Compute 32016 mod 11. Hint: This is an application of Euler's Theorem.
Answers
Answer:
6(mod11)
Step-by-step explanation:
By Euler's Theorem,
a^10 ≡1 (mod 11) for all a.
Therefore,
32016 ≡ 32016^10 ≡6^10 ≡ 6(mod11)
According to Euler's Theorem, 32016 mod 11 is equivalent to the remainder when 1 is divided by 11 i.e., 1.
To compute 32016 mod 11 using Euler's Theorem, we can first find the value of φ(11), where φ is Euler's totient function. For a prime number like 11, φ(p) = p - 1.
φ(11) = 11 - 1 = 10
Now, we can apply Euler's Theorem, which states that for any positive integer "a" coprime to "m" (where "m" is a positive integer), we have:
a^φ(m) ≡ 1 (mod m)
In this case, we want to find 32016 mod 11. Since 32016 and 11 are coprime (they don't share any factors other than 1), we can apply Euler's Theorem.
Using Euler's Theorem:
32016¹⁰ ≡ 1 (mod 11)
Therefore, 32016 mod 11 is equivalent to the remainder when 1 is divided by 11, which is simply 1.
Hence, 32016 mod 11 is equal to 1.
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Related Questions
Find the measure of the indicated angle. Need help please.
I also need explanation...
Thank you!!!
Answers
Answer:
The measures of interior angles of a triangle sum to 180°.
63+60=123
180-123=57
Angle AB is 57°
in a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. a number of beads are then removed from the container. if the product of the point values of the removed beads is 147,000, how many red beads were removed?
Answers
Based on the mentioned informations and provided values, 21 red beads were removed.
Let the number of red beads removed be x. Then we have:
Total points = (7x + 5y + 3z + 2w) = 147000, where y, z, w are the number of yellow, green, and blue beads removed, respectively.
We can also write the above Linear equation as:
7x = 147000 - 5y - 3z - 2w
Since 147000 is divisible by 1000, we can divide both sides by 1000 to get:
7x = 147
x = 21
Therefore, 21 red beads were removed.
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5+5=10-10-10-10-10+1
Answers
Answer:
Your answer is -29
Step-by-step explanation:
Hope this helps : )
Evaluate the expression 9x for x = 2
Answers
The value of expression 9x for x= 2 is 18.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression = 9x
For x=2
Value of expression=9*2
=18
Hence,
After evaluating 9x for x=2 value will be 18.
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1.True or false: all variable terms can be combined, regardless of exponents
2. Polynomials in standard form…
a. Are in ascending order of monomial degrees
b. Are in descending order of monomial degrees
c. Are in whatever order in which they are given
Answers
Answer:
b
Step-by-step explanation:
Standford form is highest exponent to lowest
Evaluate
a - b + 3C when
a = 4, b = -2, and
4b =
C = 3.
Answers
Answer:
19
Step-by-step explanation:
Plugin a =4 ; b = -2 & c =3 in the expression
a - b + 3c = 4 - (-2) + 3*3
= 4 + 6 + 9
= 19
allen and ben are painting a fence. the ratio of the amount of work allen does to the amount of work ben does is $3:5$. if the fence requires a total of $240$ square feet to be painted, how many square feet does ben paint?
Answers
The fence Ben paints is 150 square feet.
Given:
ratio of the amount of work allen does to the amount of work ben does is 3:5
allen : ben = 3:5
total work done in ratio = 3 + 5 = 8
Count the fence Ben paints
Since , fence requires a total of 240 square feet to be painted
Thus, ben = ratio of ben/ total ratio × total of works
ben = 5/8 × 240
ben = 1,200/8
ben = 150
Hence , The fence Ben paints is 150 square feet .
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The triangle below is equilateral. That means all the sides are the same length. What is the value of y?
Answers
Answer:
y = 7
Step-by-step explanation:
3x = 5x - 8
8 = 2x
x = 4
3x = 5 + y
3(4) = 5 + y
12 = 5 + y
7 = y
#teamtrees #WAP (Water And Plant)
Answer:
7
Step-by-step explanation:
As all sides are equal,
3x=5x-8
2x=8
x=4
5+y=3x
5+y=3*4
5+y=12
y=12-5
y=7
find the exact values of the sine, cosine, and tangent of the angle. 255° = 300° − 45°
Answers
The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.
To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.
By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.
We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.
Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.
For 45°:
sin(45°) = cos(45°) = 1/√2
tan(45°) = 1
Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.
Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.
Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.
Therefore, for the angle 255°:
sin(255°) = -1/√2
cos(255°) = 1/√2
tan(255°) = -1
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Cassie rolls a fair number cube with 6 faces labeled 1 through 6. She rolls the number cube 300 times. Which result is most likely?
Answers
Answer:
she mostly likely found 1 result .
Find when and .Both values are .Both values are . and and
Answers
from the question;
we to find |x| when x = 15 and when x = -15
by definition of absolute value we have
\(\lvert x\rvert\text{ = x}\)Thats for every value of x, the absolute value is always positive
Hence,
\(\begin{gathered} \text{when x = 15} \\ \lvert15\rvert=\text{ 15} \end{gathered}\)Also
\(\begin{gathered} \text{when x = - 15} \\ \lvert-15\rvert\text{ = 15} \end{gathered}\)Therefore the correct answer is
Both values are 15
option B
There are 42 runners in a race. How many different ways can the runners finish first, second, and third?
Answers
Answer:
There are 68,640 different ways the runners can finish first, second, and third in the race.
Concept of Permutations
The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.
Brief Overview
Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.
Calculations
To calculate the total number of different ways, we multiply the number of choices for each position:
42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.
Concluding Sentence
Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.
Hari can do a piece of work in 8 days. In how many days would he do one-fourth of the same work ? Can anyone show the process as well ? Will matk brainlieast
Answers
Answer:
2 days
Step-by-step explanation:
I figured out what 1/4 of 8 was by taking 2 and multiplying it by 4. You can also get this same answer by dividing 8 by 4.
In 12 games, Jeffrey scored 252 points. What is his scoring rate in points per game?
Answers
Answer: His scoring rate was 21 points per game.
Step-by-step explanation: Find his scoring rate by dividing 252 by 12.
252/12 = 21
Which equation correctly describes the relationship between the
measure of the inscribed angle and the measure of the
intercepted arc in the figure?
m JKL= mJL
1/2m JKL = mJL
2(m JKL) =mJL
m JKL = 360° – mJL
Answers
The relationship that describes the measure of the inscribed angle and the measure of the intercepted arc is: 2(m∠JKL) = m(JL)
What is the Inscribed Angle Theorem?The inscribed angle theorem states in a circle, the measure of the angle that is inscribed is always half of the arc that is intercepted. Which means that the intercepted arc is twice the measure of the inscribed angle.
In the image given:
m∠JKL is the inscribed angle.m(JL) is the intercepted arcTherefore, the relationship that describes the measure of the inscribed angle and the measure of the intercepted arc is: 2(m∠JKL) = m(JL)
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Answer:
2(m∠JKL)=mJL
Step-by-step explanation:
I took the test :)
7. The quality control division of Rothschild's Blueberry Farm randomly inspects 100 of the containers in the truck being
sent to Stop and Shop. Identify the population and sample given in this scenario.
Answers
The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Population: The containers of blueberries that are being sent to Stop and Shop.
Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
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V=IR
In an experiment I and R are both measured correct to 1 decimal place.
When I= 4.0 and R=2.7, find the lower bound for V.
Answers
Answer:
10.75
Step-by-step explanation:
4.0×2.7=10.8
lower bound of 10.8 is 10.75
A Ferris wheel at the local fair has a diameter of 52 meters. Which expression can be used to find its circumference, C, in meters
A. C= 26 x π
B. C= 52 x π
C. C= 2 x 52 x π
D. C= 26²π
And how did you get the answwr
Answers
Where am I to put the points? help?
Answers
we know that a has to be a number less than 0 and c has to be a number greater than 0. so a has to go before the number 0 and b can go before or after 0, as long as it satisfies the equation
Consider the sequence \( u_{n}=\frac{1}{n} \). c Find the values of \( n \) such that \( S_{n}>3 \). For each of the following sequences: i Write down an expression for \( S_{n} \). if Find \( S_{5} \
Answers
The expression for \(S_n\) is \(S_n = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}\). And for the specific case of \(S_5\), we have \(S_5 = \frac{137}{60}\).
The sequence \(u_n = \frac{1}{n}\) represents a series of terms where each term is the reciprocal of its corresponding natural number index.
To find the values of \(n\) such that \(S_n > 3\), we need to determine the partial sum \(S_n\) and then identify the values of \(n\) for which \(S_n\) exceeds 3.
The partial sum \(S_n\) is calculated by adding up the terms of the sequence from \(u_1\) to \(u_n\). It can be expressed as:
\[S_n = u_1 + u_2 + u_3 + \ldots + u_n\]
Substituting the value of \(u_n = \frac{1}{n}\), we get:
\[S_n = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}\]
Now, we need to find the values of \(n\) for which \(S_n > 3\). We can evaluate this by calculating the partial sums for increasing values of \(n\) until we find a value that exceeds 3.
Let's find \(S_5\). Substituting \(n = 5\) into the expression for \(S_n\), we have:
\[S_5 = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}\]
Calculating this sum:
\[S_5 = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}\]
Adding the fractions, we get:
\[S_5 = \frac{60}{60} + \frac{30}{60} + \frac{20}{60} + \frac{15}{60} + \frac{12}{60} = \frac{137}{60}\]
Therefore, \(S_5 = \frac{137}{60}\).
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Estimate the line of best fit using two points on the line.
A. y= -3/2x + 12
B. y= 3/2x + 12
C. y= -2/3 + 12
D. y= 2/3 + 12
Answers
Answer:
?
Step-by-step explanation:
Answer: c
Step-by-step explanation:
A p e x
Which of the following equations correctly describes how to calculate net income?
a. net income = (cost of goods sold) - (net sales) - (operating expenses)
b. net income = (operating expenses) - (cost of goods sold) - (net sales)
C. net income = (operating expenses) + (cost of goods sold) - (net sales)
d. net income = (net sales) - (cost of goods sold) - (operating expenses)
Answers
Answer: D
Step-by-step explanation:
The equation that correctly describes the net income is; a. net income = (cost of goods sold) - (net sales) - (operating expenses)
What is gross profit?Gross profit is the profit a firm makes after deducting the costs of manufacturing and selling its products or providing its services from the revenue the company made.
The equation that correctly describes the gross profit is given by;
gross profit = (net sales) - (cost of goods sold)
Gross profit is defined as the profit a firm makes after deducting the costs of manufacturing.
Thus, the correct option is A.
Hence, The equation that correctly describes the net income is; a. net income = (cost of goods sold) - (net sales) - (operating expenses)
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Christy starts doing her homework at home. After every fifteen minutes of studying, she gets up and takes a five minute stretch break. If she has 2 hours of homework to do. how long will it take her?
ASAP
Answers
Answer:
160 minutes or two hours and 40 minutes
Step-by-step explanation:
First, let's divide 2 hours of total work by the 15 minutes chunks she does.
2 hours = 120 minutes
120 minutes / 15 minutes = 8
She will have 8 sessions of studying with a break. Now we can calculate the total.
[] 120 minutes of studying
[] 8 * 5 minute break = 40 minutes of break
[] 120 + 40 = 160 minutes
In State College, PA the average outside temperature during the month of January was 35 degrees F. Calculate the HDD for the month of January.
Answers
The HDD for the month of January in State College, PA is 930.
To calculate the HDD (Heating Degree Days) for the month of January in State College, PA, we need to subtract the average daily temperature from 65 degrees Fahrenheit, which is considered the standard temperature for indoor heating.
HDD = 65°F - 35°F
HDD = 30°F
Therefore, the HDD for the month of January in State College, PA is 30 degrees Fahrenheit.
Hi! To calculate the Heating Degree Days (HDD) for the month of January in State College, PA with an average outside temperature of 35 degrees F, follow these steps:
1. Determine the base temperature: In the US, the base temperature is commonly 65 degrees F.
2. Subtract the average temperature from the base temperature: 65 - 35 = 30 degrees.
3. Multiply the difference by the number of days in the month: January has 31 days, so 30 * 31 = 930.
So, the HDD for the month of January in State College, PA is 930.
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To calculate the HDD for the month of January in State College, PA, we need to first determine the base temperature. The base temperature is the temperature below which a building needs to be heated in order to maintain a comfortable indoor temperature. In this case, we will use a base temperature of 65 degrees F.
To calculate the HDD, we need to subtract the average daily temperature from the base temperature and sum up the values for each day of the month. If we assume that January has 31 days, we can calculate the HDD as follows:
HDD = (65 - 35) x 31
HDD = 930
So the HDD for the month of January in State College, PA is 930. This means that during the month of January, there were 930 heating degree days, which indicates the amount of heating required to maintain a comfortable indoor temperature. It is important to note that the HDD can vary depending on the base temperature used, so it is important to choose a base temperature that is appropriate for the climate and the building being heated.
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which of the following statements is true?a trapezoid must have one pair of congruent rectangles are trapezoids are parallelograms. all squares are parallelograms.
Answers
The true statement is trapezoids are parallelograms. Option b is correct.
A trapezoid is a quadrilateral with at least one pair of parallel sides, but it does not necessarily have congruent sides or right angles. Therefore, the statement "A trapezoid must have one pair of congruent sides" is false.
On the other hand, a trapezoid can be classified as a special type of parallelogram because it has one pair of parallel sides. So, the statement "Trapezoids are parallelograms" is true.
As for the last statement, it is incorrect to say that all squares are parallelograms. A square is a special type of rectangle, but it is not a parallelogram because its opposite sides are not parallel.
Therefore, b is correct.
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Is 8/6 a mix number since it cannot be simplified? I’m using it in an equation y=-8/6x-1 and I need to simplify any fractions before submitting an answer
Answers
Step-by-step explanation:
Yes, 8/6 is an improper fraction, which means the numerator is greater than or equal to the denominator. To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2:
8/6 = (8 ÷ 2) / (6 ÷ 2) = 4/3
So, we can replace 8/6 with 4/3 in the equation y = -8/6x - 1 to get:
y = -4/3x - 1
15. What is the value of m?
Answers
Ordena de menos a mayor las siguientes fracciones:
2
3
,
5
6
,
7
12
,
3
4
Answers
What is the purpose of making a geological timeline Quora?.
Answers
Geological timeline is based on the presence of fossils on the rocks of various sequences, and also the classification of rock types and the correlation of rocks of different locations.
The purpose that geological timeline serve and reason scientist do make it, is portray the history of the Earth.
A geological timeline can be regarded as a system which gives the relationship between geological strata as well as events based on chronological time.This helps the scientist in studying events as well as frequency of events to Know if there are chances of recurrence of that particular event.Examples of this event could be eclipse of sun that usually occur at some point in time.The geologic time scale also helps in portraying the history of the Earth such as rocks and fossils.Therefore, geologic time scale serves as events as regards Earth history.
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The classification of rock types, the correlation of rocks from diverse locations, and the presence of fossils on the rocks of distinct sequences are all used to create the geological timeline.
What is a Geological timeline?Geological timelines have a purpose, and scientists create them in order to depict Earth's history.
(A) The relationship between geological strata and events based on chronological time can be shown using a geological timeline.
(B) The scientist can use this information to investigate events and their frequency and determine whether there is a possibility that a specific event will occur again.
(C) A sun eclipse, which often happens at some point in time, could serve as an illustration of this occurrence.
(D) Rocks and fossils that depict Earth's past can be found thanks to the geologic time scale.
(E) As a result, the geologic time scale provides information about historical events on Earth.
Therefore, the classification of rock types, the correlation of rocks from diverse locations, and the presence of fossils on the rocks of distinct sequences are all used to create the geological timeline.
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Please answer this question for a lot of points to see if u do good.
9 - 3 divided by 1/3 + 1
I already know this answer just solve and see.
Answers
Answer:
Would the answer be 9?
Step-by-step explanation:
Use PEMDAS.
3/1/3=1
9-1-8
8+1=9
\(9 - 3 \div \frac{1}{3} + 1\)
solution:you can follow the PEDMAS rule where,
P= Parenthesis
E= Exponents
D= Division
M= Multiplication
A= Addition
S= Subtraction
Let's solve:\(3 \div \frac{1}{3} = 1\)
\(9 - 8 = 1\)
\(8 + 1 = 9\)