Using Fermat's little theorem, 82035 mod 17 is equal to 1. Fermat's Little Theorem states that when a prime number (denoted as p) divides an integer (denoted as a), the remainder obtained when a raised to the power of p-1 is divided by p will always be 1.
In simpler terms, it asserts that if a and p are numbers that meet specific conditions, then a to the power of p-1 will have a remainder of 1 when divided by p.
In this case, we have p = 17 and a = 82035.
Since 17 is a prime number and 82035 is not divisible by 17, we can apply Fermat's Little Theorem to find 82035 mod 17.
The theorem tells us that (82035)^(17-1) is congruent to 1 modulo 17.
Now, let's calculate the exponent:
17 - 1 = 16
Therefore, we have:
82035^16 ≡ 1 (mod 17)
To find 82035 mod 17, we can reduce the exponent to the remainder when divided by 16.
82035 mod 16 = 3
So, we have:
82035 ≡ 82035^1 ≡ 82035^16 ≡ 1 (mod 17)
Hence, 82035 mod 17 is equal to 1.
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30 in.
10 in.
10 in.
30 in.
20 in.
Find the area of the arrow above.
square inches
Answer: 45
Step-by-step explanation:
Month Change in Water Level (in.) March 8 April –3 May –9 June 5 The water level for a lake was recorded for four months. The data is shown in the table. Which month shows the greatest change in water level? A) March B) April C) May D) June
Answer: May
Step-by-step explanation: 9 is greater than 8 don't worry about the signs
Does the following improper integral converge or diverge? Show your reasoning. 1 те dax (b) Apply an appropriate trigonometric substitution to confirm that san 4V1 - 22 d. = = (c) Find the general solution to the following diff ential equation. dy (22+-2) dc 3, 7-2, 1
(a)The power is 1/2, which is less than 1 the improper integral ∫(1 / √(x)) dx from a to infinity diverges.
b)The value of the integral of ∫(1 / √(x)) dx from 1 to infinity is ln(√2 + 1).
c) The general solution to the differential equation dy/dx = (2x - 2) / (x² + 3x - 2) is y = ln|x - 1||x + 2| + C, where C is a constant.
To determine if the improper integral converges or diverges, to evaluate the integral:
∫(1 / √(x)) dx from a to infinity
This integral represents the area under the curve of the function 1/√(x) from x = a to x = infinity.
To determine convergence or divergence, the p-test for improper integrals. For the p-test, the power of x in the denominator, which is 1/2.
If the power is greater than 1, the integral converges. If the power is less than or equal to 1, the integral diverges.
To confirm the result using a trigonometric substitution, let's substitute x = tan²(t):
√(x) = √(tan²(t)) = tan(t)
dx = 2tan(t)sec²(t) dt
substitute these values into the integral:
∫(1 / √(x)) dx = ∫(1 / tan(t))(2tan(t)sec²(t)) dt
= ∫2sec(t) dt
To determine the limits of integration. Since the original integral was from 1 to infinity, to find the corresponding values of t.
When x = 1, tan²(t) = 1, which implies tan(t) = ±1. the positive value because dealing with positive values of x.
tan(t) = 1 when t = π/4
The integral with the appropriate limits:
∫(1 / √(x)) dx = ∫2sec(t) dt from t = 0 to t = π/4
Evaluating the integral:
∫2sec(t) dt = 2ln|sec(t) + tan(t)| from t = 0 to t = π/4
Plugging in the limits:
2ln|sec(π/4) + tan(π/4)| - 2ln|sec(0) + tan(0)|
ln(√2 + 1) - ln(1)
ln(√2 + 1)
The given differential equation is:
dy/dx = (2x - 2) / (x^2 + 3x - 2)
To find the general solution, by factoring the denominator:
dy/dx = (2x - 2) / [(x - 1)(x + 2)]
decompose the fraction into partial fractions:
dy/dx = A/(x - 1) + B/(x + 2)
To find the values of A and B, both sides of the equation by the denominator (x - 1)(x + 2):
2x - 2 = A(x + 2) + B(x - 1)
Expanding the right side and collecting like terms:
2x - 2 = Ax + 2A + Bx - B
Matching the coefficients of x and the constant terms on both sides, the following system of equations:
A + B = 2 (coefficient of x)
2A - B = -2 (constant term)
Solving this system of equations, A = 1 and B = 1.
Substituting these values back into the partial fraction decomposition:
dy/dx = 1/(x - 1) + 1/(x + 2)
integrate both sides with respect to x:
∫ dy = ∫ (1/(x - 1) + 1/(x + 2)) dx
Integrating each term separately:
y = ln|x - 1| + ln|x + 2| + C
Combining the logarithmic terms using properties of logarithms:
y = ln|x - 1||x + 2| + C
This is the general solution to the given differential equation.
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The expression represents a polynomial with terms. The constant term is , the leading term is , and the leading coefficient is .
There is no polynomial attached ; considering the hypothetival
Answer:
x³ = leading term.
2 = leading Coefficient
1 = constant term.
Step-by-step explanation:
Considering an hypothetical situation ;
For any polynomial such as 2x³ + 3x + 1
The polynomial is represented as : ax³ + bx + c
Where a = leading Coefficient ;
x³ = leading term
c = constant term
Therefore ;
The leading term in this hypothetical question is :
x³ = leading term.
2 = leading Coefficient
1 = constant term.
Given a population with standard deviation 8. how large a random sample should you take so that the probablity is 0.8664 that the sample mean is within 0.8 of the population mean
.
we need a sample size of at least 248 to have a probability of 0.8664 that the sample mean is within 0.8 of the population mean.
Given a population with standard deviation 8, we have to calculate the sample size required so that the probability is 0.8664 that the sample mean is within 0.8 of the population mean.To solve the problem, we have to use the formula as follows:$$n = \frac{z^2\sigma^2}{d^2}$$
Where, n = sample sizeσ = population standard deviation d = precision level z = z-score
So, z can be found using the standard normal table. In this case, we need to find the z-score that corresponds to the probability of 0.8664 plus half of the remaining probability of 1 - 0.8664, which is equal to 0.0668.Using the standard normal table, we find the z-score that corresponds to the 0.9334 probability, which is 1.48 (approximately).Now, we can substitute all the values into the formula and solve for n.$$n = \frac{z^2\sigma^2}{d^2}$$$$n = \frac{(1.48)^2 \cdot 8^2}{(0.8)^2}$$$$n = 247.15$$
Therefore, we need a sample size of at least 248 to have a probability of 0.8664 that the sample mean is within 0.8 of the population mean.
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The needed sample size is given as follows:
n = 250.
How to use the normal distribution?We first must use the z-score formula, as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).
The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.
By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
The p-value of the z-score in this problem is given as follows, considering the symmetry of the normal distribution:
0.5 + 0.8864/2 = 0.9432.
Hence the z-score is given as follows:
z = 1.58.
Then the sample size is obtained as follows:
[tex]1.58 = \frac{0.8}{\frac{8}{\sqrt{n}}}[/tex]
[tex]\sqrt{n} = 15.8[/tex]
n = 15.8²
n = 250.
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Another translation that I need help on T__T
The translation for this problem is classified as follows:
2 units left -> horizontal translation.4 units down -> vertical translation.What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a. -> horizontal translation.Right a units: x -> x + a. -> horizontal translation.Up a units: y -> y + a. -> vertical translation.Down a units: y -> y - a. -> vertical translation.For this problem, we have a translation 2 units left, which is an horizontal translation, and then a translation 4 units down, which is a vertical translation.
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Answer:
A would be the answer I would choose
find the area of the following figure round to the nearest
Answer:
lets divide the figure into two parts.
triangle base=2ft+2ft+6ft
triangle base=10ft
area of triangle = 1/2×base×height
area of triangle = 1/2×10ft×12ft
area of triangle =60ft²
area of square=side²
area of square=(6ft)²
area of square=36ft²
Two angles are supplementary. One angle measures 132 degrees. Find the measure of the other angle.
Answer:
48 degrees
Step-by-step explanation:
Supplementary angles add up to 180 degrees.
If one angle is 132 degrees, the other must be 48 degrees.
how can you write a quadratic function in
standard form, given its vertex form?
Given a starting guess of [90, yo] = [1, 2], how many iterations does Newton's method for optimization take to find a minimum of the function f(, y) = 12a2 – 7x + 7 +10y? – xy to a tolerance of 10-8? If needed, you may assume quadratic convergence. iterations = integer
The number of iterations required is 6.
Given a starting guess of [90, yo] = [1, 2], Newton's method for optimization takes 6 iterations to find a minimum of the function f(x, y) = 12a^2 – 7x + 7 +10y – xy to a tolerance of 10^-8.Step-by-step explanation:
Newton's method is an iterative process to approximate the roots of an equation or optimization of a function.
To solve this problem, we need to apply Newton's method to the function f(x, y) = 12a^2 – 7x + 7 +10y – xy as follows:
Given a starting guess of [90, yo] = [1, 2], we can find the solution using the following formula:xn+1 = xn - f'(xn)/f''(xn)where xn is the current guess, f'(xn) is the derivative of f at xn, and f''(xn) is the second derivative of f at xn.
Here, f(x, y) = 12a^2 – 7x + 7 +10y – xy, so we have (x, y) = [-7 - y, 10 - x]f''(x, y) = [0, -1; -1, 0]
We need to apply this formula until the difference between xn and xn+1 is less than or equal to the tolerance of 10^-8.
This means that we need to keep iterating until |xn+1 - xn| <= 10^-8.
Given the assumption of quadratic convergence, we can also calculate the number of iterations required as follows:|xn+1 - xn| ≈ |xn - xn-1|^2/|xn+1 - 2xn + xn-1|
Using this formula, we can calculate the number of iterations required to reach the tolerance of 10^-8.
Here are the results of the first six iterations:x1 = [1, 2]x2 = [4.125, 2.9]x3 = [4.223382352941176, 2.979411764705882]x4 = [4.223639551849474, 2.979707510729614]x5 = [4.223639551862697, 2.979707510767132]x6 = [4.223639551862697, 2.979707510767132]
We can see that the difference between x5 and x6 is less than 10^-8, so we have found a solution to the desired tolerance.
Therefore, the number of iterations required is 6.
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the waiting time at an elevator is uniformly distributed between 30 and 200 seconds. what is the probability a rider must wait between 1 minute and 1.4 minutes?
The probability that a rider must wait between 1 minute and 1.4 minutes at the elevator can be determined by calculating the proportion of the uniform distribution that falls within this time interval.
The given information states that the waiting time at the elevator follows a uniform distribution between 30 and 200 seconds. To find the probability of waiting between 1 minute and 1.4 minutes, we need to convert these time values to seconds.
1 minute is equal to 60 seconds, and 1.4 minutes is equal to 84 seconds. Therefore, we are interested in finding the probability that the waiting time falls between 60 seconds and 84 seconds.
Since the waiting time follows a uniform distribution, the probability of waiting within a specific interval is equal to the length of that interval divided by the total length of the distribution.
The total length of the distribution is 200 seconds - 30 seconds = 170 seconds.
The length of the interval between 60 seconds and 84 seconds is 84 seconds - 60 seconds = 24 seconds.
Thus, the probability that a rider must wait between 1 minute and 1.4 minutes is 24 seconds / 170 seconds, which is approximately 0.1412 or 14.12%.
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I need this answer b/6=3
The answer is b=18. To solve, multiply 6 by 3 to get 18. This is called doing the inverse operation. Since the equation is a division equation, we would have to multiply in order to find the missing variable.
What is the Surface Area of the Triangular Prism below?
Answer:
c ) 2480 cm²
Step-by-step explanation:
Surface Area of a Triangular prism =
S = bh + lb + 2ls
b = 30cm
h = 8cm
s = 17 cm
l = 35cm
The surface area = 30cm × 8 cm + 35 × 30 cm + 2(35 × 17)
= 240 cm² + 1050 cm² + 1190 cm²
= 2480 cm²
Option c is the correct option
The table below shows the score
Analisa and Luke earned on four science
projects.
Science Project Scores
Project Analisa Luke
95 90
2
81 84
3
76 95
4
88 91
5
2
?
Analisa and Luke worked on a fifth
science project together. They each
carned the same score on the project.
When the fifth score is included in the
table, Analisa's mean score does not
change
Which of the following statements
describes how Luke's mean score
changes when the fifth score is included
in the table?
Answer:
It increases by 2.5
Step-by-step explanation:
yeah
4
The equation below has no solution.
2
2 - 72 + 3 + 4x = ax + b
True
False
it is True ..............................................
Answer:
True
Step-by-step explanation:
2-72+3+4x=ax+b
73 + 4x = ax + b
Since there are 3 variables in this equation you need 3 equations. Since there is only 1 you cannot continue solving this equation after you simplified.
Hope this helps!
Help PLEASEE!!!!!!!!!!
I think it’s the third one. Hope that helps!
Answer:
the answers are B or C x>4/19
Can someone explain why the statement is true. Will Mark brainliest.
Answer:
The triangle is isosceles.
Step-by-step explanation:
This means that one angle's sine is the same as the other's cosine.
Mr. Adams drove his delivery truck 151.2 miles during 24 days. He drove the same number of miles each day.
How many miles did Mr. Adams drive each day?
Divide total miles by number of days:
151.2 / 24 = 6.3 miles per day
5. Find the circumference of a circle with a radius
of 15 feet.
Answer:
94.25 feet.
Step-by-step explanation:
Rudy makes 4 baskets out of every 10 attempts. At this rate, how many baskets would he score in a season when he attempted 75 shots?
Natalia and Sun are 14.5 m apart and looking up at the top of a radio tower. They are on the same side of the tower. If Natalia is looking up at an angle of 289, and Sun is looking up at the tower at an angle of elevation of 31°, how tall is the tower to the nearest tenth of a metre? Assume their eyes are 1.6 m above the ground.
The height of the radio tower to the nearest tenth of a metre is 6.9 m.
Let the height of the radio tower be h metresFrom Sun's point of view, the top of the radio tower is right-angled to the horizontal line through his eye. This implies that the length of the radio tower is opposite the angle of elevation.
Thus, the distance of Sun from the radio tower is equal to the length of the adjacent side of the right-angled triangle formed.
Thus, from the tangent ratio:tan 31° = h / 14.5 + 1.6 (since Sun's eye level is 1.6m above the ground)h = (14.5 + 1.6) tan 31° = 6.9 m (to one decimal place)From Natalia's point of view,
the radio tower makes an acute angle with the line of sight from her eye to the top of the radio tower. This implies that the length of the radio tower is adjacent to the angle of elevation.
Thus, the distance of Natalia from the radio tower is equal to the length of the hypotenuse of the right-angled triangle formed.
Thus, from the sine ratio:sin 89° = h / 14.5 - 1.6 (since Natalia's eye level is 1.6m above the ground)
h = (14.5 - 1.6) sin 89° = 12.9 m (to one decimal place)
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convert 50 percentage into fraction
Answer:
50/100, simplified to 1/2
Step-by-step explanation:
50% means half of 1.
1/2=.5 which is half of 1.
1=100%
.5=50%
1/2=50%
Answer:
[tex] \displaystyle \frac{1}{2} [/tex]
Step-by-step explanation:
we are given a parcentage
we want to convert it into fraction
remember that,
[tex] \displaystyle \% = \frac{1}{100} [/tex]
therefore
substitute:
[tex] \displaystyle 50 \times \frac{1}{100} [/tex]
reduce fraction:
[tex] \displaystyle \cancel{50} \times \frac{1}{ \cancel{100} \: ^{2} }[/tex]
[tex] \displaystyle 1 \times \frac{1}{2} [/tex]
simplify multiplication:
[tex] \displaystyle \frac{1}{2} [/tex]
hence,
[tex] \displaystyle 50\% = \frac{1}{2} [/tex]
If the width of the fridge is 4 inches and cost of one square inch is five dollars find the total cost of the blanket
Answer:
$20
Step-by-step explanation:
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Answer:
Only the mean increased.
Step-by-step explanation:
The mean is the total divided by the number of scores, and since adding 21 will increase the total score significantly, the mean increases.
The median is still 7.
**Jane found money in her pocket. She went to a convenience store and spent 1/4 of her money on chocolate milk, 3/5 of her money on a magazine, and the rest of her money on candy. What fraction of her money did she spend on candy?
Answer:
3/20
Step-by-step explanation:
1/1-1/4-3/5= (money spent)
1×4×5/(1×4×5)-1×1×5/(1×4×5)-3×1×4/(1×4×5)
20/20-5/20-12/20
(20-5-12)/20=3/20
Answer:
$y - $0.85
Step-by-step explanation:
y represents how much money he had.
[tex]\frac{3}{5}+\frac{1}{4} =\frac{17}{20}[/tex]
$y - $0.85
Use the benchmark 1/2 to compare 5/8 and 2/7
Answer:
what?
Step-by-step explanation:
Particle size is a very important property when working with paints. Take 13 measurements of a population of paint cans that have a population standard deviation of 200 angstroms, and find a sample mean of 3978.1 angstroms, construct a 98% confidence interval for the average size of particles in the population. and then answer the following;
confidence coefficient
a.2.09
b.1.65
c.1.96
D.2.33
The confidence coefficient for a 98% confidence interval is 2.33, indicating the number of standard deviations away from the mean.
To construct a confidence interval, we use a critical value that corresponds to the desired level of confidence. In this case, the confidence level is 98%, which means there is a 98% chance that the true population parameter falls within the confidence interval.
The critical value for a 98% confidence interval can be found using the standard normal distribution. Since the sample size is relatively small (13 measurements), we typically use the t-distribution instead. However, when the sample size is large (typically considered to be greater than 30), the t-distribution closely approximates the standard normal distribution.
For a 98% confidence level, the critical value is 2.33. This value represents the number of standard deviations away from the mean that includes 98% of the distribution.
Therefore, the correct answer is (D) 2.33 as the confidence coefficient for a 98% confidence interval.
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what is the diameter ?
Answer:
37.999749573966
Step-by-step explanation:
Brainliest?
A computer programmer charges $30 for an initial consultation and $35 per hour for programming. Write a formula for her total charge for h hours of work. *
1 point
A) (30 + 35)h
B) 30 + 35h
C) 35 + 30h
D).65h