The set builder form of the set b = {1/10, 1/00, 1/1000} is b = {x | x = 1/10ⁿ, where n is a positive integer}
In mathematics, set builder notation is a concise way of describing a set using a rule or a formula.
Let's explore how we can use set builder notation to write the set b={1/10, 1/100, 1/1000}.
To begin, we need to identify the common property that these elements share. In this case, we can observe that each element is a rational number with a power of ten as the denominator. So, we can write the set b as follows:
b = {x | x = 1/10ⁿ, where n is a positive integer}
In this notation, the vertical bar represents "such that" and separates the description of the element from the rule that defines the set. The letter x is a variable that represents any element that satisfies the rule. We use the power of ten as a common property to describe the set b.
In this set builder form, we can see that b is a set of elements that can be expressed as 1/10 to the power of a positive integer. We can also use set builder notation to define other sets with different properties, such as sets of even numbers or sets of prime numbers.
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Explain why the denominator 6 in 3/6 is not changed when adding fractions
The denominator 6 in 3/6 is should not be changed when adding fractions if other fractions have a denominator of 6, to make the addition easy because 6 will be the lowest common multiple.
Why are denominators not changed when adding fractions?
One of the reasons why the denominator will always stay the same when adding fraction is because the size of the equal pieces does not change when you combine the two fractions together.
For example say you want to add 3/6 + 1/6 + 2/6,
you will notice that all the fractions have equal denominator, so adding the fractions together will have the following result.
3/6 + 1/6 + 2/6 = (3 + 1 + 2 ) / 6
= 6/6
= 1
So the 6 in 3/6 should not be changed if all other fractions you wish to add to 3/6 have 6 as their denominator, because the 6 is lowest common multiple.
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Monique , vic, and Ramon played a card game . Monique had one- third the number of point that Ramon had. Vic had one- half the points that Ramon had. If Ramon had 240 points , how many points did Monique and Vic have.
A rectangle i formed by placing two identical quare ide by ide. The area of the rectangle i 288 quared cm. What i the perimeter of one quare?
The perimeter of one square which combined with other to form a rectangle of 288 cm² is 12 cm.
The area of rectangle is given by the formula -
Area = length × width
Now we know that all the sides of square are same. Also, the identical squares have been kept side by side. So, let us represent one dimension of square with b. Thus, length of rectangle will be (b + b)
Length of rectangle = 2b
Width of rectangle will be b. Now, finding the value of b first.
288 = 2b×b
Performing multiplication
2b² = 288
b² = 288/2
Performing division
b² = 144
b = ✓144
Taking square root
b = 12 cm
The perimeter of one square = 2(length + width)
Perimeter of one square = 2 ( 12 + 12)
Perimeter = 2 × 24
Performing multiplication
Perimeter = 48 cm
Thus, perimeter of one square is 48 cm.
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Suppose that a motorboat is moving at ​ft/s when its motor suddenly​ quits, and that s later the boat has slowed to ​ft/s. assume that the resistance it encounters while coasting is proportional to its​ velocity, so that ​dv/dtkv. How far will the boat coast in​ all?
the boat will coast for a distance of 400 ln(2) ft, which is approximately 277.3 ft.
To find how far the boat will coast, we need to use the concept of differential equations. The equation that describes the velocity of the boat at any time "t" after its motor quits is given by:
dv/dt = -k*v
where "v" is the velocity of the boat at time "t", "k" is the proportionality constant, and the negative sign indicates that the velocity is decreasing with time.
We can solve this differential equation to obtain the velocity of the boat as a function of time:
v(t) = v(0) * e^(-k*t)
where "v(0)" is the initial velocity of the boat (40 ft/sec).
Using the given information, we can set up two equations:
v(10) = 20 (velocity after 10 sec)
v(0) = 40 (initial velocity)
Plugging these values into the equation, we get:
20 = 40 * e^(-10k)
Solving for "k", we get:
k = ln(2)/10
Now, we can integrate the velocity equation to find the distance the boat travels during the coasting period:
d = [tex]\int\limits^{\infty}_{10} {v(t)} \, dt[/tex]
Plugging in the values, we get:
d = (40/k) * [e^(-k*10) - 0] = 400 ln(2) ft
To explain the solution, we used the concept of differential equations to model the motion of the boat as it coasts after its motor quits. We used the given information to solve for the proportionality constant "k", which allowed us to find the velocity of the boat at any time.
Finally, we integrated the velocity equation to find the distance the boat travels during the coasting period. The key to this problem was using the concept of differential equations to model the motion of the boat and setting up the appropriate equations to solve for the unknowns.
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Complete question is:
Suppose that a motorboat is moving at 40 ft/sec when its motor suddenly quits, and then 10 sec later the boat has slowed to 20 ft/sec. Assume, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?
How many solutions does this system have?
Answers:
None
1
2
3
Infinite
How are lim p(x) and lim p(x) calculated if p is a polynomial function?
Limits function lim p(x) can be calculated if p is a polynomial function by:
Identify the degree of the polynomial.Substitute the defined limits with xSimplify and solve the limits function.To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:
Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.
Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:
Lim p(2) = a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀
Then, we just need to simplify our finding:
Lim p(2) = 8a₃ + 4a₂ + 2a₁ + a₀
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Suppose normal distribution has a mean of 98 and a standard deviation of
6. What is P(x ≥ 92)?
O A. 0.16
B. 0.475
C. 0.84
D. 0.975
The probability expressed as P(x ≥ 92) in the normal distribution is; C: 0.84
How to find the probability in normal distribution?We are given that the normal distribution has;
Population mean: μ = 98
Population standard deviation; σ = 6
Sample mean; x' = 92
Thus, z-score is;
z = (x' - μ)/σ
z = (92 - 98)/6
z = -1
Thus, from z-score tables we have;
P(z ≥ -1) = 0.84
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Help ASAP................................
Answer:
Step-by-step explanation:
Top problem:
A = πr² = (22/7)(21)² = 1386 ft²
Bottom problem:
r = D/2 = 20/2 = 10 in
A = (22/7)(10)² = 314 in²
ANSWER ASAP
Three points of a parallelogram are (4, 3), (-4 3), and (2, -3).
What are the coordinates of the 4th point that would complete the parallelogram?
Given parallelogram points are (4,3),(-4 3), and (2, -3).
Let's say A= (4,3) , B=(-4 3) ,C=(2, -3) and D=(x, y)
Parallelogram defined as opposite sides are equal and parallel to each other.
From the properties of parallelogram :
We can say diagonals bisect each other.
From this we can easily find 4th point of parallelogram by using mid point concept.
Mid point formula
(X,Y)=[tex](\frac{x_{1} +x_{2}}{2},\frac{y_{1} +y_{2}}{2})[/tex]
Find mid point between AC line
midpoint (X,Y)= [tex](\frac{4 +2}{2},\frac{3-3}{2})[/tex]
(X,Y)=[tex](\frac{6}{2},\frac{0}{2})[/tex]
(X,Y)=(3,0)
Find mid point between BD Line
Mid point (X,Y)= [tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]
Mid point of AC and BD are equal to each other
(3,0)=[tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]
Equate x-coordinate and y-coordinate.
[tex]3=(\frac{-4 +x}{2})[/tex] and [tex]0=(\frac{3+y}{2})[/tex]
6=-4+x and 0=3+y
x=10 and y=-3
Therefore ,the coordinates of the 4th point is D(x, y)=(10,-3)
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The coordinates of the fourth point that would complete the parallelogram are (10, -3).
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
We know A, B, and C, where A = (4, 3), B = (-4, 3), and C = (2, -3).
To determine the fourth point, which represents D.
First, we need to find the vector representing side AB.
Subtracting the coordinates of point B from the coordinates of point A. So:
AB = A - B = (4, 3) - (-4, 3) = (8, 0)
Next, we need to find a point that is on the line that is parallel to AB and passes through point C.
The vector CD (where D is the point) is equal to AB. So:
CD = AB = (8, 0)
We know that C = (2, -3),
We can start by adding CD to C to get D:
D = C + CD = (2, -3) + (8, 0) = (10, -3)
Therefore, the coordinates of the fourth point are (10, -3).
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suppose 4 math majors and 6 computer science majors randomly take seats in the front row of a classroom. a. what's the probability the math majors are seated together? b. what's the probability the math majors are seated together and the computer science majors are seated together?
The probability the math majors are seated together is 0.028 and all seated togeather with their group is 0.0047.
Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.
Probability determines the likelihood of an event occurring.
P(A) = f / N. Odds and probabilities are related, but odds depend on probabilities. Before we can determine the probability that an event will occur, we first need the probability.
total number of teacher is 10
so number of ways total 10 teacher seat = 10!/(6!*4!)
= 210
and
the number of ways the math majors are seated together
= 6
probability = 6/210 = 0.028
the number of ways the math majors are seated together and the computer science majors are seated together
= 1
probability = 1/210
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Segment has endpoints (−7, 14) and (11, 5). Point lies on at (−3, 12).
What is the ratio of to ?
Last time I asked the question Brainly decided to delete like 90% of my question.
The ratio of the coordinate point on the line is 2 to 7.
What is the ratio of the point on the coordinate?The ratio of the coordinate point on the line is calculated as follows;
Let the coordinate points = (xp, yp)
Let the ratio of the line = a:b
xp = x₁ + (a/(a+b) (x₂ - x₁)
yp = y₁ + (a/a+b) (y₂ - y₁)
-3 = -7 + ( a/a+b)(11 - - 7)
-3 = -7 + (a/a+b)(18)
-3(a + b) = -7(a+b) + 18a
7(a + b ) - 3(a+b) = 18a
7a + 7b - 3a - 3b = 18a
4b = 14a
4/14 = a/b
2/7 = a/b
2 : 7 = a : b
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Express 0.10670.10670, point, 1067 as a fraction.
Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.
Step-by-step explanation:
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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Jordan bought a $300,000 house, paying 10% down, and getting a 30 year loan with 3% interest for the remaining amount.
How much is the loan amount going to be?
What will her monthly payments be?
How much interest will she pay over the life of the loan?
Answer:
The down payment that Jordan made on the house was $300,000 x 10% = $30,000. So, he financed $300,000 - $30,000 = $270,000.
where
M = monthly payment
P = loan amount ($270,000)
r = monthly interest rate (3% / 12 months = 0.003)
n = number of payments (30 years x 12 months/year = 360)
This comes out to a monthly payment of approximately $1,173.38.
To simplify
The loan amount is- $270,000
Her monthly payment will be- $1,173.38
The amount of interest she will pay is- $8,100
A phone sells for $230. It is now on sale for 30% off. How much money will April save if she buys the phone on sale?
If the phone is in sale of 30% off, the money April save if she buys the phone on sale is $69.
A sale is a reduction of the basic price of a good or a service. It can occur on any stage in the process of production.
It is given that a phone sells for $230. It is now on sale for 30% off.
Now, Cost price = $230
sale percentage = 30%
so, the sale price = [tex]230 \times 30\%\\[/tex]
or [tex]230 \times \frac{30}{100}[/tex] = $69
therefore, the money April will save if she buys the phone on sale is $69.
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You want to carpet your 12 ft. by 16 ft room. If the carpet you have chosen cost $10 per square foot, how much will it cost to carpet your room?
At a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.
What are the parameter for determining square foot?The rectangle's area in square meters The area's width and length should be measured in feet. To calculate area, multiply your length by your width. Use our length converter to convert your measures if they aren't already in feet.
Area is length times breadth, or 12 feet by 16 feet, or 192 square feet. The cost of the carpet is $10 per square foot. By dividing the square footage of the room by the price per square foot, we can get the overall cost to carpet it.
Total cost is equal to Area. Cost per square foot is $1920 or 192 square feet (around 18 m2) times $10 per square foot.
Therefore, at a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.
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A 3 inch radius circle is drawn inside a 7 inch radius circle. If you throw a dart at these circles, what is the probability AS A PERCENT that you land inside the smaller circle? Round to the nearest whole percent. Use 3.14 for pi.
Answer:
Step-by-step explanation:
Help ASAP please. !!!!
What do a the answer to x+30=4x+9
find x or x= blank
Answer:
Step-by-step explanation:
4x + 9 = x + 30
3x + 9 = 30
3x = 21
x = 7
x + y = -5 is it a solution
Answer: The equation X + y = -5 represents a straight line in a two-dimensional plane. To determine whether a specific point (X, y) is a solution of the equation, you can substitute the values of X and y into the equation and see if it holds true. If the equation is satisfied, then the point (X, y) is a solution. If the equation is not satisfied, then the point (X, y) is not a solution.
For example, if X = 2 and y = -7, then the equation becomes:
2 + (-7) = -5
-5 = -5
Since the equation holds true, the point (2, -7) is a solution of the equation X + y = -5.
Step-by-step explanation:
Please help with 3 4 and 5
What is the area of the shaded region? Round to the nearest tenth of a centimeter.
The area of the shaded region found using trigonometric ratios is about 86.6 square centimeters
What are trigonometric ratios?Trigonometric ratios are expressions of the relationship between the interior angle of a right triangle and the ratio of two of the sides of the triangle.
Whereby, the inscribing figure of the quadrilateral is a regular hexagon, we get;
Interior angle of a regular hexagon = 120°
The 10 cm segment bisects the top vertex angle of the regular hexagon, which together with the 5·√3 cm side and trigonometric ratios, indicates that we get;
sin(60) = s/(5·√3) = (√3)/2
Where;
s = The side length of the regular hexagon
(5·√3)/s = (√3)/2
s = (5·√3)/((√3)/2) = 10
The side length of the regular hexagon, s = 10
The area of the regular hexagon, A = ((3·√3)/2) × s² = (1/2)×6 ×s ×a
Where;
a = The apothem = 5·√3
Therefore; A = ((3·√3)/2) × 10² = 150·√3
A = (1/2)×6 ×10 × 5·√3 = 150·√3
Area of the quadrilateral = 4 × (1/2) × 5·√3 × 10 = 100·√3
Area of the shaded region = Area of the hexagon - Area of the quadrilateral
Therefore;
Area of the shaded region = 150·√3 - 100·√3 = 50·√3 ≈ 86.6
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What is the range of function f?
A.{y|4 < y < ∞}
B. {y|-∞}< y < ∞}
C. {yl-∞ < y < 0}
D.{y|-∞< y < 4}
sophia paid $3,360,00 in taxes in 2010. her taxes rose to $4,848,60 in 2011 what was the percentage increase in her taxes from 2010 to 2011
The percentage increase in her taxes from 2010 to 2011 is 44.30%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Sophia paid $3,360,00 in taxes in 2010 and her taxes rose to $4,848,60 in 2011.
So, The amount of tax increase is $(484860 - 336000) = $148860.
Therefore, The percentage increase is,
= (148860/336000)×100%.
= 44.30%.
The net amount change will now be divided by the starting total, and the result will be multiplied by 100% to determine the percentage change.
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Describe how the volume of three tennis balls, each with a diameter of 2.7 inches compares to the volume of their packaging, which is a cylinder that has the same diameter and a height of 8.1 inches. Explain or show your work.
Answer:
Step-by-step explanation:
The volume of the three tennis balls combined is approximately 4.88 cubic inches. The volume of the packaging cylinder is approximately 50.33 cubic inches. Thus, the volume of the three tennis balls is about 9.7% of the volume of their packaging cylinder.
To calculate this, we can use the formula for the volume of a sphere (V = 4/3 x π x r3) and the formula for the volume of a cylinder (V = π x r2 x h).
The radius of each tennis ball is half the diameter, or 1.35 inches. So, the volume of each tennis ball is 4/3 x π x (1.35)3 = 4.88 cubic inches.
The radius of the cylinder is the same as the diameter of each tennis ball, or 2.7 inches. The height of the cylinder is 8.1 inches. So, the volume of the cylinder is π x (2.7)2 x 8.1 = 50.33 cubic inches.
The volume of the three tennis balls is 4.88 x 3 = 14.64 cubic inches. The volume of the packaging cylinder is 50.33 cubic inches. Thus, the volume of the three tennis balls is 14.64 ÷ 50.33 = 0.097 = 9.7% of the volume of their packaging cylinder.
answer the following question in the space provided to move forward.
1. What function did you enter?
2. What was the "y" or "f(x)" when x = 2 for your function?
1. The function for this problem is defined as follows: y = 2x + 3.
2. The numeric value of the function at x = 2 is given as follows: y = 7.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
We define a function as follows:
y = 2x + 3.
At x = 2, the numeric value is found replacing the lone instance of x by 2, hence:
y = 2(2) + 3
y = 7.
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__ % of 90 is 90?
O 90%
O 100%
O 10%
O 50%
Answer:
100
Step-by-step explanation:
I hate that I have to use 20 characterz
How do you find the measure of each angle indicated? m
The thermostat in Steffi’s storage room is set to 56°F. The actual temperature variance in her house can be modeled by the inequality |t − 56| ≤ 3. Plot the range of possible temperatures in her storage room.
The range of possible temperatures in Steffi's storage room is between 53°F and 59°F, inclusive.
What is Inequality?
An inequality is a mathematical statement that compares two values, expressing that they are not necessarily equal. It is often represented using one of the following symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
For example, "x > 5" is an inequality that states that the value of x is greater than 5. Similarly, "y ≤ 10" is an inequality that states that the value of y is less than or equal to 10.
Inequalities are commonly used in algebra and other areas of mathematics, as well as in many real-world applications, to express relationships between values that are not necessarily equal.
The inequality |t − 56| ≤ 3 represents all temperatures within 3 degrees of 56°F, including both those above and below 56°F.
We can represent this range graphically as a horizontal line segment centered at 56°F with a length of 6 units (3 units on either side of 56°F).
Thus, the range of possible temperatures in Steffi's storage room is between 53°F and 59°F, inclusive.
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Describe a sequence of transformations that exhibits the similarity between the pair of figures shown.
Answer:
Reflection across the x-axis followed by dilation by a scale factor of with the center of dilation at the origin
Step-by-step explanation:
Rectangle EFGD has vertices at points E(-6,8), F(0,8), G(0,1) and D(-6,1).
1 transformation - reflection across the x-axis with the rule
So, the image rectangle E''F''G''D'' has vertices with coordinates
2 transformation - dilation by a scale factor of with the center of dilation at the origin. This transformation has the rule
Thus,
These are exactly vertices of rectangle E'F'G'D'.
