Prove or disprove the following statement: if A, B, and C are
sets with finite cardinalities that satisfy A ∩ B ∩ C = ∅, then |A
∪ B ∪ C| = |A| + |B| + |C|.

Answer:

Phoebe: 180

Andy: 60

Polly: 30

Step-by-step explanation:

Let Polly's money be P  

Then Andy's money = P * 2 = 2P  

Then Pheobe's money = 2P * 3 = 6P  

There are 9 P's (P + 2P + 6P)

270 / 9 P's = 30

Therefore P = 30

Polly gets $30

Andy gets 30 * 2 = $60

Phoebe gets 60 * 3 = $180

Checking:    

180 + 60 + 30 = 270

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

Step-by-step explanation:

Remark

You are trying to convert the base function f(x) = x^2 into the child function g(x) = -(x + 3)^2 + 5

UP

Start with the simplest part of the transformations. + 5

If you have g(x) = f(x)+5 what you have done is move the function up 5 units on your grid.

Up side Down

Next is the - sign.

f(x) = x^2

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

This has the affect of turning x^2 upside down. It looks like a cup opening towards the counter or down.

Left right

The last step is left / right. This is the hard one. It moves in the opposite direction that you think it should. x +3 moves the parabola left, not right. If you want it to move right, use (x - 3)

Graph

I have enclosed a graph to show you exactly what is going on. The red  line is f(x)=x^2

The blue line is g(x) = -(x + 3)^2 + 5

Answer:

19 months

Step-by-step explanation:

First off 682- 55 = 627. 627/33 = 19

Each machine will print 760 pages

What is arithmetic ?

Arithmetic is an elementary part of mathematics that consists of the study of the parcels of the traditional operations on figures addition, deduction, multiplication, division, exponentiation, and birth of roots.

Main body:

As there are total 6 printing machines

but one of the machines is out of order

which means left working machines = 6-1 = 5

pages to be printed = 3800

so total pages need to be printed by each machine =

3,800 ÷ 5 = 760

Hence, Each machine will print 760 pages

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The question states that 1/4 of students at International are in the blue house, with 1/5 votes for Adam and 1/4 for Franklin. To analyze the results, calculate the fraction of votes for each candidate and multiply by the total number of students.

Based on the information provided, 1/4 of the students at International are in the blue house. The vote went as follows: 1/5 of the votes were for Adam, and 1/4 of the votes were for Franklin.

To analyze the vote results, we need to calculate the fraction of votes for each candidate.

Let's start with Adam:
- The fraction of votes for Adam is 1/5.
- To find the number of students who voted for Adam, we can multiply this fraction by the total number of students at International.

Next, let's calculate the fraction of votes for Franklin:
- The fraction of votes for Franklin is 1/4.
- Similar to before, we'll multiply this fraction by the total number of students at International to find the number of students who voted for Franklin.

Remember, we are given that 1/4 of the students are in the blue house. So, if we let "x" represent the total number of students at International, then 1/4 of "x" would be the number of students in the blue house.

To summarize:
- The fraction of votes for Adam is 1/5.
- The fraction of votes for Franklin is 1/4.
- 1/4 of the students at International are in the blue house.

Please note that the question is incomplete and doesn't provide the total number of students or any additional information required to calculate the specific number of votes for each candidate.

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Answer:

C

Step-by-step explanation:

Use the pythagorean theorem.

32^2+b^2=48^2

1024+b^2=2304

Subtract 1024

b^2=1280

Square root

b=sqrt(1280)

Now simplify sqrt(1280)

sqrt(1280) = sqrt(256*5)

You can take the square root of 256 since it is a perfect square so take it out of the radical.

sqrt(256*5)=16sqrt(5)

So the answer is c, 16\(\sqrt{5}\)

Answer:

C. 16/5

Step-by-step explanation:

pythagorean theorem

a^2 + b^2 = c^2

divide 48 and 32 by 16

a= 2 c= 3

4 + b^2 = 9

b^2 = 5

b = √5

then multiply 16 with √5

which =

16√5

Answer:

b = \(\frac{ac-2c}{2a}\)

Step-by-step explanation:

Given

\(\frac{1}{2}\) = \(\frac{1}{a}\) + \(\frac{b}{c}\)

Multiply through by 2ac to clear the fractions

ac = 2c + 2ab ( subtract 2c from both sides )

ac- 2c = 2ab ( divide both sides by 2a )

\(\frac{ac-2c}{2a}\) = b

Darrol needs to work for at least 63 hours to save enough money to buy the $3200 television set.

The cost of the television set is $3200.

Darrol has $700 saved up.

Let's define x as the number of hours Darrol needs to work to save enough money to buy the television set.

Darrol earns $40 per hour.

Therefore, the amount of money he will earn in x hours is: 40x

If he adds this amount to his savings, he will have enough money to buy the television set.

We can set up the following equation:

40x + 700 = 3200

Simplifying the equation, we get:

40x = 2500

Dividing both sides by 40, we get:

x = 62.5

Therefore, Darrol needs to work for at least 63 hours to save enough money to buy the $3200 television set.

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Answer: If there are 60 questions and the student has to answer 75% of questions then the number of questions the student must answer is 45

Step-by-step explanation:

No of questions= 60,

Answers to be given= 75%

then no of questions to pass the exam= No of questions*Answers to be given in percentage

=60*75/100\

=45

The height of the building is approximately 62.4369 feet. The solution involves using trigonometry and solving for the opposite side of the triangle using the tangent function.

Let h be the height of the building, and x be the distance between the first point and the base of the building. Then we have:

tan(26.8°) = h/x ----(1)

tan(19.5°) = h/(x + 43.9) ----(2)

From equation (1), we have x = h/tan(26.8°)

Substituting this value of x in equation (2) and solving for h, we get:

h = (43.9 tan(19.5°) tan(26.8°))/(tan(26.8°) - tan(19.5°))

Plugging in the values, we get:

h ≈ 62.4369 feet

Therefore, the height of the building is approximately 62.4369 feet.

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Answer:

The number is 7

Step-by-step explanation:

To find the missing number, subtract 5 from 12.

12 - 5 = 7

The given statement "In one scene in 8 1/2, Guido steps onto an elevator that takes on the characteristics of a confession booth" is True.

What is 8 1/2?8 1/2 is an Italian drama movie which was released in the year 1963. It was directed by Federico Fellini. The movie is widely recognized as a highly influential classic of world cinema. The story is about a renowned filmmaker named Guido Anselmi. He is in the middle of making a film but is struggling to come up with a plot for it. In one scene of the movie, Guido steps onto an elevator that takes on the characteristics of a confession booth.MAIN ANS:True, In one scene in 8 1/2, Guido steps onto an elevator that takes on the characteristics of a confession booth.The elevator in 8 1/2 takes on the characteristics of a confession booth as a result of its setting and characters. The elevator setting in the film emphasizes that Guido is in a confessional box and is confessing his sins. It was a unique way of depicting Guido's guilt. The way the elevator shook and rattled, making him feel like he was in a confessional box, was symbolic of how he felt. It was as if he was being taken to a higher power who was listening to him.

The scene emphasizes the religious imagery in the movie. It allows us to gain insight into Guido's psyche and the struggles he was having. The religious imagery in the movie suggests that Guido is trying to connect with a higher power to overcome his guilt. The scene also shows the extent to which he is willing to go to gain clarity.

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The values of function g(x) are as follows:

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

Given, a relation between two functions in terms of variables

      the value of g(x) = x* f(x) = -2 *1 = -2

      the value of g(x) = x* f(x) = 0 *-2 = 0

      the value of g(x) = x* f(x) = 1 *-5 = -5

      the value of g(x) = x* f(x) = 3 *-4 = -12

Therefore, The values of the given function are -2, 0, -5, and -12.

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Complete question:

g(x) = x f(x)

Answer:

x = 3

Step-by-step explanation:

\(2(4x + 3) = 2(18 - x) \\ 8x + 6 = 36 - 2x \\ 8x + 2x = 36 - 6 \\ 10x = 30 \\ x = \frac{30}{10} \\ x = 3\)

The solutions of  Ax = 0 in parametric vector form, where A is a row equivalent to the given matrix are : x_1 = 2x_3 + 2x_2,x_2 = x_2 + x_3,x_3 = x_3,x_4 = 2x_3 + 6x_2,x_5 = -3x_3 - 6x_2,x_6 = -4x_3 - 2x_2

The given matrix is row equivalent, which means that it can be reduced to row echelon form using elementary row operations. To solve for the parametric vector, we start by performing the same operations to the identity matrix. First, we divide the first row by 2 to get the leading coefficient of 1 on the leftmost column. Then, we add the first row to the second row, and the third row to the fourth row to eliminate the elements below the leading coefficients.

Finally, we multiply the first row by -4 and add it to the third row to get the leading coefficient of 1 on the third column. After performing the same operations on the identity matrix, we get the parametric vector x_2 + x_3. This means that x_1 = 2x_3 + 2x_2, x_2 = x_2 + x_3, x_3 = x_3, x_4 = 2x_3 + 6x_2, x_5 = -3x_3 - 6x_2, and x_6 = -4x_3 - 2x_2. Essentially, the parametric vector is the sum of the two columns of the identity matrix that correspond to the two leading coefficients in the row echelon form of the original matrix.

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Answer:

give me points an d i will give u points

Step-by-step explanation: yufikdx

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

510

Step-by-step explanation:

153/3=51 (words per min)

51x10=510 (words per 10 min)

Answer:510

Step-by-step explanation:

The two most commonly used measures of variability are variance and standard deviation.

1. Variance: Variance measures how spread out a set of data points is from the mean. It calculates the average of the squared differences between each data point and the mean. The formula for variance is sum of squared differences divided by the number of data points.

Example: Let's say we have a set of data points: 2, 4, 6, 8, and 10. The mean of these data points is 6. The differences between each data point and the mean are: -4, -2, 0, 2, and 4. Squaring these differences gives us: 16, 4, 0, 4, and 16. The sum of these squared differences is 40. Dividing this sum by the number of data points (5) gives us a variance of 8.

2. Standard Deviation: Standard deviation is the square root of variance. It measures the average distance between each data point and the mean. Standard deviation is often preferred over variance because it is in the same unit as the data points, making it easier to interpret.

Example: Using the same set of data points as above, the variance is 8. Taking the square root of 8 gives us a standard deviation of approximately 2.83.

In summary, variance measures how spread out the data points are from the mean, while standard deviation gives us a more intuitive understanding of the variability by providing a measure in the same unit as the data points. These measures help us understand how the data is distributed and how much it deviates from the average.

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The amount of the worker monthly tax will equals to K4,850.

An income tax refers to the tax imposed on individuals or entities in respect of the income earned by them. It is computed as the product of a tax rate times the taxable income. They may vary by type or characteristics of the taxpayer and the type of income

To calculate the worker's monthly tax, we need to determine the amount of salary that falls into each tax bracket and then calculate the tax owed for each bracket:

The worker's monthly tax is then computed as:

=  K1,500 + K3,000 + K350

= K4,850.

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The values of the missing angles and sides after dilation are:

m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'

m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC  (dilation)

m∠C'B'D = 180° - 34° - 51° = 95°

Thus, by way of scale factor we can say that:

BC/B'C' = BD/B'D' = 36/18 = 2

B'D' = ¹/₂BD = ¹/₂ * 22 = 11

ΔC'P'Q ∼ ΔCPQ

Thus:

C'Q'/CQ = C'D'/CD = D'Q'/DQ

CQ = 2C'Q' = 2 * 3 = 6

Therefore, m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

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Answer:

-7.34 repeating

Step-by-step explanation:

A rational number is described as a number that can be expressed as a fraction or ratio of two integers and -7.34 repeating is the only option that does not fit this description. Repeating decimals can not be rational.

Answer:  \(-\sqrt{14}\) in the lower right corner

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

Explanation:

A rational number is any fraction like 2/3 or 7/9. Pick any two integers, divide them, and you get a rational number. Zero cannot be in the denominator.

Based on that, we can see that 129/999 is rational, which is crossed off the list of potential answers.

Furthermore, \(\sqrt{16} = 4 = \frac{4}{1}\) is also rational since we can form a fraction of integers. Cross this off the list as well. Always try to simplify the expression as much as possible.

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

When converting a fraction to decimal form, it turns out that any rational number has either two cases:

This means the number \(-7.\overline{34}\) = -7.3434343434... is also rational, which is crossed off the list also.

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

The only thing left is \(-\sqrt{14}\) which is not rational, and therefore we consider it irrational. We cannot form a fraction of integers to represent this square root value. Note how 14 is not a perfect square.

Answer:

angles J and N

Step-by-step explanation:

vertical angles are congruent angles that are vertically across from each other

angle j and angle n are both right angles and they are both vertically across from each other therefore A is your answer

Answer:

The total weight of the pool when it is full of water is 690.2 pounds.

Step-by-step explanation:

We know that total weight of the wading pool (\(m_{T}\)) is the sum of the weight of empty pool (\(m_{pool}\)) and the weight of water (\(m_{w}\)), all measured in pounds, that is:

\(m_{T} = m_{pool} + m_{w}\)

The weight of water can be determined by definition of density, as we know the geometry of the wading pool and density of water:

\(m_{w}=\rho_{w}\cdot (w\cdot h\cdot l)\)

Where:

\(\rho_{w}\) - Density, measured in pounds per cubic foot.

\(w\), \(h\), \(l\) - Width, height and length of the wading pool, measured in feet.

Now, we are noticed that \(\rho_{w} = 6.24\,\frac{pd}{ft^{3}}\), \(w = 7\,ft\), \(h = 6\,ft\), \(l = 2.5\,ft\) and \(m_{pool} = 35\,pd\) and the total weight of the pool when it is full of water is:

\(m_{w} = \left(6.24\,\frac{pd}{ft^{3}} \right)\cdot (7\,ft)\cdot (6\,ft)\cdot (2.5\,ft)\)

\(m_{w} = 655.2\,pd\)

\(m_{T} = 35\,pd + 655.2\,pd\)

\(m_{T} = 690.2\,pd\)

The total weight of the pool when it is full of water is 690.2 pounds.

Answer:The answer is in the attached file below

Step-by-step explanation:

Answer:

angle 7=100 ,angle 8=80

Step-by-step explanation:

For angle 7:

By using definition of alternate interior angles:

angle 4=angle 6

Subtitute values of angles:

x+2y=3y+20

x+2y-3y=20

x-y=20.......(1)

Now by using definition of alternate opposite angles:

angle 4= angle 2

angle 2=x+2y

Angle 1 and angle 2 are the angles of straight line ,there sum will be 180.

2x+y+x+2y=180

3x+3y=180

x+y=60......(2)

Add (1) and (2):

x-y=20

x+y=60

_______

2x=80

x=40

subtitute x=40 in (2):

40+y=60

y=60-40

y=20

For angle 7:

By using definition of alternate exterior angle:

angle 1=angle 7

angle 7=2x+y

subtitute x and y:

angle 7=2(40)+20

=100

For angle 8:

By using definition of alternate opposite angle:

angle 8=angle 6

angle 8= 3y+20

angle 8=3(20)+20

=80

Answer:

The quotient of -27/9 is -3 hope this helps <3

Step-by-step explanation:

9 goes into 27, 3 times, since 27 is negative, it would be -3

The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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