The element of this group is {0, 1, 2, 3, ...., 25}, this group is a cyclic group, and 16 is not a generator for this group but 5 is a generator for this group.
How to find element of group under addition modulo?
[tex]Z_{26}[/tex] ≡ Group of integers under addition modulo 26
addition modulo is all addition of integer in ordinary way than remove integral multiple. For example, addition modulo a+mb is a+b than remove all integral multiple m and the result is lower than m (residue).
a) The elements of this group is all the integers remainder after mod 26. So,
x = k (mod 26) where 0 ≤ k < 26
or we can write each of them as {0, 1, 2, ..., 23, 24, 25}
b) Cyclic group is a group that is generated by 1 element. Since, the group is integers under addition modulo with all integers can be generated by adding 1 repeatedly, so the group [tex]Z_{26}[/tex] is cyclic group.
c) As 1 ∈ [tex]Z_{26}[/tex] but there is no m ∈ N such that [tex]16^m[/tex] = 1, but for [tex]5^m[/tex] is
{0, 5, 10, 15, 20, 25, 4, 9, 14, 19, 24, 3, 8, 13, 18, 23, 2, 7, 12, 17, 22, 1, 6, 11, 16, 21}
or in simply way, we can say there is m ∈ N for [tex]5^m[/tex] = 1. So, 16 is not generator of this group, but 5 is generator of this group.
Thus, the number of {0, 1, 2, 3, ...., 25} is the element for this group, cyclic group is a type of this group, and 5 is a generator for this group but 16 is not a generator for this group.
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The graph shows the number of laps kailee ran around a track over a given number of minutes.
(a) What is the slope of the line? Use the slope formula and show your work.
(b) How many laps did Kailee run per minute?
(c) If she continued to run at the same rate, how many laps would she run in 30 min?
The slope of the line is 0.4, Kyle runs (2/5)th of a lap in a minute, and In 30 minutes, she would run 12 laps.
As per the given graph, the slope of the line as:
m = (4.4 - 2.2)/(11 - 5.5)
m = 0.4
The equation of line as:
y = 0.4x + 0
y = (2/5)x
So, Kyle runs (2/5)th of a lap in a minute.
In 30 minutes, she would run:
y = (2/5) x 30
y = 12 laps
Therefore, the slope of the line is 0.4, Kyle runs (2/5)th of a lap in a minute, and In 30 minutes, she would run 12 laps.
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The question seems to be incomplete the correct question has been attached
you roll two fair dice. find the probability that the first die is a 6 given that the minimum of the two numbers is a 4.
The probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.
What is the probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
Two dice are rolled.
Then the sample space (n) = 36
Possible outcomes = {(6,1), (6, 2), (6, 3), (6, 4)}
Probability = 4/36
= 0.11
Hence, the probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.
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The following multiple regression output was generated from a study in which two independent variables are included. The first independent variable (X1) is a quantitative variable measured on a continuous scale. The second variable (X2) is qualitative coded 0 if Yes, 1 if No.Based on this information, which of the following statements is true?If tested at the 0.05 significance level, the overall model would be considered statistically significant.The variable X1 has a slope coefficient that is significantly different from zero if tested at the 0.05 level of significance.The model explains nearly 63 percent of the variation in the dependent variableAll of the above are true.
All of the claims about the multiple regression output are correct. The first independent variable (X1) was a continuous-scale quantitative variable, whereas the second variable (X2) was coded 0 if Yes and 1 if No.
Multiple regression is an effective statistical approach for analyzing the associations between multiple independent variables and a single dependent variable. Multiple regression has numerous uses in the social sciences, and recent research used it to analyze the connection between two independent factors and a single dependent variable.
Finally, the total model is statistically significant, the slope coefficient for variable X1 is considerably different from zero, and the model explains almost 63% of the variance in the dependent variable.
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On September 12, Jody Jansen went to Sunshine Bank to borrow $2,300 at 9% interest Jody plans to repay the loan on January 27. Assume the loan is on ordinary interest: (Use Days in a year table) a. What interest will Jody owe on January 27? (Do not round intermediate calculations. Round your answer to the nearest cent:) Interest 866.00 2 decimal places required. b. What is the total amount Jody must repay at maturity? (Do not round intermediate calculations Round your answer to the nearest cent:) Maturity value 3,166.00 2 decimal places required.
Jody will be forced to repay a total of $2,377.69 when the loan matures.
Ordinary interest, commonly referred to as simple interest, is computed by dividing the annual marginal rate by the 365 days that make up a year. It does not take compounding into account.
The number of days can be calculated as follows:
19(Sep), 31(Oct), 30(Nov), and 31(Dec) add up to 111 days in year 1.
Second-year days: 26 (Jan)
137 days in total
Rate = 0.09 Principal = $2,300
time = 137 ÷ 365
Interest = 2300 × 0.09 × (137 ÷ 365) = $77.69
Amount due at maturity is $2,300 plus $77.69, for a total of $2,377.69.
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please help me with this. Ahhh sooon
Answer:
9x + 16
Step-by-step explanation:
When you are finding the perimeter of each shape, you are essentially combining all of the shape's side measurements together.
In this case, you are given a triangle, which has 3 sides. Add the 3 side's measurements together to obtain the perimeter of the given triangle.
P (Perimeter of triangle) = (3x + 10) + (3x) + (3x + 6)
Combine like terms. Like terms are terms that have the same variables:
P = (3x + 3x + 3x) + (10 + 6)
P = (9x) + (16)
P = 9x + 16
9x + 16 is your answer.
~
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What does negative 4 over 7 > −2 indicate about the positions of negative 4 over 7 and −2 on the number line? (4 points) a is located on the right of −2, and −2 is located on the right of 0 b is located on the left of −2, and −2 is located on the right of 0 c is located to the right of −2 d is located on the left of −2
Answer: Negative 4 over 7 is located to the right of -2
In the number line, the numbers are written in ascending order or from left to right in increasing order,
That is if a < b, where a and b are any real number
⇒ b is located on the right side of an in the number line,
Here, given expression,
negative 4 over 7 > −2
That is,
⇒ Negative 4 over 7 is located to the right of -2
Step-by-step explanation:
Which is the last sentence of the proof? because f + e = 1, a2 + b2 = c2. Because f + e = c, a2 + b2 = c2. Because a2 + b2 = c2, f + e = c. Because a2 + b2 = c2, f + e = 1.
The latest sentence of proof by using the triangle congruence method we can conclude that f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex].
Given that ΔABC and ΔCBD are right triangles
Therefore, one angle of both triangle is of 90°
So, ∠B is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.
Consequently, ∠A is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.
Similarly, When two triangles are similar then their corresponding angles are equal and their corresponding sides are also equal.
Therefore , the two proportions can be rewritten as
a² = cf ( equation 1 )
b² = ce ( equation 2 )
By adding b² on both side of equation 1 then we can write equation 1 as
[tex]a^{2} + b^{2} = b^{2}+cf[/tex]
[tex]a^{2} + b^{2} = ce+cf[/tex]
Because b² and ce are equal and substitute on the right side of equation 1
Using the converse of distributive property in above equation then we get a new equation. That is,
[tex]a^{2} +b^{2} = c(f+e)[/tex]
Because distributive property is a(b+c)=a(b+ac)
a² + b² = c²
Because e + f = c²
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Juan buys 13 bottles of apple juice at the corner store for a total cost of $5.07. Assume
each bottle of juice is the same price. If c represents the total cost in dollars and cents
of the juice for any number, j, of bottles of juice, write a proportional equation for c in
terms of j that matches the context.
The proportional equation for c in terms of j as per the question statement will be equal to c = 0.39(j).
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given information in the question,
Price of 13 bottles = $5.07
Then, the price of each bottle = 5.07/13 = $0.39
As per the statement in the question,
The total cost is represented by c and the number of bottles will be j.
Then, the proportional equation will be,
c = 0.39(j)
As the number of bottles will increase, the total price will also increase with it.
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Which function matches the graph?
-5
-2
3/
7
A. f(x) =
(x + 3)(x - 5)(x + 7)²(x - 2)²
B. f(x) = (x - 3)²(x + 5)²(x-7)(x + 2)
C. f(x) = (x - 3)(x + 5)(x - 7)²(x + 2)²
D. f(x) = (x - 3)²(x + 5)(x-7)(x + 2)²
E. f(x) = (x + 3)²(x - 5)(x-7)²(x + 2)
The local movie theater charges $13 for adult tickets and $7 for children's tickets Yesterday they sold
115 tickets and made $943. How many adult and children tickets did they sell?
Answer:
23 adult tickets and 92 children tickets
Step-by-step explanation:
Answer:
he sold 23 adults tickets and 93 children
Step-by-step explanation:
A fence is to enclose a field and divide it into 3 equal areas. If there is 1600m of fencing available. Find the dimensions of the field that will allow for the maximum area.
The length of the whole field will be 400 while the width will be 200 meters.
What is the perimeter?Perimeter is the addition of an external measure of sides it will always positive.
Perimeter of square = side + side + side + side
The perimeter of the circle = πd where d is the dia of the circle.
As per the given three equal areas have been drawn,
The perimeter of this area will be as,
2x + 4y = 1600
Area A = xy
A = x(1600 - 2x)/4
A = 400x - 1/2x²
To find the maximum area take the first derivative,
dA/dx = =0
400(1) - (1/2)2x = 0
400 - x = 0
x = 400 meter
And, 4y = 1600 - 2(400)
y = 800/4 = 200 meter
Hence " The length of the whole field will be 400 while the width will be 200 meters".
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a variable is normally distributed with mean 22 and standard deviation 7. use your graphing calculator to find each of the following areas. write your answers in decimal form. round to the nearest thousandth as needed. a) find the area to the left of 25. 0.274 incorrect b) find the area to the left of 17. 0.159 incorrect c) find the area to the right of 22. 0.788 incorrect d) find the area to the right of 27. 0.055 incorrect e) find the area between 17 and 30.
The area to the left of 25 is 0.6664, the area to the left of 17 is 0.2389, the area to the right of 22 is 0.5000, the area to the right of 27 is 0.2389, and the area between 17 and 30 is 0.6340.
How to calculate area from normal distribution?
μ = population mean = 22
σ = standard deviation = 7
The area from normal distribution can be calculated using z test or normal distribution formula.
a) The area to the left of 25 is
P(x ≤ 25) = P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= P(z ≤ [tex]\frac{25-22}{7}[/tex])
= P(z ≤ 0.43)
using z table and we get,
= 0.6664
b) The area to the left of 17 is
P(x ≤ 17) = P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= P(z ≤ [tex]\frac{17-22}{7}[/tex])
= P(z ≤ -0.71)
using z table and we get,
= 0.2389
c) The area to the right of 22 is
P(x > 22) = 1 - P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= 1 - P(z ≤ [tex]\frac{22-22}{7}[/tex])
= 1 - P(z ≤ 0.00)
using z table and we get,
= 1 - 0.5
= 0.5000
d) The area to the right of 27 is
P(x > 22) = 1 - P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= 1 - P(z ≤ [tex]\frac{27-22}{7}[/tex])
= 1 - P(z ≤ 0.71)
using z table and we get,
= 1 - 0.7611
= 0.2389
e) The area between 17 and 30 is
P(17 ≤ x ≤ 22) = P([tex]\frac{x-\mu}{\sigma}[/tex] ≤ z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])
= P([tex]\frac{17-22}{7}[/tex] ≤ z ≤ [tex]\frac{30-22}{7}[/tex])
= P(-0.71 ≤ z ≤ 1.14)
= P(z ≤ 1.14) - P(z ≤ -0.71)
using z table and we get,
= 0.8729 - 0.2389
= 0.6340
Thus, the area is 0.6664 for area in the left of 25, the area is 0.2389 for area in the left of 17, the area is 0.5 for area in the right of 22, the area is 0.2389 for area in the right of 27, and the area is 0.634 for area between 17 and 30.
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a rectangular pasture has a perimeter of 1200 feet. the pasture's length is 200 feet more than its width. what is the area of the pasture?
The area of the rectangular pasture is found to be 80,000 ft².
Explain the term Rectangle?A rectangular is a flat, two-dimensional object with four sides. A rectangle has two opposite sides that are parallel to one another and have the same length. A rectangle with the dimensions l and w has an area of l w. The rectangle's perimeter is 2(l + w).Given:
A rectangular pasture does have a 1200 foot circumference. The width of the meadow is 200 feet wider than its length.Let the pasture's rectangular length be l feet.
Given that the rectangular pasture's length being 200 feet longer than its breadth, its width must be w = l200 feet.
The pasture's boundary is;
2(l + w) = 1200
2(l + l - 200) = 1200
2l - 200 = 600
l = 400 feet
Width; w = l - 200
w = 400 - 200 = 200 feet
Rectangular area;
A = l x w
A = 400 x 200
A = 80,000 ft²
Thus, the area of the rectangular pasture is found to be 80,000 ft².
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What are 7 groups of ten + 2 more groups of 10?
Answer: 90
Step-by-step explanation:
7 * 10 = 70
2 * 10 = 20
70 + 20 = 90
consider the triangle formed by the side of the house, the ladder, and the ground. find the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall?
The rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall is [tex]\frac{527}{24}ft^2/sec[/tex].
What is triangle?
Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.
Given:
dx / dt = 2 feet / sec
We have to find dA/dt when x = 7.
Since,
Area = 1/2 x (xy)
A = 1/2 x (xy)
Differentiating both sides with respect to t
[tex]\frac{dA}{dt} = \frac{1}{2}(\frac{dx}{dt}y+\frac{dy}{dt}x)\\[/tex] ..(1)
We have,
x^2 + y^2 = 25^2
plug x = 7
⇒ y = √(25^2 - 7^2)
y = √(625 - 49)
y = √576
y = 24
Now plug x = 7, y = 24, dx/dt = 2 and dy/dt = -7/12 in equation (1)
[tex]\frac{dA}{dt} = \frac{1}{2} (2(24) + (-\frac{7}{12})(7)) \\ \frac{dA}{dt} = \frac{527}{24} ft^2/sec[/tex]
Hence, the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall is [tex]\frac{527}{24}ft^2/sec[/tex].
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What is the sum of three fourths and
seven fourths?
Dylan divided 1/2 pound of butter into 4 equal parts. How much butter was in each part?
Mark as brainiest
Answer:
1/8 pounds
because half of 1/2 is 1/4 and half of that is 1/8 so into 4 eqaula parts ots would be 1/8
Robert swims a lap in the pool. His coach graphs his distance from the starting block.
A. Determine whether each graph is a function. Justify your answer.
B. Construct Arguments - Which graph must be incorrect. Explain
A) Both the graphs A and B are functions, here the vertical lines can intersect the curve A and B more than once. So, A and B graphs are functions.
B) The incorrect graph is A
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
A) Examine the graph to determine whether any vertical lines generated meet the curve more than once. If such a line exists, the graph does not reflect a function. The graph represents a function if no vertical line intersects the curve more than once.
A and B are functions, according to this.
B) A is the incorrect graph.
Because Robert's acceleration will change
Curved lines have varying slopes; they can begin with a very modest slope and then curve quickly (either upwards or downwards) towards a huge slope. In either case, the curving line with a changing slope indicates fast motion (i.e., changing velocity).
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please hurry 121314151617181920
(7 , -3) : Quadrant 4
(0 , 1) : y-axis
(-3 , -2) : Quadrant 3
(4 , 4) : Quadrant 1
Jonah has recorded 32 shows using his cable television service. Each week he records 6 new shows
Answer: he need 6 day to get the 32 show
7x−3(x−1) as another equation
The expression 7x−3(x−1) written as another expression is 4x + 3
How to represent the expression in another form?From the question, we have the following expression that can be used in our computation:
7x−3(x−1)
There are brackets in the above expression
So, the first step is that we remove the bracket
So, we have the following representation
7x−3(x−1) = 7x − 3x + 3
Looking at the equation closely, we have like terms
So, the next step is to evaluate the like terms
Solving further, we evaluate the like terms
7x−3(x−1) = 4x + 3
The above equation cannot be further simplified
Hence, the solution or equivalent of the expression is 4x + 3
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melissa is using synthetic division to divide 3x3−x2−9x+7 by x−1.
Synthetic division yields the result 3x^2 + 2x - 7 when the equation
3x^3 - x^2 - 9x + 7 is divided by x - 1.
What is synthetic division?
Synthetic division in algebra is a technique that requires less writing and calculation than long division to manually divide polynomials into their Euclidean parts. The method can be applied to division by any polynomial, although it is typically taught for division by linear monic polynomials.
Consider the given polynomial 3x^3 - x^2 - 9x + 7.
We have to divide this polynomial by x - 1 using synthetic division.
3x^2 + 2x - 7
________________________
(x - 1)√(3x^3 - x^2 - 9x + 7)
3x^3 - 3x^2
______________________
2x^2 - 9x + 7
- 2x^2 - 2x
__________________________
-7x + 7
- -7x + 7
_________________________
0 + 0
Hence, Synthetic division yields the result 3x^2 + 2x - 7 when the equation 3x^3 - x^2 - 9x + 7 is divided by x - 1.
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Determine whether the pair of lines appear to be parallel or perpendicular.
1. The lines are perpendicular because they are always the same distance apart and never intersect.
2. The lines are parallel because they are always the same distance apart and never intersect.
3. The lines are parallel because they intersect at a right angle.
4. The lines are perpendicular because they intersect at a right angle.
The correct statement about the pair of lines will be;
''The lines are perpendicular because they intersect at a right angle.''
Option 4 is true.
What is Line segment?
Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The pair of lines are shown in figure.
Now,
By figure, we see that;
The lines are perpendicular because they intersect at a right angle.
Thus, The correct statement about the pair of lines will be;
''The lines are perpendicular because they intersect at a right angle.''
Option 4 is true.
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Suppose the original quantity is and the new quantity is . Estimate the percent change. Is this an example of a percent increase or a percent decrease?
There is percent decrease is 12%.
What is Percent decrease?The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease.
Given:
original quantity is 100
new quantity is 88
So, change in quantity = 100-88= 12
and, percent decrease = 12 / 100 x 100 = 12%
Hence, there is percent decrease is 12%.
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suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 6 cubic feet per minute. if the pool has radius 3 feet and height 8 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 6 feet?
The pool's water is changing height at a pace of 0.283 feet per minute.
Given,
Right circular cylinder shaped pool.
The radius of the pool = 3 feet
The height of the pool = 8 feet
Imagine that 6 cubic feet of water per minute is continuously being poured into a swimming pool in the shape of a right circular cylinder.
We have to find the rate of change of the height of the water in the pool when the depth of the water in the pool is 6 feet;
Here,
Due to the swimming pool's right circular cylinder shape, its volume equals;
V(c) = π × r² ×h
Where r is the radius of the base and h the height
We take differentiation on both sides of the equation to get:
dV/dt = π × r² × dh/dt
Since the pool is a right circular cylinder and dV/dt is constant at 6 ft3/min, the rate of change in water height in the pool is independent of water height.
Then:
6 = π × r² × dh/dt
dh/dt = 6 / π × 3²
dh/dt = 8/113,04
dh/dt = 0.283 ft/min
Therefore,
The rate of change of the height of the water in the pool is 0.283 feet/min
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25 POINTS PLS ANSWER WITH GIVE BRAINLY PPLEASE HELPP
The constant of proportionality for the given set of values of x and y is found as 1/2.
Explain the term constant of proportionality?The ratio connecting two given numbers in what is described as a proportional relationship is the constant of proportionality. Constant ratio, rate constant, unit rate, constant of variation, and even rate of change are other terms for the proportionality constant.As k = y/x, just use equation to determine k, the proportionality constant.We say that y changes directly as x or that y is inversely proportional the x if y = k x for some constant k. The proportionality constant for the connection is denoted by the integer k.For the given question,
The table for the two value of x and y are given below.
The value of constant of proportionality for every pair of values will be same.
Thus,
k = x/y
For x = 2 and y = 4
k = 2/4
k = 1/2
Thus, the constant of proportionality for the given set of values of x and y is found as 1/2.
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For what value of x is line m parallel to line n?
Answer:
x=20
Step-by-step explanation:
6x+10 and 130 are equal to each other so to solve for x we set them equal
6x+10=130
-10. -10
6x=120
x=20
Hopes this helps please mark brainliest
Plot each point on the coordinate grid
Answer:
ur not showing the points u need to plot
Step-by-step explanation:
Manuel found a wrecked Trans-Am that he could fix. He bought the car for 65% of the original price of $7200. What did he pay for the car (round answer to the nearest dollar)?
Answer:
4680
Step-by-step explanation:
how many four-digit numbers greater than $2999$ can be formed such that the product of the middle two digits exceeds $5$?
A total of 4970 four-digit numbers that are greater than 2999 can be created so that the middle two digits' product is greater than 5.
Combinations are mathematical operations that count the number of possible combinations for a set of elements when the order of the selection is irrelevant. One can choose the components of combinations in any order. Here, we have to find four-digit number combinations.
The digit in the thousands place should be greater than 2 so that the four-digit number be will greater than 2999. So the possible numbers are 3, 4, 5, 6, 7, 8, and 9. Therefore, this occurs in 7 ways.
The digit in the one's place can be any number from 0 to 9. Therefore, this occurs in 10 ways.
For the middle two digits, the combinations are given by,
If the hundreds digit is 1 then, the tens digit can be 6, 7, 8, and 9. This occurs in 4 ways.
If the hundreds digit is 2 and the tens digit can be from 3 to 9. This occurs in 7 ways.
If the hundreds digit is 3 and the tens digit can be from 2 to 9. This occurs in 8 ways.
If the hundreds digit is 4 and the tens digit can be from 2 to 9. This occurs in 8 ways.
If the hundreds digit is 5 and the tens digit can be from 2 to 9. This occurs in 8 ways.
If the hundreds digit is 6 and the tens digit can be from 1 to 9. This occurs in 9 ways.
If the hundreds digit is 7 and the tens digit can be from 1 to 9. This occurs in 9 ways.
If the hundreds digit is 8 and the tens digit can be from 1 to 9. This occurs in 9 ways.
If the hundreds digit is 9 and the tens digit can be from 1 to 9. This occurs in 9 ways.
The total ways for the middle two digits are 4+7+8+8+8+9+9+9+9=71 ways.
Therefore, the total number of four-digit numbers greater than 2999 is 7×10×71=4970.
The answer is 4970.
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