To calculate[tex]2^2873686243768478237864767208[/tex] mod 101 using Fermat's little theorem, we can simplify the exponent by taking it modulo 100, since 100 is the Euler's totient function value of 101. Therefore,[tex]2^2873686243768478237864767208[/tex] mod 101 is equal to 57.
Fermat's little theorem states that if p is a prime number and a is any integer not divisible by p, then a^(p-1) ≡ 1 (mod p). In this case, p = 101, and we need to find[tex]2^2873686243768478237864767208[/tex]mod 101.
First, we simplify the exponent by taking it modulo 100, since 100 is the Euler's totient function value of 101. The exponent 2873686243768478237864767208 is congruent to 8 modulo 100. So, we need to calculate 2^8 mod 101. Applying Fermat's little theorem, we know that 2^(101-1) ≡ 1 (mod 101), since 101 is prime. Therefore, 2^100 ≡ 1 (mod 101).
We can express [tex]2^8[/tex] in terms of 2^100 as [tex](2^100)^0.08[/tex]. Simplifying this, we get [tex](2^100)^0.08 ≡ 1^0.08[/tex]≡ 1 (mod 101).
Thus, we conclude that[tex]2^8[/tex] ≡ 1 (mod 101), and therefore 2^2873686243768478237864767208 ≡ [tex]2^8[/tex] (mod 101).
Finally, evaluating [tex]2^8[/tex] mod 101, we find that [tex]2^8[/tex] ≡ 57 (mod 101).
Therefore,[tex]2^2873686243768478237864767208[/tex] mod 101 is equal to 57.
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specify a codomain for each of these functions in exercise 16. under what conditions is each of these funtions with the codomain you specified onto?
The codomain of a function is the set that contains all possible values that the function can map to. It represents the range of possible output values. To specify a codomain for a function, you need to consider the nature of the function and the type of values it can produce.
A function is considered onto (or surjective) if every element in the codomain has at least one corresponding element in the domain that maps to it. In other words, for each value in the codomain, there exists an input in the domain that produces that particular output.
To determine if a function is onto, you need to ensure that every element in the codomain is reached by the function. This can be achieved by satisfying certain conditions, such as:
The range of the function (the actual set of output values) is equal to the codomain. This means that the function covers all possible values in the codomain.
The function is defined for every element in the codomain. There are no "gaps" or missing elements that the function does not cover.
The function is one-to-one (injective). This means that each element in the domain maps to a unique element in the codomain, preventing any overlap or repetition.
These conditions ensure that every value in the codomain is covered by the function, making it onto.
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is 1563/25 a rational number
Answer:
Yes, it's a rational number
Step-by-step explanation:
can be written as fraction and integers
The center and a point on a circle are given. Find the circumference to the nearest tenth.
center:(5, −5);
point on the circle: (25, 10)
The circumference is about ?
Answer: 50pi or about 157
Step-by-step explanation: Find the distance between the two points using the Pythagorean theorem, and since that is the radius double it to get the diameter, then multiply that by pi to get the answer. Hope this helps!
Answer:
Circumference ~ 157
Step-by-step explanation:
Use the distance formula to find the radius. The radius is 25. Plug 25 into the formula 2(pi)r to get 50pi or about 157.
The cost of a car rental is $40 per day plus $0.22 per mile. You are on a daily budget of $84. Write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. Use pencil and paper. Find 2 other two-step inequalities with the same solutions.
Answer:
200 miles
Step-by-step explanation:
Given data
cost of car rental per day= $40
cost per mile= $0.22
We are told that the budget is $84
The expression for the total cost is given as
y= 40+0.22x
where x = the distance travelled
now for y=$84, by substituting we can get x
84=40+0.22x
84-40=0.22x
44=0.22x
divide both sides by 0.22
x= 44/0.22
x=200
Hence the distance that $84 will go is 200 miles
A researcher wanted to investigate the relationship between gender and career choice (career choice is classified as either predominantly male, predominantly female, or neutral). One-hundred males and one-hundred females were randomly selected and their profession was classified into one of the three career types. Which of the following procedures is most appropriate for the above example?
Chi-square test of independence
One-way within subjects ANOVA (Repeated measures ANOVA)
One-way between subjects ANOVA
Correlation
Chi-square goodness of fit test
The most appropriate procedure for the given example is the Chi-square test of independence.
Chi-square test of independence: This statistical test is used to determine if there is a significant association between two categorical variables. In this case, the researcher wants to investigate the relationship between gender (male or female) and career choice (predominantly male, predominantly female, or neutral). The test will help determine if there is a dependency between gender and career choice.
a. Formulate hypotheses: The null hypothesis (H0) states that there is no association between gender and career choice, while the alternative hypothesis (Ha) states that there is an association.
b. Set the significance level (alpha): Typically, it is set to 0.05 or 0.01, depending on the desired level of confidence.
c. Create a contingency table: Construct a table that shows the observed frequencies of career choices for each gender.
d. Calculate expected frequencies: Compute the expected frequencies under the assumption of independence between gender and career choice.
e. Calculate the chi-square statistic: Determine the chi-square statistic based on the observed and expected frequencies.
f. Determine the critical value: Look up the critical value from the chi-square distribution table using the degrees of freedom and chosen alpha level.
g. Compare the chi-square statistic and critical value: If the chi-square statistic is greater than the critical value, reject the null hypothesis and conclude that there is a significant association between gender and career choice. If it is not, fail to reject the null hypothesis.
h. Interpret the results: Based on the conclusion, provide an interpretation of the findings, indicating whether there is evidence of a relationship between gender and career choice.
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Choose two things that a rigid motion preserves.
Two things that a rigid motion preserves are: length and angle.
The two things that a rigid motion preserves are:
1. Length: A rigid motion preserves the length of objects. This means that the distances between points or the lengths of line segments remain the same after the rigid motion is applied.
For example, if you have a line segment AB of length 5 units, a rigid motion such as translation, rotation, or reflection will not change the length of AB.
2. Angle: A rigid motion preserves angles between lines or line segments. This means that the measure of an angle remains the same after a rigid motion is applied.
For example, if you have an angle ABC with a measure of 60 degrees, a rigid motion will not change the measure of angle ABC.
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Suppose that V₁, V2, , Um are linear dependent in a vector space V. For every & EV, show that 7₁, V2, , Um, 7 are also linearly dependent. 9
By supposing that V₁, V2, and Um are linearly dependent in a vector space V. For every & EV. V₁, V₂, ..., Uₘ are linearly dependent in a vector space V. As 7₁V₁ = 7(c₂V₂ + c₃V₃ + ... + cₘUₘ)
To show that 7₁V₁, 7₂V₂, ..., 7ₘUₘ, 7 is also linearly dependent for every 'c' in V, we can use the following approach: If V₁, V₂, ..., Uₘ are linearly dependent, then we can write at least one vector as a linear combination of the other vectors.
Let's assume V₁ can be written as a linear combination of the other vectors as follows:
V₁ = a₂V₂ + a₃V₃ + ... + aₘUₘ
where a₂, a₃, ..., aₘ are constants. Now, we can express the vector 7₁V₁ as:
7₁V₁ = 7₁a₂V₂ + 7₁a₃V₃ + ... + 7₁aₘUₘ
Since 7 is a constant, we can take it outside the bracket as:
7₁V₁ = 7(a₂7₁V₂ + a₃7₁V₃ + ... + aₘ7₁Uₘ)
Let's assume the sum inside the bracket is equal to 'b'. Then,
7₁V₁ = 7b
Since we know that V₁, V₂, ..., Uₘ are linearly dependent, we can write b as a linear combination of the other vectors as follows:
b = c₂V₂ + c₃V₃ + ... + cₘUₘ
where c₂, c₃, ..., cₘ are constants. Now, substituting the value of b in the equation for 7₁V₁, we get:
7₁V₁ = 7(c₂V₂ + c₃V₃ + ... + cₘUₘ)
This shows that 7₁V₁, 7₂V₂, ..., 7ₘUₘ, 7 are also linearly dependent. Therefore, we have proved that for every 'c' in V, 7₁V₁, 7₂V₂, ..., 7ₘUₘ, 7 are also linearly dependent.
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5. Arrange these numbers in ascending order (from least to greatest) -2.6 -2.193 -2.2 -2.01 I
Answer:
see below
Step-by-step explanation:
-2.6
-2.2
-2.193
-2.01
Since they are negatives, the higher number it is, the smaller it actually is. The smaller the number is, that number will be closer to 0 and will actually be higher than the rest.
Hope this helps! :)
Use the rule x + 9 to write a sequence. Start with x = 0.
Be sure to write a sequence of at least six numbers, each separated by commas:
0, ___, ___, ___, ___, ___
Answer:
9, 10, 11, 12, 13, 14, 15
Step-by-step explanation:
0 + 9 = 9
1 + 9 = 10
2 + 9 = 11
3 + 9 = 12
4 + 9 = 13
5 + 9 = 14
6 + 9 = 15
The sequence of at least six numbers, by using rule x + 9 Start with x = 0 is 9, 10, 11, 12, 13, 14.
What is sequence?An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given:
x + 9
First sequence, Put x = 0
0 + 9 = 9
Second sequence, put x = 1
1 + 9 = 10
Second sequence, put x = 2
2 + 9 = 11
Second sequence, put x = 3
3 + 9 = 12
Second sequence, put x = 4
4 + 9 = 13
Second sequence, put x = 5
5 + 9 = 14
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When a coin is flipped 20 times and lands heads up 11 times, what is the
experimental probability? Write your answer as a decimal.
Answer:
0.55
Step-by-step explanation:
11 (the time it lands on heads) /20 (the number of times it was flipped) = 0.55
please help i’m desperate
Answer:
4.52
Step-by-step explanation:
volume of cone is
[tex]\pi {r}^{2} \frac{h}{3} [/tex]
h is 2.2
and
r is 1.4
How do the number of faces, vertices, and edges of a cube compare to the number of faces, vertices, and edges of a tetrahedron? A cube has more faces than a tetrahedron. A cube has more vertices than a tetrahedron. A cube has more edges than a tetrahedron.
Answer:
it is 2, 4 and 6
Step-by-step explanation:
p=(w+2)/3w solve for w
Answer: w = 2/3p-1
Step-by-step explanation: You must subtract w from both sides and then factor the equation
Anyone know this and if do pls help
70% of the trip length, t, is 35 miles. Find t:
0.70t = 35. Dividing both sides by 0.70, we get:
35
t = ----------- = 50
0.70
The total trip length is 50 miles.
Which of the following
represents 9!
A. 9
B. 9*8*7*6*5*4*3*2*1
C. 9+8+7+6+5+4+3+2+1
Rearrange t= 5s + 4 to make s the subject.
What is the value of x?
5(x+2)=11
Answer:
X=1.8
Step-by-step explanation:
Step one: 5 times 1.8 equals 9.
Step two: 9+2=11
Can some one tell me what is: B X H, cause its apart of my assignment
Answer:
Step-by-step explanation:
it is about math then b=base
and h =height
A social researcher wants to test the hypothesis that college students who drink alcohol while text messaging type a different number of keystrokes than those who do not drink while they text. The social researcher studies a sample 50 drinking texters and 50 non-drinking texters. The sample mean number of keystrokes for drinking texters was 142 with a sample standard deviation of 7.45. The sample mean number of keystrokes for non-drinking texters was 120 with a sample standard deviation 6.81. Test the null hypothesis of no difference in mean keystrokes between the population of students who drink while texting and the population of students who do not drink while texting.
What is the null hypothesis in this study?
There is no difference in mean keystrokes between the populations of students who drink and text and students who do not drink and text.
There is a difference in mean keystrokes between the populations of students who drink and text and students who do not drink and text.
The sample mean keystrokes for drinking texters is ______ and the sample mean keystrokes for non-drinking texters is _______
The sample variance for drinking texters is _____ and the sample variance for non-drinking texters is ________
What is the standard error of the difference between means?
What is the calculated t? _____
What is the critical t? ______
Based on the comparison of calculated t and critical t, what must we do?
Retain the null hypothesis of no difference in mean keystrokes between the populations of drinking texters and non-drinking texters.
Reject the null hypothesis and conclude there is a difference in mean keystrokes between the populations of drinking texters and non-drinking texters.
The null hypothesis in this study is that there is no difference in mean keystrokes between the populations of students who drink and text and those who do not.
The null hypothesis in this study states that there is no difference in mean keystrokes between the populations of students who drink and text and those who do not. It assumes that the mean keystrokes for both groups are equal.
The sample means keystrokes for drinking texters is stated as 142, while for non-drinking texters, it is 120.
The sample variances for drinking and non-drinking texters are not provided in the question. Without the sample variances, it is not possible to calculate the standard error of the difference between means.
The calculated t-value and critical t-value are not given in the question. The comparison between the calculated t-value and critical t-value is necessary to determine the appropriate action.
Based on the comparison of the calculated t-value and critical t-value, the appropriate action to take is not specified in the question. It is usually done by comparing the calculated t-value with the critical t-value at a specific significance level. If the calculated t-value exceeds the critical t-value, the null hypothesis is rejected, suggesting a significant difference in mean keystrokes between the populations. If the calculated t-value is less than the critical t-value, the null hypothesis is retained, indicating no significant difference in mean keystrokes between the populations.
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The volume of a triangular pyramid is 13.5 cubic meters. What is the volume of a triangular prism with a congruent base and the same height?
Answer:
The prism is 3 by 3 by 1.5.
Step-by-step explanation:
The prism has a length x and a width x. Since it is a square at the base both length and width are the same amount x. The height is "half the length of one edge of the base". Since the base is x, this makes it 1/2x.
The volume's prism is found using V = l*w*h. Substitute and simplify.
13.5 = x*x*1/2x
13.5 = 1/2 x^3
27 = x^3
3 = x
The prism is 3 by 3 by 1.5.
brainliest?
2x+4 and 5x-8 help please
Answer:
7x - 4
Step-by-step explanation:
2x + 4 + 5x - 8
7x + 4 - 8
7x - 4
The ecology club plans to increase the size of a rectangular green space by adding 6 feet to each dimension of the green space. a. The ecology club wants to put fencing around the proposed green space. How many more feet of fencing will the club need to buy for the proposed green space than it would have bought for the current green space? b. The ecology club wants to cover the proposed green space with a layer of sod. How much greater is the area of the proposed green space than the area of the current green space? a a. 9 more feet of fencing b. 441 square feet greater b a. 24 more feet of fencing b. 276 square feet greater c a. 36 more feet of fencing b. 624 square feet greater d a. 12 more feet of fencing b. 129 square feet greate
Answer:
gg
Step-by-step explanation:
gfg
Type the correct answer in the box. Use numerals instead of words.
Consider this equation.
10*+25
How many valid solutions does the equation have?
The equation has
valid solution(s).
The original equation (10x + 25) / (3x + 12) = 5x / (x + 4) has no valid solutions.
We have,
To determine the number of valid solutions for the equation
(10x + 25) / (3x + 12) = 5x / (x + 4), we need to solve the equation and check if there are any values of x that satisfy the equation while not causing any division by zero.
Let's solve the equation step by step:
(10x + 25) / (3x + 12) = 5x / (x + 4)
Cross-multiply to eliminate the fractions:
(10x + 25)(x + 4) = (3x + 12)(5x)
Expand both sides:
10x² + 40x + 25x + 100 = 15x² + 60x
Combine like terms:
10x² + 65x + 100 = 15x² + 60x
Subtract 10x² + 60x from both sides:
5x² + 5x + 100 = 0
Now we have a quadratic equation.
To solve it, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
For the equation 5x² + 5x + 100 = 0, a = 5, b = 5, and c = 100.
Calculating the discriminant (b² - 4ac):
Discriminant = (5²) - (4 x 5 x 100)
Discriminant = 25 - 2000
Discriminant = -1975
Since the discriminant is negative (-1975), the quadratic equation has no real solutions.
Therefore,
The original equation (10x + 25) / (3x + 12) = 5x / (x + 4) has no valid solutions.
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What are the distances between the pair of points
G(0,-3) and H(0,-6)
Answer:
the distance is 3 units
Step-by-step explanation:
Answer:
3 units
Step-by-step explanation:
The sum of two numbers is 37 . The smaller number is 15 less than the larger number. What are the numbers?
Answer:
11 and 26
Step-by-step explanation:
x+x-15=37
x+x-15+15=37+15
x+x=52
2x=52
2x÷2=52÷2
x=26
26+26-15=37
37=37
In a luck experiment the sample space is N = {1, 2, 3, 4]. We define the possibilities A = {1, 2}, B = {1, 3}, C = {1, 4}. If the elementary possibilities are equally probable, consider whether possibilities A, B, C are in pairs independently and if possibilities A, B, C are every three independently that is, completely independent.
Given,In a luck experiment the sample space is N = {1, 2, 3, 4]. We define the possibilities A = {1, 2}, B = {1, 3}, C = {1, 4}.
If the elementary possibilities are equally probable, we need to determine whether possibilities A, B, C are in pairs independently and if possibilities A, B, C are every three independently, i.e., completely independent.
An independent event is an event that is not affected by any other event or occurrence. When two events are independent, the probability of one event occurring does not affect the probability of the other event occurring.So, if we define three events, A, B, and C, then A and B, A and C, and B and C may be independent of each other, or they may be dependent on each other.
To determine whether they are independent or not, we need to find the probability of each event and its combinations.
Here, the probability of each elementary possibility is equally probable, i.e., 1/4.If we consider events A and B, then we see that they have 1 as their common element.
Hence, P(A and B) = P({1}) = 1/4.Now, P(A) = P({1, 2}) = 2/4 = 1/2, and P(B) = P({1, 3}) = 2/4 = 1/2.Then, P(A) × P(B) = (1/2) × (1/2) = 1/4 = P(A and B).Since P(A and B) = P(A) × P(B), we can say that events A and B are independent.Similarly, we can calculate for events A and C, and B and C. We get,P(A and C) = 1/4 = P(A) × P(C)P(B and C) = 1/4 = P(B) × P(C)Therefore, events A, B, and C are pairwise independent.
If events A, B, and C are completely independent, then their joint probability, i.e., P(A and B and C) is the product of their individual probabilities, i.e., P(A) × P(B) × P(C).If this holds, then A, B, and C are completely independent.
Now, we can calculate,P(A and B and C) = P({1}) = 1/4 = P(A) × P(B) × P(C)Since P(A and B and C) = P(A) × P(B) × P(C), we can say that events A, B, and C are completely independent.
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According to the given luck experiment, the events A, B, and C are all independent of each other.
The sample space is N = {1, 2, 3, 4}.
It is defined that the possibilities A = {1, 2}, B = {1, 3}, and C = {1, 4}.
If the elementary possibilities are equally probable, let's consider the independence of the possibilities A, B, and C as follows;
The event A and B are independent if and only if P(A ∩ B) = P(A)P(B).
Probability of A = P(A) = n(A) / n(S) = 2/4 = 1/2
Probability of B = P(B) = n(B) / n(S) = 2/4 = 1/2
Possibility of A ∩ B = {1}
P(A ∩ B) = n(A ∩ B) / n(S) = 1/4
Now, P(A)P(B) = (1/2) (1/2) = 1/4
Hence, P(A ∩ B) = P(A)P(B).
Therefore, the events A and B are independent.
The event A and C are independent if and only if P(A ∩ C) = P(A)P(C).
Probability of C = P(C) = n(C) / n(S) = 1/2
Probability of A = P(A) = n(A) / n(S) = 1/2
Possibility of A ∩ C = {1}
P(A ∩ C) = n(A ∩ C) / n(S) = 1/4
Now, P(A)P(C) = (1/2) (1/2) = 1/4
Therefore, P(A ∩ C) = P(A)P(C)
Thus, the events A and C are independent.
The event B and C are independent if and only if P(B ∩ C) = P(B)P(C).
Probability of B = P(B) = n(B) / n(S) = 1/2
Probability of C = P(C) = n(C) / n(S) = 1/2
Possibility of B ∩ C = {1}
P(B ∩ C) = n(B ∩ C) / n(S) = 1/4
Now, P(B)P(C) = (1/2) (1/2) = 1/4
Hence, P(B ∩ C) = P(B)P(C)
Thus, the events B and C are independent.
So, we have concluded that the events A, B, and C are all independent of each other.
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The Z score for the observation of 500 has meaning that: a. Z score is always equal to the mean b. Z score is by one standard deviation smaller than the mean c. The observation is by one standard deviation greater than the mean d. The observation is equal to the mean
However, we know that the correct option is c, because the observation is one standard deviation greater than the mean.
The Z score for the observation of 500 has the meaning that the observation is one standard deviation greater than the mean. Therefore, the correct option is c. The Z score is a measure of how far a data point is from the mean, in terms of the number of standard deviations.
It's calculated by subtracting the mean from the observation, then dividing by the standard deviation. So, if the Z score is positive, it means the observation is above the mean, while a negative Z score means the observation is below the mean.
In this case, we are told that the observation has a Z score of 1. This means that the observation is 1 standard deviation above the mean. Since the mean is not given, we cannot say whether option a or option d is correct.
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The Z score for the observation of 500 has meaning that the observation is by one standard deviation greater than the mean.
To find the Z-score.
A Z-score, also known as a standard score, is the number of standard deviations from the mean that a data point.
The formula for calculating the Z-score is: Z = (X - μ) / σ, where X is the raw score being transformed, μ is the mean of the population, σ is the standard deviation of the population.
Given that Z-score is the number of standard deviations from the mean that a data point is, the Z score for the observation of 500 has meaning that the observation is by one standard deviation greater than the mean.
Therefore, option (c) is the correct answer: The observation is by one standard deviation greater than the mean.
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I've done everything I can, I cant figure this out pls help asap
1. H
2. A
3. E
4. C
I have to type extra words to turn this in so basically I just found the slop of the line then matched it with the letters...
HELP PLEASE!! (No links)
A plane slices horizontally through a cone as shown, which term best describes the cross-section?
es )
A)
circle
B)
rectangle
C)
rhombus
D)
triangle
If the vibrating string is subject to viscous damping, the governing equa- tion can be written as du(x, t) J²u(x, t) Ət² ²u(x, t) x2 2h = 7 Ət where h is a constant.
The given equation represents the governing equation for a vibrating string subject to viscous damping. The equation involves the partial derivatives of the displacement function u(x, t) with respect to both time t and position x. The left-hand side of the equation captures the effects of inertia and elasticity of the string, while the right-hand side represents the damping term.
The term du(x, t)/dt^2 describes the acceleration of the string at a specific point (x, t) and is proportional to the second derivative of u with respect to time. The term d^2u(x, t)/dx^2 represents the curvature or bending of the string at that point and is proportion to the second derivative of u with respect to position.
The constant h represents the damping coefficient, which determines the level of damping present in the system. Higher values of h indicate stronger damping effects, while lower values imply less damping.
The equation states that the sum of the damping term and the terms related to inertia and elasticity is equal to 7 times the partial derivative of u with respect to time.
By solving this governing equation, one can determine the behavior of the vibrating string over time and space, taking into account the effects of viscous damping.
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