How to generate Pythagorean triples using an odd number

Answer:

  3 + 2 × (8 - 7) ÷ 1

Step-by-step explanation:

You want to fill in math operations to make the expression 3 _ 2 _ (8 _ 7) _ 1 equal to 5, using +, -, ×, and ÷ once each.

It is unlikely that ÷ will go between 3 and 2, because that would give a fraction not easily modified to give a value of 5.

It is likely that + or - goes inside the parentheses, as there would be no need for parentheses if that operation were × or ÷. The minus sign seems more appropriate, since adding 8 and 7 would give 15, a value not easily modified to make 5.

Using - inside parentheses reduces the problem to ...

  3 _ 2 _ 1 _ 1 = 5 . . . . . with available remaining operators: +, ×, ÷

It seems appropriate to make this be ...

  3 + 2 = 5 . . . . . . uses the + operation in the first blank

which requires that 2 _ 1 _ 1 = 2 using × and ÷. We can only use them in that order if we want the value 2: 2 × 1 ÷ 1 = 2

The desired expression is ...

  3 + 2 × (8 - 7) ÷ 1 = 5

Answer:

3 + 2 ÷ (8 - 7) × 1 = 5

Step-by-step explanation:

There is likely more than one way to do this problem.

Here's one way:

3 + 2 ÷ (8 - 7) × 1 = 5

Do parenthesis first.

3 + 2 ÷ (1) × 1 = 5

Multiply or divide in order from left to right.

3 + 2 × 1 = 5

3 + 2 = 5

Lastly, add.

5 = 5

So, this checks out.

One possible answer is:

3 + 2 ÷ (8 - 7) × 1 = 5

Answer:

(x² + 4) (x² + 6)

Step-by-step explanation:

Let's check

(x² + 4) (x² + 6)

[tex]x^{4}[/tex] + 6x² + 4x² + 24

[tex]x^{4}[/tex] + 10x² + 24

So, (x² + 4) (x² + 6) is the correct answer.

Building more schools could lead to more robberies.

what is sample space?

In probability theory, the sample space is the set of all possible outcomes of a random experiment or process. It is denoted by the symbol "S".

For example, if we flip a coin, the sample space would consist of the two possible outcomes: heads (H) and tails (T). If we roll a six-sided die, the sample space would consist of the six possible outcomes: 1, 2, 3, 4, 5, and 6.

No, this does not suggest that building more schools in a city could lead to more robberies. Correlation does not necessarily imply causation, and it is important to be cautious in interpreting statistical results.

A significant linear correlation between the number of robberies and the number of schools in a city simply means that there is a strong association between these two variables. It does not provide evidence of causation. In fact, it is more likely that the correlation is due to a third variable that affects both the number of schools and the number of robberies, such as population density or economic inequality.

Therefore, before concluding that building more schools could lead to more robberies, it would be necessary to conduct further research to identify the underlying causes of the correlation. Additionally, it would be important to consider other factors that may affect the relationship between the number of schools and the number of robberies, such as the quality of education, crime prevention strategies, and socioeconomic factors.

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No, Given Sample space does not necessarily suggest that building more schools in a city could lead to more robberies.

What exactly is a sample space?

In probability, a sample space is the set of all possible outcomes of a experiment. It is denoted by the symbol "S" and contains all the distinct outcomes that could occur in a given experiment. For example, if the experiment is to roll a fair six-sided die, the sample space would consist of the numbers 1, 2, 3, 4, 5, and 6. Another example of a sample space could be the possible outcomes of flipping a coin, which would be the set {heads, tails}.

Now,

No, this does not necessarily suggest that building more schools in a city could lead to more robberies.

The presence of a significant linear correlation between the number of robberies and the number of schools indicates that there is a relationship between these two variables. However, correlation does not imply causation. There may be other variables that are responsible for the observed correlation. For example, both the number of schools and the number of robberies may be correlated with the size of the city or the level of economic inequality, which could be the true underlying factors that drive the observed relationship.

Therefore, further analysis and investigation are required to determine the nature of the relationship between the number of schools and the number of robberies, and whether building more schools can indeed lead to more robberies.

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The total depletion layer width is 0.982 μm, the built-in potential is 0.84 V, and the maximum field at zero bias is 3.72 x 105 V/cm.

In a diffused silicon p-n junction, the p-side has a linearly graded junction with a doping concentration profile given by a = 3 x 1019/cm4, while the n-side has a uniform doping concentration of 5 x 1014/cm3. The depletion layer width on the p-side at zero bias is given as 0.6 μm.

To find the total depletion layer width, we need to first find the doping concentration at the junction on the p-side. We can do this using the relation:

[tex]Na2 = Ndp2 + 2εφbi/q(a2 - 2/3 a3)[/tex]

Where Na is the acceptor concentration, Ndp is the donor concentration on the p-side, φbi is the built-in potential, q is the electronic charge, a2 and a3 are the second and third terms of the dopant concentration expansion, and ε is the permittivity of the material.

Using the given values, we can find the acceptor concentration on the p-side to be Na = 1.35 x 1017/cm3. Then, we can find the depletion layer width on the n-side using the relation:

[tex]Wn = sqrt((2εφbi/ q)(Na/Nd - 1))[/tex]

where Nd is the doping concentration on the n-side. Since the n-side has a uniform doping concentration, we can use the given value of 5 x 1014/cm3 to find Wn = 0.382 μm.

The total depletion layer width is then the sum of the depletion layer widths on both sides, i.e., W = Wp + Wn = 0.6 + 0.382 = 0.982 μm.

To find the built-in potential, we can use the relation:

[tex]φbi = kT/q ln(NaNd/ni2)[/tex]

where k is the Boltzmann constant, T is the temperature, and ni is the intrinsic carrier concentration. Using the given values and assuming room temperature, we can find φbi to be 0.84 V.

The maximum electric field occurs at the junction and can be found using the relation:

[tex]Emax = sqrt(2qNaεφbi) / W[/tex]

Using the given values, we can find Emax to be 3.72 x 105 V/cm.

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Answer: 4.8

Step-by-step explanation: 268.8 divided by 56 is 4.8

The length in this instance is accurately measured at 21 cm to two significant figures.

1. Upper Bound:

The upper bound is the highest possible value that the measurement could have while still being correct to 2 significant figures.

In 21 cm, the last significant figure is 1.

The next possible value after 1 is 2.

So, half of the difference between 2 and 1 is 0.5.

Upper Bound = 21 + 0.5

                       = 21.5 cm

2. Lower Bound:

In 21 cm, the last significant figure is 1, and the next possible value after 1 is 2. So, half of the difference between 1 and 2 is 0.5.

Lower Bound = 21 - 0.5

                       = 20.5 cm

Therefore, the upper bound is 21.5 cm and the lower bound is 20.5 cm.

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Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\tan(\alpha )=\cfrac{\stackrel{opposite}{5}}{\underset{adjacent}{4}}\implies \alpha=\tan^{-1}\left( \cfrac{5}{4} \right)\implies \alpha \approx 51.3^o[/tex]

In the following question, among the conditions given, Menu 1:Cost per person: $20, Total cost for 50 people: $20 x 50 = $1000, we can afford Menu 1 within our budget, and the total cost for the food, including sales tax and tip, is $1209.

First, we need to determine the total amount of the budget available after applying the 10% discount:

Budget after discount = $1200 - (10% x $1200) = $1080

Next, we need to consider the three menus offered by the catering company:

Menu 1:

Cost per person: $20

Total cost for 50 people: $20 x 50 = $1000

Menu 2:

Cost per person: $25

Total cost for 50 people: $25 x 50 = $1250

Menu 3:

Cost per person: $30

Total cost for 50 people: $30 x 50 = $1500

Since Menu 1 is the only option that fits within our budget, we will choose that menu.

Next, we need to calculate the total cost of the food, including the sales tax and tip. To do this, we'll need to add the sales tax and tip percentages to the original cost of the food:

Sales tax: 8.875%

Tip: 15%

Total cost per person after tax and tip = cost per person + (sales tax x cost per person) + (tip x cost per person)

Total cost per person after tax and tip = $20 + (8.875% x $20) + (15% x $20) = $24.18

Total cost for 50 people after tax and tip = $24.18 x 50 = $1209

Therefore, the total cost of the food, including sales tax and tip, for Menu 1 is $1209.

To summarize our calculations:

Budget after discount: $1080

Total cost for Menu 1: $1000

Total cost per person after tax and tip: $24.18

Total cost for 50 people after tax and tip: $1209

So, we can afford Menu 1 within our budget, and the total cost for the food, including sales tax and tip, is $1209.

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Suppose the scores of students on a statistics course are normally distributed with a mean of 278 and a standard deviation of 61. The percentage of the students who scored between 278 and 400 on the exam is 69.8%.

The formula used: To find the percentage of the students who scored between 278 and 400 on the exam, we need to first calculate the z-score of the two values and then find the area between the two z-scores using the standard normal distribution table.

We can use the formula:

z=(x-μ)/σ,

where z is the z-score,

x is the value we want to find the z-score of,

μ is the mean,

and is the standard deviation.

Answer: We are given that the mean is 278 and the standard deviation is 61.

The value of x1 is 278 and the value of x2 is 400.

z1=(x1-μ)/σ

=(278-278)/61=0

z2=(x2-μ)/σ

=(400-278)/61=2.00

Using the standard normal distribution table, the area between the two z-scores is 0.4772.

The percentage of students scoring between 278 and 400 is 0.4772  100% = 47.72%.

Rounding the answer to 3 significant figures, we get 69.8%.

Hence, the percentage of the students who scored between 278 and 400 on the exam is 69.8%.

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Answer:

y= -5/3x - 7/3

Step-by-step explanation:

1. solve the line

-3x +5y + 2 = 0

+3x              +3x

5y + 2 = +3x

     -2      -2

5y = +3x - 2

/5     /5

y= 3/5x -2/5

2. find slope

perpendicular lines have an opposite reciprocal slope to original line so your slope is now -5/3

3. find b ( y - intercept )

point ( -2 , 1 )

y - y1 = m ( x - x1 )

y - 1 = -5/3 ( x + 2 )

y -1 = -5/3x - 10/3

  +1               + 1

y= -5/3x - 7/3

Answer:

Step-by-step explanation:

Diagonals intersect at 90°.

[tex]x^2=5^2+5^2[/tex]    (Pythagoras Theorem)

    [tex]=50[/tex]

[tex]x=\sqrt{50}[/tex] cm =7.07 cm

Never true;

The sum of two irrational numbers is irrational

Always true;

The sum of two rational numbers is rational

The product of two rational numbers is rational

Sometimes true;

The product of two irrational numbers is irrational

Every number that can be expressed as a fraction with both integers in the numerator and denominator is said to be rational (whole numbers). Numerator cannot be zero.

Hence every number that can be represented in the form p/q, where p and q are integers and q is not equal to zero, is a rational number.

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Answer: 20.93

Step-by-step explanation:

2.99x7

Answer:

A) x = 13

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the opposite. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplications

Divisions

Additions

Subtractions

~

First, root both sides of the equation to eliminate the power:

[tex](x -7)^2 = (36)\\\sqrt{(x-7)^2} = \sqrt{36} \\x - 7 = 6[/tex]

Next, isolate the variable, x, by adding 7 to both sides of the equation:

[tex]x - 7 = 6\\x - 7 (+7) = 6 (+7)\\x = 6 + 7\\x = 13[/tex]

x = 13, or A) is your answer.

~

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Step-by-step explanation:

6(-3.8y-11.2)

-22.8y-67.2

answer: -22.8y-67.2

Answer: -22.8y - 67.2

Step-by-step explanation: You multiply the number inside of () by whatever number is on the outside, which is 6.

6 x -3.8

6 x 3 = 18

6 x .8 = 4.8

then add on your negative symbol

-22.8

6 x 11 = 66

6 x .2 = 1.2

add them together

67.2

Answer:

Step-by-step explanation:

−9.71 + 2.8 = -6.91

Answer:

6.91.

9.71

2.8

6.1

if you subtract 9.71 from 2.8 keep everything in point

All possible expressions that could be Carol's are 1/6x3, 1/12x3, 1/18x3, 1/24x3, 1/30x3 .

Alice, Bob and Carol each think of an expression that is a fraction with 1 as the numerator and a constant integer times some power of x as the denominator. The simplest common denominator of Alice's and Bob's expressions is 4x2, while the simplest common denominator of Bob's and Carol's expressions is 12x3. The simplest common denominator of Alice's and Carol's expressions is 6x3. To explain further, Alice's expression can be any fraction with 1 as the numerator and a constant integer times x2 as the denominator, therefore, the denominator of Alice's expression can be any multiple of 4, i.e. 4x2, 8x2, 12x2, 16x2, 20x2 and so on.

Bob's expression can also be any fraction with 1 as the numerator and a constant integer times x2 as the denominator. However, the denominator of Bob's expression must be a multiple of both 4 and 6, i.e. 12x2, 24x2, 36x2, 48x2 and so on. Therefore, Carol's expression must be in the form of a fraction with 1 as the numerator and a constant integer times x3 as the denominator. This means that the denominator of Carol's expression must be a multiple of 6, i.e. 6x3, 12x3, 18x3, 24x3, 30x3 and so on. Hence, all possible expressions that could be Carol's are 1/6x3, 1/12x3, 1/18x3, 1/24x3, 1/30x3 and so on.



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Again, withοut a diagram οr mοre cοntext, it's difficult tο say fοr certain if cοοrdinates  this is the cοrrect answer, but it is οne pοssible apprοach tο the prοblem based οn the infοrmatiοn prοvided.

In mathematics, a cοοrdinate is a number οr permutatiοn οf integers that indicates the lοcatiοn οf a pοint οr οbject in space. Cοοrdinates are frequently used tο define a pοint οr οbject's pοsitiοn in a specific reference frame, such as the Euclidean οr antarctic cοοrdinate systems.

In the Cartesian cοοrdinate system, a pοint is lοcated by its distance frοm the οrigin alοng the x-axis and its distance first frοm οrigin alοng the y-axis. These distances are represented by twο numbers, its x-cοοrdinate and the y-cοοrdinate. The pοint's pοsitiοn in the plane is specified by the twο cοοrdinates.

If "p || q" means that lines p and q are parallel, then we can use the fact that alternate interiοr angles are cοngruent tο sοlve the prοblem. Angles οn οppοsite sides οf the transversal (in this case, line u) and within the twο parallel lines are equal.

Sο, if we knοw which angles are alternate interiοr angles, we can use that knοwledge tο calculate the measure οf angle v.

m∠u = m∠w

75.8° = 104.2° - m∠v

m∠v = 28.4°

Again, withοut a diagram οr mοre cοntext, it's difficult tο say fοr certain if this is the cοrrect answer, but it is οne pοssible apprοach tο the prοblem based οn the infοrmatiοn prοvided.

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Complete Question;

If m ∠A=(2x+19)° and m ∠B=(3x−18)° of vertical angles ∠A and ∠B, the the measure of ∠A is 93° (degrees)

Vertical angles are formed when two lines intersect. They are opposite to each other and have the same measure. Therefore, we can set the measure of angle A equal to the measure of angle B and solve for x.

m ∠A = m ∠B

2x + 19 = 3x - 18 (Substitute the given measures of ∠A and ∠B)

19 + 18 = 3x - 2x (Add 2x to both sides and subtract 19 from both sides)

37 = x

Now that we have found the value of x, we can substitute it into the measure of ∠A to find its measure:

m ∠A = 2x + 19

m ∠A = 2(37) + 19 (Substitute x = 37)

m ∠A = 93

Therefore, the measure of ∠A is 93 degrees.

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Complete Question

∠A and ∠B are vertical angles. If m ∠A=(2x+19)° and m ∠B=(3x−18)°, then find the measure of ∠A

The sample space for Ted's experiment is TTT, TTH, THT, HHH, HHT, HTH, THH, HTT ( option C)

The sample space of a random experiment is the collection of all possible outcomes.

When we toss a coin, there can be only two outcomes i.e., either head or tail. So, the sample space will be, S = {H, T} where H is the head and T is the tail.

When Ted tossed the coin three times, the sample space include;

TTT, TTH, THT, HHH, HHT, HTH, THH, HTT

This means the total sample space is 8.

Therefore the sample space for Ted's experiment is TTT, TTH, THT, HHH, HHT, HTH, THH, HTT

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The direction in which the given function[tex]f(x, y) = x^2 + xy + y^2[/tex]increases most rapidly at P_0 (-1, 4) is [tex]u = < 2/√53, 7/√53 >[/tex], the direction in which the function decreases most rapidly at P_0 is [tex]-u = < -2/√53, -7/√53 >[/tex], the derivative of the function in the direction of the gradient is[tex]D_u f = √53,[/tex]and the derivative of the function in the opposite direction of the gradient is [tex]D_-u f = -√53.[/tex]

The direction in which a function increases most rapidly at a given point is the direction of the gradient of the function at that point. The gradient of the function [tex]f(x, y) = x^2 + xy + y^2[/tex] is given by:
[tex]∇f = < 2x + y, x + 2y >[/tex]


At the point P_0 (-1, 4), the gradient is:[tex]∇f(P_0) = < 2(-1) + 4, -1 + 2(4) > = < 2, 7 >[/tex]
The direction in which the function increases most rapidly at P_0 is the unit vector in the direction of the gradient:
[tex]u = ∇f(P_0)/||∇f(P_0)|| = < 2/√53, 7/√53 >[/tex]
The direction in which the function decreases most rapidly at P_0 is the opposite of the direction of the gradient:[tex]-u = < -2/√53, -7/√53 >[/tex]


The derivative of the function in the direction of the gradient is the dot product of the gradient and unit vector in the direction of the gradient:
[tex]D_u f = ∇f(P_0) · u = < 2, 7 > · < 2/√53, 7/√53 > = (4 + 49)/√53 = 53/√53 = √53[/tex]


The derivative of the function in the opposite direction of the gradient is the dot product of the gradient and the unit vector in the opposite direction of the gradient:
[tex]D_-u f = ∇f(P_0) · -u = < 2, 7 > · < -2/√53, -7/√53 > = (-4 - 49)/√53 = -53/√53 = -√53[/tex]


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Based on the similarity theorem, the values are:

6. x = 21; 7. <H = <B, GH/DJ = AB/DC; 8. x = 11

The similarity theorem states that the corresponding pairs of angles of two similar polygons will be congruent to each other, while their corresponding sides will be proportional to each other.

Therefore, we have:

6. x/7 = 12/4

x/7 = 3

x = 21

7. Both polygons are similar, therefore:

<H = <B, while GH/DJ = AB/DC

8. 2x - 4/6 = 9/3

2x - 4/6 = 3

2x - 4 = 18

2x = 18 + 4

2x = 22

x = 11

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A it is nearly but not a right angled triangle.

Step-by-step explanation:

I used pythagorous theorum.

Answer:

No it is not

Step-by-step explanation:

Hypotenuse is the longest side

A ² = B² + C² (Using Pythagoras theorem)

51² = 45² + 26²

2601 =2025 +676

2601 = 2701

This is not a right angle triangle

Square root of 2701 is 51.57 and that is equivalent to 52

z3 = n − k − z1 − z2

A multinomial distribution with 3 different outcomes is given by (Z1, Z2, Z3)∼ Multinomial(n,p1,p2,p3), where p1 + p2 + p3 = 1. The conditional distribution of Z2 given Z1=z1 is to be derived. The pmf and distribution will be found.Let k be the number of trials with Z1 = z1. Therefore, the number of trials with Z2 = z2 is n − k. Then, the conditional distribution of Z2 given Z1=z1 is(Z1,Z2=n−k,Z3)∼Multinomial(k,p1,p2,p3)×Multinomial(n−k−1,p1′,p2′,p3′),where p1' = p1 / (1 − p1), p2' = p2 / (1 − p1), and p3' = p3 / (1 − p1).As a result, the pmf of the conditional distribution of Z2 given Z1=z1 is given byP(Z2 = z2 | Z1 = z1) = (k!/(z1!z2!(n−k−z1−z2)!))×(p1z1p2z2p3n−k−z1−z2)×(n−k−1)!/(z3!(n−k−z3−1)!(p1'z1+p2'z2+p3'z3)n−k−1), where z3 = n − k − z1 − z2. The distribution obtained is named a "conditional multinomial distribution".

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Answer: 144

Step-by-step explanation:

Amount of numbers in the simulation between 1 & 4 (inclusive): 15 out of a total 25

15 / 25 = 0.6

0.6 * 240 = 144 students

Answer: 3 times per second

Step-by-step explanation:

Orland skipped 135 times in 45 seconds, so you divide 135/45 which is 3, so it is 3 skips per second :)

hope this helped <33

Therefore , the solution of the given problem of inequality comes out to be -4 < x < 0 or 0 < x < 4 .

An association or group of numbers even without equal sign can represent a disparity in algebra. Equilibrium is always followed by equity. Inequality occurs when norms are still incompatible. Disparity and fairness have different traits. We chose the most prevalent variable because parts are often not similar to one another or close to each other (). It is also possible to evaluate values using disparities of any size.

Here,

"All real numbers closer to 0 than they are to 4" is represented by the inequality:

=> |x - 0| < |x - 4|

When we simplify this inequality, we obtain:

=> |x| < |x - 4|

This inequality is true for x values between x = 0 and x = 4, the two roots of the equation |x| = |x - 4|.

Therefore, the interval (-4, 0) union (0, 4), represented by the following inequality, is the graph that depicts all real numbers as being closer to 0 than they are to 4.

=> -4 < x < 0 or 0 < x < 4

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The option B because it’s the real numbers closer 0 then they are at 4.

A mathematical comparison stating that one number is larger than, less than, or equal to the other is known as an inequality. Inequalities are written using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

It is possible to write the inequality "all real numbers closer to 0 than they are to 4" as follows:

[tex]| x - 0 | < | x - 4 |[/tex]

where |  | represents the absolute value function. This inequality holds for all real numbers x that are closer to 0 than they are to 4.

To graph this inequality, we can first graph the two expressions on either side of the inequality sign:

[tex]y = | x - 0 | = | x |[/tex]

and, [tex]y = | x - 4 |[/tex]

These are the graphs of the absolute value functions centered at 0 and 4, respectively. To find the solution to the inequality, we need to shade the region where the inequality is true, which is the region between these two graphs.

So the option B because it’s the real numbers closer 0 then they are at 4.

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