To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element. All elements in the set have a multiplicative inverse except for 0.
To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element (usually 1).
For example, in the set {1, 2, 3, 4, 5} under multiplication modulo 6, we have:
The multiplicative inverse of 1 is 1 (1 x 1 = 1 mod 6).
The multiplicative inverse of 2 is 4 (2 x 4 = 8 = 1 mod 6).
The multiplicative inverse of 3 is 5 (3 x 5 = 15 = 3 x 1 = 1 mod 6).
The multiplicative inverse of 4 is 2 (4 x 2 = 8 = 2 x 4 = 1 mod 6).
The multiplicative inverse of 5 is 3 (5 x 3 = 15 = 3 x 5 = 1 mod 6).
Note that every element in the set has a multiplicative inverse except for 0. This is because any number multiplied by 0 is 0, not 1.
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1. What is the rule for the following geometric sequence? 64, -32, 16, -8...
an=64(-2)n-1
an = 64(1)-1
an=64(-1)-1
an=64(2)-1
The rule for the given geometric sequence as required to be determined is; a (n) = 64 (-1/2)^(n-1).
Which rule represents the geometric sequence?By observation, the first term of the sequence is; 64.
Also, the common ratio of each successive terms is as follows;
-32 / 64 = 16 / -31, -8 / 16 = -1/2.
On this note, the ratio is; -1/2.
Consequently, it follows that the answer choice which correctly represents the rule for the geometric sequence is; an = 64(-1/2)^n-1.
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Please help meeh:
Find the first four terms and stated term given the arithmetic sequence, with a, as the 1" term.
an = 25 - 10n, a5
an = 11 + 9n, a6
an = 65 - 35n, a9
The first four terms and the stated term, with an as the first term, are given the arithmetic sequence: 11 + 9n, a6.
What is an arithmetic sequence?The difference between any succeeding term and its preceding term remains constant throughout an arithmetic progression or arithmetic sequence, which is a set of numbers. That arithmetic progression's common difference is the constant difference. A series of numbers in the following format is an arithmetic sequence: a, a + d, a + 2 d, a + 3 d, a + 4 d,... The common difference between the terms in the sequence is d, and number an is the first term. An = a + (n - 1)d gives the nth term of an arithmetic series. A sequence is considered to be arithmetic if there is a constant difference between each subsequent term.To learn more about arithmetic sequence refer to:
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Which statement describes the relationship between −2 and −4? Responses −2 is located to the left of −4 on a horizontal number line because −2>−4. negative 2 is located to the left of negative 4 on a horizontal number line because negative 2 is greater than negative 4. −2 is located to the left of −4 on a horizontal number line because −2<−4. negative 2 is located to the left of negative 4 on a horizontal number line because −2<−4. −2 is located to the right of −4 on a horizontal number line because −2>−4. negative 2 is located to the right of negative 4 on a horizontal number line because negative 2 is greater than negative 4. −2 is located to the right of −4 on a horizontal number line because −2<−4. negative 2 is located to the right of negative 4 on a horizontal number line because −2<−4.
−2 is located to the right of −4 on a horizontal number line because −2>−4. Therefore, option C is the correct answer.
What is number line?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.
Given that, -2 and -4 is located on number line.
Negative integers on the number line located left to zero.
If the greater integer with negative sign and go farther on left of 0 on number line, the value of integers decreases.
Therefore, option C is the correct answer.
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a statistics professor finds that when he schedules an office hour for student help, an average of students arrive. find the probability that in a randomly selected office hour, the number of student arrivals is
The probability of 3 students arriving at a randomly selected office hour is 0.27(27%). This can be calculated by using the Poisson distribution equation which is P(x)=e^(-λ)*(λ^x/x!).
In the above equation, λ is equal to the average number of arrivals which is 3.3. Plugging these values into the equation gives us P(3)= e^(-3.3)*(3.3^3/3!) = 0.27, this means that the probability of 3 students arriving in randomly selected office hours is 0.27.The Poisson distribution is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space. It is commonly used in engineering, economics, and other fields.
This equation is especially useful in situations like this one where the arrival rate is known and the probability of a certain number of arrivals needs to be determined.
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A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 3.
in a shipment of 66 vials, only 14 do not have hairline cracks. if you randomly select 4 vials from the shipment, what is the probability that all 4 of the selected vials have hairline cracks?
that the probability of selecting 4 vials with hairline cracks is approximately 0.0375, or 3.75%
We can solve this problem using the hypergeometric distribution, which is used when sampling without replacement from a finite population. In this case, we have a population of 66 vials, out of which 14 are good (do not have hairline cracks) and 52 are bad (have hairline cracks). The probability of selecting all 4 bad vials (with hairline cracks) can be calculated as follows: P(4 bad vials) = (number of ways to choose 4 bad vials) / (total number of ways to choose 4 vials)
The number of ways to choose 4 bad vials from 52 is: C(52,4) = 52! / (4! × (52-4)!) = 270725
The total number of ways to choose 4 vials from 66 is: C(66,4) = 66! / (4! × (66-4)!) = 7219420
Therefore, the probability of selecting all 4 bad vials is: P(4 bad vials) = 270725 / 7219420 = 0.0375
This means that the probability of selecting 4 vials with hairline cracks is approximately 0.0375, or 3.75%
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five times a number is 120
Answer: The Number is 24.
Step-by-step explanation:
1) Set unknown number to a variable (I'm going to do x).
2) Set up equation: 5x = 120.
3) Simplify by dividing both sides by 5: 5x/5 = 120/5 = 24.
Help please it's urgent
Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
The required formula that describes the given variation is F = 1.6d².
What is the general formula to describe the given variation?The general formula to describe the variation that F is directly proportional to the square of d is F = kd²,
where k is a constant of proportionality.
To determine the value of k, we can use the given information that F = 40 when d = 5:
40 = k(5)²
40 = 25k
k = 40/25
k = 1.6
Substituting this value of k into the general formula, we get:
F = 1.6d²
Therefore, the formula that describes the variation is F = 1.6d².
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k
m
(x-30)°
y
n
(x+50)
Find the values of x and y that make k || j and
m || n.
x=
y =
0
The value of variables x and y are,
⇒ x = 80°
⇒ y = 130°
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Since, A parallelogram is forming here,
Then, Opposite angels are going to be equal.
Thus, We get;
⇒ y = (x + 50)°
Now, As you know that sum of all angles of a quadrilateral equals 360°
Hence, We get;
2 {(x + 50) + (x - 30)} = 360°
(x + 50) + (x - 30) = 180°
2x + 20 = 180
2x = 160
x = 80°
So, We get;
⇒ y = (x+50)
= 80 +50
= 130°
And,
⇒ x = 80°
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Consider the function f(x) = (x - 3)^2
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.
Answer:
Step-by-step explanation:
a) As the function is a quadratic you could restrict the domain by taking only values either side of the line x = 3. This means the domain will be
a) 3<x<∞
Or
b) -∞<x<3
b) the graph is attached below.
c) The equation of the inverse of f(x) can be found by switching x and y:
X = (y-3)²
√x = y - 3
y = √x + 3
However this takes in positive and negative values of the square root function. So in order to restrict this, we can take the positive square root only.
Thus y = +√x + 3
Find the gradient of the line that passes through (3, 7) and (1, 10).
Answer:
-1.5
Step-by-step explanation:
The gradient of a line can be found using the formula:
gradient = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
So for the line that passes through (3, 7) and (1, 10), the gradient can be found as:
gradient = (10 - 7) / (1 - 3)
gradient = 3 / -2
gradient = -1.5
So the gradient of the line that passes through (3, 7) and (1, 10) is -1.5.
Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
Answers:
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
A general formula to describe is F = 1.6×d² will be correct answer.
What in math is a proportional?A relationship is considered proportional if the ratio remains constant. For instance, the average number of apples produced per tree is a measure of proportionality, and the number of trees in an orchard is inversely related to the number of apples produced in a harvest. When two quantities are proportionate with one another, then expand and contract at the same pace, keeping the relationship constant.
Finding the general formula we obtain:
F=kd²
40=k×5²
k=1.6
so, F =1.6×d².
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A circle has a diameter of 26 feet what is the circumference
Use 3.14 for pie and do not round your answer be sure to include the correct unit in it in your answer
The circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.
What is the circumference?
The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated as a pole.
The formula for the circumference of a circle is 2 * π * r, where r is the radius of the circle.
To find the circumference, we first need to find the radius of the circle.
The diameter of the circle is 26 feet, so the radius can be calculated by dividing the diameter by 2:
r = 26 feet / 2 = 13 feet
Now that we know the radius, we can find the circumference:
C = 2 * π * r = 2 * 3.14 * 13 = 81.64 feet
Therefore, the circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.
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The price of Stock A at 9 A.M. was $13.52. Since then, the price has been increasing at the rate of $0.05 each hour. At noon the price of Stock B was $14.27. It begins to decrease at the rate of $0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
The number of hours that the prices of the two stocks be the same will be 4 hours.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
Let 'x' be the number of hours and 'y' be the price of stocks. Then the equations are written as,
y = 13.52 + 0.05x ...1
y = 14.27 - 0.14x ...2
From equations 1 and 2, then we have
13.52 + 0.05x = 14.27 - 0.14x
0.14x + 0.05x = 14.27 - 13.52
0.19x = 0.75
x = 3.947 ≈ 4 hours
The number of hours that the prices of the two stocks be the same will be 4 hours.
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Classify each ordered pair as a solution or not a solution of the inequality y
a inequality y <2/7 x − 5.
The ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is y<2/7x-5.
Here,
Put (x, y)=(21, 0) in the given inequality, we get
0<2/7(21)-5
0<1
So, it is solution
Put (x, y)=(6, -4) in the given inequality, we get
-4<2/7(6)-5
-4<12/7-5
-4<1.7-5
-4<-3.3
So, it is solution
Put (x, y)=(0, -5) in the given inequality, we get
-5<2/7(0)-5
-5<-5
Which is not true, it is not a solution
Put (x, y)=(7, -3) in the given inequality, we get
-3<2/7(7)-5
-3<-3
Which is not true, it is not a solution
Therefore, the ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.
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What is the azimuth of an object that is ten degrees south of east?
Answer:
Step-by-step explanation:
135°
Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero.
Translate the following sentence into an equation: "The product of 3 and x increased by 7 equals 25 ."
What is the answer to this equation (5+12i)+(7-5i)
The answer to the equation (5+12i) + (7-5i) is found to be 12-7i.
The provided equation is a simple algebraic relation between two complex numbers.
The given complex numbers are 5+12i and 7-5i.
We have to add these two complex numbers.
We will add the real part of the complex number to the real part and complex part of one complex number to the complex part of the complex number.
Sum of number = (5+12i) + (7-5i)
Sum of number = 12-7i
The sum of the two complex numbers is also complex number that has a real part has 12 and the imaginary or the complex part as -7.
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Shawn's retirement party will cost $6 if he invitês 3 guests. If there are 8 guests, how much
will Shawn's retirement party cost? Assume the relationship is directly proportional.
Step-by-step explanation:
Shawns party will cost $16 if there are 8 guest
Juan the trainer offers two solo workout plans: Plan A and Plan B. Each client does either one or the other (not both). Juan trained on Wednesday and Thursday last week. The table below shows the number of Plan A and Plan B clients Juan trained each day and the total time (in hours) he trained.
Wednesday Thursday
Number of
Plan A workouts
Number of
Plan B workouts
Total time
(in hours)
Let be the length (in hours) of each Plan A workout.
Let be the length (in hours) of each Plan B workout.
(a) Write a system of equations that could be used to find the length (in hours) of each type of workout.
(b) How long (in hours) was each type of workout?
A system of equations that could be used to find the length (in hours) of each type of workout
7a + 9b = 12
5a + 3b = 6
Solve this system of equations by multiplying both sides of one of the equation so that when the equations are added or subtracted there will only be one variable.
-I will multiply both sides of the 2nd equation by -3
-3*(5a + 3b) = 6*-3
-15a - 9b = -18
-Now I will get rid of the variable b by adding the two equations together.
7a + 9b = 12
+ -15a - 9b = -18
-8a = -6
a = -6/-8
a= 3/4 (45 minutes)
-Now plug 3/4 into one of the original equations as a to solve for b.
-I will use the 2nd original equation.
5a + 3b = 6
5(3/4) + 3b = 6
15/4 + 3b = 6
3b = 9/4
b = 9/12 = 3/4 (45 minutes)
Both workout plans last the same amount of time.
Plan A lasts 45 minutes.
Plan B lasts 45 minutes.
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Calculate the volume of this cylinder, giving your answer to 1 decimal point
The volume of the cylinder is approximately 1413.7 cubic centimeters.
The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height or length of the cylinder.
Since the base of the cylinder has a diameter of 9cm, the radius is half of that, or r = 4.5cm.
The length of the cylinder is given as 20cm.
Therefore, the volume of the cylinder is:
V = πr²h
= π(4.5)²(20)
= 1413.72 cubic centimeters (rounded to 1 decimal place)
Thus, the volume of the cylinder is approximately 1413.7 cubic centimeters.
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Complete question:
Calculate the volume of this cylinder. give your answer to 1 decimal place. Base is 9cm. Length is 20cm.
David biked 12\frac{7}{8}12
8
7
miles on Tuesday and 5\frac{3}{8}5
8
3
miles on Wednesday.
How much farther did David bike on Tuesday than on Wednesday?
David biked [tex]7\frac{1}{2}[/tex] miles farther on Tuesday than on Wednesday.
We are given that David biked [tex]12\frac{7}{8}[/tex] miles on Tuesday and [tex]5\frac{3}{8}[/tex] miles on Wednesday.
In order to find the number of miles David biked farther on Tuesday than on Wednesday, we will subtract the miles biked by him on Wednesday from the miles biked by him on Tuesday as follows -
[tex]12\frac{7}{8} - 5\frac{3}{8}[/tex]
So, first, we will subtract the whole number of parts as follows -
12-5 = 7
Then, we will subtract the fractional parts as follows -
7/8 - 3/8 = 4/8 = 1/2
so we get,
[tex]12\frac{7}{8} - 5\frac{3}{8} = 7\frac{1}{2}[/tex]
Therefore, David biked [tex]7\frac{1}{2}[/tex] miles farther on Tuesday than on Wednesday.
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The accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency. a) Which would you expect to be larger: the median or the mean? Explain briefly. b) Which would you report: the median or the mean? Explain briefly.
Say you have a 92% in a class and you do 2 assignments and they are both worth 50% of your grade. And you get a 2/5 on one of them and a 5/5 on the other. Whats the resulting grade?
Answer:
70%
Step-by-step explanation:
The taj Mahal in India is a square about 95.4 on each side.What is the area of the taj mahal?
The area of the Taj Mahal is 9092.16 square meters (97,890.56 square feet).
What is area of a square?The quantity of square units required to completely cover a square is known as the area of a square. The territory that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square meters serving as the standard unit.
The Taj Mahal has an area of 9092.16 square meters (97,890.56 square feet). We utilise the formula for calculating the area of a square, which is length x width. The Taj Mahal's length and width are both 95.4 metres, therefore we just multiply these two values together. 9092.16 square meters = 95.4 × 95.4 square meters (97,890.56 square feet). This is the Taj Mahal's area.
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The Son has got his Crown On The pharaoh’s outfitters, ‘Cloaks and Crowns’, sell Cloaks and Crowns in 3 sizes – prince, king and emperor (in increasing size order). He wants to kit out his three sons for the forthcoming festival of Ra. Ahmose chooses a bigger cloak than Kamose, but a smaller crown than Thutmose. Both Thutmose’s cloak and crown are larger than Kamose’s, but the size of Thutmose’s crown matches the size of Kamose’s cloak. Which sizes did the pharaoh’s sons each get?
The only possible solution for system is A = 2, B = 1, and C = 3, which means Thutmose got the emperor size crown and cloak, Kamose got the prince size cloak and king size crown, and Ahmose got the king size cloak and prince size crown.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Let's us consider the sizes of the cloaks by C (prince), B (king), and A (emperor)
The sizes of the crowns by 1 (prince), 2 (king), and 3 (emperor).
Now let us write the following system of inequalities:
B > C
A > B
3 = C (Thutmose's crown matches Kamose's cloak)
2 > C
A > 3
A > 2 (Thutmose's crown is larger than the king size crown)
From the fifth inequality, we know that Thutmose's cloak is the largest of all three cloaks, so A must equal C.
Therefore, we can simplify the system of inequalities to:
B > C, A > B, C = 3, 2 > C, A > 3 and A > 2
Hence, the only possible solution for system is A = 2, B = 1, and C = 3, which means Thutmose got the emperor size crown and cloak, Kamose got the prince size cloak and king size crown, and Ahmose got the king size cloak and prince size crown.
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903-814 with solution
Answer:
89
Step-by-step explanation:
903 - 814 =
= (900 + 3) - (800 + 14) =
= 900 + 3 - 800 - 14 = 100 - 11 =
= 89
I hate math why is this necessary
Answer:
3
Step-by-step explanation:
Slope = rise/ run = change in y / change in x = 3 / 1 = 3
this is VERY necessary in all of the engineering and physics worlds of which you have yet to be acquainted...... these fields enable you to have a smart phone, a car, a bank account, a computer , rockets etc.
simplify
1/2 - 1/4 + 1/8
688588478685758486759+2345678909876545355=
Answer:
6.9x10^20
Step-by-step explanation:
688588478685758486759+2345678909876545355=
6.90934158E20
the diagram below shows the graph of y=x^2+2x-3 for the domain -4 2. use the graph to determine the scale used on the x- axis, the value of y for which x= 1.5, the values of x for which y=0 and the range of values of y, giving your answer in the form a
Answer:
no sisiejdirjr diendieje jdisjeidi
Answer:
awnser is b
Step-by-step explanation:
eg 2023 ........................................
