Use Wilson's theorem to find the least nonnegative residue modulo m of each integer n below. (You should not use a calculator or multiply large numbers.) n = 861, m = 89 (b) n = 64!/52!, m = 13 m=
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The least nonnegative residue of 64!/52! modulo 13 is 4.
Wilson's theorem states that for any prime number 'p', the factorial of (p-1) is congruent to -1 modulo p. This can be written as (p-1)! ≡ -1 (mod p).
Using Wilson's theorem, we can find the least nonnegative residue modulo 89 for the integer 861.
For n = 861 and m = 89, we need to calculate (n mod m) as follows:
861 mod 89 = 861 - (89 * (861 // 89))
= 861 - (89 * 9)
= 861 - 801
= 60
Therefore, the least nonnegative residue of 861 modulo 89 is 60.
Now let's move on to the second part.
For n = 64!/52! and m = 13, we can simplify the expression using cancelation:
64!/52! = (64 * 63 * 62 * ... * 53 * 52!)/52!
Most of the terms in the numerator and denominator cancel out, leaving:
64 * 63 * 62 * ... * 53
To find the least nonnegative residue modulo 13, we can calculate the product of the remaining terms and take the result modulo 13.
(64 * 63 * 62 * ... * 53) mod 13 ≡ (11 * 12 * 1 * 2 * ... * 3) mod 13
≡ (11 * (-1) * 1 * 2 * ... * 3) mod 13
≡ (-11 * 1 * 2 * ... * 3) mod 13
Since (-11) ≡ 2 (mod 13), we have:
(-11 * 1 * 2 * ... * 3) mod 13 ≡ (2 * 1 * 2 * ... * 3) mod 13
Calculating the product, we find:
(2 * 1 * 2 * ... * 3) mod 13 ≡ 4 (mod 13)
Therefore, the least nonnegative residue of 64!/52! modulo 13 is 4.
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Related Questions
How much time has passed from the first clock to the second clock?
The time passed is less than 12 hours. 4:20 and 8:55
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if you have to pay 4125 per semester how much do you have to pay to attend a four-year College
Answers
1 semester $4125
In a year we have 2 semesters
In 4 years we 2(4)=8 semesters
So we need to multiplicate $4125 by 8
4125 * 8 =33000
You need to pay $33000 to attend a four- year college
Answer: 3 años
Step-by-step explanation:
por que si
Select all that apply.
Chandler can mow 2 lawns per hour. If L represents lawns and H represents hours, which of the following equations represent this rate relationship?
Answers
Answer:
H=2L
Step-by-step explanation:
In one hour= CHandler can mow 2 lawns
1H=2L
H=2L
Answer:
L = 2 x H
H = 1/2 x L
Step-by-step explanation:
please, please help me with this!! it’s very important.
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The parabola's vertex is located at (-2, 8). The parabola's graph is then depicted below.
Let a be the leading coefficient and the parabola's vertex be the point (h, k). The parabola's equation will therefore be stated as,
y = a(x - h)² + k
The parabola's equation is stated as,
y = -(x + 2)² + 8
The downward-pointing parabola is represented by the negative sign.
The vertex of the parabola is at (-2, 8), according to the equation above. The parabola's graph is then depicted below.
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The distance around a circular pool is 39.25 m. How does the lifeguard have to walk from the edge of the pool to the centre of the pool?
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Answer:
d = 6.246 m
Step-by-step explanation:
Given that,
The distance around a circular pool is 39.25 m.
We need to find how does the lifeguard have to walk from the edge of the pool to the centre of the pool. It means we need to find the radius r of the circle.
ATQ,
Circumference = 2πr = 39.25 m
r is radius
\(r=\dfrac{39.25 }{2\pi}\\\\r=6.246\ m\)
So, the required distance is 6.246 m.
Find the missing value in the table.
Answers
Answer:
we're just multiplying X × 2 every time so (y=80)
It costs $2 per person to ride the Ferris wheel. Write an equation relating the cost, c, to the number of people, n.
Please help.
Answers
Answer:
c =2n
Step-by-step explanation:
cost c is given by cost of each person multiplied by number n of people
PLS HELP ME ASAP I DONT HAVE TIME IT ALSO DETECTS IF ITS RIGHT OR WRONG
Answers
Answer:
yes its linear
Step-by-step explanation:
What does the presence of residuals in our regression model suggest?
[We should expect residuals in our model. It is very unlikely to see data that the model can describe perfectly.]
[The presence of even small residuals shows that the model fits poorly.]
[Large residuals are better than small residuals. Thus, the presence of large residuals is a sign of a great fit.]
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The presence of residuals in a regression model suggests that there is some difference between the predicted values and the actual observed values. This is expected, as it is very unlikely to see data that the model can describe perfectly.
The size of the residuals can indicate the quality of the fit - smaller residuals generally suggest a better fit, while larger residuals may indicate a poorer fit. However, some level of residuals is normal and expected in any regression model.
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Find the points of inflection of the curve y = (1 + x)/(1 + x2). (Hint: All three lie on one straight line.) x = (smallest x-value) x = . x = . (largest x-value)
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The points of inflection are x = 0, x = -∞, and x = ∞. These three points lie on the vertical line x = 0.
To find the points of inflection, we need to take the second derivative of the function y = (1 + x)/(1 + x²):
y' = (1 - x²)/[(1 + x²)²]
y'' = (-6x)/[(1 + x²)³]
To find the points of inflection, we need to set y'' = 0 and solve for x:
0 = (-6x)/[(1 + x²)³]
0 = -6x
This gives us three possible values for x: x = 0 (where the second derivative changes sign), and x = ±∞ (where the second derivative approaches 0).
To determine which of these points are points of inflection, we need to look at the sign of the second derivative on either side of each point. If the sign changes, then it is a point of inflection. If the sign stays the same, then it is not a point of inflection.
At x = 0, the second derivative changes sign from negative to positive, so this is a point of inflection.
At x = ±∞, the second derivative is always 0, so these are not points of inflection.
Therefore, the points of inflection are x = 0, x = -∞, and x = ∞. These three points lie on the vertical line x = 0.
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If y = 4 find slope, X-intercept and y-intercept.
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Answer:
An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero
Gwen runs back and forth along straight track: During the time interval 0 < t < 45 seconds, Gwens 250ain velocity; In feet per second, is modeled by the function given by v (t) What is the first time;t1 , that Gwen changes direction? Find Gwens average velocity over the time interval 0 < t
Answers
The average velocity of Gwen over the time interval 0 < t is zero. We need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer.
Given that Gwen runs back and forth along a straight track and her velocity, in feet per second, is modeled by the function v(t) during the time interval 0 < t < 45 seconds; We are to determine the first time at which Gwen changes direction and find her average velocity over the time interval 0 < t.Firstly, we know that velocity is a vector quantity and has both magnitude and direction.
Since she is running back and forth along a straight track, her displacement at any given time t is given by the function s(t), which is the integral of her velocity function v(t).That is, s(t) = ∫v(t)dtWe can find the displacement by taking the definite integral of v(t) from 0 to t. Since Gwen is running back and forth, her displacement will be zero at the times when she changes direction.
Therefore, we need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer. Therefore,t = 45n/πwhere n is an integer. Since we are looking for the first time at which Gwen changes direction, we need to take the smallest positive value of n, which is n = 1.
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Problem 21 Is there a linear filter W that satisfies the following two properties? (1) W leaves linear trends invariant. (2) All seasonalities of period length 4 (and only those) are eliminated. If yes, specify W. If no, justify why such a moving average does not exist. Note: A moving average that eliminates seasonalities of length 4 will, of course, also eliminate seasonalities of length 2. However, this property is not important here and does not need to be considered. It is only necessary to ensure that the moving average does not, for example, also eliminate seasonalities of length 3, 5, 8 or others. >
Answers
No, there is no linear filter W that satisfies both properties.Based on the analysis above, it is not possible to find a linear filter W that simultaneously satisfies both properties.
To analyze the problem, let's consider the frequency response of the filter W. A linear trend in a signal corresponds to a DC component, while seasonalities of period length 4 correspond to a frequency component at 1/4 of the sampling rate.
Property (1) states that W should leave linear trends invariant. This means that the DC component of the frequency response of W should be 1 at all frequencies.
Property (2) states that W should eliminate seasonalities of period length 4. This implies that the frequency response of W should be zero at the frequency corresponding to 1/4 of the sampling rate.
Now, if a linear trend is to be preserved (property 1), the DC component of the frequency response must be 1. However, if the filter also eliminates seasonalities of period length 4 (property 2), the frequency response must be zero at the frequency corresponding to 1/4 of the sampling rate. These two requirements are contradictory, as it is not possible for the frequency response to be both 1 and 0 at the same frequency.
Based on the analysis above, it is not possible to find a linear filter W that simultaneously satisfies both properties. The existence of a moving average that leaves linear trends invariant while eliminating only seasonalities of length 4 is not feasible due to the conflicting requirements imposed by the properties.
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1 2) Simplify x^-6 * x^2
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hello
to solve this question, we can simply use laws of indicies on it
\(a^m\times a^n=a^{m+n}\)so going by that, we can use this template to solve our problem
\(x^{-6}\times x^2=x^{-6+2}=x^{-4}=\frac{1}{x^4}\)from the calculation above, the answer to this question is 1 / x^4 and this corresponds to option D
Use the previous information to answer the follow ing questions about the news program. a. I · Identify the variable measured on each participant in the survey. Us is the variable categorical or quantitative? identify at least one statistic that the news program use to summarize the variable. wh is d. Identify at least on at least one graph that the news program could use to summarize the variable. ne news program wishes to test whether there is evidence that more than three-quarters of U.S. adults are opposed to the verdict. Five hundred and sixty-two partici- pants participated in the survey, of which 82% said that they were unhappy with the verdict. a. State the null and alternative hypotheses for this test. b. What is the value of the statistic?
Answers
The news program surveyed 562 participants on their opinion on the verdict, and the variable measured was their opinion, which is a categorical variable. The statistic used to summarize this variable was 82%.
a. The variable measured on each participant in the survey is the opinion on the verdict, which is a categorical variable. The news program could use the statistic of 82% to summarize the variable, which indicates that 82% of participants said that they were unhappy with the verdict. The news program could also use a graph, such as a bar graph, to visualize the results of the survey.
b. The null hypothesis for this test is that three-quarters or less of U.S. adults are opposed to the verdict, and the alternative hypothesis is that more than three-quarters of U.S. adults are opposed to the verdict. The value of the statistic is 0.82, which represents the percentage of participants who said that they were unhappy with the verdict. This statistic can be calculated by dividing the number of participants who were unhappy with the verdict (462) by the total number of participants (562), and multiplying the result by 100.
Therefore, 0.82 = (462/562)*100 = 82%.
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the heights of the peach trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.8 feet.
what is the height of a peach tree with a z-score of -0.5?
Enter your answer rounded to the nearest tenth, in the box.
Answers
Answer:
i think 1.8 not sure tho
Answer:
Z-score Formula: z = (x - μ)/σ
Plug in: -0.5 = (x - 12.5)/1.8
Solve: -0.5 * 1.8 = x - 12.5
-0.9 = x - 12.5
-0.9 + 12.5
x = 11.6
Therefore, the height of a peach tree with a z-score of -0.5 is 11.6 feet.
Steve ran a 12-mile race at an average speed of 8miles per hour. If Adam ran the same race at an average speed of 6 miles per hour, how many minutes longer did Adam take to complete the race than did Steve?
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Lines a, b, c, and d are in the same plane. Line a is parallel to line c. Lines b and e are
perpendicular to line d. Based on this, tell how lines a and b are related, Justify your answer.
Answers
Using the equivalance rule, a is parallel to c so c is parallel to b so a is parallel to b.
In the given question, Lines a, b, c, and d are in the same plane.
Line a is parallel to line c.
Lines b and e are perpendicular to line d.
We have to find how lines a and b are related.
As a,b,c and d lie on the same plane, When b and c are perpendicular to d, b and c are parallel.
As a is parallel to c so c is parallel to b.
Since c is parallel to b so a is parallel to b.
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Two right triangular gardens each have a shorter leg 20 feet. The length of the longer leg of one garden is twice the length of the longer leg of the other garden. The perimeter of the larger garden is 1.6 times the perimeter of the other garden. What is the approximate length of the longer leg of the smaller garden? Use a graphing calculator to help you determine the answer.
Answers
Answer:
about 24.38 feet
Step-by-step explanation:
Graphing window: [0, 30] by [-20, 160]
y1 = 20 + 2x + √(400 + 4x^2)
y2 = 1.6(20 + x + √(400 + x^2))
y1 = y2 when x = 24.3798.
So the length of the smaller garden's longer leg is about 24.38 feet.
a diagram is shown, with angels labeled in degrees complete the sentences about the diagram
Answers
Answer:
Equation: 5x = 90
x = 18
<LNM = 54degrees
Step-by-step explanation:
From the diagram shown;
<JNK + <KNL + <LNM = 90
x + x + 3x = 90
5x = 90
x = 90/5
x = 18
The equation 5x = 90 can be used to solve for x
Get <LNM = 3x
<LNM = 3(18)
<LNM = 54 degrees
HELP ASAP!
Consider right triangle DEF below.
Answers
This is how too apply it in trig when trying to find a side with only the degree and the side.
The trigonometric relation is solved and the length of side DE is given by the relation DE = 3.8 ( tan 40° )
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔEFD
Now , the measure of side EF = 5 units
The measure of side DF = 3.8 units
And , from the trigonometric relations , we get
tan θ = opposite / adjacent
On simplifying , we get
tan 40° = DE / DF
Multiply by DF on both sides , we get
DE = 3.8 ( tan 40° )
Hence , the trigonometric relation is solved
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The vertices of quadrilateral DEFG are D(-2, 6), E(-4, 6), F(-6, 9), and G(-1, 9). Find the coordinates of the image of quadrilateral DEFG after a translation using the rule (x, y) → (x + 1, y - 6), a reflection over the x-axis, and a reflection over the y-axis
Answers
Answer:
the coordinates from all of the transformations are (1,0) (3,0) (5,-3) (0,-3)
Step-by-step explanation:
after using the first rule the coordinates were (-1,0)(-3,0)(-5,3)(0,3)
after reflectiong it over the x-axis (-1,0)(-3,0)(-5,-3)(0,-3)
after reflecting it over the y-axis it gave the final answer of (1,0) (3,0) (5,-3) (0,-3)
Can someone help me. I don't get this
Answers
Hope this helps good luck u can do thisss :)
I just need to know number 5 please
Answers
Step-by-step explanation:
y=4*x
when x is 2 y=8
when x is 4 y=16
find the length of the unknown side
Answers
if leg b is unknown, then. b = √(c² - a²)
for hypotenuse c missing, the formula is. c = √(a² + b²)
my sample distribution has alot of really high scores. i would describe this distribution as (a) positively skewed (b)normal (c) leptokurtic (d) negatively skewed
Answers
The main answer: (a) positively skewed.
A positively skewed distribution means that the tail of the distribution extends towards the higher end of the values, indicating that there are more low scores and a few extremely high scores.
This description aligns with the scenario you provided, where you mentioned having a lot of really high scores. In a positively skewed distribution, the mean will typically be larger than the median, indicating the influence of the high scores on the overall shape of the distribution.
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mark is 11 3/4 years old.marian is 1 1/2 years older than mark and jane is 1 1/5 years older than marian.how old is jane?
Answers
Jane is 19 9/20 years old. If Marian is 11/2 years bigger then Mark, you would have to add both ages up and then get the answer of 17 1/4. Then it said that Jane is 11/5 years older than Marian which means that you would have to add again to find the final answer. 11/5=2 1/5 and then add 17 1/4 which you get 19 9/20. So Jane is 19 9/20 years old.
Answer:
22/3 years old jane
Step-by-step explanation:
add 11+11 =22
2+5=7
7-3=4
so, she's 22/3 years old
what is the equation of the least squares regression line that describes the rela- tionship between operating cost per hour and number of passenger seats in the
Answers
The relationship between operating cost per hour and the number of passenger seats is shown by the equation of the least squares regression line, where y=1136+14.673x is the expected operating cost per hour and x is the number of passenger seats.
Why do you use the word "square"?a plane figure in geometry with four equal sides and four right angles of 90 degrees. A square is both an equilateral rectangle and a special kind of parallelogram (an equilateral and equiangular one).
the parallelogram in detail.In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.
based on the available facts;
y=1136+14.673x
where
x= number of passenger seat
y=predicted operating cost per hour.
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Write the expression in simpliest form WILL GIIVE BRAINLIEST
3 (2x - 3)
Answers
Answer: The answer is 6x–9, please mark me as brainliest and have a wonderful weekend. :D
Step-by-step explanation:
A bag of potatoes costs $4.60 for 40 ounces. How much does a 10lb-bag of potatoes cost?
$46.00
$18.40
$10.20
$20.30
Answers
Answer:
$18.4
Step-by-step explanation:
40oz=2.5lb
10lb=4*2.5lb=4*4.6=18.4