et A={a,b,c},B={b,c,d}, and C={b,c,e} (a) Find A∪(B∩C),(A∪B)∩C, and (A∪B)∩(A∪C). (Enter your answer in set-roster notation.) A∪(B∩C)= (A∪B)∩C= (A∪B)∩(A∪C)=

Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.

To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.

To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:

168 = 1 * 120 + 48

120 = 2 * 48 + 24

48 = 2 * 24 + 0

Therefore, the GCD of 120 and 168 is 24.

Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0

Therefore, the GCD of 120, 168, and 192 is 24.

So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:

Total number of items = 120 + 168 + 192 = 480

Number of bags = 480 / 24 = 20

Therefore, Thomas can get a maximum of 20 bags.

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Answer:

(0, 3) & (4, 1):  y = -1/2x + 3

(-2, -3) & (2, -1):  y = 1/2x -2

 (1, 3) & (4, 9) y = 2x + 1

Step-by-step explanation:

(0, 3) represents the y-intercept of its respective line and since only one line has a y-intercept of 3 (i.e., y = -1/2x + 3), we can eliminate this option.

The easiest way to find which lines the other four points lie on is by finding their slopes using the slope formula.

(-2, -3) & (2, -1):

\(\frac{-1-(-3)}{2-(-2)}=\frac{-1+3}{2+2}=\frac{2}{4}=\frac{1}{2}\)

Since there is only one line with a slope of 1/2, we can also eliminate that option.

The last only line on which the points (1, 3) & (4, 9) can lie is y = 2x + 1

The solution is she can cover 5/18 of her lawn.

Here, we have,

to determine how much of Sierra's lawn she can cover:

We first need to find the total amount of grass seed she has in terms of the amount needed to cover the whole lawn.

We start by converting the amount of grass seed she has to the same unit as the amount needed to cover the whole lawn.

1/3 lb = 1/3 x (5/6) = 5/18 lb

So, Sierra has 5/18 of the amount of grass seed needed to cover the whole lawn.

Therefore, she can cover 5/18 of her lawn.

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complete question:

Sierra spreads grass seed on her lawn. She needs lb of grass seed to cover her

5/6

whole lawn. She has 1/3 lb of grass seed. How much of her lawn can she cover?

Show your work.

The gambler's payoff has a standard deviation of $1. The gambler can expect to win or lose $1 on average for each coin flip, and there is a high degree of variability in the possible outcomes of the game.

The standard deviation of the gambler's payoff can be calculated using the following formula:

σ = √(Σ(xi - μ)^2 * P(xi))

where σ is the standard deviation, xi is the possible outcome of the game, μ is the expected value of the game, and P(xi) is the probability of each outcome.

In this case, there are two possible outcomes: winning $1 with probability 1/2 and losing $1 with probability 1/2. The expected value of the game is:

μ = (1/2 * $1) + (1/2 * -$1) = $0

To calculate the standard deviation, we need to determine the variance first. The variance can be calculated as:

σ^2 = Σ(xi - μ)^2 * P(xi)

= (1 - 0)^2 * 1/2 + (-1 - 0)^2 * 1/2

= 1

Therefore, the standard deviation is:

σ = √1 = 1

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\(2\sqrt[3]{x^2}\cdot \sqrt{16x}\\\\=2\sqrt[3]{x^2} \cdot 4\sqrt x\\\\=8x^{\tfrac 23} \cdot x^{\tfrac 12}\\\\=8\cdot x^{\tfrac 23 + \tfrac 12}\\\\=8\cdot x^{\tfrac 76}\\\\=8\sqrt[6]{x^7}\\\\=8\sqrt[6]{x^6 \cdot x}\\\\=8x\sqrt[6]{x}\)

\(\text{Hence the answer is A}\)

Answer:

\( \sf \: Option \: A \: \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8x \sqrt[6]{ {x}}\)

Step-by-step explanation:

\( \sf \: if \: x > 0 \\ \sf \: 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 2 \sqrt[3]{ {x}^{2} } \cdot \: 4 \sqrt{x} \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{2}{3} } \cdot \: {x}^{ \frac{1}{2} } \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} =8 {x}^{ \frac{2}{3} + \frac{1}{2} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{4 + 3}{3 \times 2} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{7}{6} } \\ \sf 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 \sqrt[6]{ {x}^{7} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 \sqrt[6]{ {x}^{6} + x } \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8x \sqrt[6]{ {x}}\)

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Answer:

5+3m

Step-by-step explanation:

The y-intercept of (f - g)(x) has the coordinates given as follows:

D. (0, −9).

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For function f(x), we have that when x increases by 2, y increases by 10, hence the slope m is given as follows:

m = 10/2

m = 5.

Hence:

f(x) = 5x + b

When x = -6, f(x) = -36, hence the intercept b is given as follows:

-36 = -30 + b

b = -6.

Hence:

f(x) = 5x - 6.

For function g(x), we have that when x increases by 2, y decays by 4, hence the slope m is given as follows:

m = -4/2

m = -2.

Hence:

g(x) = -2x + b

When x = -6, y = 15, hence the intercept b is given as follows:

15 = 12 + b

b = 3.

Hence:

g(x) = -2x + 3.

The subtraction function is given as follows:

(f - g)(x) = 5x - 6 + 2x - 3

(f - g)(x) = 7x - 9

Hence the coordinates of the intercept are given as follows:

D. (0, −9).

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Answer: i would like to sad it varies

Step-by-step explanation: the number of people required for a Vehicle to be an HOV i would say exactly 2 and greater. The state Laws also applies, so i'll add that onto it varies

The answer to this Question is (5^7)*(x^7/5), the question is based on exponents laws

What are exponent laws?

These are some basic laws in maths that helps us to simplify the complicated expressions easily

Solution:

Here we can first distribute the power 7 to both 5 and 5th root of x by exponent laws

we get 5^7 * 5th root(x)^7

now we know nth root(x) = x ^1/n

we will do the same as

we get 5^7 * x^7/5 which is our required answer and there many more properties of exponents that we study in higher classes

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The best statement that describes the function of the logic variable X is: A. X is a variable whose value is 1 or 0.

Logic variables typically represent binary states or conditions, where 1 represents "true" or "on" and 0 represents "false" or "off". Therefore, option A accurately describes the function of the logic variable X as having a value of either 1 or 0. Logic variables are often used in the field of logic and computer science to represent binary states or conditions. The value of a logic variable can only be one of two possibilities: 1 or 0.

In this context, 1 typically represents "true" or "on," indicating that a certain condition is satisfied or a certain state is active. On the other hand, 0 represents "false" or "off," indicating that the condition is not satisfied or the state is inactive.

By using logic variables, we can model and manipulate binary logic in a precise and systematic manner. The values of logic variables are fundamental in logical operations, such as AND, OR, and NOT, which are essential in designing and analyzing digital circuits, programming, and logical reasoning.

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The Quadrilateral that matches the listed characteristics is a rectangle.

A rectangle is a quadrilateral with four right angles, and two pairs of opposite sides that are parallel. It is also a parallelogram because it has two pairs of parallel sides. However, not all parallelograms are rectangles.

A rectangle also has four congruent angles which makes it a special case of parallelogram. In a rectangle, opposite sides are congruent to each other. Therefore, answer option C. Rectangle matches the given characteristics.

What is a quadrilateral?A quadrilateral is a polygon with four sides. Examples of quadrilaterals include parallelograms, rhombuses, rectangles, squares, and trapezoids. The angles of a quadrilateral add up to 360 degrees.What is a rectangle?

A rectangle is a four-sided figure with four right angles.

Opposite sides of a rectangle are parallel to each other. The length and width of a rectangle are perpendicular to each other. The formula for finding the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. The area of a rectangle is A = lw, where A is the area, l is the length, and w is the width.

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The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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What operation is used. Is a multiplicarion between irrational numbers.

What is the amount collected

It must be multiplied 15.5 x 3.98

Replace 15.5 = 15+ 0.5

3.98 = 4-0.02

then 15x 4 + 0.5x4 - 15x(0.02) - 0.5x(0.02)

Then result 60 + 2 - 0.30 - 0.01

62 - 0.31 = 61.69

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Answer:

310

Step-by-step explanation:

Answer: 310

Step-by-step explanation: 2% equals 10, so just keep counting up until you get 62%.

Hopefully this helped! :D

The probability that 0 < Z < 2.03 is approximately 0.4788. This means that about 47.88\% of the values in a standard normal distribution are between 0 and 2.03.

To find the probability using a z-score, you need to use a formula that involves subtracting the mean and dividing by the standard deviation of the normal distribution. Then, you can look up the corresponding probability in a z-table, which shows the probability of a value being less than, greater than, or between certain z-scores.¹²

To answer your question, you need to use the formula and the z-table.

The formula for finding a z-score is:

z = \frac{x - \mu}{\sigma}

where x is the value, \mu is the mean, and \sigma is the standard deviation of the normal distribution.

Since you are given that Z follows a standard normal distribution, you can assume that \mu = 0 and \sigma = 1. Therefore, the formula simplifies to:

z = x

To find the probability that 0 < Z < 2.03, you need to find the area under the curve between these two values. You can do this by using the z-table.

First, look up the value 0 in the z-table. You will find that the probability that Z < 0 is 0.5. This means that half of the area under the curve is to the left of 0.

Next, look up the value 2.03 in the z-table. You will find that the probability that Z < 2.03 is 0.9788. This means that most of the area under the curve is to the left of 2.03.

To find the probability that 0 < Z < 2.03, you need to subtract these two probabilities:

P(0 < Z < 2.03) = P(Z < 2.03) - P(Z < 0)

P(0 < Z < 2.03) = 0.9788 - 0.5

P(0 < Z < 2.03) = 0.4788

Therefore, the probability that 0 < Z < 2.03 is approximately 0.4788. This means that about 47.88\% of the values in a standard normal distribution are between 0 and 2.03.

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the complete question is:

Find The Specified Probability. Round Your Answer To Four Decimal Places, If Necessary. P(0<Z&Lt;2.03)

we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

The error is in step 2 in step 2 Susu forgot to divide 8 by 4 for finding the solution of a quadratic equation.

The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x2). It is also called an "Equation of Degree 2"

Susu is solving the quadratic equation \(4x^2-8x-13=0\) by completing the square

To apply to completing the square method we need to get x^2 alone

Susu added 13 on both sides. So step 1 is correct

When we factor out 4, we divide both terms by 4

\(4(\dfrac{4x^2}{4}-\dfrac{8x}{2})=13\)

\(4(x^2-2x)=13\)

Susu forgot to divide 8 by 4

So , error in step 2

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Answer:

Step-by-step explanation:

2

The determinant of q is 4cos^2(0)sin^2(0) - 1.

The matrix q represents a combination of rotation and reflection. To find the determinant of q, we can use the following formula:

det(q) = det([ cs -sin0; sm0 cos0]) * det([ 1 - 2 cos2 0 -2 cos 0 sin 0; -2cos0sin0 1- 2sin2 0])

The first matrix represents a rotation by an angle of θ, where θ is the value of 0 in the given matrix q. The determinant of a rotation matrix is always 1, so we have:

det([ cs -sin0; sm0 cos0]) = cos^2(0) + sin^2(0) = 1

The second matrix represents a reflection along the line y = x tan(θ/2) - d/2. The determinant of a reflection matrix is always -1, so we have:

det([ 1 - 2 cos^2(0) -2 cos(0) sin(0); -2cos(0)sin(0) 1- 2sin^2(0)]) = -[1 - 2 cos^2(0) -2 cos(0) sin(0)][1 - 2 sin^2(0) -2 cos(0) sin(0)]

= -(1 - 4cos^2(0)sin^2(0) - 4cos^2(0)sin^2(0)) = -1 + 4cos^2(0)sin^2(0)

Therefore, the determinant of q is:

det(q) = det([ cs -sin0; sm0 cos0]) * det([ 1 - 2 cos^2(0) -2 cos(0) sin(0); -2cos(0)sin(0) 1- 2sin^2(0)])

= 1 * (-1 + 4cos^2(0)sin^2(0))

= 4cos^2(0)sin^2(0) - 1

So the determinant of q is 4cos^2(0)sin^2(0) - 1.

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Answer: imaginary axis

Step-by-step explanation:

The members of each set are A = {2, 3, 5, 7, 11, 13, 17} and B = {}

A n B = {}

A u B = {2, 3, 5, 7, 11, 13, 17}

The members of each set

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

U = (1,2,3,4,.... 18)

A = {Prime numbers)

B = (Odd numbers greater than 31)

This means that the universal set is from 1 to 18

So, we have

A = {2, 3, 5, 7, 11, 13, 17}

B = {}

The sets of the following

A n B: This is the elements common in both sets

So, we have A n B = {}

A u B: This is the list of all elements without repetition

So, we have A u B = {2, 3, 5, 7, 11, 13, 17}

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complete question:

U

=(1,2,3,4,.... 18); A= {Prime numbers) and B= (Odd numbers greater than 31. a) If A and B are subsets of the universal set, &, list the members of A and B Find the set b) c) i) AnB ii) AUB i) Illustrate U, A and B on a Venn diagram. ii) Shade the region for prime factors of 18 on the Venn diagram.

​

The mean time it takes Diane and her three friends to complete the obstacle course is approximately 45.75 seconds.

To find the mean of the times it takes Diane and her three friends to complete the obstacle course, we need to add up the times and then divide by the number of people who completed the course.

Let's assume that the times (in seconds) it took each person to complete the course were:

Diane: 42 seconds

Friend 1: 55 seconds

Friend 2: 39 seconds

Friend 3: 47 seconds

To find the mean, we add up all of the times and then divide by the total number of people who completed the course (in this case, four people):

Mean time = (42 + 55 + 39 + 47) / 4

= 183 / 4

= 45.75 seconds

It's important to note that the mean can be impacted by outliers or extreme values in the data set. In this case, if one person had a much longer time to complete the course, it could significantly impact the mean time. It's important to consider the distribution and range of the data in addition to the mean when analyzing data.

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Given:

Consider the number as x.

The objective is to represent algebraic expression for, 2 is subtracted from the square of a number.

Explanation:

Since the number is given as x, the square of the number can be represented as,

Now, subtract 2 from the above expression,

Hence, the required expression is x²-2.

Answer: A student who owns a cell phone is more likely to have brought a personal device than not to have brought one.

Step-by-step explanation:

Using the ratio principle, the longest stage is Prophase with a duration of 456 minutes

The amount of time spent in each stage of Mitosis can be calculated thus :(Number of onion per stage / total number of onions) × total time spent.

Total time spent = 24 hours = (60 × 24) = 1440 minutes

Time spent per stage :

Anaphase :

(12 / 60) × 1440 = 288 minutes

Prophase :

(19 / 60) × 1440 = 456 minutes

Metaphase :

(14 / 60) × 1440 = 336 minutes

Telophase :

(15 / 60) × 1440 = 360 minutes

Therefore, the stage with the longest duration is the Prophase stage and the duration is 456 minutes

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\(\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}\)

\(\Huge \textsf{Step-by-step explanation}\)

\(\LARGE \bold{\textsf{Step 1: Assign Variables}}\)

\(\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}\)

\(\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}\)

\(\large \bold{ \textsf{From the problem, we know that:}}\)

\(\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}\)

\(\large \bold{ \textsf{We can use this information to write two equations:}}\)

\(\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}\)

\(\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}\)

\(\LARGE \bold{\textsf{Step 3: Solve the system of equations}}\)

\(\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}\)

\(\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}\)

\(\large \textsf{Simplifying this expression gives us:}\)

\(\textsf{10\textit{p} + 10 = 260}\)

\(\large \textsf{Subtracting 10 from both sides:}\)

\(\textsf{10\textit{p} = 250}\)

\(\large \textsf{Dividing both sides by 10}\)

\(\textsf{\textit{p} = 25}\)

\(\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}\)

\(\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}\)

\(\large \textsf{So, 25 pizzas and 80 sodas were sold.}\)

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

There are 40 chickens and 16 pigs on the farm. Let's assume the number of chickens is represented by "C" and the number of pigs is represented by "P."

We know that the total number of animals is 56, so we can write the equation C + P = 56.

Each chicken has 2 feet, and each pig has 4 feet. The total number of feet on the farm is 178, so we can write the equation 2C + 4P = 178.

Solving these two equations simultaneously, we can find the values of C and P. By substituting the value of C from the first equation into the second equation, we get 2(56 - P) + 4P = 178. Simplifying this equation gives us 112 - 2P + 4P = 178. Combining like terms, we have 2P = 66, which leads to P = 33.

Substituting the value of P into the first equation, we get C + 33 = 56, and by solving for C, we find C = 23.

Therefore, there are 23 chickens and 33 pigs on the farm.

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