Recall that, fixed a set U (which we call the universe of discourse), we have certain operations on subsets of U so that, for all A, B, C CU the following equivalences and equalities hold. >> AC BUC, ABCC CCA⇒B >> CnACB, A" = A, (AUB)* = A*n B', (An B)* = A*UB*. ACB →B'CA, You can answer just one of the following parts, not both. You can support your answer with drawings of Venn diagrams, but you need to give an argument according to the specifications for full credit. (a) Prove that for any given sets A, BCU, we have that B\A= (AB)* using only the above equations and equivalences. (Hint: Notice that two sets X, Y CU are equal if and only if, for every CCU, we have XCC YCC.) (b) Prove that for any given sets A, BCU, we have that B* A* = (AB)* using the definitions of the operations (). \, and in terms of the elements of U, A, and B.

Answer:

a

Step-by-step explanation:

x² - 3 = 2x ( subtract 2x from both sides )

x² - 2x - 3 = 0 ← in standard form

consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)

the factors are - 3 and + 1 , since

- 3 × + 1 = - 3 and - 3 + 1 = - 2 , then

x² - 2x - 3 = (x - 3)(x + 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

To be able to make x/y table, we substitute any number as x in the given equation y = -1/3x - 2.

Let's create a table,

x solution y

-6 -1/3(-6) - 2 = 2 - 2 0

-3 -1/3(-3) - 2 = 1 - 2 -1

0 -1/3(0) -2 = 0 - 2 -2

3 -1/3(3) - 2 = -1 - 2 -3

6 -1/3(6) - 2 = -2 - 2 -4

Answer:

68°/•

Step-by-step explanation:

100°/• - 32°/•

=68°/•

Step-by-step explanation:

Hey,

I'm sorry, this is not correct. For a reflection, all you have to do is count the number of points from that specific point to the line. So, for example, w is 6 units away from the line, in order to draw that, count 6 units and graph. It's pretty hard to explain, but remember the shape is being reflected, so the orientation must change. I suggest searching this up.

Let me know if you have any more questions and I'll be more than glad to help.

- Lena :)

Answer:

102 yards.

Step-by-step explanation:

If she walked 30 yards and 72 all you have to do is add them together wich is 102 yards. If thats how far she walked in all she probably walked the same length back unless she took a longer way or a short cut.

I hope this helps!

Answer:

it would be 2

Step-by-step explanation:

Answer:

A=75, B=60, C=45

Step-by-step explanation:

5x+4x+3x=180

12x=180

x=15

plug them in and get

A=5(15)=75

B=4(15)=60

C=3(15)=45

Answer:

False.

Inflation occurs in an economy when there is an increase in the overall price level of goods and services over time. It is usually caused by factors such as an increase in the money supply, higher demand for goods and services, or a decrease in the supply of goods and services. Therefore, a reduction in the total amount of money in an economy would generally lead to deflation, which is the opposite of inflation.

All the measures of central tendency are, The median, The mode, and The mean.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some measures,

A. The median

B. A sample statistic

C. The mode

D. The lowest value

E. The mean

We know that;

The four measures of central tendency are mean, median, mode and the midrange.

Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.

Hence, All the measures of central tendency are, The median, The mode, and The mean.

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Validation of the model and answering the question "what are my options" occur in the design phase of the IDC (Intelligence, Design, and Choice) framework.

The IDC framework is a decision-making process that consists of three phases: Intelligence, Design, and Choice. Each phase corresponds to a specific set of activities and objectives.

In the intelligence phase, the focus is on gathering information, identifying the problem or decision to be made, and understanding the factors and variables involved. This phase involves data collection, analysis, and exploration to gain insights and knowledge about the problem domain.

In the design phase, the emphasis is on developing and evaluating potential options or solutions to address the problem or decision at hand. This phase involves creating models, prototypes, or simulations to represent the problem and exploring different alternatives.

Validation of the model is an important aspect of this phase to ensure that the proposed solutions align with the problem requirements and objectives.

The question "what are my options" is a fundamental question that arises during the design phase. It implies the exploration and generation of various possible choices or solutions that can be evaluated and compared.

Therefore, the design phase of the IDC framework encompasses the activities of validating the model and answering the question "what are my options." It involves refining and testing potential solutions to make informed decisions in the subsequent choice phase.

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The probability of matching 6 randomly chosen integers is 1/593,775.

According to the statement

we have to find that the probability of winning a lottery.

So, For this purpose,

The given information is :

Total numbers are 30 and they are the positive integers and we have to pick 6 integers from them.

So, use the combination here

Combination is the number of possible arrangements in a collection of items where the order does not matter.

And

There are C(30, 6) = 30!/(6!*(30-6)!)

C(30, 6)= 593,775

So, There are 593,775 ways to pick 6 numbers from the first 30 positive integers.

And

The probability of winning a lottery is with 6 integers is :

1/593,775

So, The probability of matching 6 randomly chosen integers is 1/593,775.

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Question:

Find the probability of winning a lottery by selecting the correct six integers where the order in which these integers are selected does not matter from the positive integers not exceeding 30.

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Answer:

11 units

Step-by-step explanation:

Just trust me!

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer:

5 because once you evaluate your functions and simplify your equations you get all 5 solutions.

Step-by-step explanation:

Answer:

Intersection means a line common to other lines and an action of intersection/intersecting.

hope it helps!

Answer:

D)

Step-by-step explanation:

Answer:

-3x + 5y + 2.

Step-by-step explanation:

Answer: a

Step-by-step explanation: simple math

Answer:

25%

Step-by-step explanation:

Piece 1 = x + y > 1 - x - y

Piece 2 = x + (1 - x - y) > y

Piece 3 = y + (1 - x - y > x

Not going to lie, I had to look up how to calculate the probability of this lol

Hopefully this is right and you do well!

If it is follow my gram Greyhasnoshame

Answer

an=a1+(n-1)d

Step-by-step explanation:

a2-a=9_2=7

a3-a2=16-9=7

a4-a3=23-16=7

a5-a4=30-23=7

Using calculator, the value of  the angle 5 sin (20 +10°) -4 = 0​ where 0 <x<90 is 17.5 degrees

You should understand that the sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle

The given angle is 5 sin (20 +10°) -4 = 0

To find the angle, first open the bracket to have

5sin(30) - 4 = 0

Collecting like terms to have

5 sin 30 = 4

Dividing both sides by 5 we have

5 sin30/5 = 4/5

This means that sin30 = 0.8

⇒sin30 - 0.8 = 0

⇒ 0.5 -0.8 = 0

-0.3

Therefore sin⁻-0.3 = 17.5⁰

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Answer:

20.84

Step-by-step explanation:

$25.36 - $4.52 = $20.84

Hope this helps

Answer:

$448.50

General Formulas and Concepts:

Pre-Algebra

Statistics

Simple Interest Rate Formula: A = P(1 + rt)

Step-by-step explanation:

Step 1: Define variables

P = 390

r = 0.03

t = 5

Step 2: Find A

And we have our final answer!

Answer:

The Answer Is: 448.50 Just did the question

Step-by-step explanation:

The normal distribution of x has a mean of 100 and a standard deviation of 20. The probability that x is greater than 145 is P(x > 145) = 0.0122.

Probability is simply the possibility that something will happen. Since we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several. Statistics is the study of events that fall into a probability distribution. The ratio of favorable events to all other outcomes in the sample space is the standard definition of probability. The probability of an event is calculated using the formula P(E) = (Number of favorable outcomes) (Sample space). Probability is the study of possible outcomes of events, together with their relative probabilities and distributions.

x ~ N (100.20), μ=100, σ= 20

So, x-100/20~ N(0,1)

P(x>145) = 1-P( x ≤ 145)     {P(x>a) = 1-P(x ≤ a)}

              = 1-P( x-100/20 ≤ 145-100/20)

              = 1-P( x-100/20 ≤ 145-2.25)

              = 1 - ∅ (2.25)    {By the standard normal distribution table}

              = 1- 0.9878

              = 0.0122

{∅(x) is the distribution function of the standard normal distribution table}

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Answer: 41.86 miles/hour

Step-by-step explanation:

Use Distance = Speed*Time to find the two missing values with the data that is provided for those two cases [in brackets].

MPH MILES     HOURS

 50            20      [0.4]

 [40]    70      1.75

Totals   90 miles   2.15 hours

Average = 90 miles/2.15 hours

     41.86 mph

The 90 %confidence interval for the mean waste recycled per person per day for the population of Texas is (0.9, 1.5)

We will solve the problem in the following way,

Let us first assume that the population of Texas is approximately normal.

We will then find the critical value that will be used in constructing the confidence interval.

We have been given the following values:

The sample mean waste recycled per person per day= x'= 1.2 pounds

The sample Standard Deviation= s= 0.99 pounds

The sample size of residents of the state of Texas= n= 24 residents

The significance level= α= 0.1

The critical value that we get is t' = 1.714

Now we will calculate the Standard Error.

The formula for Standard error is

Error= \(\frac{s}{\sqrt{n} }\)

Substituting the values we know, we get

Error = \(\frac{0.99}{\sqrt{24} }\)

Error = 0.2021

Now we will calculate the margin of error

The formula for the Margin of error is

Margin= \(t' *\)\(\frac{s}{\sqrt{n} }\)

Substituting the known values, we get

margin= 1.714*0.2021

margin= 0.3463

Now we will calculate the lower limit and upper limit

Lower limit= x' - margin of error

= 1.2 - 0.3463

= 0.9

Upper limit = x' + margin of error

= 1.2 + 0.3463

=1.5

The 90% confidence interval is (0.9, 1.5) or 0.9 ≤ μ ≤ 1.5

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Answer:  Rational

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

To find the maximum profit, we can look for the vertex of the parabolic function representing the profit.

The given profit function is:

\(Z = -3x^2 + 12x + 25\)

We can see that the coefficient of the \(x^2\) term is negative, which means the parabola opens downwards. This indicates that the vertex of the parabola represents the maximum point.

The x-coordinate of the vertex can be found using the formula:

\(x = \frac{-b}{2a}\)

In our case, a = -3 and b = 12. Plugging these values into the formula, we get:

\(x = \frac{-12}{2 \cdot (-3)}\\\\x = \frac{-12}{-6}\\\\x = 2\)

To find the maximum profit, we substitute the x-coordinate of the vertex into the profit function:

\(Z = -3(2)^2 + 12(2) + 25\\\\Z = -12 + 24 + 25\\\\Z = 37\)

Therefore, the maximum profit is 37.

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Answer:

The time it takes to earn an amount A with a given principal P invested for a time period t is t = (A/P - 1)/r

Step-by-step explanation:

In order to calculate the time it would take to earn a certain amount of interest on a principal amount in an investment with simple interest, we use the simple interest formula as follows;

A = P·(1  + r·t)

A = The final amount after the number of periods of investment

P = The principal or initial amount

r = The interest rate per period

t = The number of the time periods

Therefore, the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest is fount by making t the subject  of the above equation, which is given as follows;

A/P = 1 + rt

rt = A/P - 1

t = (A/P - 1)/r

Therefore, the time it takes to earn an amount A with a given principal P invested for a time period t is given by t = (A/P - 1)/r.