Water is flowing from Tower #1 to Tower #2 in the diagram below at a rate of 20 gallons per minute. Initially, Tower #1 contained 1650 gallons and Tower #2 contained 570 gallons. (a) How many gallons does each tower contain after 5 minutes? Show your work. (b) Let m be the number of minutes it takes for the two towers to contain the same number of gallons. Set up and solve an equation for m. PLEASE HELP

There are three solutions for the system of equations.

Now, The system of equations have:

x - y = -4   __(1)

\(y = \sqrt{2x+3}-2\) ___(2)

=> From equation (1)

x + 4 = y

Substitute the values of y as 4 + x

x + 4 = \(\sqrt{2x+3}-2\)

Now, Collect like terms:

x + 4 + 2 = √ 2x + 3

x + 6 = √ 2x + 3

Squaring on both sides:

\((x+6)^2=(\sqrt{2x+3} )^2\)

(x + 6)(x + 6) = 2x + 3

\(x^{2} +12x+36\) = 2x + 3

\(x^{2}\) + 12x - 2x + 36 - 3 = 0

\(x^{2}\) - 10x + 33 = 0

Factories the common factor:

\(x^{2} -\) 5x -5x + 25 + 8 = x (x -5)-5(x - 5) + 8 = (x -5)(x - 5)+ 8

= (x-5)^2 + 8

Therefore, x = 5 and 8

When we put x = 5 in eqn (1) we get:

5 - y = -4

-y = -4 - 5

y = 11

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Answer:

48 × 9.20 = 441.60

Step-by-step explanation:

gross wages can be calculated by multiplying the number of hours worked by the employee's hourly wage.

The dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

In the question,

The function is \(B(x) = 0. 06x^2 - 0. 2x^3\)

To find the maximum or minimum, take the derivative and set it equal to zero.

⇒ \(B'(x) = 2(0. 06)x - 3(0. 2)x^{2}\)

Setting it equal to zero, we get

⇒ \(0.12x - 0.6x^{2}=0\)

⇒ 0.6x (0.2-x) = 0

⇒ x = 0 or x = 0.2

Now substitute x = 0.2 in B(x), we get

⇒ \(B(0.2) = 0. 06(0.2)^{2} - 0. 2(0.2)^{3}\)

⇒ B(0.2) = 0.0024 - 0.0016

⇒ B(0.2) = 0.0008

To know B(0.2) is maximum, let us find the values for x = 1 and x = 0.01.

For x = 1,

⇒ \(B(1) = 0. 06(1)^{2} - 0. 2(1)^{3}\)

⇒ B(1) = 0.06-0.2

⇒ B(1) = -1.04

For x = 0.01,

⇒ \(B(0.01) = 0. 06(0.01)^{2} - 0. 2(0.01)^{3}\)

⇒ B(0.01) = 0.000006 - 0.0000002

⇒ B(0.01) = 0.0000058

Thus, x = 0.2 is the maximum.

Hence we can conclude that the dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

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The concept that a message gives different meanings to different objects is called option (b) polymorphism.

Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.

This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.

Therefore, the correct option is (b) polymorphism

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Answer:

1) 3.21 by itself if rational, I don't know if the dots mean anything, but if they do, then it is irrational.

2) Pi is an irrational number as it repeats forever.

False. The bandwagon fallacy is when someone believes that an argument is valid because most people believe it to be true.

The idea is that since everyone believes it, then it must be true. It is also called an argument from popularity, argumentum ad populum, appeal to the masses, appeal to belief, and consensus fallacy.The fallacy occurs when one claims that an idea is true or false because many other people believe it to be so.

The fallacy works because humans are social animals and they tend to believe things that others believe. Therefore, when people see that many others believe in an idea, they are more likely to accept it as true without giving much thought to whether it is actually true or not. The bandwagon fallacy is a logical error because the truth of an idea does not depend on how many people believe it.

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Step-by-step explanation:

If u assume x=y=1, then x+y=2 and x^2+y^2=2

And now, xy=1.

Therefore x=y=1.

Let me know, if anyone come with other answers too.

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Step-by-step explanation:

(*) x^2 + y^2 - 2xy = 64

<=> (x - y)^2 = 64

<=> x - y = 8 or x - y = -8

(**) x^2 - y^2 = 40

<=> (x - y)(x + y) = 40

Case 1: x - y = 8

(**) <=> 8(x + y) = 40

<=> x + y = 5

we have: x+y = 5 and x-y = 8

--> x = (5+8)/2 = 6.5

--> y = x - 8 = 6.5 - 8 = -1.5

so (x,y) = (6.5 , -1.5)

Case 2: x - y = -8

(**) <=> -8(x + y) = 40

<=> x + y = -5

we have: x + y = -5 and x - y = -8

--> x = [ (-5) + (-8) ]/2 = -6.5

--> y = -5 - x = -5 + 6.5 = 1.5

so (x,y) = (-6.5 , 1.5)

Answer: (x,y) = (6.5 , -1.5) and (-6.5 , 1.5)

The value of the the function h(x) at x = 4 is given as follows:

8.7.

The quadratic regression equations for each table are given as follows:

The function for the first item is defined as follows:

h(x) = 50/(5.5 + 8e^(-0.9x)).

At x = 4, the value assumed by the function is obtained replacing the lone instance of x by 4, hence:

h(4) = 50/(5.5 + 8e^(-0.9(4))).

Then a calculator is used to obtain the exact value due to the exponential, hence:

h(4) = 8.7.

The regression equations are obtained inserting the points of each table into a quadratic regression calculator.

For the first table, the points are given as follows:

(16, 15), (18, 15.6), (20, 15.7), (21, 15), (23, 13.1), (26, 8.9), (27, 6.6).

Hence the equation is of:

y = -0.127x² + 4.699x - 27.777.

For the second table, the points are given as follows:

(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).

Hence the equation is of:

y = 32.86x² - 379.14x + 1229.14.

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The cost of the item in 5 years is $25.53

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

Initial value, a = $20

Rate, r = 5%

Time, t = 5 years

The cost can be calculated using the following exponential function

C(t) = a * (1 + r)^t

Substitute the known values in the above equation, so, we have the following representation

C(5) = 20 * (1 + 5%)^5

Evaluate

C(5) = 25.53

Hence, the cost is 25.53

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Answer:

a)  0.356

b)  1.1397

Step-by-step explanation:

a) log₇2

b) log₇ (¹⁴⁷/₁₆)

          log (7)

Answer:

X= 0.5

Step-by-step explanation:

Answer:

101.8 lb

Step-by-step explanation:

1760 sq ft are covered by 40 lb

4480 sq ft are covered by x

1760/40 = 4480/x

1760x = 40 × 4480

x = 179,200/1760

x = 101.818181...

Answer: 101.8 lb

Answer:

Red Gold

Step-by-step explanation:

Assuming you mean 9/40

Red gold = 25%

Pink Gold = .2 which is 20%

Rose gold is \(\frac{9}{40}\) = .225 which is 22.5%

The area of this figure is the sum of areas of the right triangle and the semi-circle

Area of the triangle = 1/2 * base * height

The base = 6 feet

The height = 8 feet

So the area of the triangle is:

Now let us find the area of the semi-circle

Area of semi-circle = 1/2 * 3.14 * r^2

Since the diameter of the semi-circle is 8 feet and the radius is 1/2 the diameter

So the radius = 8/2 = 4 ft

Area of semi-circle is:

Let us add the two areas to find the area of the figure

Area of the figure = 24 + 25.12 = 49.12 square feet

The missing is 49.12

the exact value of \(sin^{-1}\)(1) is π/2 or 90 degrees. However, sin^-1(3/2) and \(sin^{-1}\) (5) are undefined as there are no angles whose sine is equal to those values.

To find the exact value of each expression, we need to use the inverse sine function or sin^-1. The inverse sine function gives us the angle whose sine equals the given value.
(a) \(sin^{-1}\) (1) = π/2 or 90 degrees. This is because the sine of 90 degrees is equal to 1.
(b)  \(sin^{-1}\) (3/2) is undefined. This is because the sine function only takes values between -1 and 1, and 3/2 is greater than 1. Therefore, there is no angle whose sine is equal to 3/2.
(c) sin^-1(5) is also undefined. This is because the sine function only takes values between -1 and 1, and 5 is greater than

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what is the probability that the sum of the numbers showing on two rolled dice is 8 is 5/36.

To find this probability, we need to first determine the total number of possible outcomes when two dice are rolled. Each die has six possible outcomes, so there are 6 x 6 = 36 possible outcomes when two dice are rolled. To determine how many of these outcomes have a sum of 8, we can create a table or list all the possible combinations:

- 2 + 6 = 8
- 3 + 5 = 8
- 4 + 4 = 8
- 5 + 3 = 8
- 6 + 2 = 8

There are 5 possible combinations that result in a sum of 8. Therefore, the probability of rolling a sum of 8 is 5/36.

In conclusion, the probability of rolling a sum of 8 when two dice are rolled is 5/36.

The probability that the sum of the numbers showing on the dice is 8 is 5/36.


To calculate the probability, we need to find the number of favorable outcomes and divide it by the total possible outcomes. When rolling two dice, there are 6 sides on each die, so there are 6 x 6 = 36 possible outcomes.

Now, let's find the favorable outcomes where the sum is 8. The possible combinations are:
1. (2, 6)
2. (3, 5)
3. (4, 4)
4. (5, 3)
5. (6, 2)

There are 5 favorable outcomes. So, the probability of the sum being 8 is:

Probability = Favorable outcomes / Total possible outcomes
Probability = 5 / 36


The probability that the sum of the numbers showing on the dice is 8 is 5/36.

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Step-by-step explanation:

From the question

Perimeter = 2L + 2W

L = 24 units

W = 11 units

Substitute the values into the above formula

That's

P = 2(24) + 2(11)

P = 48 + 22

P = 70 units

Therefore the perimeter of the rectangle cannot be 60 units since the values when substituted into the above formula will give us 70 units

Hope this helps you

So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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They both make 3 baskets. The number of points Norma and vincent have after first time out are 6 points and 9 points respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.

If the number of basket is x, and the total point is y, thus

for Norma, the total point = 19+2x=y equation 1

for vincent, the total point = 16+3x= y equation 2

subtract equation 1 from 2

16-19+3x-2x = 0

-3+x = 0

x= 3

substitute 3 for x in equation 1

19+2(3)= y

25= y

y = 25

therefore they both made 3 basket after the first time out and Norma make extra 6 points and Vincent made extra 9 points

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Answer:

8

Step-by-step explanation:

Since the two horizontal lines are parallel, we have that triangle CDG and triangle CEF are similar (corresponding points in that order). Therefore, using similarity, CD/CG = CE/CF. Therefore 3/4 = 9/(4+x).

So 12 = 4+x, and x = 8.

The conditions that must be met to use the normal approximation for the confidence level are np>5 and n(1-p)>5

Sampling Distribution: A sampling distribution is a probability distribution of a statistic that is obtained through repeated sampling of a specific population. It describes a range of possible outcomes for a statistic, such as the mean or mode of some variable, of a population.

Given that the sampling distribution of the population proportion is based on a binomial distribution.

The conditions that must be met to use the normal approximation for the confidence level are np>5 and n(1-p)>5

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Answer: Your answer is 61.25cm hope this helps!

Step 1: Write out the expression to simplify

Step 2: Remove the bracket using distribution property

Step 3: Rewrite the resulting expression in order of degree and state the degree and the number of terms

The degree is 3 (third degree) as the highest power of the variable is 3, there are three terms in the expression

Hence, the expression is a cubic expression (degree 3) and a trinomial (3 terms)

The expected return on James's portfolio is 18%.

The expected return on Siebling Manufacturing Company's common stock is 8.4%.

To calculate the expected return on James's portfolio, we need to take the weighted average of the expected returns of MSFT and AAPL based on their respective investments.

Let's assume James invests x% in MSFT and (100 - x)% in AAPL.

The expected return on James's portfolio can be calculated as:

Expected Return = (x * Expected Return of MSFT) + ((100 - x) * Expected Return of AAPL)

Substituting the given values:

Expected Return = (x * 12%) + ((100 - x) * 24%)

To find the value of x that makes James's investments equal, we set the weights equal:

x = 100 - x

Solving this equation gives us x = 50.

Now we can substitute this value back into the expected return equation:

Expected Return = (50% * 12%) + (50% * 24%)

Expected Return = 6% + 12%

Expected Return = 18%

Therefore, the expected return on James's portfolio is 18%.

To calculate the expected return on Siebling Manufacturing Company's common stock, we can use the Capital Asset Pricing Model (CAPM).

The CAPM formula is:

Expected Return = Risk-Free Rate + Beta * Market Premium

Risk-Free Rate = 2%

Market Premium = 8%

Beta = 0.8

Expected Return = 2% + 0.8 * 8%

Expected Return = 2% + 6.4%

Expected Return = 8.4%

Therefore, the expected return on Siebling Manufacturing Company's common stock is 8.4%.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

The mean (μ) for the given binomial distribution is 0.50.

To calculate the mean (μ) of a binomial distribution, we multiply the number of trials (n) by the probability of success in a single trial (π). Let's examine each scenario in detail:

a. When n = 5 and π = 0.10:

μ = 5 * 0.10

  = 0.50

For this binomial distribution, with 5 trials and a success probability of 0.10, the mean (μ) is 0.50. This means that, on average, we would expect to have 0.50 successes per trial.

b. When n = 3 and π = 0.40:

μ = 3 * 0.40

  = 1.20

In this case, the mean (μ) of the binomial distribution is 1.20. It indicates that, on average, there would be 1.20 successes per trial when there are 3 trials and a success probability of 0.40.

c. When n = 5 and π = 0.50:

μ = 5 * 0.50

  = 2.50

For a binomial distribution with 5 trials and a success probability of 0.50, the mean (μ) is 2.50. This means that, on average, we would expect to have 2.50 successes per trial.

d. When n = 3 and π = 0.80:

μ = 3 * 0.80

  = 2.40

In this scenario, the mean (μ) of the binomial distribution is 2.40. It suggests that, on average, we would expect to have 2.40 successes per trial when there are 3 trials and a success probability of 0.80.

The mean (μ) provides a measure of the central tendency or the average number of successes in a binomial distribution based on the given parameters.

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Answer:

z/y

Step-by-step explanation:

The Probability that rose identifies all 3 cards in the correct order is 1/66300.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Number of Card drawn without replacement= 3

Total cards = 52

As, there is no description about cards then the total number of ways to choose is

= \(^{52}P_3\)

= 52!/ 3! 49!

= 66300

and, Favorable Condition= 1( pick one card at a time)

Now, Probability that rose identifies all 3 cards in the correct order

= 1/ \(^{52}P_3\)

= 1/ 66300

Hence, the probability is 1/66300.

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The range of possible values of the measurement is:

[45.97cm, 48.03cm]

Here we have the measurement:

measurement 47 cm ± 2.2%

The 2.2 percent of 47cm is:

47cm*( 2.2%/100%) = 47cm*(0.022) = 1.034 cm

Then the minimum of the measurement is:

47cm - 1.034cm = 45.97cm

The maximum of the measurement is:

47cm + 1.034cm = 48.03cm

we conclude that the correct option is the second one:

[45.97cm, 48.03cm]

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