The correct answer is cycle. A sine or a cosine function represent periodic functions where the value of the function is repeats after a definite interval.
What do you mean by periodic function?
A periodic function can be defined as:
A function returning to the same value at regular intervals. Though periodic motion and oscillatory motion sound the same, not all periodic motions will be oscillatory motion.
Image result for periodic function
If a function has a repeating pattern like sine or cosine, it is called a periodic function. The period is the length of the smallest interval that contains exactly one copy of the repeating pattern.
A motion that repeats itself at regular intervals is termed periodic motion. 1. A motion that does not repeat itself at regular intervals is termed non-periodic motion. 2. After a certain period of time, an object exhibiting periodic motion returns to its original position.
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the quality-control manager of a large factory is concerned about the number of defective items produced by workers. thirty workers at the factory agree to participate in a study of three different incentive plans to help reduce the number of defective items produced. the plans will be randomly assigned to the workers so that 10 workers received each plan. the reduction in the number of defective items produced by each worker will be recorded two weeks after the plans are implemented. which of the following best describes why a completely randomized design is an appropriate design to use in this situation? responses
A completely randomized design is an appropriate design to use in this situation because There is no blocking variable, and incentive plans will be randomly assigned to the workers.
A completely randomized design (CRD) is the simplest design for comparative experiments because it employs only two basic experimental design principles: randomization and replication.
By randomization, we mean that the experimental units' run sequence is determined at random.
Treatments are assigned to experimental units or plots in a completely random manner in CRDs. CRD can be used for either single-factor or multifactor experiments.
According to the question,
The quality control manager of a large factory wants to find out the number of defective items . For that 10 workers are selected Randomly and these worker will work on item according 3 incentive plans Means Replication is 3.
Hence , A completely randomized design is an appropriate design to use in this situation because There is no blocking variable, and incentive plans will be randomly assigned to the workers.
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A set of 3 consecutive even integers adds up to 6. What are the integers?
Situation:
An archaelogist in Turkey discovers a
spear head that contains 55% of its
original amount of C-14.
PLS HELP AHHHHH
The age of the spear head to the nearest year is 8 years.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since the archaelogist in Turkey discovers a spear head that contains 55% of its original amount of C-14. The amount will be:
= 55% × 14
= 0.55 × 14
= 7.7
The age of the spear will be 8 years.
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Complete question
An archaelogist in Turkey discovers a spear head that contains 55% of its original amount of C-14. Find the age of the spear head to the nearest year.
i need help it's hard
The teeth on the key are busted and now they must be readjusted and the code is 12y×2x^2.
What is code?Coding in Math is a series of the independent, standalone modules to that is use coding to reinforcement and extended by to the students' understandings of to the math.! As students learning major programming is concepts, they will development math-related to the projects that is demonstrate their proficiency by math and to the computer science.
18xy^2z^2=2xy^2 z×9xz
20xy^2z= 2xy^2z×10x^2
11xy^z=xyz^2×11
180y=9y×2x
24xy =12y×2x^2
(Take the greatest common factor)
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Write the equation of each line in slope-intercept form.
Answer:
24. y= -1/3x+1
25. y= -2/-1x+3
Solve for the lengths of XZ and YZ
how would you explain finding the slope to classmate
Answer/Step-by-step explanation:
Since the axes are labelled and there are nice points marked on the line, you can practically SEE the slope here without any calculating, just by counting. Start with a point and find the directions to the next point. To get from one point to the next, go UP2 and OVER3.
"UP2 and OVER3" is the slope 2/3. Double check that you get a slope that is positive because the line is going up to the right, it should have positive slope.
If the teacher is insisting that you use the slope formula, then name two of the points, such as (0, 4) and (3, 6). First subtract the y's, 6 - 4 is 2, put that on top of a fraction. Then subtract the x's, 3 - 0 is 3, put that on the bottom of a fraction. You get 2/3 again. Doesn't matter what points you use, since they are all on the same line it will come out the same.
Write this set using interval notation.
Please help me!!!
Answer:
Step-by-step explanation:
The set {x | x < 0 or x > 3 } can be written in interval notation as (-∞, 0) ∪ (3, ∞).
The set {x | x < 0 or x > 3 } consists of all real numbers that are either less than 0 or greater than 3. This set can be represented as the union of the set of all numbers less than 0, which can be written as (-∞, 0), and the set of all numbers greater than 3, which can be written as (3, ∞).
Therefore, the set {x | x < 0 or x > 3 } can be written in interval notation as (-∞, 0) ∪ (3, ∞).
I need help with this question. I know the answer I jsut don't know how to get there. Please help!
The graph of f(x)=x2 is shown.
Use the parabola tool to graph g(x).
g(x)=(x+2)2−1
(Answer is (-2,-1) and (-3,0) )
Answer:
The graph of f(x) = x^2 is shown.
Use the parabola tool to graph g(x).
9(x)= (1 + x)^2 – 2
graph the parabola by first plotting its vertex and then plotting a second point on the parabola
when approximating the area below a curve, using midpoint rectangles always produces the best approximation.
The statement given is true. When approximating the area below a curve, using midpoint rectangles always produces the best approximation.
A good way to estimate areas with rectangles is to make each rectangle cross the curve at the midpoint of that rectangle's top side. Midpoints always the best approximate for the area under the curve using a finite number of rectangles.
What to use the midpoint rule?The midpoint rule, also known as the rectangle method or mid-ordinate rule, is used to estimate the area under a simple curve. There are other methods to estimate the area, such as the left rectangle or right rectangle sum, but the midpoint rule gives the better approximate compared to the two methods.
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using traditional methods it takes 90 hours to receive an advanced driving license. a new training technique using computer aided instruction (cai) has been proposed. a researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. after performing the test on 190 students, the researcher fails to reject the null hypothesis at a 0.02 level of significance.
The conclusion is that there is no sufficient evidence at the 0.02 level of significance that the new technique lengthens the training time.
Given,
The mean time taken to receive advanced driving license, through traditional methods [tex]\mu = 90[/tex] hours
The researcher believes the new technique may lengthen the training time
Researcher conducts hypothesis test of n = 190 students
The researcher fails to reject the null hypothesis at significance level, [tex]\alpha = 0.02[/tex]
Test hypothesis :-
[tex]H_0[/tex] :The mean time it takes for the new technique to receive an advanced driving license is 90 hours, i.e. [tex]\mu = 90[/tex].
[tex]H_a[/tex]: The mean time it takes for the new technique to receive an advanced driving license is greater than 90 hours, i.e. [tex]\mu > 90[/tex].
Failure to reject the null hypothesis means that our sample did not provide enough evidence to conclude that the effect exists. However, the lack of evidence does not prove that the effect does not exist.
As a result, the average time for the new technique to obtain an advanced driving licence is less than 90 hours.
Thus,, the researcher's belief that the new technique would lengthen training time was incorrect.
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a bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed v/2. Thependulum bob is suspended by a stiff rod of length and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle?
Sell Order 5: Price: $20, Quantity: 400
Since this order has the same price as Sell Order 2, it will be executed fifth.
1: Sell Order 3: Price: $30, Quantity: 300
2: Sell Order 1: Price: $25, Quantity: 500
3: Sell Order 4: Price: $25, Quantity: 100
4: Sell Order 2: Price: $20, Quantity: 200
5: Sell Order 5: Price: $20, Quantity: 400
1: Sell Order 3: Price: $30, Quantity: 300
Since this order has the highest price, it will be executed first.
2: Sell Order 1: Price: $25, Quantity: 500
Since this order has the second highest price, it will be executed second.
3: Sell Order 4: Price: $25, Quantity: 100
Since this order has the same price as Sell Order 1, it will be executed third.
4: Sell Order 2: Price: $20, Quantity: 200
Since this order has the third highest price, it will be executed fourth.
5: Sell Order 5: Price: $20, Quantity: 400
Since this order has the same price as Sell Order 2, it will be executed fifth.
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Of the animals on a farm 60% are cows and the rest are sheep. When 260 more cows and sheep are added to the farm, the percent of cows increases by 20% and the number of sheep doubles. Find the number of sheep originally on the farm.
The number of sheep originally on the farm will be equal to 200.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from.
Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Let the number of animals originally at the farm is x.
60% of the animals are cows.
So, 0.6x are cows.
If there are 60% cows, then there are 40% of sheep.
So, 0.4x are sheep.
The quantity of sheep multiplies when many cows and sheep were introduced to the property.
As a result, the farm now has the same amount of sheep that it did before.
Number of sheep added = 0.4x
There are total 260 animals added to the farm.
So,
Number of sheep added = 260-0.4x
Total number of animals = x + 260
The percentage of cows increased to 20%.
Initial number of cows at farm + cows added = Initial number of cows at farm + 20% of the total cows initially at the farm.
0.6x + (260-0.4x) = 0.6x + 0.2(0.6x)
0.6x+260-0.4x = 0.6x+0.12x
0.2x+260 = 0.6x+0.12x
0.2x+260 = 0.72x
260 = 0.52x
x = 260/0.52
x = 500
Thus, the farm's initial animal population was 500.
0.6x = the amount of cows that were first on the farm= 0.6(500) = 300 cows
0.4x = the amount of sheep that were initially on the farm = 0.4(500) = 200 sheep
0.4x = Sheep added = 200
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An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. The accompanying table shows the number of students who obtained the indicated points for X (rows) and Y (column). The class is composed of 100 students. Y 10 15 6 2 10 15 20 10 10 1 15 14 1 Compute the correlation between the scores of students from the two parts of the quiz.
E(max(X, Y )) = PxPy max(x, y)p(x, y)
= max(0, 0)p(0, 0)+max(0, 5)p(0, 5)+· · ·+max(10, 10)p(10, 10)+max(10, 15)p(10, 15)
= 0 ∗ 0.02 + 5 ∗ 0.06 + · · · + 10 ∗ 0.14 + 15 ∗ 0.01 = 9.6.
fX(x) = R 10(2x + y − 2xy)dy = x +12, 0 ≤ x ≤ 1.
fY (y) = R 10
(2x + y − 2xy)dx = 1, 0 ≤ y ≤ 1.
Since f(x, y) 6= fX(x)fY (y), X and Y are not independent.
Column=A column is a recurring piece or article in a newspaper, magazine or other publication, where a writer expresses their own opinion in few columns allotted to them by the newspaper organisation. Columns are written by columnists.
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NO LINKS!! Please help me with this statement Part 6 ll
Answer:
C) Domain: all real numbers x except x = ±2
E) f(x) → ∞ as x → -2⁻ and as x → 2⁺, f(x) → -∞ as x → -2⁺ and as x → 2⁻
Step-by-step explanation:
Given function:
[tex]f(x)=\dfrac{3x^2}{x^2-4}[/tex]
The domain of a function is the set of all possible input values (x-values).
A rational function is undefined when the denominator is equal to zero.
The denominator of the given function is zero when:
[tex]\implies x^2-4=0[/tex]
[tex]\implies x^2=4[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{4}[/tex]
[tex]\implies x= \pm 2[/tex]
Therefore the domain of the function is:
all real numbers x except x = ±2The excluded x-values are x = -2 and x = 2.
To find the behaviour of the function near the excluded x-values, input values of x that are very near either side of excluded values:
[tex]x \rightarrow -2^-: \quad f(-2.001)=\dfrac{3(-2.001)^2}{(-2.001)^2-4}=3002.250...[/tex]
[tex]x \rightarrow -2^+: \quad f(-1.999)=\dfrac{3(-1.999)^2}{(-1.999)^2-4}=-2997,750...[/tex]
[tex]x \rightarrow 2^-: \quad f(1.999)=\dfrac{3(1.999)^2}{(1.999)^2-4}=-2997.750...[/tex]
[tex]x \rightarrow -2^+: \quad f(2.001)=\dfrac{3(2.001)^2}{(2.001)^2-4}=3002.250...[/tex]
Therefore, the behaviour of the function near the excluded x-values:
f(x) → +∞ as x → -2⁻f(x) → -∞ as x → -2⁺f(x) → -∞ as x → 2⁻f(x) → +∞ as x → 2⁺Compute the orthogonal projection of [-2 2] onto the line through [ -1 5] and the origin. The orthogonal projection is [ __ __ ]
the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75] using unit vector.
First, we need to calculate the unit vector of the line. This can be done by subtracting the two given points and dividing the result by the magnitude of the vector:
[-1 5] - [0 0]
= [-1 5]
|[-1 5]| = sqrt(1^2 + 5^2) = sqrt(26) = 5.1
Unit vector = [-1/5.1 5/5.1] = [-0.196 0.980]
Next, we need to calculate the dot product of the vector [-2 2] and the unit vector [-0.196 0.980]. This will give us the scalar projection.
(-2)(-0.196) + (2)(0.980) = -0.392 + 1.960 = 1.568
Finally, we can calculate the orthogonal projection by multiplying the scalar projection by the unit vector.
[-0.196 0.980] (1.568) = [-0.301 1.527]
Rounding to two decimal places, the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75].
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The sum of the first 15 terms of the sequences 7, -14, 28, -56, 112,...
The sum of the first 15 terms of the geometric sequences will be 76,456.33.
What is the sum of a geometric sequence?The aggregate to boundless GP implies, the number of terms in a limitless GP.
Let a₁ be the first term, n be the total number term, and r be a common ratio.
Then the sum of the geometric sequence will be
Sₙ = [a₁ (1 - rⁿ)] / (1 - r)
The geometric sequence is given below.
7, -14, 28, -56, 112,...
The first term of the geometric sequence is 7 and the common ratio of the geometric sequence is given as,
r = - 14 / 7
r = - 2
Then the sum of the first 15 terms of the sequences will be given as,
S₁₅ = [7 (1 - (-2)¹⁵)] / (1 - (-2))
S₁₅ = [7(1 + 32,768)] / 3
S₁₅ = -229,369 / 3
S₁₅ = 76,456.33
The sum of the first 15 terms of the geometric sequences will be 76,456.33.
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What is the rule that describes the translation ABC → A' B' C' ?
The rule that describes the translation will be as T<-3, 2>
Given,
Translation;-
Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same.
Here,
In order to move from A = (-3,3) to A' = (-6, 5), we must first move 3 units to the left and 2 units up.
Step 1's change causes x to become x-3.
Step 2's change causes y to become y+2.
When you combine these, (x, y) becomes (x-3, y+2).
That is equivalent to writing T<-3, 2>.
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The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y).
Temp 170 172 173 174 174 175 176 177 Ratio 0.76 1.27 1.48 0.99 0.99 1.02 1.12 1.70 Temp. 180 180 180 180 180 181 181 182 Ratio 1.43 1.50 1.57 2.15 2.11 0.88 1.33 0.84 Temp. 182 182 182 184 184 185 186 188 Ratio 1.73 2.04 2.70 1.59 2.62 3.10 1.89 3.18 (a) Determine the equation of the estimated regression line. (Round all numerical values to five decimal places.) y = . 1017x-16.592 レ 19174x (b) Calculate a point estimate for true average efficiency ratio when tank temperature is 182. (Round your answer to four decimal places.) 1.9174 (c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 182. (Round your answers to four decimal places.) (182, 0.84) 1581 (182, 1.73) (182, 2.04) (182, 2.70)
The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate.
a) The equation of the estimated regression line is ŷ = - 16.592 + 0.1017x.
b) A point estimate is 1.9174 for true average efficiency ratio when tank temperature is 182.
c) The values of the residuals from the least squares line for the four observations for which temperature is 182 are -1.0774, -0.1874, 0.1226, 0.7826..
We have given the accompanying data on tank temperature (x) and efficiency ratio (y).
a) We have to find out the equation of the estimated regression line. Consider the calculations shown in the above table:
ΣΧ= 4308 ; ΣΥ= 39.99 ; ΣΧΥ = 7229.47 ;
ΣX² = 773790
Determine the slope and intercepts using the following formulas,
Slope b₁ = (n ΣΧΥ - ΣX ΣΥ)/(nΣΧ² - (ΣX)²)
=> b₁ = [24 (7229.47) - (4308) (39.99)]/(24(773790)-(4308)²)
=> b₁ = 1230.36/12096 = 0.10171626984
=> b₁ ≈ 0.1017
Intercept, b₀ = ΣY /n - b₁ΣΧ /n
=> b₀ = 39.99/24 - 0.1017×4308/24
= -16.592
Thus, the estimated regression equation of the form, ŷ = b₀ + b₁ x
ŷ = - 16.592 + 0.1017x
b) Calculate the point estimate for true average efficiency ratio when tank temperature is 182.
y = -16.592 + 0.1017x
=> y= -16.592 +0.1017 (182)
=> y= 1.9174
Therefore, the point estimate for true average efficiency ratio when tank temperature is 182 is 1.9174..
c)We have to find out the values of the residuals from the least squares line for the four observations for which temperature is 182.
From part (b), the value of ŷ is 1.9174.
The table below shows the residuals.
Vi ŷ e = y₁ - y
0.84 1.9174 -1.0774
1.73 1.9174 -0.1874
2.04 1.9174 0.1226
2.70 1.9174. 0.7826
Hence, we got all the required values.
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A line passes through the point (9, 1) and has a slope of -4/3
Write an equation in slope-intercept form for this line.
Answer:
Step-by-step explanation:
the answer is y= -4x/3 + 13
Solve the equation.
9(z + 3) = 45
Answer:
Step-by-step explanation:
9z + 27 = 45
9z= 18
z= 18/9
z = 2
Answer:
[tex]z=2[/tex]
Step-by-step explanation:
[tex]9(z+3)=45\\9z+27=45\\9z=45-27\\9z=18\\z=\frac{18}{9}\\ z=2[/tex]
Hope it helps you
solving systems using substitution 4y=x ; 3x-y=70
Answer:
x= 56/3
y= 14/3
Step-by-step explanation:
for process look at provided image
A figure dilated by a factor of 6. By what factor will the perimeter of the figure change.
Point M is the midpoint of PQ, and LM is the perpendicular bisector of PQ. Write a two-column proof to show that LP = LQ.
The two column proof below has shown us that the LP ≅ LQ by definition of segment congruence.
How to write a two column proof?We are told that Point M is the midpoint of PQ, and LM is the perpendicular bisector of PQ. Thus, the two-column proof to show that LP = LQ is as follows;
Statement 1; PM ≅ QM, LM ⊥ PQ
Reason 1; Given
Statement 2; LM ≅ LM
Reason 2; Reflexive Property of Congruence
Statement 3; ∠PML ≅ ∠QML
Reason 3; Right angle congruence theorem
Statement 4; ΔPML ≅ ΔQML
Reason 4; SAS congruence theorem
Statement 5; ∠PML ≅ ∠QML
Reason 5; Corresponding parts of congruent triangles are congruent
Statement 6; LP ≅ LQ
Reason 6; Definition of segment congruence
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The heights of two different children were recorded in the chart.
a cart of two children's heights from age 0 months to 60 months
Draw a conclusion based on the data provided.
Answer:
based on the data i can draw a conclusion that child two and child one both grow taller as their time (months) increases. child 2 grows at a faster rate than child 1.
Step-by-step explanation:
Use the given information to prove that ∠QPR ≅ ∠SPR.
Given: QR ≅ SR
PQ ≅ PS
Prove: ∠QPR ≅ ∠SPR
By SSS rule of congruence
∠QPR ≅ ∠SPR
"Information available from the question"
In the question:
Use the given information to prove that ∠QPR ≅ ∠SPR.
Given: QR ≅ SR
PQ ≅ PS
Prove: ∠QPR ≅ ∠SPR
Now, According to the question:
In triangle PQR and triangle PRS
We can see that
QR ≅ SR (given)
PQ ≅ PS (given)
PR = PR (Common line)
By SSS rule of congruence
When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. This method is called side-side-side, or SSS for short.
Hence, ∠QPR ≅ ∠SPR
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Using the MGFs that you have derived in problem 1 above (and/or in lecture notes), identify the distributions of the random variables with the following moment-generating functions.
a) M(t)=(1−4t)^2 b) M(t)= 1/(1−3.2t)
c) M(t)= e^(−5t∣6t^2)
MGFs means moment generating function. Every distribution function has a unique mgf
Make X a random number. We say that X has a moment generating function, and the function
Mₓ(t) = E(e^tx) is referred to as the moment generating function of X
However, not all random variables have a moment generating function. However, every random variable has a unique function—an additional transform with properties comparable to those of the mgf.
The second creating capability (mgf) is a capability frequently used to describe the circulation of an irregular variable.
The moment-generating function is extremely useful for the following reasons:
1. Moments can be easily calculated with it; At zero, its derivatives are equivalent to the random variable's moments;
2. The mgf of a probability distribution is what makes it unique.
The question is incomplete so, I've answered in general
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Noah went into a movie theater and bought 9 drinks and 4 candies, costing a total of $60. Nachelle went into the same movie theater and bought 10 drinks and 2 candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Answer:
Drink: $5
Candy : $3.75
Step-by-step explanation:
Let d = the cost of a drink
Let c = the cost of a candy
9d + 4c = 60
10d + 2c = 57.50 ⇒ Mult. by -2 ⇒ -20d -4c = -115 Add this to the first equation
-20d - 4c = -115
9d + 4c = 60
-11d = -55 Divide both sides by -11
d = 5
A drink costs $5.00.
Plug in 5 for d in either of the two equations to solve for c
9d + 4c = 60
9(5) + 4x = 60
45 + 4c = 60 Subtract 45 from both sides
4c = 15 Divide both sides by 4
x = 3.75
A candy costs $3.75
Simplify for all questions
The required simplified solution of the expression is given as,
1. -2√15 2.3c 4. -5
3. √6 5. 2a
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
1.
[tex]=\sqrt{(3 -\sqrt{15} )^2} - \sqrt{(3 +\sqrt{15} )^2} \\=3 -\sqrt{15} - (3 +\sqrt{15})\\=3 -\sqrt{15} -3 -\sqrt{15}\\= -2\sqrt{15}[/tex]
Similarly, the solution of the various expression can be determined.
2.3c
3. √6
4. -5
5. 2a
Thus, the solution of the expression are given above
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In this exercise we want to identify primitive elements (generators) of a multiplicative group since they play a big role in the DHKE and many other public-key schemes based on the DL problem. You are given a prime p = 4969 and the corresponding multiplicative group Z*_969. Determine how many generators exist in Z*_969. What is the probability of a randomly chosen element a Z*_969 being a generator? Determine the smallest generator a Z*_969 with a > 1000. What measures can be taken in order to simplify the search for generators for arbitrary groups Z*_p?
1. Number of generators of Z*4969 = 1584
2. Probability of a randomly chosen element a Z*_969 being a generator = [tex]\frac{1584}{4968}[/tex]
3. 1001 is the smallest generator
4. Number of generators
∅(n) = n [tex](1 - \frac{1}{p_{1} } )(1 - \frac{1}{p_{2} } ).........(1 - \frac{1}{p_{n} } )[/tex]
1. Every relative prime of 4968 offers a generation if a is the generation of Z.
4968 = 4 × 1242
= 4 × 3 × 414
= 4 × 3 × 2 ×207
= 4 × 3 × 2× 3× 69
= 4 × 3 × 2 × 3 × 3 ×23
[tex]= 2^{3} * 3^{3} * 23[/tex]
Number of generators ∅ (4968) = 4968[tex](1 - \frac{1}{2} )(1 - \frac{1}{3} )(1 - \frac{1}{23} )[/tex]
Number of generators of Z*4969 = 1584
2. When a Z*4969 value is set, it becomes a generation and belongs to one of the 1584 elements.
The probability that a element is selected from Z*4968 becomes a generation is
= favorable elememt / total element
= [tex]\frac{1584}{4968}[/tex]
= 0.3188
3. To find the smallest generator a Z*_969 with a > 1000.
a > 1000
Every relative prime of 4968 gives a generation of Z*4969
G C D (1001 4968) = 1
Hence, 1001 is the smallest generator
4. Number of generators
∅(n) = n [tex](1 - \frac{1}{p_{1} } )(1 - \frac{1}{p_{2} } ).........(1 - \frac{1}{p_{n} } )[/tex]
To learn more about probability check the given link
https://brainly.com/question/6649771
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