Answer:
1/3
Step-by-step explanation:
There are 12 students in total and 4 liked Midsummer Night's Dream
Therefore 4 out of the 12 students like the play the best which can be represented in a fraction
4/12 - When you represent this as a fraction, it is also the probality, when randomly selected, a Shakespeare student likes the play the best.
This probability can then be simplified by dividing the denominator and numerator by 4
4/4 = 1 and 12/4 = 3
So, the answer is 1/3
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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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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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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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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What are the zeros of the polynomial 4x 2 }+ 52 √ 2x 3 ?`?
The zeros of the polynomial are 1/2√2 and -3/√2.
What is a zero of a polynomial?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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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])
What is Complex Number?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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Question In picture
this was an accident how do I delete?
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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What number is 10 more than 37?
10 more than 37 will be Addition of 10 and 37 which is supposed to be 10 plus 37 = 47.
Addition is the process of combining items and counting them as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.
The SUM is the result or conclusion that results from adding two or more integers. Addends are the numbers that are added.
We simply changed "more than" to "plus" and found the answer to the straightforward math issue. It is equivalent to 10 + 37 to add 10 to 37. Therefore, the answer is 47 once more.
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Hi! i need some help:)
Answer:
y=1/2x+-2
Step-by-step explanation:
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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What are the 4 types of translations in math?
The four fundamental translations or transformations in geometry are translation, reflection, rotation, dilation, and resizing.
How many translations are there in math?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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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 .
what is range ?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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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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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.
What is a banquet hall?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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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.
What is Rational Number?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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two angles form a linear pair. one angle measure is 36° more than the other. find both angle measures.
The measures of the angles are 72°, and 108°.
What is Angle Sum Property?
The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angles.
We have,
two angles form a linear pair. one angle measure is 36° more than the other.
If two angles form a linear pair, then the sum of the degree measure of the angles is 180°.
Let x be the measure of the smaller angle.
Then,
36° + x is the measure of the other angle.
So,
36° + x + x = 180°
2x = 180° - 36°
2x = 144°
x = 144°/2
x = 72°
the measure of the smaller angle is x = 72°,
the measure of the other angle is
36° + 72° = 108°
Hence, the measures of the angles are 72°, and 108°.
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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
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 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.
What is function?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.
What is domain of a function?The domain of a function is the set of all possible value of independent variables. It is also called the input of a function.
What is the domain of the function y= 3x-1?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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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
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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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
what is divisibility test?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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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.
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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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.
What is whole number?Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.
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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
How to calculate inequality ?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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(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 !
Given expression:-[tex](x + y)( x{}^{2} + xy + y {}^{2}) [/tex]
stepsDistribute parentheses
[tex] = xx {}^{2} + xxy + xy {}^{2} + yx {}^{2} + y {}^{2}x + y {}^{2} [/tex]
simply[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!!!
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The product of (x+y)(x²+xy+y²) gives x³ + 2x²y + 2xy² + y³.
What is Algebra?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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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.
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