Use the Extended Euclidean Algorithm to show that the inverse of 177 in mod 901 is 56 by hand calculations ?

Answer:

✓73 or approximately 8.54

Step-by-step explanation:

✓ 8²+3² = ✓ 73 or approximately 8.54

The side length of the square is 2/3 foot.

A number system is defined as a system of writing to express numbers.

To find the side length of a square, we can take the square root of its area.

Given that the area of the square is 16/36 square foot

we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 4:

16/36  

=(16 ÷ 4) / (36 ÷ 4)

= 4/9 square foot.

Taking the square root of 4/9 gives us the side length of the square:

√(4/9) = 2/3 foot.

Therefore, the side length of the square is 2/3 foot.

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The volume of space that was not used= Volume of each box × number of boxes not packed into the truck= 6ft³ × 6 2/3= 40ft³.

In order to determine the amount of space that was not used in the pick up truck, we have to calculate the maximum number of boxes that can fit into the truck.

The pick up truck has a length of 8ft, width of 10ft and height of 2ft. Therefore, the volume of the pick up truck can be calculated as follows;

Volume of the pick up truck= length × width × height= 8ft × 10ft × 2ft = 160ft³

On the other hand, the dimensions of each box are length of 2ft, width of 2ft and height of 1.5ft. Therefore, the volume of each box can be calculated as follows;Volume of each box= length × width × height= 2ft × 2ft × 1.5ft = 6ft³.

Hence, the total number of boxes that can fit into the pick up truck can be calculated by dividing the volume of the truck by the volume of each box.

This is as follows;

Total number of boxes that can fit into the pick up truck= Volume of the truck ÷ Volume of each box= 160ft³ ÷ 6ft³ = 26.67.

From the calculation above, we can see that a total of 26 boxes and 2/3 of a box can be loaded into the pick up truck with a cover. Since we have packed 20 boxes, it implies that the remaining number of boxes that was not packed into the pick up truck is;

Number of boxes that was not packed into the truck = 26 2/3 - 20 = 6 2/3 boxesWe can then determine the volume of space that was not used by multiplying the volume of each box by the number of boxes not packed into the truck.

Hence;Volume of space that was not used= Volume of each box × number of boxes not packed into the truck= 6ft³ × 6 2/3= 40ft³.Therefore, the amount of space that was not used is 40ft³.

The amount of space that was not used in the pick up truck with a cover is 40ft³.

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Answer: Displacement=12 m north

Step-by-step explanation:

12 m north

Let’s assume

north= positive

south=negative

12+(-16)+22+(-6)=12

Answer:mn

jjjj  jj ii 5668jjj Step-by-step explanation:

Answer:

• \(x\) = 42°

• \(y\) = 74°  

• \(z\) = 114°

Step-by-step explanation:

To solve these problems, we have to use the triangle sum theorem, which states that "the sum of all the interior angles of a triangle is 180°".

A)

\(x\) + 90° + 48° = 180°

⇒ \(x\)  + 138° = 180°

⇒ \(x\) + 138° - 138° = 180° - 138°      [Subtracting 138° from both sides]

⇒ \(x\) = 42°

B)

The triangle in this question is an isosceles triangle, therefore the two angles at the base of the triangle are equal and have measures of \(y\).

\(y\) + \(y\) + 32° = 180°

⇒ 2\(y\) + 32° = 180°

⇒ 2\(y\) = 180° - 32°

⇒ 2\(y\) = 148°

⇒ \(\frac{2}{2} y\) = \(\frac{148^{\circ}}{2}\)             [Dividing both sides by 2]

⇒ \(y\) = 74°                    

C)

\(z\) + 28° + 38° = 180°

⇒ \(z\) + 66 = 180°

⇒ \(z\)  = 180° - 66°

⇒ \(z\) = 114°

A system of linear equations: y + 2x = -5 and 8x + 4y = -20  has infinitely many solutions.

The 3 possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

The given linear system is:

y + 2x = -5           ....... (equation 1)

8x + 4y = -20     ..........(equation 2)

Rearrange equation 1 to:

2x + y = -5

Multiply both sides by 4:

8x + y4 = -20

Hence, equation 1 is equivalent to equation 2. Hence, the given linear system has infinitely many solutions.

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The probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.

To find the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

- P(X = k) is the probability of exactly k successes,

- n is the number of trials,

- k is the number of successes,

- p is the probability of success in a single trial, and

- C(n, k) is the combination of n choose k.

In this case, n = 12, k can be 0, 1, or 2, and p = 0.59 (the probability of using smartphones in meetings or classes).

Now we can calculate the probabilities for each value of k and sum them up:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)

P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)

P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)

Calculating these probabilities and summing them up will give us the desired probability that fewer than 3 out of 12 users use their smartphones in meetings or classes.

Let's calculate the probabilities.

P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)

Using the combination formula, C(12, 0) = 1, and simplifying the equation:

P(X = 0) = 1 * 1 * (1 - 0.59)^12 = 0.0003159

P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)

Using the combination formula, C(12, 1) = 12, and simplifying the equation:

P(X = 1) = 12 * 0.59^1 * (1 - 0.59)^11 = 0.0065294

P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)

Using the combination formula, C(12, 2) = 66, and simplifying the equation:

P(X = 2) = 66 * 0.59^2 * (1 - 0.59)^10 = 0.0470972

Now, let's sum up these probabilities to find P(X < 3):

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.0003159 + 0.0065294 + 0.0470972 = 0.0539425

Therefore, the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.

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The two solutions of the system are:

(5, 6)

(-4, -3)

Here we have the system of equations:

y - x = 1

x^2 + y^2 = 41

So we have a linear eqation and a circle equation.

We can write:

y = 1 + x

From the first one, and replace that in the second equation:

x^2 + (x + 1)^2 = 41

x^2 + x^2 +2 x + 1 = 41

2x^2 + 2x - 40 = 0

x^2 + x - 20 =0

The solutions are given by the quadratic formula:

\(x = \frac{1 \pm \sqrt{1^2 - 4*1*-20} }{2} \\\\x = \frac{1 \pm 9 }{2}\)

So we have two values:

x = (1 + 9)/2 = 5

x = (1 - 9)/2 = -4

And we know that:

y = 1 + x

Replacing the solutions of x there we will get:

y = 1+ 5 =  6

y = 1 - 4 = -3

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

Step-by-step explanation:

is there a height? Is the triangle with a 90 degrees angle? Is there any other conditions that are given?

To predict the cost of damage for a house that is 3.1 miles from the nearest fire station, we need to use the given equation y = 4920x + 10277.

The equation\(y = 4920x + 10277\) represents a linear relationship between the distance from the nearest fire station (x) and the predicted cost of damage (y) for a house. In this equation, the coefficient 4920 represents the rate of change in the cost of damage per unit increase in distance, and the constant term 10277 represents the intercept or the predicted cost of damage when the distance is zero.

To predict the cost of damage for a house that is 3.1 miles from the nearest fire station, we substitute x = 3.1 into the equation. The calculation would be\(y = 4920 * 3.1 + 10277.\) By evaluating this expression, we can determine the predicted cost of damage for a house at that distance.

However, it's important to note that without additional information about the context or specific data related to the equation, it is not possible to provide a precise numerical value for the cost of damage. The equation is only a mathematical representation of a relationship and would require more data or specific parameters to make an accurate prediction. Therefore, the answer "not appropriate" would be the appropriate response in this case.

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Answer:

i dont know if its a typo but here

Step-by-step explanation:

Answer:

34.24

Step-by-step explanation:

when dividing by a decimal, the original number increases

To divide 8.56 by 0.25, we can perform the calculation as follows:

8.56 ÷ 0.25 = 34.24

Therefore, the correct answer is D) 34.24.

Using trigonometry, the angle of elevation of the top of the building from A is 36.87 degrees

The angle of elevation of the building from A, we can apply the concept of trigonometry;

tan(θ) = opposite/adjacent

tan(θ) = height/180m

Since we're given that the angle of the top of the building is 45 degrees when the man is 180m away from point A, we can set up the equation:

tan(45°) = height/180m

The tangent of 45 degrees is 1, so the equation becomes:

1 = height/180m

Solving for the height:

height = 180m

Using the tangent of the angle;

tan(θ) = height/distance

tan(θ) = 180m/240m

Simplifying:

tan(θ) = 0.75

θ = tan⁻¹(0.75)

θ = 36.87 degrees

Therefore, the angle of elevation of the top of the building from point A is approximately 36.87 degrees.

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Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,

and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.

They need to think about how their technology could be used, and whether it could be used to harm people or the environment.

They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,

and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.

For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.

In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.

This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.

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Step-by-step explanation:

9+16×+3

28×<7

35x it's answer can I help

Answer:

Starting with the expression n² - 2 - (n - 2)², we can simplify it by expanding the second term using the formula for the square of a binomial:

n² - 2 - (n - 2)² = n² - 2 - (n² - 4n + 4)

Next, we can combine like terms:

n² - 2 - (n² - 4n + 4) = n² - n² + 4n - 6

Simplifying further, we get:

n² - 2 - (n - 2)² = 4n - 6

To prove that this expression is always even, we can show that it can be written in the form 2k, where k is an integer.

So, let's rewrite the expression as:

4n - 6 = 2(2n - 3)

Since 2n - 3 is an integer (because n is an integer greater than 1), we have shown that 4n - 6 can be written in the form 2k, where k is an integer.

Therefore, we have proved algebraically that n² - 2 - (n - 2)² is always an even number.

Answer:

The same as the person above me

Step-by-step explanation:

1.

- 2,3

2.

-X=2

Y=3

Answer:

Line up the decimal points. **Answer is Least to greatest: 10.5 , 11, 19**

Step-by-step explanation:

You need to line each number up.

10.5

11.0

19.0

The reason why 11 and 19 have a decimal point and zero at the end is because you need to do that in order to compare the numbers.

This problem is also a little common sense because 10.5 is the smallest, 19 is the largest while 11 is in the middle.

Answer:

B) 3b. 10b

Step-by-step explanation:

B) 3b. 10b = (3x10)(bxb) = 30b²

Answer:

-1.0

Step-by-step explanation:

dont no the explanation

Answer:

B

Step-by-step explanation:

Answer:

Angle 1 = 123 degrees

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:

it is wrong because he forgot to subtract the 5x

Step-by-step explanation:

I think this right I really hope it is though :-)

In the probability , the answers are,

a) Number of ways that each person has at least one pear =286 ways.

b) Number of ways that each person has at least one distinct pear =131220 ways.

The probability is a statistic for determining the likelihood of an event occurring. It determines the likelihood of an event. The probability calculation is P(E) = Number of Favourable Outcomes/Number of Total Outcomes.

a) There are 7 apples and 6 pears that are identical.

So the total number of fruits in this case is 7+6 = 13 identical fruits.

The number of ways to divide 13 fruits among three separate people is provided by methods.

=> \(13C_3\) = 286 ways.

Hence the number of ways is 286.

b) I assume that "distinct" in this case means that we care which person got which particular piece of fruit; swapping apples, for example, between two people produces a different distribution (as far as our count goes) even if they wind up with the same numbers of apples.

The apples are easy. Each one can go to one of 3 people, and there are 5 of them, so there are

\(3^5\) = 243 ways to distribute them.

The pears are a little harder, because we have to eliminate some of the possibilities. But we start with the total possible distributions:

\(3^6\) = 729

and subtract the ones that leave someone without any pears.

Obviously, there are 3 ways to leave two people without pears: each consists of giving all 6 pears to one person.

How many ways are there to leave just one person without any pears? There are 3 possible choices for the person so treated, and there are in these cases 2 possible recipients for each pear, so there are

\(2^6\) = 64 ways to distribute them between the two.

There's a hidden trap here! Each of those 64 ways includes two in which all the pears go to one or the other of those two people. Those duplicate the three all-to-one-person cases we've already figured, so we don't want to count them again. So the number of cases where exactly one person gets no pears is actually

3 * 62 = 186

Total number of ways to distribute the pears so that each person gets at least one is therefore

\(3^6\) - 3 - 3 * 62 = 729 - 3 - 186 = 540

We can combine any of these permissible distributions of the pears with any of the possible distributions of the apples, so the total number of ways to perform this combination is

243 * 540 = 131,220

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Rounding the value to the nearest whole number, the charge transferred is approximately 3880 C.

To calculate the charge transferred, we can use the formula:

Q = I * t

where:

Q is the charge transferred,

I is the current, and

t is the time.

Substituting the given values:

I = 61.9 A (current)

t = 62.9 s (time)

Q = 61.9 A * 62.9 s = 3880.11 C

Rounding the value to the nearest whole number, the charge transferred is approximately 3880 C.

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Answer: 16.308

Step-by-step explanation:brainiest please

Answer:

40 mph

Step-by-step explanation:

160÷4 = 40 miles per hour

Answer:

40miles per hour

Step-by-step explanation:

distance traveled/time spent=speed(velocity)

160/4=speed (velocity)

40mph

There would be 20 more of us (620-600). There would have been a day when more than 20 people would have been born.

A counting-based argument is known as a combinatorial argument or combinatorial proof. This line of reasoning has already been used, for instance in the section on Stirling numbers of the second sort.

It is mentioned that 620 persons shared the same month of birth. Assume that there were 30 days in the month to avoid losing generality. We'll demonstrate that through contradiction, assuming there were no more than 20 births on any one day throughout that month.

(Beyond that, we have the outcome.)

Now within Thirty Days, 30 * 20 births made up the total. However, since the population was 621 strong, another 21 persons had to be born on a day within that month. Note that the pigeon-hole principle was used in this instance. As a result, someday x, more than twenty people will be born. Consequently, there are at least 21 people who share a birthday.

The outcome would be the same whether there were 620 people. The discussion we had led to this. Keep in mind that in this scenario, we would have 20 more people (620-600). Therefore, a day when more than 20 people were born would have come.

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