Construct an algebraic proof for the given statement. Cite a property from Theorem 6.2.2 for every step. (A - B) u (An B) = A Theorem 6.2.2 Set Identities Let all sets referred to below be subsets of a universal set U. 1. Commutative Laws: For all sets A and B, (a) AUB = BUA and (b) An B = BNA. 2. Associative Laws: For all sets A, B, and C, (a) (A U BUC = AU (BUC) and (b) (ANB) NC = An (BNC). 3. Distributive Laws: For all sets, A, B, and C, (a) AU (BNC) = (AUB) N (AUC) and (b) A N (BUC) = (ANB) U (ANC). 4. Identity Laws: For all sets A, (a) A UØ = A and (b) A NU = A. 5. Complement Laws: (a) AU AC = U and (b) An A = 0. 6. Double Complement Law: For all sets A, (A) = A. 7. Idempotent Laws: For all sets A, (a) AU A = A and (b) An A = A. 8. Universal Bound Laws: For all sets A, (a) A UU = U and (b) Ang=0. 9. De Morgan's Laws: For all sets A and B, (a) (AUB) = A n Bº and (b) (ANB) = ACU B. 10. Absorption Laws: For all sets A and B, (a) A U(ANB) = A and (b) AN (AUB) = A. 11. Complements of U and Ø: (a) U = 0 and (b) Ø¢ = U. 12. Set Difference Law: For all sets A and B, A - B = ABC.

Answer:

90

Step-by-step explanation:

It is a right angle

Answer:

8.944

Step-by-step explanation:

Use the Pythagorean theorem to find the unknown side.

\(a^{2} +b^{2} =c^{2} \\x^{2} +8^{2} =12^{2} \\x^{2} = 12^{2} -8^{2}\\x=8.944\)

Answer:

I feel like its that but im rlly not sure.

Step-by-step explanation:

Leanne's list is incorrect and  there are 3 different sides a person can choose. So, there are a total of 6 possible ways a person could choose their dinner.

The given parameters are:

Main Dish: B, C and P

Sides: A and F

Using the above parameters, the combination of dishes are:

BA, BF, CA, CF, PA and PF

Hence, we can conclude that Leanne list is incorrect

Also, we have:

Dish = 3

Sides = 2

So, the number of dinner to choose is:

Dinner = 3 * 2 = 6

Hence, a person could choose their dinner in 6 ways

Read more about combination at:

https://brainly.com/question/11732255

#SPJ2

Answer:

d) 32.4%

Step-by-step explanation:

p(chance of winning general election) = (chance of winning primary)x(chance of winning general) = 60% x 54% = 0.6 x 0.54 = 0.324 = 32.4%

\(\huge\text{Hey there!}\)

\(\large\text{40 is 20\% of what time number?}\\\\\\\bullet \large\bold{We\ are\ looking\ for\ your\ UNKNOWN\ number; we\ can\ the\ value}\\\large\bold{is\ \underline{a}\ for\ our\ answer!}\\\bullet\large\bold{REMEMBER: Percentages\ are\ out\ 100\ \& the\ word\ \underline{of}\ means\ \underline{multiply}}\)

\(\huge\text{NOW LETS SOLVE FOR YOUR ANSWER!}\)

\(\bold{Equation: 20\%\ \times \ a\ =\ 40}\\\\\bold{a = \dfrac{40}{20\%}}}\\\\\bold{20\% = \dfrac{20}{100}\rightarrow 0.2}}}\\\\\bold{Equation: a = \dfrac{40}{0.2}}\\\\\bold{\dfrac{40}{0.2}=200}\\\\\bold{a=200}\\\\\boxed{\boxed{\bold{Answer: 200}}}\huge\checkmark\)

\(\large\textsf{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

Im not sure if the numbers in the title were included, but the answer would be: 8.5, 9, 9.5, 10, 10, 10, 11.5, 12, 12, 70, 70, 72, 105.

Step-by-step explanation:

If Francine adds 8.0 ml of 3.0 m KOH to 4.0 ml of 6.0 m HBr, then the resulting mixture will be neutral in nature.

To determine whether the mixture is acidic, basic or neutral, litmus test is done or some other tests can also be performed. However, the mathematical calculations help in understanding the reason behind the result of litmus test.

In the given problem, the volume and molarity of the solutions are given, so number of moles can be easily calculated.

Number of moles of KOH = (8.0 mL) x (3.0 mol/L) / 1000 mL/L = 0.024 mol

Number of moles of HBr = (4.0 mL) x (6.0 mol/L) / 1000 mL/L = 0.024 mol

Considering the chemical reaction between KOH (which is a strong base) and HBr ( which is a strong acid), the resulting product will be a salt along with water (in the form of vapors).

KOH + HBr → KBr + H2O

Since, the number of moles of KOH and HBr is same, therefore the resultant solution will have salt with neutral pH.

Learn more about chemical reaction at:

brainly.com/question/11231920

#SPJ4

Answer:

Step-by-step explanation:

Formulas to Calculate Area of Rhombus

Using Base and Height A = b × h

Using Trigonometry A = b2 × Sin(a)

A = ½ × d1 × d2

1/2 × 25 × 20 =

250 cm²

As no explicit alternative hypothesis is supplied, we should use the two-tailed test, which includes both possibilities of the proportion being less or greater than 62%. As a result, the correct answer is (c) two-tailed test.

To determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed, let's consider the possible alternatives to the researcher's claim:

1. The proportion of voters favoring gun control is less than 62%.
2. The proportion of voters favoring gun control is more than 62%.
3. The proportion of voters favoring gun control is not equal to 62%.

If we were to test against alternative 1, it would be a right-tailed test.
If we were to test against alternative 2, it would be a left-tailed test.
If we were to test against alternative 3, it would be a two-tailed test.

Since we are not provided with any specific alternative hypothesis, it is most appropriate to choose the two-tailed test, as it covers both possibilities of the proportion being either less or more than 62%. Therefore, the answer is (c) two-tailed test.

You can learn more about two-tailed tests at: brainly.com/question/31327677

#SPJ11

Expressing x² + 4x – 7 in the form (x + p)² - q, where p and q are integers, we get p = 2 and Q= 11

Integer:

An integer is the number zero (0), a positive natural number (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). A negative number is the additive inverse of the corresponding positive number. In the language of mathematics, sets of integers are usually denoted by a bold Z.

To find: To express x² + 4x - 7 in the form (x+ p)² - q and determine the values of p and q.

The values of p and q are 2 and 11 respectively.

By completing the square method;

⇒ p = (4/2) = 2.

Therefore,

by expanding (x+ p)² i.e., (x+2)²

By expanding the above (x+2)² We have;

x² + 4x + 4

However,

The question is given as x²+4x-7

Therefore, by comparison between;

x² + 4x + 4 and x²+4x-7; we have:

x² + 4x + 4 = x²+4x-7

⇒ 4 - q = -7,

and, q = 7+4

⇒ q = 11

The values are p =2 and q = 11.

Learn more about Integer:

https://brainly.com/question/15276410

#SPJ4

Answer:

If jacob is broke then he needs to mow 2 lawns for $20 to pay his brother back.

Step-by-step explanation:

Answer:

\(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \sqrt{x} \left \{ {{y=2} \atop {x=2}} \right. \frac{x}{y} \alpha \alpha \alpha =\beta\)

Step-by-step explanation:

Answer:

just put out + from the question.

Answer:

8 3/10

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

a)

The value of the term deposit after 4.5 years is $68,950.53.

Calculation of the value of the term deposit after 4.5 years:
The compound interest formula is: $A=P(1+r)^n

Where:

P is the initial amount

r is the interest rate per compounding period,

n is the number of compounding periods

A is the final amount.

Given:

P=$45000,

r=8.8% per annum, and

n = 4.5 years (annually compounded).

Now substituting the given values in the formula we get,

A=P(1+r)^n

A=45000(1+0.088)^{4.5}

A=45000(1.088)^{4.5}

A=45000(1.532234)

A=68,950.53

Therefore, the value of the term deposit after 4.5 years is $68,950.53.

b)

The interest earned is $23950.53

Interest is the difference between the final amount and the initial amount. The initial amount is $45000 and the final amount is $68,950.53.

Thus, Interest earned = final amount - initial amount

Interest earned = $68,950.53 - $45000

Interest earned = $23950.53

Therefore, the interest earned is $23950.53.

To know more about term deposit refer here:

https://brainly.com/question/28024749

#SPJ11

complete question:

The compound interest formula is given by A=P(1+r)^n where P is the initial amount, r is the interest rate per compounding period, n is the number of compounding periods, and A is the final amount. Suppose that $45000 is invested into a term deposit that earns 8.8% per annum. (a) Calculate the value of the term deposit after 4.5 years. (b) How much interest was earned?

Answer:

40.6428571429

Step-by-step explanation:

To evaluate the expression for the given value of the variable when t = -1/2, we just need to substitute the value of t into the expression:

41 + 5/7 * (-1/2) = 41 - 5/14
41 - 5/14 = 40.6428571429

So the answer is 40.6428571429.

Answer:

option B

-5/2

Step-by-step explanation:

______________________

In the attached diagram the perimeter of the hall way is

The perimeter of the hall way is calculated by adding all the sides of the hallway

The perimeter of the hall way  = 2x - 7 + x + 1 + 4x - 9 + x - 2 + x + 2 + 3x - 11 + x - 2 + 3x - 11 + x + 4

adding like terms results to

The perimeter of the hall way  =  17x + (-34)

Finally, the simplified expression is:

17x - 34

Learn more about perimeter at

https://brainly.com/question/19819849

#SPJ1

Answer:

6 pounds

Step-by-step explanation:

Answer:

beat your meat??? also you are bad!!!!

Step-by-step explanation:

Answer:

3A
4C

5B

6C

7A

8A

Step-by-step explanation:

If I'm wrong

Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

a. the number of patients in a hospital

A discrete random variable is a variable that can only take on a finite or countably infinite set of distinct values. In this case, the number of patients in a hospital can only be whole numbers (e.g., 0, 1, 2, 3, etc.), which is a countable set of values. Therefore, it is a discrete random variable.

b. the average amount of electricity consumed

The average amount of electricity consumed is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range, and it is not restricted to specific distinct values.

c. the amount of paint used in repainting a building

The amount of paint used in repainting a building can be measured in continuous quantities (e.g., liters or gallons). It is not restricted to specific distinct values, and therefore, it is not a discrete random variable.

d. the average weight of female athletes

Similar to the average amount of electricity consumed, the average weight of female athletes is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range and is not restricted to specific distinct values.

Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

To know more about variable follow the link:

https://brainly.com/question/28248724

#SPJ11

The set g={2,4,6,8} in Z10 under the operation * is a group.

To determine whether the set g={2,4,6,8} in Z10 is a group under the operation *, we need to verify four properties: closure, associativity, identity element, and inverse element.

Closure: For any two elements a and b in g, the product ab should also be in g. In this case, multiplying any two elements in g (mod 10) will result in another element in g, satisfying closure.

Associativity: For any three elements a, b, and c in g, the operation * should be associative. Since multiplication in Z10 is associative, the operation * on g is also associative.

Identity Element: An identity element e exists in g such that for any element a in g, ae = ea = a. The element 2 serves as the identity element in g since 2a = a2 = a for all elements a in g.

Inverse Element: For every element a in g, there exists an inverse element b in g such that ab = ba = e. In this case, each element in g has an inverse within g. For example, 28 = 82 = 6, 46 = 64 = 4, 64 = 46 = 6, and 82 = 28 = 2.

Since the set g={2,4,6,8} in Z10 satisfies all four group properties, it is indeed a group under the operation *.

Learn more about operation

brainly.com/question/30581198

#SPJ11

Answer:

4/6 or 2/3

Step-by-step explanation:

probability is successful out of total. The total is 1,2,3,4,5,6, or 6 ways, and the successful is 2,4,5,6, or 4 ways

Answer:

10cm -4cm=6cm

Step-by-step explanation:

answer=6cm

Answer:

y=−9

Step-by-step explanation:

Let's solve for y.

y=(2)(−8)+7

Answer:

y=-9

Step-by-step explanation:

Y=2(-8)+7

first multiply

Y=-16+7

add like terms

y=-9

Answer:

25

Step-by-step explanation:

percentage calculator 40 is what percent of 160=25;)

Answer:

40/100×160

Step-by-step explanation:

2/5×160

320/5

64

After buying tickets and drinks the total cost is 29.18 and using 5.00 off coupon, the cost of one drink is 11.59

As per the question statement, 2 tickets cost 11.00 and they bought 2 drinks and used a 5.00 off coupon. The total cost was 29.18. We are supposed to find out the cost of one drink.

Let the cost of one drink be "x"

Cost of 2 tickets = 11

Off coupon is of 5.00

Cost of two drinks = \(2x\)

Total money paid = 29.18

Hence, \(11+2x-5=29.18\\2x=29.18+5-11=23.18\\x=\frac{23.18}{2} \\x=11.59\)

Therefore the cost of one drink is \(x=11.59\)

This question was a classic example of how to form equations when all the given conditions are in statements.

To learn more about it, click on the link given below:

https://brainly.com/question/953809

#SPJ9

Answer:

69............ I see 69

Step-by-step explanation: