List the elements in the set . Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. (B ∪ A)'

Answer:

Bigcity United lost 12 games.

Step-by-step explanation:

Since you know the percentage of games Bigcity United won, first you need to determine the percentage of games that they lose by subtracting the percentage of games they won from 100%:

100%-60%=40%

Now, you know that they lost 40% of the games and you can calculate 40% of the number of games they played last season:

30*40%=12

According to this, the answer is that Bigcity United lost 12 games.

let's firstly convert the mixed fractions to improper fractions and then get their difference.

\(\stackrel{mixed}{8\frac{7}{8}}\implies \cfrac{8\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{71}{8}} ~\hfill \stackrel{mixed}{6\frac{3}{4}}\implies \cfrac{6\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{27}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{8}-\cfrac{27}{4}\implies \cfrac{1(71)~~ -~~2(27)}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{71-54}{8}\implies \cfrac{17}{8}\implies 2\frac{1}{8}\)

The answer is 237.55

Define Percentage

A ratio or figure stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

Given expression is,

125.8% of £188.83

Rewrite it as,

⇒ 125.8 / 100 * 188.83

⇒ 1.258 * 188.83

⇒ 237.54814

⇒ 237.55 (rounded to 2 Decimal places)

Hence, the answer is 237.55

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Since the values for x and y are not given, we cannot calculate the commission.

To solve for the commission in dollars earned by the salesperson, we need the actual values for the first x and the number of sales that are greater than x.

Let x be the value of the first x the salesperson has in sales.

Let y be the number of sales that are greater than x.

Then, the salesperson earns a commission on the first x and on the number of sales that are greater than x.

The commission can be calculated as follows:

Commission = (commission rate on the first x) + (commission rate on y)

where the commission rate on the first x and on y is the same.

We are not given the values for x and y.

Hence, we cannot calculate the commission.

Part A cannot be solved with the given information.

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The statistical method that would be best to use in this situation is b) Regression analysis.

Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.

Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.

Hence the answer is Regression analysis.

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Given:

The general equation is

The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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4c is 50a/c % of the expression 2a

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

Expression = 2a

Percentage = 4c

Represent the percentage expression with x

So, we have the following equation

x% * Percentage  = Expression

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

x% * 4c = 2a

Evaluate

x = 50a/c %

Express as percentage

Hence, the percentage is 50a/c %

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No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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Answer:

A

Step-by-step explanation:

Answer:

x² + x - 8

Step-by-step explanation:

(f . g)(x) is same with (f(g(x))

so insert the g(x) equation into f(x) and change the x on it

f(g(x)) = g(x) - 2

f(g(x)) = (x² + x - 6) - 2 = x² + x - 6 - 2 = x² + x -8

so

(f.g)(x) is x² + x - 8

Answer:x=-7

Step-by-step explanation:

Step-by-step explanation:

I'm not sure it's probably x=-2

Answer: 64m

Step-by-step explanation: first,lets use the formula to find a trapezoids area. the formula is 1/2 x (b1 +b1) x h. well then if add on the numbers it would be 1/2 x (5+11) x 8. so lets start solving. as you know parenthesis comes first. so 1/2 x (5+11) x 8 turns into 1/2 (16) x 8. then you multiply the base (16) with the height (8). then 1/2 (16) x 8 turns into 1/2 x 128. now lets divide 128 by 2 ( now this is a method for multiplying by 1/2, if you do not believe me search it up.). the answer is 64.

Answer:

We bought 10 Pounds of Chocolate, and 5 Pounds of Candy.

Step-by-step explanation:

Hey!

==================================================================

Let's make a chart!

                 Lbs     Price  Cost

Chocolate | x      | 2.50 | 2.50x

Candy       | 15-x | 3.00  | 3.00(15-x)

Equation:

2.50x + 3.00(15-x) = 40

--------------------------------------------------------------------------------------------------------------

⇒ 2.50x + 3.00(15-x) = 40

-Distribute 3 over 15-x

⇒ 2.50x + 45 - 3x =40

-Combine Like Terms

⇒ -0.5x + 45 = 40

-Subtract 45 from both sides.

⇒ -0.5x + 45 = 40

            -45   -45

--------------------------

⇒ -0.5x = -5

-Divide by -0.5 on both sides

⇒ -0.5x/-0.5 = -5/-0.5

⇒ x = 10

That means we bought 10 Pounds of Chocolate.

---------------------------------------------------------------------------------------------------------------Since Candy was 15-x, we can Substitute 10 as x, and Solve:

⇒ 15 - 10

⇒ 5

That means we bought 5 Pounds of Candy.

--------------------------------------------------------------------------------------------------------------

We bought 10 Pounds of Chocolate, and 5 Pounds of Candy.

==================================================================

Hope I Helped, Feel free to ask any questions to clarify :)

Have a great day!

More Love, More Peace, Less Hate.

       -Aadi x

Answer:

8 Tickets

Step-by-step explanation:

40 / 5 = 8

Answer:

answer is 20+12x^6

Step-by-step explanation:

Multiply x^2+2x-3 by 2

length equals 2x^4+4x-6

simplify. 6x^5-6

multiply 2x2+3x+5 by 2

width equals 4x4+6x+10

simplify. 16+6x+10

simplify again. 26+6x

add length and width- 20+12x^6

Answer:

true

Step-by-step explanation:

Answer:

Answer:

3) -82 4)-70 5) -15 6)-14 7)5 8)15 9)16 10)16 11)64 12)21 13)1500 in the middle 14)450

Step-by-step explanation:

The force required to keep a hockey puck sliding at a constant velocity, neglecting ice friction and air resistance, is equal to its weight. The correct option is "equal to its weight."

When a hockey puck is set in motion across a frozen pond and there is no ice friction or air resistance, the only force acting on the puck is its weight, which is the force due to gravity pulling it downward. According to Newton's first law of motion (the law of inertia), an object at a constant velocity will continue to move at that velocity unless acted upon by an external force.

Since the puck is already in motion and we want to maintain its constant velocity, the force required to counteract its weight and keep it sliding is equal to its weight. This is because the weight of an object is the force exerted on it by gravity, and in the absence of other forces, an equal and opposite force is needed to maintain the object's motion without acceleration.

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Answer:

4(3x+7)

Step-by-step explanation:

12x+28

Bot numbers are divisible by 4

4*3 *x + 4*7

Factor out the 4

4(3x+7)

Step-by-step explanation:

x+66+52=180

x=180-66-52

x=180-118

x=62

a)  the Reynolds number for the flow of metal into the mold is given by:

\($Re = \frac{(1.798)(0.014)}{0.0012} \\= 21.008$\)

Since the Reynolds number is less than 2300, the flow is laminar.

b) the time taken for a 300,000 $mm^3$ casting to be filled with a runner of diameter 1.328 mm.

a)  The velocity and rate of the flow of the metal into the mold, and whether the flow is turbulent or laminar, are determined using Bernoulli's equation and Reynolds number.

Bernoulli's equation is given by the following formula:  

\($P_1 +\frac{1}{2}\rho v_1^2+\rho gh_1 = P_2 +\frac{1}{2}\rho v_2^2+\rho gh_2$\) where \($P_1$\) and \($P_2$\) are the pressures at points 1 and 2, \($v_1$\) and \($v_2$\) are the velocities at points 1 and 2, \($h_1$\) and \(V\) are the heights of the liquid columns at points 1 and 2, and $\rho$ is the density of the fluid, which is 7500 kg/m³ for molten metal, and \(V\) is the gravitational acceleration of the earth, which is 9.81 m/s².

We know that the height difference between the metal level in the pouring basin and the mold is $320\ mm$ and the diameter of the runner is \($14\ mm$\).

Therefore, the velocity of the flow of the metal into the mold is given by: \($v_2 = \sqrt{2gh_2} \\= \sqrt{2(9.81)(0.32)} \\= 1.798\ m/s$\)

The Reynolds number is used to determine whether the flow is turbulent or laminar, and it is given by the following formula: \($Re = \frac{vD}{h}$\) where \($v$\) is the velocity of the fluid, \($D$\) is the diameter of the pipe or runner, and $h$ is the viscosity of the fluid, which is \($0.0012\ Ns/m^2$\) for molten metal.

Therefore, the Reynolds number for the flow of metal into the mold is given by:

\($Re = \frac{(1.798)(0.014)}{0.0012} \\= 21.008$\)

Since the Reynolds number is less than 2300, the flow is laminar.

b)  We know that Reynolds number is given by \($Re = \frac{vD}{h}$\).

We need to find the diameter of the runner which will ensure a Reynolds number of 2000.  

\($D = \frac{Reh}{v} \\= \frac{(2000)(0.0012)}{1.798} \\= 1.328\ mm$\)

Therefore, the diameter of the runner needed to ensure a Reynolds number of 2000 is 1.328 mm.

The volume of the casting is 300,000 $mm^3$, and the cross-sectional area of the runner is

\($A = \frac{\pi D^2}{4}\\= \frac{\pi(1.328)^2}{4}\\= 1.392\ mm^2$\).

The time taken for the casting to be filled is given by:

\($t = \frac{V}{Av} \\= \frac{300,000}{1.392(1.798)} \\= 118,055\ s$\)

Therefore, the time taken for a 300,000 $mm^3$ casting to be filled with a runner of diameter 1.328 mm.

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For a particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s, the displacement is -11.53 m

For given question,

A particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s.

We can observe that, for t1 = 1.82 s and t2 = 3.81 s

object is moving from right to left along the x axis.

We know that, the displacement of a particle moving in a straight line is the change in its position.

so, d = 4.97 - 16.5

d = -11.53

The negative sign indicates that the object is moving from right to left along the x axis  for t1 = 1.82 s and t2 = 3.81 s

Therefore, for a particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s, the displacement is -11.53m.

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A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.


A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.

Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.

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Answer:

X=6

Step-by-step explanation:

2x-3/3=X/2

or, (2x-3)×2= 3x ( cross multiplication )

or, 4x-6=3x

or,4x-3x=6

... 1x=6

hence ...... x=6

Therefore, the y-intercept of the transformed function is -8.

A quadratic function is a mathematical function of the form f(x) = a\(x^{2}\) + bx + c, where "a", "b", and "c" are constants, and "x" is the variable.

The graph of a quadratic function is a parabola, which can either open upwards or downwards, depending on the value of "a". The vertex of the parabola is the point where the graph changes direction, and it is given by the formula (-b/2a, f(-b/2a)).

by the question.

The vertex form of a quadratic function is:

\(f(x)=a(x-h)^{2}+k\)

where (h,k) is the vertex of the parabola and a determines the direction and degree of the stretch or compression.

To reflect the function over the x-axis, we need to multiply the entire function by -1. To stretch it vertically by a factor of 3, we need to multiply it by 3. To shift it left 1 unit and down 5 units, we need to subtract 1 from x and subtract 5 from the y-intercept.

Therefore, the vertex form of the transformed function is:

f(x) = -3\((x+1)^{2}\) - 5

The vertex of the original function was at (-b/2a, c-b^2/4a). Since the original function is in standard form, we have a = 1, b = 0, and c = 0. So, the vertex of the original function is at (0,0).

To find the y-intercept of the transformed function, we can substitute x=0: f (0) = -3\((0+1)^{2}\) - 5 = -8

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Jacob will need 7 months to spend all the money.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits into his savings account each week. when summer vacation is over, he plans to spend $180 per month.

The number of months will be calculated as:-

Total money in the account = 180 + 12(145-55)

Total money in the account = $1260

Total months = 1260 / 180

Total months = 7 months

Therefore, Jacob will need 7 months to spend all the money.

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Using proportions, it is found that Ms. Grant had $18,896 of his total savings left after making the donation.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, she saved $80 a month for 22 years = 22 x 12 months, hence the total amount saved is given by:

T = 80 x 22 x 12 = $21,120.

She donated 20% of her savings to a charity, hence she retained 80% of the total amount, which is given by:

R = 0.8 x 21,120 = $18,896.

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