If "p" is prime and "a" is positive integer, then a^(p) ≡ a (mod p). Explain to me how we can derive this alternative theorem from Fermat’s Little Theorem
Fermat’s Little Theorem: If p is prime and a is an integer not divisible by p, then a^(p−1) ≡ 1 (mod p)
Answers
The alternative theorem states that if "p" is a prime number and "a" is a positive integer, then \(a^{(p)}\) is congruent to "a" modulo p. This theorem can be derived from Fermat's Little Theorem.
Fermat's Little Theorem states that if "p" is a prime number and "a" is an integer not divisible by p, then \(a^{p-1}\) is congruent to 1 modulo p. To derive the alternative theorem, we can start by applying Fermat's Little Theorem to the case where "a" is not divisible by p, resulting in \(a^{p-1}\) ≡ 1 (mod p).
Now, consider the case where "a" is divisible by p. In this scenario, "a" can be written as a = kp, where k is a positive integer. Substituting this into the alternative theorem, we have \((kp)^p\) ≡ kp (mod p). Expanding the left side using the binomial theorem, we get \(k^p * p^{p-1}\) ≡ kp (mod p).
Since "p" is a prime number, p^p-1 is congruent to 1 modulo p by Fermat's Little Theorem. Therefore, the equation simplifies to \(k^p\)k^p ≡ kp (mod p). We can cancel the common factor of p on both sides, giving \(k^p\) ≡ k (mod p). Finally, recognizing that k is a positive integer, we conclude that this congruence is valid for any positive integer k.
Hence, we have derived the alternative theorem, which states that if "p" is a prime number and "a" is a positive integer, then \(a^{(p)}\) is congruent to "a" modulo p, regardless of whether "a" is divisible by p or not.
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Related Questions
The length of one side of a square City block is 462 what is the perimeter of the block
Answers
Answer: 1,848
Step-by-step explanation:
One side is 462. Since a square has 4 sides, we do 462*4 which is 1,848.
P=4s
P=4(462)
P=1,848
Write a function that takes as input three real numbers a,b,c and prints out solutions for the quadratic equation ax 2
+bx+c=0. Please note that there are three possible situations.
Answers
function that takes three real numbers, `a`, `b`, and `c`, and prints out the solutions for the quadratic equation `ax^2 + bx + c = 0`:
```python
import math
def quadratic_equation(a, b, c):
# Calculate the discriminant
discriminant = b**2 - 4*a*c
# Check the value of the discriminant
if discriminant > 0:
# Two real and distinct solutions
x1 = (-b + math.sqrt(discriminant)) / (2*a)
x2 = (-b - math.sqrt(discriminant)) / (2*a)
print("The quadratic equation has two real and distinct solutions:")
print("x1 =", x1)
print("x2 =", x2)
elif discriminant == 0:
# One real solution (repeated root)
x = -b / (2*a)
print("The quadratic equation has one real solution:")
print("x =", x)
else:
# Complex solutions
real_part = -b / (2*a)
imaginary_part = math.sqrt(abs(discriminant)) / (2*a)
print("The quadratic equation has two complex solutions:")
print("x1 =", real_part, "+", imaginary_part, "i")
print("x2 =", real_part, "-", imaginary_part, "i")
```
The function first calculates the discriminant, which is the value inside the square root in the quadratic formula. Based on the value of the discriminant, the function determines the nature of the solutions.
- If the discriminant is greater than 0, there are two real and distinct solutions.
- If the discriminant is equal to 0, there is one real solution (a repeated root).
- If the discriminant is less than 0, there are two complex solutions.
The function prints out the solutions based on the nature of the discriminant, providing the values of `x1` and `x2` for real solutions or the real and imaginary parts for complex solutions.
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Find the greatest common factor of 18 ,12 and 42 .
Answers
The Factors of the numbers are as follows;
\(\begin{gathered} 18=2\times3\times3 \\ 12=2\times2\times3 \\ 42=2\times3\times7 \end{gathered}\)The common factors are 2 and 3.
Therefore, the Greatest Common Factor is (2 x 3) 6
Find the coordinate of the given point.
The point Y between X(1,-2) and Z(11, 3) such that the ratio of XY to YZ is 3:2
Answers
\(\textit{internal division of a line segment using ratios} \\\\\\ X(1,-2)\qquad Z(11,3)\qquad \qquad \stackrel{\textit{ratio from X to Z}}{3:2} \\\\\\ \cfrac{X\underline{Y}}{\underline{Y} Z} = \cfrac{3}{2}\implies \cfrac{X}{Z} = \cfrac{3}{2}\implies 2X=3Z\implies 2(1,-2)=3(11,3)\)
\((\stackrel{x}{2}~~,~~ \stackrel{y}{-4})=(\stackrel{x}{33}~~,~~ \stackrel{y}{9}) \implies Y=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{2 +33}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-4 +9}}{3+2} \right)} \\\\\\ Y=\left( \cfrac{ 35 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies {\Large \begin{array}{llll} Y=(7~~,~~1) \end{array}}\)
3 friends ordered 2 pizzas of 6 slices each and ate equal amounts, how many slices did each person eat?
A 1
B 2
C 3
D 4
Answers
Answer:
Option D, 4
Step-by-step explanation:
2 pizzas x 6 slices per pizza = 12 slices of pizza
12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend
Option D, 4, is your answer
Topology question. Answer only subpart a. Need Asap.
3. Let (X, Jx) and (Y, Ty) be topological spaces defined as follows: X = {D, O, R, K} Tx = {Ø, {0}, {D, O}, {O, R}, {D, O, R}, X} Y = {M, A, T, H} Jy = {0, {M}, {M, A}, {M, A, T}, Y} (a) Let E= {0, K
Answers
Given the topological spaces X = {D, O, R, K} with the topology Tx and Y = {M, A, T, H} with the topology Jy, we are asked to determine whether the set E = {0, K} is open in X and open in Y.
To determine whether the set E = {0, K} is open in the topological spaces X and Y, we need to check if E belongs to the respective topologies, Tx and Ty.
In X, the topology Tx is given by: Tx = {Ø, {0}, {D, O}, {O, R}, {D, O, R}, X}. We can see that E = {0, K} is not explicitly listed in Tx. Therefore, E is not open in X since it does not belong to the topology.
In Y, the topology Ty is given by: Jy = {0, {M}, {M, A}, {M, A, T}, Y}. Again, E = {0, K} is not explicitly listed in Ty. Hence, E is not open in Y as it does not belong to the topology.
In both cases, the set E = {0, K} is not open in the respective topological spaces X and Y because it is not a member of the defined topologies.
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Ciara measured the length, x, of each of the insects she found underneath a rock. She recorded the lengths in the table below. Calculate an estimate of the mean length of the insects she found. Give your answer in millimetres (mm). Length (mm) 0≤x≤10 10≤x≤20 20≤x≤30 Frequency 5 6 9
Answers
The estimate of the mean length of the insects Ciara found is 17 millimeters (mm).
To calculate an estimate of the mean length of the insects Ciara found, we need to find the weighted average of the lengths using the given frequencies.
Let's denote the lower limits of the length intervals as L1 = 0, L2 = 10, and L3 = 20.
Similarly, denote the upper limits as U1 = 10, U2 = 20, and U3 = 30.
Next, we calculate the midpoints of each interval by taking the average of the lower and upper limits.
The midpoints are M1 = (L1 + U1) / 2 = 5, M2 = (L2 + U2) / 2 = 15, and M3 = (L3 + U3) / 2 = 25.
Now, we can calculate the sum of the products of the frequencies and the corresponding midpoints.
This gives us (5 \(\times\) 5) + (6 \(\times\) 15) + (9 \(\times\) 25) = 25 + 90 + 225 = 340.
Next, we calculate the sum of the frequencies, which is 5 + 6 + 9 = 20.
Finally, we divide the sum of the products by the sum of the frequencies to find the weighted average, which is 340 / 20 = 17.
Therefore, the estimate of the mean length of the insects Ciara found is 17 millimeters (mm).
Thus, the mean length of the insects Ciara found is approximately 17 millimeters (mm).
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What is K-map A. method used to minimize Boolean expressions with having to use Boolean algabra B. pictoriat nethod used to aininize soolesn expressions without having to use Hootean atgabra theorens and exation asnipulations Q.pictorial wethod used to minimize Bootean expresstons with having to use Booleen algobra theormen and eqution manipulations
Answers
Karnaugh maps or K-maps are pictorial methods used to minimize Boolean expressions without having to use Boolean algebra theorems and equation manipulations. Option Q is the correct answer.
They provide a visual aid for determining the optimal grouping of terms. Karnaugh maps reduce logic functions more quickly and easily than Boolean algebra simplification. It is a practical tool to use for problems that require minimizing Boolean expressions. There are two common versions of Karnaugh maps: 2-D Karnaugh maps and 3-D Karnaugh maps. A Karnaugh map consists of squares in which each square represents a product term or minterm.
In a two-variable Karnaugh map, there are four squares, whereas in a three-variable Karnaugh map, there are eight squares. Karnaugh maps are read and interpreted from left to right and top to bottom. Terms that are adjacent or touching in the map can be combined to produce a simplified expression. K-maps can minimize up to 4 variables in a 2-D map and up to 6 variables in a 3-D map. Karnaugh maps help reduce the complexity of Boolean expressions and make it easier to implement logic circuits.
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a manufacturer of batteries would like to insure that their defective rate is less than 5%. in order to be sure that their batteries meet this quality control standard, the supervisor randomly samples 100 batteries and finds that 4 are defective. is there significant statistical evidence that the manufacturer is meeting their quality control standards?? find the p-value rounded to 4 decimal places.
Answers
Since the p-value (0.1021) is greater than the significance level (0.05), we fail to reject the null hypothesis.
What is null hypothesis?The null hypothesis is a type of hypothesis that describes the population parameter and is used to examine the validity of experimental results.
To test whether the manufacturer's defective rate is less than 5%, we can use a one-tailed hypothesis test with a significance level of 0.05.
Let p be the true proportion of defective batteries in the population. The null hypothesis is that p >= 0.05, and the alternative hypothesis is that p < 0.05.
We can use the normal approximation to the binomial distribution, since n = 100 and p₀ = 0.05 > 10. The test statistic is:
z = (x - np₀) / √(np₀(1-p₀))
where x is the number of defective batteries in the sample, n is the sample size, and p₀ is the hypothesized proportion under the null hypothesis.
Plugging in the values, we get:
z = (4 - 100*0.05) / √(100*0.05*0.95) = -1.2649
The p-value for this test is the probability of getting a test statistic as extreme as -1.2649 or less, assuming the null hypothesis is true. From a standard normal distribution table, the probability of getting a z-score of -1.2649 or less is 0.1021.
Since the p-value (0.1021) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the manufacturer is not meeting their quality control standards.
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A fitness center piloted two new programs to help people reduce stress levels and maintain a healthy lifestyle. after one month, 112 of the 125 people who volunteered for a program in mindfulness reported a reduction in stress levels, and 110 of the 135 people who volunteered for a yoga program reported a reduction in stress levels. the fitness center wants to investigate whether there is a significant difference between the proportions of all people in the two programs who would report reductions in stress levels. have the conditions for inference been met?
Answers
Yes, all requirements have been satisfied for drawing conclusions from statistics. would note a reduction in stress. whether the prerequisites for inference are present.
Describe statistics.It is common practice to start with a statistical population or a statistical model that needs to be investigated when applying statistics to a problem in science, business, or society. The field of statistics is concerned with the collection, arrangement, organization, analysis, interpretation, and presentation of data.
The conditions for making judgments about a single proportion are Random: A random experiment or sample must have produced the data. For the sample distribution of pp with hat on top to be considered normal, there must be nearly equal numbers of expected successes and failures.
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Can someone help me
Answers
Answer:
1/5 x (6 x 4) goes to less than 24 (ps I’m not sure sorry)
2 x 6 x 4 goes to great than 24
(4 x 6) x (3 - 2) goes to equal to 24
(6 x 4) divide 2 goes to less than 24
(6 x 8) - (6 x 4) goes to equal to 24
6 x (5 - 4) goes to less than 24
9 x 6 / 5 - 3 goes to greater than 24
5 x 1/5 x (6 x 4) goes to equal to 24
Answer:
the answers are in the picture because I wrote them on paper. Hope it helps!
I used a calculator on every problem so they should be correct
The measures of angle B and angle B' are equal. True or false?
100 POINTS. PLEASE ANSWER ASAP.
Answers
Answer:
I think its true
Step-by-step explanation:
hope it helps and you have a greate Day
Please help me out!!!
Answers
Suppose you learn a word embedding for a vocabulary of 10000 words. Then the embedding vectors should be 10000 dimensional, so as to capture the full range of variation and meaning in those words.
True
False
Answers
False. The statement is not necessarily true. While it is possible to have word embeddings that are 10000 dimensional for a vocabulary of 10000 words.
It is not a requirement to capture the full range of variation and meaning in those words. The dimensionality of word embeddings is not solely determined by the size of the vocabulary, but rather by various factors such as the complexity of the underlying semantic relationships and the specific modeling techniques used.
In practice, word embeddings are often created using techniques like Word2Vec or GloVe, which typically produce lower-dimensional embeddings (e.g., 100 to 300 dimensions). These lower-dimensional embeddings have been shown to effectively capture important semantic relationships and patterns in language, while also reducing the computational complexity and memory requirements. The choice of dimensionality depends on the specific application and the trade-off between capturing sufficient information and computational efficiency.
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JGR-MST. Which statement is not always true? someone pls helpp
Answers
Answer:
It is D, I think it’s because the letters need to be around in the same order
The angle corresponding to each other of different triangle are equal.
What are similar triangle ?"Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion".
Here given,
\(\triangle JGR\) is similar to triangle \(\triangle MST\)
So, from the definition of similar triangle ,
angle J ≅ angle M
angle G ≅ angle S
angle R ≅ angle T
Hence, option D is correct.
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PLEASE Answer!!! I'll give you a thanks + 5.0-star rating and a BRAINLIEST to whoever gives the most explained answer ( must be 2 answers! )
Find the value of each unknown angle. Write each angle to the nearest tenth of a degree.
Answers
Answer:
look at the photo................
You bought your friend's bike and owe $60.00 to your friend to finish paying for it. You do chores and earn $4.00 per day (7 days per week). If you give your friend all your money how much money would you have after 3 weeks of working?
Answers
Answer:
$24.
Step-by-step explanation:
I multiplied 4 by 7 to get 28. Then I multiplied $28 by three weeks and got $84. Since $84 is more than I owe I subtracted $84 by $60 and got $24. I would give my friend $60 and keep $24. Hope this helps! Have a great day!
A statue in the park is 24 feet tall and has a width of 36 inches. Chase was in
ceramics class and decided to make a model of the statue. The model is 16 inches
tall. How wide is the model (to the nearest tenth of an inch)?
Answers
Answer:
22.33 feet tall / 267.96 inches tall
Step-by-step explanation:
The statue is 36 inches wide. If Chase made his model of the statue 16 inches wide, he decreased it by 20 inches. Now change the inches into feet. 36 inches would be 3 feet, 16 inches would be 1.33 feet and 20 inches would be 1.67 feet. 24ft - 1.67 = 22.33ft. Now change the answers to inches. 22.33ft will be 267.96 inches tall.
if you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a heart or 7?
Answers
The probability which represents the likelihood of randomly selecting a card that is a heart or a 7 from a well-shuffled standard deck is 4/13.
To calculate the probability of selecting a card that is either a heart or a 7 from a standard deck of 52 cards, we need to determine the number of favorable outcomes (cards that are hearts or 7s) and the total number of possible outcomes (all the cards in the deck).
Let's break it down:
Number of favorable outcomes:
- There are 13 hearts in a deck (one for each rank).
- There are four 7s in a deck (one for each suit, including the 7 of hearts).
- However, we need to subtract one card (the 7 of hearts) from the count since it has already been counted as a heart.
So, the number of favorable outcomes is 13 + 4 - 1 = 16.
Total number of possible outcomes:
- There are 52 cards in a deck.
Therefore, the probability of selecting a card that is either a heart or a 7 is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 16 / 52
= 4 / 13
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III An airline reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, determine the probability that there will be fewer than 20 no-shows. Use the normal distribution to approximate the binomial distribution. Include the correction for continuity.
Answers
The probability that there will be fewer than 20 no-shows among 150 advanced reservations, using the normal approximation with continuity correction, is approximately 0.116.
What is the probability of having fewer than 20 no-shows among 150 advanced reservations?To determine this probability, we can use the normal distribution as an approximation to the binomial distribution with the given parameters. The continuity correction is applied to account for the fact that the binomial distribution is discrete while the normal distribution is continuous.
Given that the rate of no-shows is 15% and there are 150 advanced reservations, we can calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the formula: μ = np and σ = sqrt(np(1-p)), where p is the probability of a no-show.
In this case, p = 0.15, so μ = \(150 * 0.15\) = 22.5 and σ = sqrt(\(150 * 0.15 * 0.85\)) ≈ 3.35.
To find the probability of fewer than 20 no-shows, we can use the normal distribution with a continuity correction. We calculate the z-score for 20 as (20 - μ + 0.5) / σ and then use a standard normal distribution table or calculator to find the corresponding cumulative probability.
Using the z-score, we find z ≈ (20 - 22.5 + 0.5) / 3.35 ≈ -0.746. Looking up this z-score in a standard normal distribution table or calculator, we find a cumulative probability of approximately 0.229.
Since we want the probability of fewer than 20 no-shows, we subtract this probability from 0.5 (to account for the area in the right tail of the distribution) and multiply by 2 to include the left tail as well: P(Z < -0.746) ≈ \(2 * (0.5 - 0.229)\) ≈ 0.542.
Therefore, the probability that there will be fewer than 20 no-shows among 150 advanced reservations is approximately 0.116 (rounded to three decimal places).
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Integrate the ODE
dy/dx = x² √y, 0 < x < 2, y(0) = 1
using Euler's method (Δx = 0, 2) to compute y(2). Obtain analytical solution to the ODE and compare y(2) obtained using Euler's method with that obtained analytically.
Answers
we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.
Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:
Step 1: For x = 0, y = 1 (initial condition).
Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.
Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.
Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.
Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.
Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.
Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.
Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.
Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.
Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.
Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.
Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.
To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:
∫(1/√y) dy = ∫x² dx
Integrating both sides gives:
2√y = (1/3)x³ + C
Solving for y:
y = (1/4)(x³ + C)²
Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:
1 = (1/4)(0³ + C)²
1 = (1/4)C²
4 = C²
C = ±2
Since C can be either 2 or -2, the general solution to the ODE is:
y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²
Now, let's evaluate y(2) using the analytical solution:
y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5
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find the distance from the given point to each of the following. (4, 7, -5) (a) the xy-plane (b) the yz-plane (c) the xz-plane (d) the x-axis (e) the y-axis (f) the z-axis
Answers
\(So distance from a) xy plane = |-5| = 5 b) yz plane = |4| = 4c) xz plane = |7| = 7d) x-axis = √[(7)^2+(-5)^2] = √[49+25]=√[74] = 8.6023e) y-axis =√[(-5)^2+(4)^2] = √[25+16] =√[41] = 6.4031f) z-axis = √[(4)^2+(7)^2] = √[16+49] = √[65] = 8.0622\)
What is axis?A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates that are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length. An axis is a line that is used to sketch, measure, rotate, etc. a curve or a figure. The Cartesian axes in the plane or in space, which are often mutually perpendicular, are the most frequently seen axes. Axes, pronounced "ax-ees," is the plural form of "axis." The phrase is also used to describe a line that passes across a group of aircraft. The line on a graph that passes 0 horizontally (left to right).
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Find the average rate of change of his annual salary between 2017 and 2020
Answers
We were told that the salary, t years after 2015 is given by the function,
S(t) = 3100t + 56000
When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2
We would substitute t = 2 into the function and find S(2)
Thus,
S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200
When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5
We would substitute t = 2 into the function and find S(2)
Thus,
S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500
Thus, we can say that
when
x1 = 2, y1 = 62200
when x2 = 5, y2 = 71500
Recall,
slope or average rate of change = (y2 - y1)/(x2 - x1)
average rate of change = (71500 - 62200)/(5 - 2) = 9300/3
average rate of change = 3100
The last option is correct
can anyone give me the right answer and not the wrong answer pls !
Answers
Answer: last one
Step-by-step explanation:
the first two make a positive product, then multiplying by a negative gives a negative
If 2A:3B=5:6 and 3B:2C=36:15, then find A:C
Answers
Answer:
A : C = 2 : 1
Step-by-step explanation:
Expressing the ratios in fractional form
\(\frac{2A}{3B}\) = \(\frac{5}{6}\) ( cross- multiply )
15B = 12A ( divide both sides by 15 )
B = \(\frac{12}{15}\) A = \(\frac{4}{5}\) A
and
\(\frac{3B}{2C}\) = \(\frac{36}{15}\) ( cross- multiply )
45B = 72C ( substitute B = \(\frac{4}{5}\) A )
45 × \(\frac{4}{5}\) A = 72C
36A = 72C ( divide both sides by C )
36 × \(\frac{A}{C}\) = 72 ( divide both sides by 36 )
\(\frac{A}{C}\) = \(\frac{72}{36}\) = \(\frac{2}{1}\)
Then
A : C = 2 : 1
Polygon JKLM is drawn with vertices J(-4,-3), K(-4,-6), L(-1,-6), M(-1,-3). Determine the image coordinates of L’ if the pre-image is reflected across y=-3.
A. L’(-3,6)
B. L’(-1,6)
C. L’(-1,0)
D. L’(1,0)
Answers
Step-by-step explanation:
If x = 1, solve for y.
y = 5 x 2^x
y = [?]
Enter
(-4, 18) is a solution to:
y = 5x – 2
Answers
Mavis is interested in whether military dependency is related to gender in american samoa. Here is data she collected about the population of american samoa in 201020102010:.
Answers
Mavis is interested in whether military dependency is related to gender in american samoa. then Male = 0.4193 and Female = 0.5087
What does distribution mean in work?
Distribution is the activity of both selling and delivering products and services from manufacturer to customer. This can also be called product distribution. As businesses become more global it becomes important to improve distribution to ensure that customers and all members of the distribution channel are happy.
To obtain the marginal distribution of gender :
Total number of civilians (male + female)
(26393 + 27330) = 53,723
Male :
P(male) = number of male / total
P(male) = 26393 / 53,723 = 0.4912793
P(Female) = number of Female / total
P(Female) = 27330 / 53,723 = 0.5087206
Complete question :
Mavis is interested in whether military dependency is related to gender in American Samoa. Here is data she collected about the population of American Samoa in 2010.
Millitary status _________ female ____ Male
In armed forces _________ 28 _______ 59
Millitary dependent ______ 928 ______ 781
Civilian _______________ 26393 ___27330
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The function f(x) is a cubic function and the zeros of f(x) are -5, -3 and 1. The y-intercept of f(x) is -45. Write the equation of the cubic polynomial in standard form.
Answers
Step-by-step explanation:
Since -5, -3 and 1 are the zeroes of f(x),
(x + 5), (x + 3) and (x - 1) are factors of f(x).
=> f(x) = a(x + 5)(x + 3)(x - 1),
where a is a real constant.
We are given that when x = 0, f(x) = -45.
=> a(0 + 5)(0 + 3)(0 - 1) = -45
=> -15a = -45, a = 3.
Hence, f(x) = 3(x + 5)(x + 3)(x - 1)
= 3x³ + 21x² + 21x - 45.
Answer:
The function f(x) is a cubic function and the zeros of f(x) are -5, -3 and 1. The y-intercept of f(x) is -45.
(x+5), (x+3) and (x-1) are the factors of f(x).
Form : f(x)=a(x+5)(x+3)(x-1)
When f(x)=-45 and x=0, we get a=3
Equation of the cubic polynomial in standard form is :---
\(f(x) = 3(x + 5)(x + 3)(x - 1)\\ =3 ( {x}^{2} + 8x + 15)(x - 1) \\=3({x}^{3} + 8 {x}^{2} + 15x - {x}^{2} - 8x - 15) \\ =3({x}^{3} + 7{x}^{2} + 7x - 15)\\=\boxed{3{x}^{3}+21{x}^{2}+21x-45}\)
3x³+21x²+21x-45 is the right answer.what are the steps to induction nsls
Answers
These steps are often referred to as the principle of mathematical induction or PMI.
The steps for mathematical induction are:
Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.
Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.
Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.
Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.
These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.
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