite of the number 1

**Answer:**

Number 5

**Step-by-step explanation:**

When the net is folded, 3 will be folded left and up, with 4 being the base. 6 will be folded right, with 2 being the top of the cube.

So, we have pairs

2 and 4

6 and 3

1 and 5

So, the opposite of the number 1 is the number 5

What are the 4 types of translations in math?

The four **fundamental translations **or transformations in geometry are translation, reflection, rotation, dilation, and resizing.

For a **function graph**, four different transformations are feasible (and translation in math is one of them). When we translate, we move a figure in any direction. When we reflect, we turn a figure or a line over. The act of rotating a figure around a point is known as rotation.

In mathematics, a translation merely moves a shape up, down, left, or right without turning it. The image or the translated shapes seem to be the same size as the original shape, proving that they are congruent. Simply said, they have changed their path or directions.

Three types of translation are described in Jakobson's On **Linguistic** Aspects of Translation (1959, 2000): intralingual (inside one language, such as rewording or paraphrasing), interlingual (between two languages), and intersemiotic (between sign systems).

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Michael breeds chickens and ducks. Last month, he sold 505050 chickens and 303030 ducks for \$550$550dollar sign, 550. This month, he sold 444444 chickens and 363636 ducks for \$532$532dollar sign, 532.

The** price **of a **single chicken** is $8 and the **price** of a **single duck **is $5.

The prices can be determined by forming the **linear equation **in two **variables.**

Given that,

Michael sold **last month**, 50 chickens and 30 ducks for $550.

**This month, **he sold 44 chickens and 36 ducks for $532.

Let the **price **of single chicken be 'a' and the price of a single duck be 'b'. Then the **linear equation** will be:

50a+30b=550 ____________(1)

44a+36b=532 ____________(2)

Solving equation (1) for the value of 'b'.

b=550-50a/30

b=55/3 - 5a/3 ____________(3)

Putting the value of 'b' in equation (2).

44a+36(55/3 - 5a/3) = 532

128 = 16a

a=8

Putting the value of a in equation (3).

b= 55/3 - 5*8/3

b=5

Thus, The price of a** single chicken** is $8 and the price of a **single duck** is $5.

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Michael sold last month, 50 chickens and 30 ducks for $550.

This month, he sold 44 chickens and 36 ducks for $532.

50a+30b=550

44a+36b=532

Solving equation (1) for the value of 'b'.

b=550-50a/30

b=55/3 - 5a/3

Putting the value of 'b'

44a+36(55/3 - 5a/3) = 532

128 = 16a

a=8

Putting the value of a

b= 55/3 - 5*8/3

b=5

Thus, The price of a single chicken is $8 and the price of a single duck is $5.

What are the 3 parameters of range function?

Three parameters, start value, stop value, and step value, are required for the range() method in Python to **function**. After incrementing the values by the amount specified in the step value .

The range of values between a given data collection's top and lowest values is known as the **statistical range**. The difference between the highest and lowest observation is another method of expressing the range. By deducting the highest value from the lowest, one may calculate the **sample interval**. A crucial indicator of variability for continuous variables is the sample range.

here

startNumber (optional): The series of integers that are returned begins with this number.

stopNumber: The list of integers that range() provides comes to an end before this one.

stepValue (opportunity): a number that is an integer and represents the difference between each integer in the series.

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How do you find the discontinuity of a hole?

The process of finding the **discontinuity **of a hole is explained below.

The term discontinuity in statistics is defined as a point on the graph that is **undefined **or is unfit for the rest of the graph.

In order to find the discontinuity of the hole we have to perform the following steps,

The first and foremost thing is to factor out the numerator and the **denominator**

Next we have to determine the common factors in the **numerator **and the denominator

After that we have to set the common **factors **equal to zero and find the value of x.

Then the final steps is to plot the **graph **and mark the point with a hole

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What are the zeros of the polynomial 4x 2 }+ 52 âˆš 2x 3 ?`?

The zeros of the **polynomial **are 1/2√2 and -3/√2.

The **zeros **of a polynomial are all the x-values that make the polynomial equal to **zero**.

Given, the **polynomial **is 4x² + 5√2x - 3.

We have to find the **zeros **of the **polynomial**,

Let 4x² + 5√2x - 3 = 0

On factoring,

= 4x² + 6√2x - √2x - 3

= 2√2x(√2x + 3) - (√2x + 3)

= (2√2x - 1)(√2x + 3)

Now, 2√2x - 1 = 0

2√2x = 1

x = 1/2√2

Also, √2x + 3 = 0

√2x = -3

x = -3/√2

Therefore, the zeros of the **polynomial **are 1/2√2 and -3/√2.

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a sampling plan in which an initial sample is selected and the audit team either draws a final conclusion or selects additional items before drawing a final conclusion is called

a** sampling plan** in which an initial sample is selected and the **audit** team either draws a final conclusion or selects additional items before drawing a final conclusion is known as ** Sequential sampling**

Sequential sampling is a non-probability sampling strategy where the **researcher** selects one or more populations within a time frame, conducts his research, evaluates the findings, and then selects further populations as necessary. This** sampling **strategy offers the researcher limitless opportunities to adjust his research procedures and obtain a keen understanding of the** study** he is currently conducting.

Sequential sampling has a number of benefits, including limitless options for sample size selection and sampling schedule, little cost and labor requirements, and the ability to make minor alterations and modifications to the primary research even during the early stages of the project.

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How many numbers between 50 and 100 are divisible by 3?

On solving the provided question, we can say that - If you put all the numbers together by **digits**, the total must be a multiple of three. so answer is 17

The **divisibility rule** is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set **divisor **without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

[tex]51, 54, 57\\60, 63, 66, 69\\72, 75, 78\\81, 84, 87\\90, 93, 96, 99[/tex]

If you put all the numbers together by digits, the total must be a multiple of three. so answer is 17

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(x+y)(x2+xy+y2)

pls solve step by step

**Answer:**

[tex]x {}^{3} + 2x {}^{2} y + 2xy {}^{2} + y {}^{2} [/tex]

**Step-by-step explanation:**

Greetings !

**[tex](x + y)( x{}^{2} + xy + y {}^{2}) [/tex]**

Distribute parentheses

[tex] = xx {}^{2} + xxy + xy {}^{2} + yx {}^{2} + y {}^{2}x + y {}^{2} [/tex]

[tex] = x {}^{3} + x {}^{2} y + xy {}^{2} + yx {}^{2} + y {}^{2} x + y {}^{2} [/tex]

Collect Like terms and further simplification

[tex] = x {}^{3} + 2x {}^{2} y + 2xy {}^{2} + y {}^{2} [/tex]

Hope it helps!!!

If you have any questions and suggestions tag it on the comments. thanks

The **product **of (x+y)(x²+xy+y²) gives x³ + 2x²y + 2xy² + y³.

A branch of mathematics known as **algebra deals **with **symbols **and the mathematical **operations **performed on them.

Variables are the name given to these symbols because they lack set values.

In order to **determine **the **values**, these **symbols **are also **subjected **to various addition, subtraction, multiplication, and division **arithmetic** **operations**.

Given:

(x+y)(x²+xy+y²)

**Multiplying **the terms

= x(x²+xy+y²)) + y(x²+xy+y²)

= x³ + x²y + xy² + yx² + xy² + y³

= x³ + 2x²y + 2xy² + y³

Hence, the **expression **gives x³ + 2x²y + 2xy² + y³.

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What is the ordered pair for Point N?

Enter the coordinates in the boxes.

The **ordered pair** for **Point **N is (6,9).

**What is the ordered pair?**

An **ordered pair **in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the **ordered pair** differs from the** ordered pair**. **Ordered pairs** are also known as 2-tuples or 2-**length **sequences.

Here, we have

Given the **graph **and we have to find the **coordinates **of all points.

N = (6,9)

M = (5,7)

R = (9,8)

D = (2,6)

C = (1,4)

B = (2,1)

A = (6,2)

Q = (7,5)

Hence, the **ordered pair** for Point N is (6,9).

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Collin states that 8+(16+9)=(8+16)+9 is always true. which of the following properties would prove Collin is correct?

Transitive Property

Associative Property of Multiplication

Associative Property of Addition

Commutative Property of Addition

Answer: Associative Property of Addition

The property states:

(a+b)+c=a+(b+c)

Thus, (8+16)+9=8+(16+9) via the associative property of addition.

The property states:

(a+b)+c=a+(b+c)

Thus, (8+16)+9=8+(16+9) via the associative property of addition.

What is the slope and y-intercept of y =- 3x 4?

The **slope** of the** linear equation** y = -3x + 4 is -3, and the y-intercept is 4.

To **calculate **the slope of a linear equation, the formula is m = (y2 - y1) / (x2 - x1). The slope is calculated by selecting two points on the line, (x1, y1) and (x2, y2), and then **subtracting** the first point's y-value from the second's and dividing the result by the first point's x-value minus the second's. For the equation y = -3x + 4, the y-intercept is 4, which is the** b-value** in the equation y = mx + b. The y-intercept is the point where the line crosses the y-axis. To calculate the** y-intercept**, set x = 0 and solve for y. For the equation y = -3x + 4, when x = 0, y = 4. Therefore, the y-intercept is 4.

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What is the domain of the function y 3x 1?

We calculated the domain of this **function **is all the real numbers of independent variable X such as 0, 1, 2, 3, 4, 5, 6 etc.

An expression that indicates a relationship between an independent variable and dependent variable. A function consists of two variables with or without numbers. A function has symbols but equal sign is mandatory.

The **domain** of a function is the set of all possible value of independent variables. It is also called the input of a function.

In the above function, the domain is all real number of independent variable x.

For each value of x that means for each domain, we get a value of y. The set of y values are called ranges.

we put x= 0, 1, 2, 3, 4, 5, 6 and so on.

we get y = 3×0-1 = -1

y = 3×1-1 = 2

y =3×2-1 = 5

y = 3×3-1 = 8

y= 3×4-1 = 11

y = 3×5-1 = 14

y= 3×6-1= 17

The set of domains are {0, 1, 2, 3, 4, 6}

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2. A swimming pool has a volume of 32,700 cubic feet. How many gallons of water doesthe pool hold?A. 4,371.66 galB. 239,360 galC. 244,596 galD. 4,278.07 gal

The pool holds about 245,000 **gallons**. Therefore, **option (c) **244,596 gal is correct.

To find the number of gallons of water the pool holds, we need to convert the volume in cubic feet to gallons.

One **cubic foot** is equal to 7.4805194805 **gallons**, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:

1 cubic foot= 7.4805194805 gallons

gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot

= 244,999.99968 gallons

Rounded to the nearest gallon, the pool holds about 245,000 **gallons.**

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One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:

1 cubic foot= 7.4805194805 gallons

gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot

= 244,999.99968 gallons

Rounded to the nearest gallon, the pool holds about 245,000 gallons.

19)

Is the product of √8 and √98 rational or irrational? Justify your answer.

**Answer:**

They are both irrational

**Step-by-step explanation:**

so the square root of 8 is 2.82842712475 which is irrational because it is not a perfect square or repeated decimal pattern.

the square root of 98 is also irrational for the same reason but the square root is 9.89949493661.

The **product **of two √8 and √98 **irrational **number is **irrational**.

A **rational **number is any number that can be **expressed **as a **ratio **(or fraction) of **two **integers.

Any real number that **cannot **be represented as the **quotient **of two integers is **irrational**.

Given:

The **rational number **are : √8 and √78

As, the √8= 2.82842712475 which is **irrational **because it is not a **perfect square **or repeated decimal pattern.

and, √98 = 9.89949493661 is also **irrational**.

Hence, the **product **of two **irrational **number is **irrational**.

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Solve for x and graph the solution on the number line below.

1≥-x-1 and -x-1≥ −13

The solution to both **inequality **is 2 ≥ -x and -x≥ 14

The idea of inequality, which is the state of **not being equal**, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

We have the equation 1≥-x-1 and -x-1≥ −13

Let us solve the inequality

1 ≥ - x - 1

1 + 1 ≥ -x

2 ≥ -x

Now, let us solve the inequality

-x-1≥ −13

-x+13 ≥ -1

-x≥ 14

Therefore the solution to both **inequality **is 2 ≥ -x and -x≥ 14

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