a) The set of all positive powers of 3 (i.e. 3, 9, 27,...) can be recursively defined as follows:
Let S be the set of positive powers of 3.
The base case is S = {3}.
For the recursive case, we can define S as the union of S with the set {3x | x ∈ S}.
In other words, to get the next element in S, we multiply the previous element by 3.
b) The set of all bitstrings that have an even number of Is can be recursively defined as follows:
Let S be the set of bitstrings that have an even number of Is.
The base case is S = {ε}, where ε is the empty string.
For the recursive case, we can define S as the union of {0x | x ∈ S} with {1x | x ∈ S}.
In other words, to get a bitstring in S with an even number of Is, we can either take a bitstring from S and append a 0 or take a bitstring from S and append a 1.
c) The set of all positive integers n such that n = 3 (mod 7) can be recursively defined as follows:
Let S be the set of positive integers n such that n = 3 (mod 7).
The base case is S = {3}.
For the recursive case, we can define S as the union of S with the set {n+7k | n ∈ S, k ∈ N}.
In other words, to get the next element in S, we can add 7 to the previous element. This generates an infinite set of integers that are congruent to 3 modulo 7.
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What should be added to x2 xy y2 to obtain 2x2 3xy class 7?
To obtain the equation 2x² + 3xy from x² xy y², you would need to add 1x² and 2xy to the original equation.
In order to obtain the equation 2x² + 3xy from x² xy y², you must add some terms to the original equation. The equation 2x² + 3xy represents a polynomial of degree 2, with x² and xy as the leading terms.
The original equation, x² xy y², is also a polynomial of degree 2, but it does not have the same leading terms as the desired equation.
By adding terms to the original equation, we can change the coefficients of the leading terms to match those of the desired equation. In this case, we need to add 1x² and 2xy to the original equation.
This can be simplified as x² + xy + y² + x² + 2xy = 2x² + 3xy. The polynomial x² and 2xy should be added to x² xy y² to get 2x² + 3xy.
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The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Determine P(at least 2 heads).
13%
25%
50%
80%
Probability of getting at least 2 heads is 50%.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given the sample space for tossing a coin 3 times as,
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Total number of outcomes in the sample space = 8
At least 2 heads means, heads can be 2 or more, for which the only possibilities are 2 heads or 3 heads.
Number of outcomes having 2 heads = 3
Number of outcomes having 3 heads = 1
P(at least 2 heads) = P(2 heads) + P(3 heads)
= 3/8 + 1/8
= 4/8
= 1/2
= 0.5 = 50%
Hence there is a 50% chance for getting at least 2 heads.
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Answer:
Probability of getting at least 2 heads is 50%.
Step-by-step explanation:
What is Probability?
Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given the sample space for tossing a coin 3 times as,
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Total number of outcomes in the sample space = 8
At least 2 heads means, heads can be 2 or more, for which the only possibilities are 2 heads or 3 heads.
Number of outcomes having 2 heads = 3
Number of outcomes having 3 heads = 1
P(at least 2 heads) = P(2 heads) + P(3 heads)
= 3/8 + 1/8
= 4/8
= 1/2
= 0.5 = 50%
Hence there is a 50% chance for getting at least 2 heads.
a cylinder with a radius of 3 cm and a height of 7 cm. What Is the volume?
Answer:
Volume: 197.92
Formula: π r² h
Step-by-step explanation:
Please help me due tommorow
Answer:
A)57 film a music video
Step-by-step explanation:
Let x represent measure of angle 1.
We have been given that measure of angle 3 is six more than twice the measure of angle 1. So measure of angle 3 would be .
We are also told that measure of angle 2 is 27 less than measure of angle 3, so measure of angle 2 would be .
We have been given that angle 1, angle 2 and angle 3 form a straight line, so the sum of angles 1, 2 and 3 would be 180 degrees.
Upon substituting the expressions for measure of angles, we will get:
Now, we will combine like terms.
The measure of angle 2 would be .
Therefore, the measure of angle 2 is 57 degrees.
How do you construct a perpendicular bisector of Class 9?
A perpendicular bisector is a line that intersects a segment of a line at its midpoint, forming two equal segments.
To construct a perpendicular bisector of a line segment in class 9, the following steps should be followed:
1. Draw the line segment and mark the midpoint of the segment.
2. Take a compass and place the point at the midpoint of the line segment.
3. Adjust the width of the compass such that it is slightly greater than half the length of the line segment.
4. Make an arc above and below the line segment.
5. Draw a line through the two points of intersection of the arc and the line segment. This line is the perpendicular bisector of the line segment.
The formula for the perpendicular bisector is (x - x1) / (x2 - x1) = (y - y1) / (y2 - y1), where (x1, y1) and (x2, y2) are the coordinates of points on the line segment.
To calculate the perpendicular bisector of the line segment:
1. Calculate the midpoint of the line segment using the midpoint formula (x1 + x2) / 2 and (y1 + y2) / 2.
2. Substitute the coordinates of the midpoint and the endpoints into the perpendicular bisector formula.
3. Solve the equation to find the equation of the perpendicular bisector.
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pls help me with thiss bru,h
Sophie plotted thee point in the coordinate plane: (1, 1), (–5, 1), (–3, 5), (–1, 5). What hape i created when thee vertice are connected?
Sophie plotted the point in the coordinate plane: (1, 1), (–5, 1), (–3, 5), (–1, 5) so, when the vertices are connected the shape formed is a rectangle.
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral.
Thus, when Sophie plotted the point in the coordinate plane: (1, 1), (–5, 1), (–3, 5), (–1, 5), the vertices connected form the shape of a rectangle.
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Please help I need help
Answer: e, a, f, c
Step-by-step explanation:
v evenly cuts through line tv and line VS. you can tell because the single line on each side....... rest should be correct
The diagram shows a sector of a circle radius 11cm angle of sector 135 degrees, show that the perimeter of the sector is greater than 47.5
the perimeter of the sector is not greater than 47.5.
What is Perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Given, a sector of a circle radius of 11 cm angle of sector 135 degrees
From the general formula of the Perimeter of the circle:
perimeter = 2 * pi * radius
In our case radius = 11 cm
Thus,
Perimeter = 2 * pi * 11
Primetime = 69.14
Since the arc is 135 degrees
Perimeter of arc = 135/360 * perimeter of whole circle
Perimeter of arc = 135/360 * 69.14
The perimeter of the arc = 25.925cm
Therefore, the perimeter of the sector is not greater than 47.5.
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Jonathan needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 3 hours and charged him $141 for parts. The total was $336. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
The required equation is x × 3 = 336 - 141. The cost of the labor per hour is $65.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x be the cost of the labor per hour.
We know that
x × 3 = labor cost
141 + x × 3 = total cost
We also know that the total cost is $336
So we can write the equation:
141 + x × 3 = 336
Solving for x:
x × 3 = 336 - 141
x × 3 = 195
x = 195/3
x = 65
Therefore, the cost of the labor per hour is $65.
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Find the length of the missing side of the triangle. CORRECT ANSWER GETS SOMETHING IN RETURN!!!
Answer:
the missing side is 29 so point D or bubble 2
Step-by-step explanation:
use the formula a^2 + b^2 = c^2
20^2 + 21^2 = ?^2 find the answer for the squared values
400 + 441 = ?^2 Add the values
841 = ?^2 in order to get rid of the power square root on both sides
_/- 841 = ? solve
29 = ?
what is the sum of the measure of the exterior angles of a regular dodecahon
Answer:
The measure of each exterior angle of a regular dodecagon will be =360∘12=30∘
Question 19xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Answer:
1Step-by-step explanation:
[tex]\mathrm{\cfrac{3^5\times\:10^5\times\:25}{5^7\times\:6^5}}[/tex]
Factor:
6^5= 2^5*3^5
10^5= 2^5*5^5
25 = 5^2
[tex]\mathrm{\cfrac{3^5\times\:2^5\times\:5^5\times\:5^2}{5^7\times\:2^5\times\:3^5}}[/tex]
3^5*2^5*5^5*5^2 = 3^5*2^5*5^7
[tex]\mathrm{\cfrac{5^7\times\:3^5\times\:2^5}{5^7\times\:2^5\times\:3^5}}[/tex]
Now, cancel common factor:-
[tex]\mathrm{3^5\times\:2^5\times\:5^7}[/tex]
[tex]\mathrm{1}[/tex]
-Hope this helps!
evaluate h/4 +(12-y)/3 when h is -12 and y is 3
A.0
B.6
C.8
D.9
Answer:
A) 0
Step-by-step explanation:
h/4+(12-y)/3
-12/4+(12-3)/3
-3+(9)/3
-3+9/3
-3+3
0
evaluate the expression
Answer:
-6
Step-by-step explanation:
−0.125x + 7 = 16
Solve for x
Show work
Answer:
-72
Step-by-step explanation:
-0.125x=16-7
-0.125x=
x=-72
Answer:
x = -72
Step-by-step explanation:
Given equation,
→ -0.125x + 7 = 16
Now we have to,
→ Find the required value of x.
Then the value of x will be,
→ -0.125x + 7 = 16
Subtract RHS with the number 7:
→ -0.125x = 16 - 7
→ -0.125x = 9
Divide RHS with the number -0.125:
→ x = 9 ÷ (-0.125)
→ [ x = -72 ]
Hence, the value of x is -72.
Three grade 8 classes decided to raise money for 2 charities by selling boxes of greeting cards. A box of cards cost $3.80 from the supplier and sold for $6.00. One class sold 150 boxes, the second 175, and the third 225. If the proceeds were divided equally between the 2 charities, how much did each receive?
The amount each charity received is $605
How much did each charity receive?The first step is to determine the total number of boxes sold.
Total boxes sold = 150 + 175 + 225 = 550
The next step is to calculate the profit made from the sales.
Profit = (selling price - cost price) x total boxes sold
Profit = ($6 - $3.80) x 550
Profit = 2.20 x 550 =1210
Amount each charity received = $121/ 2 = $605
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What’s the answer to this math question?
Answer:
Step-by-step explanation:
So we know what a gradient is = y=mx+c So you have to make a triangle with the 2 numbers touching a line and make a triangle the conects to both of them. and then you will get the answer
Write an equation that represents the line.
Use exact numbers.l
An equation that represents the line is Y is (-4/3)x+2 is the solution.
How can you determine a line's precise equation?Y = mx+b, where m is the slope and b is the y-intercept, is the formula for a line's slope-intercept (the point on the y-axis where the line crosses it). Replace m with the value you determined for your slope. In our case, the formula might be written as y = 1x+b or y = x+b if the slope value were substituted.
y=(-4/3)
We have two points since x+2 = -1.33x+2:
(3) and (2) are calculated from the graph.
We are aware that the line's equation is
y=mx+b
m=slope
m=(y2-y1)/(x2-x1)
m=(2-(-2))/(0-3)
therefore the slope is what we have
m=4/-3
m=-4/3
-4/3=-1.3333
We must track down "b"
using the example (0,2)
There are
2=m*0+b
2=b
Finally, here is
Y=(-4/3)x+2 is the solution.
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Give an equation for a logarithmic function that has the following features.
1. The range of the function is (-∞, ∞).
2. The domain of the function is (2, ∞).
3. The vertical asymptote of the function is = 2.
4. The graph does not cross through the point (3, 0).
Any equation in the variable x that contains a logarithm is called a logarithmic equation.
What are the features logarithmic function?The graphs of all logarithmic functions will have the following characteristics: The graph of logarithmic functions passes through the points (1,0). If the base of a logarithmic function is greater than 1, then the graph increases.Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ayLogarithms were invented in the 17th century as a calculation tool by Scottish mathematician John Napier (1550 to 1617), who coined the term from the Greek words for ratio (logos) and number (arithmos)Two kinds of logarithms are often used in chemistry: common (or Briggian) logarithms and natural (or Napierian) logarithms. The power to which a base of 10 must be raised to obtain a number is called the common logarithm (log) of the number.To learn more about logarithmic function refers to:
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Translate the sentence into an algebraic equation. Use x for the variable.
“The sum of a number and 4 is multiplied by 2 and the result is -30.”
Answer:
2(x+4)=-30
Step-by-step explanation:
What is quadrant class 9?
Quadrant Class 9 is a level of mathematics taught in secondary school in the United Kingdom. It is the equivalent of Algebra 1 and Geometry combined in the United States.
This class teaches students how to graph equations, solve equations, and use the properties of shapes to solve problems. Quadrant Class 9 also covers the basics of calculus, such as derivatives, integrals, and limits.
The main focus of Quadrant Class 9 is on graphing equations. Students learn how to plot points on a graph, connect the points to make a line or curve, and solve equations by finding the intersection of two lines. They also learn how to graph the solutions of inequalities and identify the domain and range of a function.
In addition to graphing, students learn how to solve equations using basic algebraic principles, such as the order of operations and the distributive property. They also learn how to solve systems of equations, manipulate polynomials, and find the roots of a quadratic equation.
Quadrant Class 9 also covers the basics of geometry, such as the Pythagorean Theorem, the properties of triangles, and the area and perimeter of shapes. Students learn how to use these skills to solve problems involving angles, area, and volume.
Overall, Quadrant Class 9 is a challenging and rewarding mathematics class that prepares students for higher-level math classes in the future.
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Find the value of the remainder. Enter the value of the remainder (only the number, you do not need to place it over the divisor)
Using synthetic division, the value of the remainder comes out to be -9.
What is synthetic division?
When the divisor is a linear factor, synthetic division is a technique used to carry out the division operation on polynomials. The ability to compute without writing variables when doing polynomial division with the synthetic division makes it an easier technique than the classic lengthy method, which is one of its advantages over the latter.
Two polynomials can be divided using the formula:
p(x)/q(x) = Q(x) + R/(q(x))
where,
The dividend is p(x).
The linear divisor is q(x).
The quotient is Q(x).
The remainder is R
Given expression is [tex]4x^{4} -3x^{3} +6x-10[/tex]
We have to divide this expression by (x + 1) by using synthetic division.
Expression given above can be written as,
4x⁴ - 3x³ + 6x - 10 = 4x⁴ - 3.x³ - 0.x² + 6x - 10
Now on dividing by x = -1 by synthetic division method, we get
-1 | 4 -3 0 6 -10
- -4 7 -7 1
4 -7 7 -1 -9
Remainder of the synthetic division will be -9.
Hence, we rewrite the given expression as, [tex]4x^{3} -7x^{2} +7x+1 -\frac{9}{x-9}[/tex]
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Is an R-squared value of 0.8 good?
In some fields, a good R-Squared reading could be required to meet criteria of 0.9 or above. An R-Squared value above 0.7 is typically regarded as indicating a high level of correlation in the financial industry, whilst a value below 0.4 would indicate a low level of correlation.
What Exactly Is Residual Value?
The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.
A good residual value is what?
Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.
A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.
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Triangulation is a method of finding the location of an object based on measurements made from two other locations.
Triangulation is the method of finding the location of an object based on the measurements made from the two other locations. The above statement is true statement.
Triangulation is the division of a face or plane polygon into a series of triangles, usually with the limitation that each side of a triangle is fully shared by two adjacent triangles. In geometry, triangulation is the division of planar objects into triangles, or more broadly, the division of high-dimensional geometric objects into simplifications. Triangulation of a 3D volume involves subdivision into packed tetrahedra that directly measure distances to points. It is a method for finding the location of the object.
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Kate was ordering the following rational numbers in math class. Please order them in ascending order:
-4.7 , 11 , 13 , -21 , 8 8/9 , 0 , -6 1/2 , 38 , -73
The numbers in the ascending order is given by A , where
-73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38
What is Ascending Order?When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.
Given data ,
Let the set of numbers be represented as set P
The value of set P is P = { -4.7 , 11 , 13 , -21 , 8 8/9 , 0 , -6 1/2 , 38 , -73 }
On simplifying the equation , we get
The larger the negative number , the lesser is its value
And , larger the positive number , the greater is its value
So ,
The ascending order of the numbers are
-73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38
Hence ,
The ascending order is -73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38
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A rectangle has side lengths, in centimetres, of r and r-3
a)Write a sentence to explain why r>3.
b)The perimeter of the rectangle is smaller than 26 cm. Use this information and your answer to part a) to write a double inequality for r.
a) The reason for which r > 3 is because a side length in a figure cannot assume a negative value.
b) The double inequality for r is given as follows: 3 < r < 8.
How to obtain the perimeter of a rectangle?The perimeter of a rectangle of base b and height h is given by the equation presented as follows:
P = 2(b + h).
The dimensions for this problem are given as follows:
b = r.h = r - 3.The perimeter of the rectangle is smaller than 26 cm, hence the inequality is defined as follows:
P < 26.
2(b + h) < 26
b + h < 13 (simplifying by 3 both sides of the inequality).
r + r - 3 < 13
2r < 16
r < 8.
Hence the double inequality is defined as follows:
3 < r < 8.
As a side length cannot be negative nor zero, hence it is also needed that r - 3 > 3 -> r > 3.
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The price of a TV is 540 omr
In a sale it is reduced by 35%
Work out the sale price.
If you get stuck, consider drawing a diagram.
You may want to use a calculator to work out 35% of
540 first...
To calculate the sale price, we need to find out how much the TV is discounted by, which we can do by multiplying the original price by the percentage discount (expressed as a decimal).
35% of the original price can be expressed as 0.35.
so,
Discount = 540 omr * 0.35 = 189 omr
To find the sale price, we can subtract the discount from the original price:
Sale price = Original price - Discount
Sale price = 540 omr - 189 omr
So the sale price is 351 omr.
Determine whether the equation is an identity or not an identity.
tan²0 cos² 0 = 1/csc^2 0
a. identity
b. not an identity
Please select the best answer from the choices provided
What is an example of dilate?
An example of dilation math is a square of side 5 units can be dilated to a square of side 15 units, but the shape of the square remains the same.
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.In mathematics, a dilation is a function f from a metric space M into itself that satisfies the identity d=rd for all points x, y \in M, where d is the distance from x to y and r is some positive real number. In Euclidean space, such a dilation is a similarity of the spaceTo dilate a figure by a scale factor, multiply both the x-coordinate and the y-coordinate of each point by the scale factor. The new points are (4, -1), (6, -10), and (10, 8)To learn more about dilation refers to:
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