[tex]-\sqrt{16y^2}[/tex] if y<0

The following can represent the gravitational potential energy U of this satellite as a function of the orbital radius r: A satellite can move in a circular orbit around a large planet with radius R.

Now that we know the alternatives for planet orbits, let's investigate why elliptical orbits are the most common.

1) The Solar system has been around for 4.6 billion years. Any planets with hyperbolic or parabolic orbits would have long since vanished.

2) To have a circular orbit, the eccentricity must be precisely zero. It's difficult.

3) An elliptical orbit's eccentricity can range from 0 to 1. Easy, that.

Here, GM/r =  [tex]V_{1} ^{2}[/tex] & GM/4r = [tex]V_{2} ^{2}[/tex]

or, [tex]V_{1} ^{2}[/tex] = 4 * [tex]V_{2} ^{2}[/tex]

or, [tex]V_{1}[/tex]= 4* [tex]V_{2} ^{}[/tex]

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(a) For a one-way function, it is easy to go from a domain element to its image but challenging to do so from a range element to its pre-image. Understanding that a one-way function doesn't need a key is essential.

(b) When two numbers are split, the modulo operation in computing yields the remainder or the signed remainder of the division

(c) Cryptographically secure hash functions and the Rabin function are examples of one-way functions.

a) In computer science, a one-way function is a function that is easy to compute for all inputs but challenging to reverse given the representation of a random input. The adjectives "easy" and "hard" should be understood in this context as they relate to computational complexity theory, particularly the notion of polynomial time problems.

(b)The C arithmetic operators now include the modulus operator, which works between two available operands. It divides the specified numerator by the supplied denominator to produce the desired result. Alternatively, it yields an integer division residual. As a result, the quantity that is left behind is also frequently an integer.

(c) Examples for one-way functions

Multiplication and factoring.

The Rabin function (modular squaring)

Discrete exponential and logarithm.

Cryptographically secure hash functions.

Other candidates.

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The second graph  represents the function [tex]f(x)=8^{\frac{1}{3} x}[/tex]

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is

[tex]f(x)=8^{\frac{1}{3} x}[/tex]

At x=0, f(0)=1

At x=1, f(1)=2

At x=2, f(2)=4

The graph of f(x) passing through the points (0,1), (1,2), (2,4),(3,8).

According to these coordinates we can say that the graph of f(x) is represented by option 2.

Therefore correct option is 2.

Hence, the second graph  represents the function [tex]f(x)=8^{\frac{1}{3} x}[/tex]

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The force that a simple machine applies to an object is known as output force. The mechanical advantage exceeds one if the output force exceeds the input force.

A basic machine's output force is indeed the pressure it puts on an item. The mechanical advantage exceeds 1 when the output force exceeds the input force. Output force minus input force equals the mechanical advantage ratio. Work is made easier by increasing the mechanical advantage.

A 630 N input force is therefore necessary.

a 3 percent mechanical advantage

It can be represented mathematically as follows:

M=f 1/f 2

the output force F1 is

The input force is F2,

and thus

F1=1890 N and 3=F1/630 N

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Answer:

the answer is D. 1,890 N!!!

Answer:

Miguel sold 18 tickets

Step-by-step explanation:

If Ajani's 36 tickets sold was twice the amount of Miguel's, you simply have to divide 36 by 2 for the right answer

36÷2=18

The types of operating system are:-

1. Batch Operating System.

2. Real-Time Operating System.

3. Time-Sharing Operating System.

4. Distributed Operating System.

5. Embedded Operating System.

6. Network Operating System.

7. Mobile Operating System.

What is an operating system?

An operating system can be thought of as a hardware and user interface. It is in charge of several different activities, including resource allocation, CPU management, file management, and the execution of all programmes. An operating system's function is to offer a setting in which a user can run programmes conveniently and effectively.

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The events that correspond to each case are given as follows:

a) Exactly one odd number: OEE, EOE, EEO.

b) More odd numbers than even numbers: OOO, OOE, OEO, EOO.

c) Two or more odd numbers: OOO, OOE, OEO, EOO.

Hence the probabilities of each event are given as follows:

a) Exactly one odd number: 3/8.

b) More odd numbers than even numbers: 1/2.

c) Two or more odd numbers: 1/2.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have three trials, each with two possible outcomes, hence the total number of outcomes is given as follows:

2³ = 8.

The meaning of the letters is given as follows:

Hence, for example, the event OEE means that an odd number was taken, then an even number and then another even number.

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Honesty can be measured by asking people to rate themselves on a scale of 1-10 for honesty, ranking their fellow participants in terms of honesty, conducting a polygraph test to assess physiological responses when presented with specific questions, and conducting interviews to assess how forthright people are in their answers.

An operational definition of honesty can be measured by asking people to rate themselves on a scale of 1-10 for honesty. This would allow participants to self-assess their own level of honesty and provide a baseline for comparison. By observing how often people tell the truth in a given situation, one can measure the level of honesty of a person.

Additionally, a polygraph can be used to measure physiological responses when asking a series of specific questions. This can provide a more accurate measurement of a person’s honesty in comparison to a self-reported scale.

Lastly, conducting interviews with participants can help to assess how forthright people are in their answers. This allows for a more in-depth assessment of honesty by allowing interviewers to observe and assess the sincerity of participants’ answers.

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Answer: Non zero solution : A solution of a set of homogeneous linear equations in which at least one of the variables has a value different from zero.

Step-by-step explanation:

Step-by-Step Explanation:

We know,

[tex] \cos(angle) = \frac{base}{hypotenuse} [/tex]

Here, angle = 60°, base = 5, hypotenuse = x

Therefore,

[tex] \cos(60) = \frac{5}{x} \\ = > \frac{1}{2} = \frac{5}{x} \\ = > x = 5 \times 2 \\ = > x = 10[/tex]

Answer:

10

Hope it helps.

The solution for x in triangle is,

⇒ x = 10

We have to given that;

A triangle is shown in figure.

Since, A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Now, We can use the trigonometry formula to find the value of x as;

⇒ cos a = Base / Hypotenuse

Substitute a = 60°, base = 5 , hypotenuse = x in above equation,

⇒ cos 60° = 5 / x

⇒ 1 / 2 = 5 / x

⇒ x = 5 × 2

⇒ x = 10

Thus, The solution for x in triangle is,

⇒ x = 10

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Answer:

Step-by-step explanation:

Answer:

D = (2x + 3)² + (x-2)(2x + 3)

Factoring D, we get:

D = (2x + 3)² + (x-2)(2x + 3)

= (2x + 3)(2x + 3 + x-2)

= (2x + 3)(3x - 2)

The statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

We have to check the given statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true or false.

Random selection is needed to eliminate bias and gives each individual the same probability of being selected.

Hence, the statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true.

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The z score for the value 66, when the mean is 51 and the standard deviation is 1 is 15.

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Z score shows by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

Given that:

mean = 51, standard deviation = 1. For a value of 66:

z = (66 - 51) / 1 = 15

The z score is 15.

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The top 10 Excel formulas are SUM, AVERAGE, COUNT, MAX, MIN, IF, VLOOKUP, CONCATENATE, INDEX and MATCH which are used for performing calculations, counting, finding the maximum and minimum values, testing a condition and returning results, combining text, and searching for a specified item.

1. SUM: Adds the values in a specified range of cells.

2. AVERAGE: Calculates the average of all the cells in a specified range.

3. COUNT: Counts the number of cells in a specified range that contain numbers.

4. MAX: Finds the largest value in a specified range of cells.

5. MIN: Finds the smallest value in a specified range of cells.

6. IF: Tests a condition and provides a value based on the results of the test.

7. VLOOKUP: Searches for a value in the first column of a specified range and returns a value from the same row from another column.

8. CONCATENATE: Combines text from two or more cells into one cell.

9. INDEX: Returns a value from a specified range of cells.

10. MATCH: Searches for a specified item in a specified range and returns its relative position.

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c. The mode is the best measure to describe the typical or central value in this data set.

The data set consists of qualitative values, which means they are not in numerical form and cannot be used to calculate the mean or median. The mode is the best measure to describe the typical or central value because it identifies the value that occurs most often in the data set.

In this case, the value that occurs most often is ‘blonde’, which would be the mode. The mean and median cannot be used because they require quantitative data, such as numerical values, to be calculated.

Additionally, the data set does not have outliers, which would cause the mean to be skewed. By using the mode, we can accurately describe the typical or central value of this data set.

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To estimate the mean number of pages per book in the fiction section of the large school library, we can use a t-test. A t-test is a statistical method for determining the probability that a given sample of data comes from a population with a certain mean value.

Given that the sample size is 35 and the standard deviation is 47.6 pages per book, we can use the t-distribution table to find the t-value for a 99% confidence level.

The t-value for a 99% confidence level and 34 degrees of freedom (sample size - 1) is 2.021.

With this information, we can construct a confidence interval for the mean number of pages per book in the fiction section of the large school library. The confidence interval is given by:

Sample mean ± t-value * (Standard deviation / √Sample size)

Therefore, the confidence interval for the mean number of pages per book in the fiction section of the large school library is:

291.8 ± 2.021 * (47.6 / √35)

The margin of error is approximately 12.2 pages per book.

So the mean number of pages per book in the fiction section of the large school library is between 279.6 and 304 pages per book with a 99% confidence level.

Answer:

Step-by-step explanation:

393,000 x 0.049

= 19257

393,000 - 19,257

=373743

Answer: 1/4

Step-by-step explanation: He plants 3/4 of the flowers in one garden. There are 1/4 left. 4/4 - 3/4= 1/4

There are 14 quarters and 25 number of pennies

Two or more expressions with an Equal sign is called as Equation.

Given that some quarters and pennies worth $3.75

0.25x+0.01y=3.75

There are 39 coins altogether

x+y=39

x=39-y

Now plug in x value in 0.25x+0.01y=3.75

0.25(39-y)+0.01y=3.75

9.75-0.25y+0.01y=3.75

9.75-0.24y=3.75

9.75-3.75=0.24y

6=0.24y

Divide both sides by 0.24

25=y

x+y=39

x=14

Hence, there are 14 quarters and 25 number of pennies

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Given the equation t = -0.0069d + 7.35, where t is the time of sunrise in hours after midnight and d is the number of the day in the year, To find the time of sunrise on December 25th, the 359th day of the year, we need to substitute 359 for d in the equation.

t = -0.0069(359) + 7.35

t = -2.4471 + 7.35

t = 4.9029

This means that the time of sunrise on December 25th is 4.9029 hours after midnight. To convert this to minutes, we can multiply 4.9029 by 60 (since there are 60 minutes in an hour).

4.9029 x 60 = 294.174

So the sun rose on December 25th at 294.174 minutes after midnight, which is equivalent to 4 hours and 54 minutes (294 minutes) after midnight. To the nearest minute, the sun rose on December 25th at 4:54 AM.

The radius of the third circle is found out to be as , 1cm.

The radius of 1st circle = 1

radius of second circle = 4

Let XYR be external tangent of the circle which is centered at C,.

Then if we will extend the line PQ to R ,

the result will be , XPR being similar to triangle YQR ,

Therefore,

RQ = x

and length of RP = x   + 5

Therefore, x / x+ 5 = 1/4

=> 4x = x + 5

=> x = 1

So , the length of QR is found out to be as 1cm.

A tangent to a circle is known as a straight line which touches the circle exactly at one point . A circle can have infinite number of tangents.

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Answer:

13.75 m.

Step-by-step explanation:

We can start by calculating the total area of the walls of the room by subtracting the area of the door and window from the total area of the room.

The total area of the room is 20m * 14m = 280 m^2

The area of the door is 1m * 1.7m = 1.7 m^2

The area of the window is 1.8m * 1.8m = 3.24 m^2

The total area of the walls is 280m^2 - 1.7m^2 - 3.24m^2 = 275.06 m^2

Now that we have the total area of the walls, we can divide it by the cost of painting per m^2 to find the height of the room.

The cost of painting per m^2 is $12165.9 / 275.06 m^2 = $44.32/m^2

So we can find the height of the room by dividing the cost by the rate of painting, $12165.9 / $44.32/m^2 = 275.06 m^2 / (20m * h) = 275.06 / 20 = 13.75m

Therefore, the height of the room is approximately 13.75 m.

Answer:

1/ 14^4

Step-by-step explanation:

Rules of Exponents

We know that a^-b = 1/a^b

14^-4  = 1/ 14^4

Answer:

[tex]{14}^{ - 4} = \frac{1}{ {14}^{4} } [/tex]

Step-by-step explanation:

To find the answer for this, you have to follow the negative rule of exponents.

That is,

1) If the number with a negative power is in it's numerator, the number with a negative exponent should be put to the denominator and make the power positive.

2) If the number with a negative power is in it's denominator, the number with a negative exponent should be put to the numerator and make the power positive.

Here, we have follow the rule 1.

Ex:

[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]

Accordingly, let us find the answer for the question.

[tex] {14}^{ - 4} = \frac{1}{ {14}^{4} } [/tex]

Answer:

To work out the cost of the council tax bill before the increase, we can use the formula:

Original cost = New cost / (1 + increase percentage)

We know that the council tax bill increased by 5% and the increase is £62. So the new cost of the council tax bill is £62 more than the original cost.

We can use the formula above to find the original cost:

Original cost = £62 / (1 + 0.05)

Original cost = £62 / 1.05

Original cost = £59.04

So the cost of the council tax bill before the increase was £59.04.

Answer:

Step-by-step explanation:

a. The area between -z and z is 0.2206, so we want to find the value of z such that P(-z < Z < z) = 0.2206.

The standard normal distribution is symmetric, so P(-z < Z < z) = 0.5 - P(Z < -z) = 0.5 - P(Z < -z) = 0.5 - 0.2206 = 0.2794

We can use a standard normal table to find the z-value such that P(Z < z) = 0.2794 which is z = 0.68.

b. The area to the left of z is 0.9951, so we want to find the value of z such that P(Z < z) = 0.9951.

We can use a standard normal table to find the z-value such that P(Z < z) = 0.9951 which is z = 2.33.

the constant rate at which the submarine dives is 30 feet per minute and 1,800 feet per hour.

feet per minute: 30 feet per minute

feet per hour: 1,800 feet per hour

We can calculate the rate of descent of the submarine by dividing the total distance it dives each time by the total time it took to dive.

For the first scenario where it dives 300 feet every 2 minutes, the rate of descent is 300/2 = 150 feet per minute.

For the second scenario, it dives 6/750 feet every 45 minutes so the rate of descent is 6/750 * 60/45 = 30 feet per minute.

Therefore, the constant rate at which the submarine dives is 30 feet per minute and 1,800 feet per hour.

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Question 10

[tex]\frac{\sin x}{7}=\frac{\sin 85^{\circ}}{8}\\\\\sin x=\frac{7\sin 85^{\circ}}{8}\\\\x \approx 60.7^{\circ}, 119.3^{\circ}[/tex]

However, the second case does not satisfy the angle sum of a triangle, so [tex]x \approx 60.7^{\circ}[/tex].

Question 12

[tex]\frac{\sin x}{19}=\frac{\sin 34^{\circ}}{12}\\\\\sin x=\frac{19\sin 34^{\circ}}{12}\\ \\ x \approx 62.3^{\circ}, 117.7^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

The proportion that represents kilometers Halona walks is 193 kilometers in 2300 minute, that is 193/ 2300.

1 kilometer / x minutes = 1.93 kilometers / 23 minutes

Let x be the kilometers Halona walks in 1 minute. If she walks at a constant speed, as speed is rate of distance covered in unit time

x kilometer / 1 minute = 1.93 kilometers / 23 minutes

So the proportion is:

x kilometer / 1 minutes = 1.93 kilometers / 23 minutes

x kilometer / 1 minutes = 193/ 2300

This proportion represents how many kilometers Halona walks per minute. To find her speed in kilometers per hour, we can multiply the proportion by 60 minutes/hour.

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