Apply the Power of a Quotient Property. (3/4)^3

The general partner actually runs the business and faces unlimited liability for the firm's debt, while the limited partner is only liable up to the amount the limited partner invested.

A limited partnership is a legal entity that consists of at least one general partner (who has unlimited personal liability) and one limited partner (whose liability is limited to their investment in the company).

In this case, the general partners are primarily responsible for managing the business and making business decisions in order to achieve the stated business goals, whereas the limited partners, also known as silent partners, are only responsible for investing in the business and not running it.

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The function, f(x) is a one to one function.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = 2x – 3

When the independent variable and dependent variable in a given relationship are switched, a relationship known as an inverse function is created.

Simply swapping the x and y coordinates will reveal it.

So,  The statement that could be used in this problem to explain why f(x) = 2x - 3 has an inverse relation.

Hence, the function f(x) is a one to one function.

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Find out your answer below:

"If a coin is tossed 7 times, what is the probability of getting 4 tails?"

Use the binomial distribution directly. Let us assume that the number of tails is represented by x  (where a result of tails is regarded as success) and in this case X = 4

Assuming that the coin is unbiased, you have a probability of success ‘p’(where p is considered as success) is 1/2 and the probability of failure ‘q’ is 1/2(where q is considered as failure). The number of trials is represented by the letter ’n’ and for this question n = 7.

Now just use the probability function for a binomial distribution:

P(X = x) = nCxpxqn-x

Using the information in the problem we get P(X = 4) = (7C5)(1/2)5(1/2)2

= 21 × 1/32 × 1/4

= 21/128

Hence, the probability of flipping a coin 7 times and getting tails 4 times is 21/128.

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The number of volunteers needed for the 5k races is 50 and the number of volunteers needed for the 10k races is 65.

The system of equations that represent the question is:

7a + 9b = 935 equation 1

7a + 7b = 805 equation 2

Where:

The elimination method would be used to determine the values of a and b.

Subtract equation 2 from equation 1

2b = 130

b = 130 / 2

b = 65

Substitute for b in equation 1 :

7a + 9(65) = 935

7a + 585 = 935

7a = 935 - 585

7a = 350

a = 350 /7

a = 50

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Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.

A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"

In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.

Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:

x + (x+4) * 3 = 84

Expanding and solving for x:

x + 3x + 12 = 84

4x = 72

x = 18

So the three consecutive even integers are 18, 20, and 22.

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Answer: I am confused by this can you explain further

Step-by-step explanation:

Answer:

Step-by-step explanation:

All of the other answers except for PQY are lines. You can assume that the answer is PQY.

The value of  y and x intercepts are 1 and -5/2

We should know that the x-intercept is the point where the x line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis respectively

The equation of the graph is give as follows

m=(y-y₁)/(x-x₊)

Taking the points (0,1) and (5,3)

We can use them to find the slope

3-1/5-0

m=2/5

Applying this to the equation of the line to get

2/5 = y-1/x-0

2/5=y-1/x

Cross and multiply to get

2x=5y-5

Rewrite the equation and make y the subject of the relation

y=2/5x+1

When y=0 2/5x=-1

This implies that x= -5/2

Also, when x=0

y=0+1 = 1

The y intercept is 1 and the x intercept is -5/2

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The value of y for the inequality is y  >  0

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

The inequality 2 times the quantity y plus one third end quantity is greater than two thirds can be written as:

2(y + 1/3) > 2/3

To determine the value of y in the inequality, you need to solve for y. That is:

2(y + 1/3) > 2/3  

y + 1/3 > 1/3     (Divide both sides by 2)

y > 1/3 - 1/3     (Collect like terms)

y > 0

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$56.4 is the cost of the 6 pairs of shoes.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that shoe store was having a back to school sale where you could buy 5 pairs of shoes for $47.40.

If a large family decided to buy 6 pairs of shoes then the cost of these 6 pair of shoes we have to find.

Let x be the cost of 6 pair of shoes.

5/47=6/x

Apply cross multiplication

5x=282

Divide both sides by 5

x=56.4

Hence, $56.4 is the cost of the 6 pairs of shoes.

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Answer:

w = 11

l = 42

Step-by-step explanation:

in word problems :

'more than' means +

'triple' means 3 times

'is' means =

perimeter means 2 times width plus 2 times the length

'length of a rectangle is nine more than triple the

width' means :

l = 9+3w

'perimeter is 106 inches' means

2l + 2w = 106

divide by 2

l + w = 53

substitute l with 9+3w to get the width

9+3w + w = 53

9 + 4w = 53

4w = 44

w = 11

go back to the perimeter equation

l + w = 53

put 11 for w

l + 11 = 53

l = 42

The true statement about students enrolled in this course from

2018 to 2019 is B The absolute change is -253 students and the relative change indicates a decrease of 7%.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Given that In the year 2018, the students enrolled were 700 and in the year 2019the students enrolled were 475.

Therefore, Initial value = 700 and Final value = 475.

The absolute change is -

Absolute change = Final value - Initial value =447 - 700 =- 253

The relative change is -

Relative change = Final value - Initial valueInitial value×100% =475-700/ 700×100% =-253

700×100% =-7%

Thus, the absolute change is -253 which indicates that there is a decrease of 7%.

The correct option is b.)

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The complete question is;

a.) The absolute change is –50 students and the relative change indicates a decrease of 11%.

b.) The absolute change is -253 students and the relative change indicates a decrease of 7 %.

c.) The absolute change is 50 students and the relative change indicates an increase of 11%.

d.) The absolute change is 50 students and the relative change indicates a decrease of 10%

The rate of speed that a vehicle must travel to cover 132 kilometers in one and a half hours is 88 kilometers per hour.

The rate of speed is the quotient of distance and time.

Similarly, the time taken to cover a distance can be determined as the quotient of distance and speed.

The formula describing the relationship between distance traveled, speed, and time is Distance = Rate of Speed x Time.

The total distance traveled = 132 kilometers

The time taken to travel the distance = 1¹/₂ hours = 1.5 hours

Rate of speed = Distance/Time

= 88 kilometers per hour (132/1.5)

Thus, the rate of speed for the vehicle to cover 132 kilometers is 88 kilometers per hour.

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Answer:

Increasing: [tex](-\infty,-\frac{4}{3})\cup(\frac{4}{3},\infty)[/tex]

Decreasing: [tex](-\frac{4}{3},\frac{4}{3})[/tex]

Step-by-step explanation:

A continuous function increases where [tex]f'(x) > 0[/tex] and decreases where [tex]f'(x) < 0[/tex], so let's find our critical points:

[tex]f(x)=3x^3-16x+2\\f'(x)=9x^2-16\\[/tex]

[tex]9x^2-16=0\\\\9x^2=16\\\\x^2=\frac{16}{9}\\\\x=-\frac{4}{3},\frac{4}{3}[/tex]

We'll use [tex]x=-2, x=0, \text{and } x=2[/tex] as test points to see how the derivative's behavior is around the critical points:

[tex]f'(-2)=9(-2)^2-16=9(4)-16=36-16=20 > 0[/tex]

[tex]f'(0)=9(0)^2-16=-16 < 0[/tex]

[tex]f'(2)=9(2)^2-16=9(4)-16=36-16=20 > 0[/tex]

Hence, we can see that f(x) increases on the interval [tex](-\infty,-\frac{4}{3})\cup(\frac{4}{3},\infty)[/tex] and decreases on the interval [tex](-\frac{4}{3},\frac{4}{3})[/tex].

Answer: B, $1.56

Step-by-step explanation:

The unit price is simply the price of a good per unit. In this case, the price per pound.

Divide the cost by the number of pounds.

18,75/12 = ~1,56

Therefore, Option B is the correct answer.

Step-by-step explanation:

. My sister asked me, "Have you seen my dog?" ____________________________________________ 2. Vijay asked "Have you gone to market?" ____________________________________________ 3. My mother asked, "Why are you crying?" ____________________________________________ The rickshaw puller asked me, "Do you speak English?" ____________________________________________

3 3/4cups,

2 1/2 cups of cranberry juice = 4 cups of club soda so we know that we would have to add 2 more cups of club soda which is equal to 1 1/4 of cranberry juice

4 = 2 1/2 and 2 = 1 1/4

2 1/2 + 1 1/4 = 3 3/4 cups

When the ferris wheel rotates once every four minutes, your seat will be above 15 meters for 77.4 seconds of each revolution.

The spikes that go through the middle of a cycle's wheel from one end to the other are an illustration of diameter. Since the diameter is the line segment that begins at one end of a circle and finishes at the other end of the circle, passing through the center, we can compare this to the diameter of a circle. The diameter of a circle cuts through the center, whereas the radius circumscribes the circle from edge to edge. The size of a circle essentially divides it in two. the distance in a straight line going from one edge of a tumor or other item, through the middle, and out the other edge.

given

d = 20 m

r = 10 m

θ = θ1 + 90°

tan θ1 = 5 /10

θ1 = 26°

θ = 26° + 90°

= 116°

that wheel was rotated 116° for you to be at 15 m elevation .

wheel rotates 360° in 4 min

time taken for the wheel to rotate 116° will be

time taken = (116° / 360°) * 4 min

1.29 min = 77.4 sec

When the ferris wheel rotates once every four minutes, your seat will be above 15 meters for 77.4 seconds of each revolution.

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The equation that can be used to solve for the price of each ticket is $296 = 16t - 92. The cost of each ticket is $24.25.

Theequqtion represents the total cost of the tickets

Total amount paid by Mrs. Perkey = total cost of the tickets - total amount saved

$296 = (16 x t) - (16 x $5.75)

$296 = 16t - 92

$296  + 92 = 16t

$388 = 16t

t = $388 / 16

t = $24.25

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The definite integral for this problem has the result given as follows:

[tex]\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}[/tex]

The definite integral for this problem is defined as follows:

[tex]\int_1^5 x^2 + 2x - \tan{x} dx[/tex]

We have an integral of the sum, hence we can integrate each term, and then add them.

For the first two terms, applying the power rule, the integrals are given as follows:

The integral of the tangent is given as follows:

ln|sec(x)|

Then the integral is given as follows:

I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.

Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:

I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)

I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 212 - ln|sec(5)| + ln|sec(1)|.

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[tex]y=\frac{1}{2}x +4[/tex]

Slope-intercept form is a common way of representing linear functions. Slope-intercept is written as y = mx + b, where m is the slope and b is the y-intercept.

Slope

To find the slope-intercept equation we first need to find the m-value. Slope is often defined as rise over run. This means the change in y divided by the change in x. So, we can find the slope by counting how much the y-value and the x-value increases between 2 points.

For example, we can take the points (2,5) and (4,6). The y-value increases by 1 and the x-values increase by 2. This means that the slope is 1/2. We can plug this into slope-intercept form to get part of the equation: [tex]y = \frac{1}{2}x+b[/tex].

Y-Intercept

Next, we need to find the b-value. The y-intercept of a graph is the y-value where the function intersects with the y-axis (the vertical axis). By looking at the graph, we can tell that the function crosses the y-axis at y = 4; this occurs at the point (0,4). The y-intercept always occurs when x = 0.  

Now, we can plug 4 in for b to get the final equation: [tex]y=\frac{1}{2}x +4[/tex].

From the table, we conclude that on Wednesday and Sunday the low temperature farthest from 0°C

The investigator must summarize the facts in tabular form after gathering them in order to study their prominent features. The presentation of data is the name given to such a configuration.

Any acquired data may be arranged in a frequency distribution table and then displayed using pictograms or bar graphs. The lengths of the equally wide bars that make up a bar graph are controlled by the frequency and scale you select.

Observing the data is represented in a table form where rows represent the number of days in a week and two columns represent the high and low temperatures of Anchorage, Alaska.

On Wednesday and Sunday, the low temperature was - 13°C and it is the farthest from 0°C.

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Answer:

☐ 3 pints

☐ 1 gallon

Step-by-step explanation:

4cups = 32 fluid ounces = 2 pints = 1 quart = 0.25 gallons

30 fl oz is less than 4 cups

2 pints is exactly 4 cups but we are looking for numbers greater than 4 cups

3 pints is more than 4 cups  so this is a correct choice

1 quart is exactly 4 cups but we are looking for numbers greater than 4 cups

1 gallon is 16 cups so a valid choice

Answer: I THINK 250

Step-by-step explanation: 125 is half and 125 times 2 is 250.

Step-by-step explanation:

2:6 = 1:3

1:3 = 1:3

5:15 = 1:3

only

7:22

cannot be reduced to 1:3.

odd one out = 7:22

The missing value in the proportion is C- 10

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that 2/5 = ?/25

Let x be the unknown number.

Here first we have the bottom half of type equation equal each other

5x=25 (2)

x= 25 (2) / 5

x = 5 (2)

x = 10

10 is the answer

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Therefore ,the solution to the given problem of equation comes out to be  y = 1/10 * x.

A formula for a mathematical equation combines two statements by using the equal sign (=) to denote equivalence. An equation in algebra is a statement proving the equality of two mathematical equations. For instance, the two numbers are connected by the relation 7x + 5 = 15. A numerical relationship is built between the sentences on either end of a letter. Usually, the symbol serves as the only variable and the only factor. For instance, 16x - 4 = 2.

Here,

Given : Every 30 minutes, an airplane makes

a 300-mile trip from Virginia to Nevada.

By taking all the information in concern,

We get,

x= time

and

y = distance

We get the equation as :

y = 1/10 * x

Therefore ,the solution to the given problem of equation comes out to be y = 1/10 * x.

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Answer:

[tex]a) \frac{d}{dx} (3e {}^{x} ) \\ [/tex]

Recall the property

[tex]\frac{d}{dx} [c \times f(x)] = c \times f'(x) \\[/tex]

[tex] = 3 \frac{d}{dx} e {}^{x} = 3e {}^{x} \\ [/tex]

[tex]b.) \: \: \frac{d}{dx} (x {}^{2} e {}^{x} ) \\ [/tex]

[tex] = x {}^{2} \times e {}^{x} +e {}^{x} \times 2x \\[/tex]

[tex] = e {}^{x} (x {}^{2} \times 2x) \\ [/tex]

[tex]c.) \: \: \frac{d}{dx}( \frac{e {}^{x} }{x {}^{3} } ) \\ [/tex]

[tex] = \frac{x {}^{3} \times e {}^{x} - e {}^{x} \times {3x}^{2} }{ {x}^{6} } \\ [/tex]

[tex]= \frac{x {}^{2} {e}^{x} (x - 3) }{ {x}^{6} } \\ [/tex]

[tex]= \frac{ {e}^{x} (x - 3) }{ {x}^{4} } \\ [/tex]

The functions f(x) = ∛x - 1 and g(x) = x³ + 1 are inverse functions.

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

Distinct Functions

The functions are represented as

f(x)=\sqrt[3]{x-1} and g(x)=x^3+1

Rewrite the functions properly

So, we have the following representations

f(x) = ∛x - 1 and g(x) = x³ + 1

Using the function compositions, the following equation must be true

f(g(x)) = x

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

f(g(x)) = ∛x³ + 1 - 1

Evaluate the like terms

f(g(x)) = ∛x³

So, we have

f(g(x)) = x

Hence, the functions are inverse functions

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