What is 900x 5 to the 5 power

An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.

In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:

Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:

89 = 1 x 55 + 34

The gcd of 55 and 89 is 1.

Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89

   The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.

To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:

   55 x 34 = 1870

   11 = 1 x 11 + 0

Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:

55 x 34 ≡ 0 |89|

Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:

55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|

Therefore, the inverse of 55 modulo 89 is indeed 34.

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The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.

To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.

A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.

To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°

Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.

The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)

So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.

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Answer:

Step-by-step explanation:

It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.

Answer:

120 minutes / 2 hours

Step-by-step explanation:

time = distance / velocity

[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98

Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.

Then the 95% confidence interval can be calculated as follows:

Upper limit: µ + Zσ

Lower limit: µ - Zσ

Where

The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.

The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.

The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore

Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880

Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.

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Answer:

x = 4

Step-by-step explanation:

Alternative interior angles means these angles are equal in magnitude and sign

[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]

The equation has two distinct real roots if 64 - 4c > 0, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.

The discriminant of a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex] is given by [tex]b^2 - 4ac[/tex]. In the given quadratic equation, a = 1, b = 8, and c = c. Therefore, the discriminant is:

[tex]b^2 - 4ac[/tex]

[tex]= 8^2 - 4(1)(c)[/tex]

[tex]= 64 - 4c[/tex]

Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). If the discriminant is negative, the equation has no real roots (two complex conjugate roots).

In this case, we do not have enough information about the value of c to determine the nature of the roots of the equation. All we know is that the discriminant is 64 - 4c.

Hence, if 64 - 4c > 0, we can state that the equation has two separate real roots, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.

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[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Lwh}{3} ~~ \begin{cases} L=\stackrel{base's}{length}\\ w=\stackrel{base's}{width}\\ h=height\\[-0.5em] \hrulefill\\ L=6L\\ w=6w \end{cases}\implies V=\cfrac{(6L)(6w)h}{3}\implies \stackrel{ \textit{36 times the volume} }{V=\cfrac{Lwh}{3}(36)}[/tex]

Answer:

Using the property of logarithms that says log_a(a^b) = b, we can simplify the expression:

7^(log_7(12)) = 12

Therefore, the value of the expression is 12.

Answer:

f(x) = (5/6)x - (1/4)

f(-8) = (5/6)(-8) - (1/4)

f(-8) = (5/3)(-4) - (1/4)

f(-8) = (-20/3) - (1/4)

f(-8) = (-80-3)/12

f(-8) = -83/12

The power dissipated by the heater is 1260 watts (W).

What is a polynomial?

A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.

Given:

Current (I) = 10.5 A

Potential Difference (V) = 120 V

Unknown:

Power (P) = ?

The formula to calculate the power is:

P = VI

Substituting the given values:

P = 120 V × 10.5 A

P = 1260 W

It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:

P = 1260 W (rounded to three significant digits).

Therefore, the power dissipated by the heater is 1260 watts (W).

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The data we get from the question is a random experiment can result in one of the outcomes {a,b,c,d} with probabilities from that information, P(A U B U C) = 0.8.
         

The given probabilities of events and outcomes are:

       P({a}) = 0.4,P({b}) = 0.1,P({c}) = 0.3,P({d}) 0.2

 So the given events are:

        A = {a,b},B = {b,c,d},C = {d}

   We have to find P(A U B U C) Using the formula of the probability of the union of two events,

    we get:

          P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Now we will find the values of all probabilities:

                  P(A) = P({a}) + P({b})

                         = 0.4 + 0.1

                         = 0.5

                   P(B) = P({b}) + P({c}) + P({d})

                          = 0.1 + 0.3 + 0.2

                           = 0.6

                   P(C) = P({d})

                            = 0.2

                      P(A ∩ B) = P({b})

                                     = 0.1

                      P(A ∩ C) = P({d})

                                     = 0.2

                      P(B ∩ C) = P({d})

                                     = 0.2

               P(A ∩ B ∩ C) = 0

 (No common event) Put all the above values in the formula:

           P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) +

                                     P(A ∩ B ∩ C)

                                 = 0.5 + 0.6 + 0.2 - 0.1 - 0.2 - 0.2 + 0

                                 = 0.8

         Therefore, P(A U B U C) = 0.8 is the required probability.

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Answer:

the chance of a blizzard tommorrow is 5%. write the complement of this event

Step-by-step explanation:

The complement of an event is the event that it does not happen, so the complement of a blizzard occurring tomorrow with a 5% chance is that a blizzard does not occur tomorrow with a probability of:

100% - 5% = 95%

Therefore, the complement event is that there is a 95% chance that a blizzard does not occur tomorrow.

Answer:

can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10​

Step-by-step explanation:

To solve sin y - cos (y + 20) = 0, we can rearrange it as sin y = cos (y + 20).

Then, we can use the identity sin (90 - x) = cos x to rewrite the right side as cos (y + 20) = sin (70 - y).

Substituting this into the equation, we get sin y = sin (70 - y).

Now, there are two possibilities:

y = 70 - y, which gives y = 35 degrees.

y = 180 - (70 - y), which gives y = 105 degrees.

To solve cos theta = sin theta - 10, we can rearrange it as cos theta - sin theta = -10 and then use the identity cos (x - 90) = sin x to rewrite it as -sin (theta - 90) = -10.

Taking the inverse sine of both

Answer:

24.4 degrees

Step-by-step explanation:

This is a right triangle so you can use trig to solve. If you take the arctan of 5/11 you get 24.4(rounded to the nearest tenth)

Answer:

169 - 144p²

Step-by-step explanation:

(13 - 12p) × (13 + 12p)

each term in the second factor is multiplied by each term in the first factor

13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis

= 169 + 156p - 156p - 144p² ← collect like terms

= 169 - 144p²

Answer:

(1,3)

Step-by-step explanation:

Given system of equations is :-

We can solve this by using substitution method by substituting the value of y from equation (1) into equation (2) as ,

2x + 1 = x + 2

Subtract x on both sides,

2x - x + 1 = 2

Simplify,

x = 2 - 1

x = 1

Substitute this value of x into equation (2) as ,

y = 1 + 2

y = 1 + 2

y = 3

Hence the required answer is (1,3) .

and we are done!

The answer is (001). This is because B (001) has h and k as non-zero integers, which does not match the criteria for the {100} family.

The question is asking which of the planes (A), (B), (C), and (D) is not part of the {100} family for a tetragonal crystal.A tetragonal crystal is a three-dimensional structure made up of four faces that intersect at right angles, forming a unit cell. Each face of the unit cell is defined by a Miller index. A Miller index is a set of three integers written in the form {hkl}, which describes the orientation of the face relative to the crystal lattice. In a tetragonal crystal, the {100} family is the set of faces described by {hkl} such that h = k = 0 and l ≠ 0.

Therefore, A (010), C (110), and E (all of these planes are in the {100} family) are all part of the {100} family for a tetragonal crystal, while B (001) is not.  because B (001) has h and k as non-zero integers, which does not match the criteria for the {100} family. In conclusion, the correct answer to the question is B (001).

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Answer:

To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (-2 - (-12)) / (0 - 5)

slope = 10 / (-5)

slope = -2

Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the given points on the line.

Let's use the point (5,-12):

y - (-12) = -2(x - 5)

y + 12 = -2x + 10

y = -2x - 2

Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.

Answer: the angle opposite the side length 9 is 74.62 degrees I think .

Step-by-step explanation:

Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.

To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.

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Answer:

x = 6

Step-by-step explanation:

Verticle angles are equal to each other...

m∠A = m∠B

Thus...

4x + 6 = 2x + 18

Now, we isolate x:

4x + 6 = 2x + 18

Subtract 6 from both sides

4x = 2x + 12

Subtract 2x from both sides

2x = 12

Divide both sides by 2

x = 6

Thus, the ratio for the number of blueberries to banana is 4:1.

A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.

A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.

The given data for preparing fruit smoothie:

Then,

ratio of  blueberries to banana:

blueberries/banana = 4/1

Thus, the ratio for the number of blueberries to banana is 4:1.

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Answer: The answer is A) Players on the basketball team are generally taller than players on the baseball team. This is the most likely conclusion we can draw based on the information given.

Step-by-step explanation:

We know that the interquartile range (IQR) is the range of the middle 50% of the data. So for the basketball team, the heights of 50% of the players lie within the range of 73 ± 2.5 (since the IQR is 5). Similarly, for the baseball team, the heights of 50% of the players lie within the range of 72 ± 3 (since the IQR is 6).

Comparing the medians, we see that the basketball team has a median height of 73, while the baseball team has a median height of 72.

Based on this information, we can conclude that:

A) Players on the basketball team are generally taller than players on the baseball team - this is the most likely answer, as the median height of the basketball team is higher.

B) Players on the baseball team are generally taller than players on the basketball team - this is not supported by the given information.

D) There is less variation in heights on the baseball team than on the basketball team - we cannot determine this based on the given information.

C) Players on the baseball team are generally the same height as players on the basketball team - this is not supported by the given information.

In set theory, two sets are considered equal if they have the same elements. In this case, A is a set containing the elements 1, 2, and 3, while B is an empty set (also known as the null set),

A contains three distinct elements, and B contains none, we can conclude that A and B are not equal, i.e., A is not equal to B.

A ≠ B

Set theory is a branch of mathematics that studies collections of objects, called sets, and the relationships between them. A set is defined as a well-defined collection of distinct objects, which can be anything from numbers and letters to more abstract concepts like functions and geometrical shapes. The set theory provides a foundation for other areas of mathematics, including algebra, topology, and logic.

One of the fundamental concepts of set theory is the notion of membership, which states that an object either belongs to a set or does not. Sets can also be combined through operations such as union, intersection, and complementation, and the relationships between sets can be represented using Venn diagrams.

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Answer:

a) We can use the given data to find the rate of change (slope) of the expenses over one year, and then use it to write the equation of a line in slope-intercept form:

Slope m = (Total Expenses in 2021-2022 - Total Expenses in 2020-2021) / 1 year

m = (23,500 - 21,211) / 1 = 2,289

Using the point-slope form of a line, we can write the equation as:

y - 21,211 = 2,289(t - t1), where t1 is the year 2020-2021.

Simplifying, we get:

y = 2,289t + 18,922

b) To estimate the Total Expenses for your first year of school, you need to know what year you will start. Let's say you will start in 2024-2025, which is 3 years from 2021-2022.

Then, plugging in t = 3 into the equation we just found, we get:

y = 2,289(3) + 18,922 = 23,789

So the estimated Total Expenses for your first year of school would be $23,789.

c) The graph of the function y = 2,289t + 18,922 is a straight line with a positive slope of 2,289. It passes through the point (0, 18,922) on the y-axis, and it will extend indefinitely in both directions.

d) The y-intercept of the graph is the point (0, 18,922), which represents the Total Expenses for the year 2020-2021. There are no vertical asymptotes, but the graph will approach a horizontal asymptote as t goes to infinity, since the expenses cannot increase indefinitely. The domain of the function is all real numbers, and the range is all values greater than or equal to 18,922. As t increases, the function increases without bound, so the end behavior is that the graph goes up to the right.

If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

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Among the given factors, global competition does not contribute to the quest for quality. The correct answer is Option A.

In today's business environment, quality has become an important factor that can make or break a company's success. A successful firm must focus on the quality of the products and services they offer, as this can help them maintain their competitive advantage and ensure customer loyalty.

Quality is important for a variety of reasons, including customer satisfaction, reduced costs, increased productivity, and increased revenue. When firms focus on quality, they can provide better products and services to their customers, which can lead to increased customer loyalty and repeat business. This can help firms build a strong reputation in the market and maintain a competitive advantage.

Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage. When firms face global competition, they need to ensure that their products and services are of high quality to compete effectively in the global market. High-quality products and services can help firms differentiate themselves from their competitors and gain a competitive advantage. This can help firms increase their market share and revenue.

Several factors contribute to the quest for quality. These include:

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The exponential distribution is a probability distribution that models the time between events in a Poisson process, where events occur randomly and independently at a constant average rate.

It is commonly used in reliability theory, queuing theory, and other fields to model the failure or waiting times of systems.

(a) The mean time to decay for Cobalt-60 is 5.27 years.

(b) The standard deviation of the decay time is 2.6355 years.

(c) The 99th percentile is 13.6825 years.

(d) The mean time of the experiment is 15.8175 years and the standard deviation is 4.86788 years.

Note: The answers are calculated based on the exponential distribution of radioactive decay with a half-life of 5.27 years for Cobalt-60.

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Answer:

Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.