U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. Which one of the following sets represents both P (A) n P (B) and P (An B)?
O a. {{1}}
O b. {0, {{1}}}
O c. {0, {1}}
O d. Not one of the above alternatives since P (A) n P (B) = P(An B)

The linear equation that relates the thickness and the number of weeks is:

y = -0.2*x + 3.36

We know that the thickness decreases at a constant rate of 0.2 meters per week, so we will have a linear function between y, the thickness, and x, the number of weeks:

y = -0.2*x + b

Where b is the initial thickness

We know that after 7 weeks the sheet is 2.4 meters thick, so we can write:

2.4 = -0.2*7 + b

Now we can solve this for b.

2.4 + 0.2*7 = b

3.36 = b

Then the linear equation is:

y = -0.2*x + 3.36

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The percentage of total deliveries made by Aldo is 60%.

A percentage is a number or ratio expressed as a fractin of 100. It is often denoted using a percent "%" sign.

It is given that,

Total number of deliveries to be made = 30

Deliveries made so far = 18

Now, for the percentage of his total deliveries we need to divide deliveries made so far with the total deliveries,multiplied by 100%.

⇒ Percentage of his total deliveries = Deliveries made so far/Total number of deliveries

⇒ Percentage of his total deliveries = 18/30*100%

⇒ Percentage of his total deliveries = 60%

Hence,the percentage of total deliveries made by Aldo is 60%.

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Answer:

45%

Step-by-step explanation:

There are 60 square tiles in total

Only 27 of the tiles have been installed

Now you're going to do 27 divided by 60

You're going to get 0.45

Now you're going to convert that decimal into a percentage by multiplying by 100

0.45×100=45

Your answer is 45%

Answer:

Second option 168= 18.X + 12.2X

Step-by-step explanation:

Area of the shape is in two parts,

Are of the larger rectangle is Lenght x width

Lenght is 12cm and width is x +2x

Area = 12 x 3x = 36x cm²

Area of the smaller rectangle = 6 x X = 6xcm²

Total area 36x + 6x = 168cm²

Another method

Find the area of the big rectangle including the cut off area

Lenght x width = 18 x (2x + X)

Area =18 x 3x or 18.3x

Calculate the white area

Length x width = 6 x 2x = 12x

Deduct the white area from the larger area

168= 18.3x - 12x

Third method

Divide the rectangle from top down

First rectangle length x width = 18x X or 18x

Second rectangle length x width = 12 x 2x

168= 18. x + 12 . 2x

The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The figure shown has a total area of 168 cm².

Now, We can find as;

Area of rectangle = Length x width

Hence, We can formulate;

⇒ 18 × x + 12 × 2x = 168

Thus, The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

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The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Answer:

d seems like the only one that would be correct

Step-by-step explanation:

lmk if this is wrong

The volume of his barn is calculated as:

= 40,000 cubic feet.

The barn as seen in the image attached below comprises of a rectangular prism and a triangular prism. Therefore:

Volume of the barn = (volume of rectangular prism) + (volume of triangular prism).

Volume of triangular prism = 1/2(base * height) * length of prism

= 1/2(40 * 10) * 50

= 10,000 cubic feet.

Volume of the rectangular prism = length * width * height

= 50 * 40 * 15

= 30,000 cubic feet.

Therefore, volume of his barn = 30,000 + 10,000 = 40,000 cubic feet.

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Amy will earn $28.70 + $3.80 = $32.50.

Profit and loss:

A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.

Amy will earn $28.70 from selling 7 large necklaces (7 x $4.10 = $28.70) and $3.80 from selling 1 small necklace, so in total, she will earn $28.70 + $3.80 = $32.50.

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The requried length of the arc MN is evaluated as 6π.

From the figure,
The area of the shaded sector is given as:

A = ∠NLM/360×πr²

27π= ∠NLM/360×π9²
∠NLM = 120

Now,

length MN = 120/360*2πr

                  = 1/3×2π×9
                  = 6π

Thus, the requried length of the arc MN is evaluated as 6π.

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The six main criteria to define normality and abnormality include statistical infrequency, personal distress, others' distress, unexpected behavior, highly consistent/inconsistent behavior, and maladaptiveness/disability.

1. Abnormality as statistical infrequency: This criterion defines abnormality based on behaviors or characteristics that deviate significantly from the statistical norm.

2. Abnormality as personal distress: This criterion focuses on the individual's subjective experience of distress or discomfort. It considers behaviors or experiences that cause significant emotional or psychological distress to the person as abnormal.

For instance, someone experiencing intense anxiety or depression may be considered abnormal based on personal distress.

3. Abnormality as others' distress: This criterion takes into account the impact of behavior on others. It considers behaviors that cause distress, harm, or disruption to others as abnormal.

For example, someone engaging in violent or aggressive behavior that harms others may be considered abnormal based on the distress caused to others.

4. Abnormality as unexpected behavior: This criterion defines abnormality based on behaviors that are considered atypical or unexpected in a given context or situation.

For instance, if someone starts laughing uncontrollably during a sad event, their behavior may be considered abnormal due to its unexpected nature.

5. Abnormality as highly consistent/inconsistent behavior: This criterion involves comparing an individual's behavior to both their own typical behavior and the behavior of others. Consistent or inconsistent patterns of behavior may be considered abnormal.

For example, if a person consistently engages in risky and impulsive behavior, it may be seen as abnormal compared to their own usually cautious behavior or the behavior of others in similar situations.

6. It considers behaviors that are maladaptive, causing difficulties in personal, social, or occupational areas. For instance, someone experiencing severe social anxiety that prevents them from forming relationships or attending school or work may be considered abnormal due to the disability it causes.

The medical model and classification systems used in physical illnesses have both value and limitations when applied to psychological disorders. They provide a structured framework for understanding and diagnosing psychological disorders, allowing for standardized assessment and treatment. However, they can oversimplify the complexity of psychological experiences and may lead to overpathologization or stigmatization.

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Answer:

  $70 or $101

Step-by-step explanation:

You want to know the savings in finance charges if a $2000 credit card balance is paid at the rate of $100 per month instead of $75 per month. The APR is 12.5%.

The finance charge each month is 1/12 of 12.5% of the outstanding balance. For the purpose here, we assume the $2000 balance earns that finance charge for the first payment.

The wording "paying $75 [or] $100 of the monthly balance" can be interpreted two ways:

The attached spreadsheet shows both solutions, so you need to decide which interpretation is expected.

If the payment amount is in addition to the finance charge, the savings is $70.

If the payment amount includes the finance charge, the payoff takes longer, so the savings is $101.

__

Additional comment

There are financial calculators that will tell you the required number of payments, depending on the scenario you are interested in. We find a spreadsheet to be the most accurate way to model the loan payments. This one rounds the interest amount to the nearest cent, just as would be the case on a credit card statement.

That rounding of intermediate values tends to change the answer slightly from what you might get using a formula. Also, the final payment amount is different from the others in most cases.

YMMV. Your best bet is to follow an example calculation from your curriculum materials. Likely that will show you the appropriate interpretation of the question.

By repaying $100 instead of $75 monthly, Taylor saves $100.86 in interest and fees.

The savings in interest and fees (finance charges) are the difference between the two payment options.

The compound interests are computed differently for the two payment options and compared.

The compound interests can be computed using an online finance calculator as follows:

I/Y (Interest per year) = 12.5%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $-75

FV (Future Value) = $0

Results:

N = 31.403

The sum of all periodic payments = $-2,355.22

Total Interest = $355.22

I/Y (Interest per year) = 12.5%

PV (Present Value) = $2,000

PMT (Periodic Payment) $-100

FV (Future Value) = $0

Results:

N = 22.544

The sum of all periodic payments = $-2,254.36

Total Interest = $254.36

Total Interest with $75 monthly repayment = $355.22

Total Interest with $100 monthly repayment = $254.36

The difference in interest = $100.86 ($355.22 - $254.36)

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Answer:

$36.00 is better because you get 54 apples

Step-by-step explanation:

36÷9= 4*12=48

Approximately 34.1% of students earn a score between 75% and 89%.
the correct answer is 34.1%.

Approximately what percent of students earn a score between 75% and 89%?

To solve this problem, we need to calculate the area under the normal distribution curve between 75% and 89%.
First, we need to convert the scores into z-scores using the formula:
z = (x - mean) / standard deviation

For 75%, the z-score is (75 - 89) / 14 = -1
For 89%, the z-score is (89 - 89) / 14 = 0

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores.

The area between -1 and 0 is approximately 0.3413, which is equivalent to 34.1%.

Therefore, approximately 34.1% of students earn a score between 75% and 89%.

So the correct answer is 34.1%.

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Answer: C

Step-by-step explanation: a^2 + b^2 = c^2

A. 6^2 + 8^2 = 10^2

B. 12^2 + 35^2 = 37^2

C. 4^2 + 6^2 does not equal 10^2.....(16 + 36 = 52   10^2 = 100)

D. 10^2 + 24^2 = 26^2

The measures of the triangles 4 cm, 6 cm, and 10 cm do not represent a right angle triangle because it does not follow the Pythagoras theorem option (C) is correct.

It is defined as a triangle in which one angle is 90 degrees and the other two angles are acute angles. In a right-angled triangle, the name of the sides are hypotenuse, perpendicular, and base.

For the triangle sides:

6 cm, 8 cm, and 10 cm

From the Pythagoras theorem:

\(10^2=8^2+6^2\)

100 = 100

These sides satisfy the Pythagoras formula.

For the triangle sides:

12 cm, 35 cm, and 37 cm

From the Pythagoras theorem:

\(37^2=35^2+12^2\)

1369 = 1369

These sides satisfy the Pythagoras formula.

For the triangle sides:

4 cm, 6 cm, and 10 cm

From the Pythagoras theorem:

\(10^2=6^2+4^2\)

100 ≠ 52

These sides do not satisfy the Pythagoras formula.

For the triangle sides:

10 cm, 24 cm, and 26 cm

From the Pythagoras theorem:

\(26^2=24^2+10^2\)

676 =  676

These sides satisfy the Pythagoras formula.

Thus, the measures of the triangles 4 cm, 6 cm, and 10 cm do not represent a right angle triangle because it does not follow the Pythagoras theorem option (C) is correct.

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Answer:

Eh, I think zero apples

Step-by-step explanation:

This is because if you eat 3 apples a day for 30 days you get,
3x30=90

Answer:

C. -2x - 2

The picture shows the work I did to get the answer.

Hope this helps!

Answer:

45 • 4 = 180

Step-by-step explanation:

1 quart = 1/4 gallon.

45 • 4 = 180

The graph of the function g(x) = −|x + 3| − 2 is added as an attachment

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

g(x) = −|x + 3| − 2

The above expression is an absolute value function that hs the following properties

Next, we plot the graph

See attachment for the graph of the function

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Answer:

Step-by-step explanation:

i thinks its 6 (im sorry if im wrong)

Answer:

z = 120º

Step-by-step explanation:

t + 2t + t + 2t = 360º

60 + 2(60) + 60 + 2(60) = 360

t = 60

2t = z

z = 120º

This is all based on the fact there there are 360º in a quadrilateral.

Rick should order part number G371-7 So the option A is the correct Answer

What is a part number ?

Part designs or materials are identified by part numbers, which are sometimes abbreviated as PN, P/N, part no., or part #. Its goal is to make referencing to that thing simpler. A part number clearly identifies a part design both inside and occasionally outside of a single organization. For instance, it is simpler to identify a screw as "HSC0424PP" rather than "Hardware, screw, machine, 4-40, 3/4" long, pan head, Phillips." The part number in this illustration is "HSC0424PP," which may be prefixed in database fields as "PN HSC0424PP" or "P/N HSC0424PP."

A serial number is a specific identifier of a specific instantiation of a part design, much as a part number identifies a component design (regardless of its instantiations). To put it another way, a part number designates each specific (physical) item as having been manufactured to a specific, original design;

As part number G371-7 fits perfectly to the desired requirement of float diameter of less than 8 inches, weigh more than 1 pound, and fit a 5/16-SAE spud connection that's why it is the correct answer

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Answer:

Answer: 7.93

Estimate: 8

Answer: 7.93, or to the nearest tenths, 7.9

The graph of g(x)=(x – 2)²+10 is a translation of the parent function f(x) = x²by² units to the right and 10 units up.

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

The graph of the function g(x) = (x-2)² +10 is a transformation of the parent function f(x) = x² that has been shifted 2 units to the right and 10 units up.

To see this, consider the vertex of the graph of g(x), which occurs at the point (2, 10). This vertex represents the minimum value of the function and is located 2 units to the right and 10 units up from the vertex of the parent function f(x), which is at the origin (0, 0). Therefore, we can say that the graph of g(x) is a translation of the graph of f(x) by a vector (2, 10).

Therefore, The graph of g(x) = (x-2)² +10 is a translation of the parent function f(x) = x²by² units to the right and 10 units up. The vertex of g(x) is located at (2, 10), which is 2 units to the right and 10 units up from the vertex of f(x) at (0, 0).

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Answer:

AB || CE, so we have triangle DEO, two of whose angles are 100° and 26° (from point D, draw DE such that CD + DE = CE intersects BO). The third angle of this triangle measures 54°, so

x = 180° - 54° = 126°.

The number of miles in the circumference of the circle on Earth parallel to the equator and passing through Lena, Wisconsin, is approximately 17,747.07 miles.

To calculate the circumference of the circle on Earth parallel to the equator and passing through Lena, Wisconsin, we need to determine the length of the circle's circumference at the given latitude.

Given:

Length of the Earth's equator = 25,100 miles

Latitude of Lena, Wisconsin = 45 degrees north

The circumference of a circle at a given latitude on a perfect sphere can be calculated using the formula:

Circumference = (Cos(latitude) * Earth's equator circumference)

First, we need to convert the latitude from degrees to radians:

Latitude in radians = 45 degrees * (π / 180)

Latitude in radians = π/4

Next, we can substitute the latitude in radians into the formula to calculate the circumference:

Circumference = (Cos(π/4) * 25,100 miles)

Using the value of the cosine of π/4 (which is √2 / 2), we have:

Circumference = (√2 / 2) * 25,100 miles

Simplifying:

Circumference ≈ 0.707 * 25,100 miles

Circumference ≈ 17,747.07 miles

Therefore, the number of miles in the circumference of the circle on Earth parallel to the equator and passing through Lena, Wisconsin, is approximately 17,747.07 miles.

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The relation c has the reflexive, symmetric, and transitive properties.

The relation c defined on the set of all people has the following properties:

1. Reflexive property:

For every person x, x is related to itself. This is because every person shares at least one common interest with themselves.

2. Symmetric property:

If x is related to y, then y is related to x. This is because if x and y share a common interest, then y and x also share that same common interest.

3. Transitive property:

If x is related to y, and y is related to z, then x is related to z. This is because if x and y share a common interest, and y and z also share a common interest, then x and z will also share that same common interest.

1. Reflexive property:

To check if a relation is reflexive, we need to verify if every element in the set is related to itself. In this case, since every person shares at least one common interest with themselves, the relation is reflexive.

2. Symmetric property:

To check if a relation is symmetric, we need to verify if for every pair (x, y) in the relation, (y, x) is also in the relation. In this case, if x and y share a common interest, then y and x will also share that same common interest, making the relation symmetric.

3. Transitive property:

To check if a relation is transitive, we need to verify if for every three elements x, y, and z in the relation, if (x, y) and (y, z) are in the relation, then (x, z) is also in the relation. In this case, if x and y share a common interest, and y and z also share a common interest, then x and z will also share that same common interest, making the relation transitive.

So, the relation c has the reflexive, symmetric, and transitive properties.

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(d) \frac{11}{27}

To determine if abc + ab + a is divisible by 3, we need to analyze the remainders of each term modulo 3. Out of the numbers 1 to 2010, exactly one-third (670 numbers) are congruent to 0 modulo 3, one-third are congruent to 1 modulo 3, and the remaining one-third are congruent to 2 modulo 3.

For abc + ab + a to be divisible by 3, we consider three cases:

Case 1: If a, b, and c are all congruent to 0 modulo 3, then abc + ab + a is divisible by 3.

Case 2: If exactly one of a, b, and c is congruent to 0 modulo 3, then abc + ab + a is divisible by 3.

Case 3: If two of a, b, and c are congruent to 0 modulo 3, then abc + ab + a is divisible by 3.

In cases 1 and 2, there are (670)^3 + 3 \times (670)^2 possible combinations, and in case 3, there are 3 \times (670)^2 possible combinations. So, the total number of successful outcomes is (670)^3 + 6 \times (670)^2, and the total number of possible outcomes is (2010)^3.

The probability is \frac{(670)^3 + 6 \times (670)^2}{(2010)^3} = \frac{11}{27}. The probability that abc + ab + a is divisible by 3 is \frac{11}{27}.

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The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .

In the question ,

it is given that ,

the number of residents in the local apartment complex is = 71

the mean electric bill for the 71 residents = $62 ;

we know that the sample mean is itself called as the best point estimate ;

So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of  local apartment complex which is given as $62 .

Therefore , the best point estimate is $62 .

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A number that goes into a greater number with no remainders is called a factor.

A factor is an integer that divides into a greater number without any remainders.

For example, the number 6 is a factor of 18 because when 18 is divided by 6, the answer is 3 with no remainders. Similarly, the number 3 is a factor of 12 because when 12 is divided by 3, the answer is 4 with no remainders.

Factors are important in mathematics because they can be used to solve equations and determine the greatest common divisor (GCD) of two or more numbers. Factors can also be used to determine prime numbers and their multiples.

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