Answer: hi
The answer will be 3x−11z
Step-by-step explanation:
have a great day ^_^
1+1+1-5+2+2+2+4-8 x 100 +1
Answer:
-792
Step-by-step explanation:
According to PEMDAS, you would multiply 8 x 100 first making the equation
1+1+1-5+2+2+2+4-800+1
then combine like terms, 8-800+1
Since 8 is smaller than 800, you would get a negative number, -792
then you add 1, making your answer -792
On the unit circle, how many radians would the point (-1,0) pass if rotated counterclockwise until it first reaches (root3/2,-1/2)?
The radians that the point (-1,0) would pass if rotated counterclockwise until it first reaches (√3/2,-1/2) is 2π/3.
How do we get the radians?When a point on the unit circle is rotated counterclockwise, it traces out an angle in radians. To find the number of radians that the point (-1,0) would pass if rotated counterclockwise until it first reaches (√3/2,-1/2), we can use the fact that the point (-1,0) corresponds to an angle of π radians on the unit circle, and the point (√3/2,-1/2) corresponds to an angle of 5π/3 radians on the unit circle.
To find the number of radians passed, we need to subtract the initial angle (π) from the final angle (5π/3), so (5π/3 - π) = 2π/3 radians.
Therefore, the point (-1,0) will pass 2π/3 radians when it is rotated counterclockwise until it first reaches (√3/2,-1/2)
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PLEASE I NEED HELP PLS THANK U SM MATH
In the given circle graph, central angle of people like to travel by boat is 72°.
What is circle graph?Circle graphs also known as pie charts are one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent real-world information. It is used to visualize information and data.
Given that, A travel magazine surveyed 500 of its adult readers about their favorite ways to travel.
The circle graph below shows that 125 people like to travel by train, 275 people like to travel by airplane, and 100 people like to travel by boat.
In a circle graph, the whole circle which subtends a 360-degree angle at the center is broken into different.
Central angle of people like to travel by train:
125/500 ×360°
= 90°
Central angle of people like to travel by airplane:
275/500 ×360°
= 198°
Central angle of people like to travel by boat:
100/500 ×360°
= 72°
Therefore, in the given circle graph, central angle of people like to travel by boat is 72°.
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560/17 participate in a football tournament if each team plays against every other team ones, how many matches will be played tota
According to the information, it can be inferred that the total matches that would be played in total are 160,461.
What is a mathematical combination?A combination is a term to refer to an arrangement of elements in no particular order. For example:
When we put together a sandwich with salami, ham and turkey. The order in which the deli meats are placed does not matter as long as they are in a sandwich. There is only one way to stack the meat on the sandwich when the order doesn't matter.
How to calculate how many matches will be played in total?To calculate how many matches will be played in total we have to perform the following procedure:
[tex]= ^{567} C_{2} \\= \frac{(567)!}{2!565!} \\= \frac{567 * 566 * (565)!}{2 * (565)!} \\= 567 * 283\\= 160,461\\\\[/tex]
As we can see after the combination, the number of games that would be played in this tournament would be 160,461.
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A depth finder shows that the water in a certain place is 620 feet deep.The difference between d,
the actual depth of the water, and the reading is |d-620] and must be less than or equal to 0.05d. Find the minimum and maximum values of d, to the nearest tenth of a foot.
Answer:
Step-by-step explanation: ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠆⠒⠒⢄⡂⠄⠀⠀⠀⠐⡓⢶⠶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⣠⠞⠁⠠⠉⠀⠂⠉⠐⠡⠪⠔⡡⣜⢢⠌⡀⠀⠂⡜⢪⡱⣋⢾⣱⢫⡗⣿⣲⠱⣏⡾⣙⣿⣿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣐⣈⣅⣩⣝⢢⣝⣣⢞⡳⢌⡓⢮⢖⡭⣚⡵⢧⣟⡾⣝⡾⣯⣟⣷⡿⣽⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⢀⣴⣾⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠰⠉⠰⠠⢍⠢⡵⡹⣬⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⣿⣷⣄⠀⠀⠀⠀
⣤⣶⣿⡿⠛⠁⠀⣾⣿⡿⠿⠿⠟⠟⠻⢛⠛⠛⠉⠉⠂⠁⠀⠀⠰⢡⠙⡬⢳⡱⢯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⣿⣧⡄⠀⠀
⣿⣿⣯⣄⡀⠀⢼⣿⣷⣶⣶⣤⣤⣤⣀⣄⣀⣀⡀⡀⢀⡀⠅⢢⣑⢪⡱⡭⢧⣻⡽⣞⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣷⣄
⠀⠉⠻⢿⣿⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⢷⣎⣧⢳⡹⡷⣭⢿⡽⣾⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣶⣾⣿⣿⣿⠟
⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣳⡾⣭⢷⣻⢽⣹⢯⣟⣿⡿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡿⠋⠉⠀⠀⠀⠀
⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣟⢷⣫⣽⢳⡝⡾⣭⣟⣾⢿⣽⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀
⠀⠙⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣛⠶⣙⢮⣓⢮⢳⡙⢴⣋⢾⡽⣿⣻⣾⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⡳⣌⠿⣱⡮⡝⣎⢧⣛⢦⣯⢿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠙⠛⠙⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⣞⣿⣟⣷⣽⣞⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣶⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣙⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
How do i solve 6/8 divided by 9/8?
JKLM is a parallelogram. JN = 5 ft, and KN = 7 ft. Solve for KM
KM= ft?
The length KM is equivalent to 8.61 ft.
What is a parallelogram?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
Given is that JKLM is a parallelogram such that JN = 5 ft and KN = 7 ft.
We can write that -
KM² = JN² + KN²
KM² = 5² + 7²
KM² = 25 + 49
KM² = 74
KM = √74
KM = 8.61
Therefore, the length KM is equivalent to 8.61 ft.
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Graph the linear inequality y < 3x using slope-intercept form.
Given inequality:
y < 3xTo graph it first, consider line:
y = 3xFind two points on the line.
x = 0 ⇒ y = 3*0 = 0, so the point is (0, 0)x = 1 ⇒ y = 3*1 = 3, the point is (1, 3)Now, plot the two points.
Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.
The last step, shade the area below (to the right) the line. Below the line because 'y <' means 'y-values less than' which appears below the line.
Answer:
See attachment.
Step-by-step explanation:
Given linear inequality:
[tex]y < 3x[/tex]
When graphing inequalities, temporarily replace the inequality sign for the equals sign:
[tex]\implies y=3x[/tex]
Find two points on the line by substituting two values of x into the equation:
[tex]x=0 \implies y=3(0)=0 \implies (0, 0)[/tex]
[tex]x=1 \implies y=3(1)=3 \implies (1,3)[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given linear inequality:
Plot points (0, 0) and (1, 3).Draw a dashed straight line through the points.Shade under the dashed line.Part B
Select the correct inequality symbol to complete the inequality.
d
Choose...
16
The complete inequality is d ≥ 3.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
We have the number line graph.
Let d be nay number in the real line.
And in the number line,
the line have the closed circle at 3 and increasing to the right to 3.
That means, the inequality,
d ≥ 3.
Therefore, the inequality is d ≥ 3.
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The complete question is given in the attached image.
A rectangle has a length tht is five times longer than its width. If the perimeter of the rectangle is 12 inches what is the width
The width of the rectangle is 1 in.
What is rectangle?A rectangle is a type of parallelogram, having each angle right angle and equal diagonal.
Given that, A rectangle has a length that is five times longer than its width. and the perimeter of the rectangle is 12 inches
Perimeter of a rectangle = 2(length+width)
Let the width be w then length will be (5w)
Therefore,
(w+5w)2 = 12
6w = 6
w = 1
Hence, the width of the rectangle is 1 in.
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A geometric sequence begins with −4, 20, −100, 405, … Which option below represents the formula for the sequence? f(n) = −5(−4)n−1 f(n) = −4(−5)n−1 f(n) = −5(−4)n f(n) = −4(−5)n
The equation that represents the formula for the sequence is f(n) = −4(−5)^n−1
What is geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
The ratio of any term to the one that precedes it should be the same for all terms. If they are all the same, then r, the common difference, is that value
The nth term of a geometric sequence is given as
a(n) = ar^n -1
where a is the first term which is -4
r is the common ratio = 20/-4 = -5
Therefore f(n) = -4(-5)^n -1
Therefore the expression that represents the formula of the sequence is f(n) = -4(-5)^n - 1
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There are 16 ounces in 1 pound, so the expression z/16, where z represents the number of ounces, can be used to find the number of pounds for any given number of ounces. How many pounds are in 40 ounces?
Answer:
40 ounces is equal to 2.5 pounds------------------------
Use the given expression z/16, substitute z with 40 and calculate:
z/16 = 40/16 = 2.5 poundsPLEASE HELP!!!!
Find the greatest common factor. 5x^2a+5xa^2
The greatest common factor of the expression 5x²a + 5xa² is 5xa
How to find greatest common factor of 5x²a + 5xa²?To find the greatest common factor (GCF) of the expression 5x²a + 5xa², we need to find the greatest term that can divide into both terms in the expression.
In this case, the GCF is 5xa, as it can divide into both 5x²a and 5xa².
We can check this by dividing both terms with 5xa:
5x²a + 5xa² = (5xa)(x) + (5xa)(a) = 5xa (x + a)
Thus, the GCF of 5x²a + 5xa² is 5xa.
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Please help I need this very quick please
Answer:
The answer is that a(t) is decreasing from 5 to 6 minutes.
Step-by-step explanation:
The other answers do not make sense, except for one which may be confusing. That answer is that a(t) is negative from 5 to 6 minutes.
The graph, however, while decreasing, is never negative, as the distance can never be a negative measurement. Nor is the graph slanted up and to the left.
If the figure below is translated in the direction described by the arrow, what will be the new coordinates of point D after the transformation?
The new coordinates of point D after the transformation(-4 -4)
How can new coordinates be found after translation?If the following figure is translated in the manner given, then - 1By adding the value of the horizontal translation to the initial x-coordinate (adding a negative amount if translating to the left), one may get the new x-coordinate of the moved point.A point moves along the x-axis when it is translated to the right or left, changing its x-coordinate. As a result, if a point is moved one unit to the right, its x-coordinate rises by one unit, changing the value of the point (x,y) to (x+a,y).The new coordinates of point D after the transformation (-4 -4).To learn more about coordinates refer to:
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Find the value of x and m
a man jumps from a great height and falls freely to the earth. another man jumps from the same height 1 second later. how’s much are the two men separated by, 2 seconds after the second man jumps
Answer:
24.53
Step-by-step explanation:
d = (1/2)gt²
First man travels 1 sec + 2 sec = 3 sec
d = (1/2)(9.81 m/s²)(3 s)² = 44.15 m
Second man travels 2 sec
d = (1/2)(9.81 m/s²)(2 s)² = 19.62 m
Distance between the 2 men:
44.15 m - 19.62 m = 24.53 m
Jewelers emphasize that the price of a diamond is
determined by cut, carat weight, color and clarity.
Draw a line that passes through the points
(0.35,1629) and (0.12,334.50).
Use your line to predict the price of a 0.17-carat
diamond.
C
Price
Check
X
Question 2
Price (U.S. $)
1500
1000
500-
T
√
On solving the provided question, we can say that the provided coordinates are(0.35 , 1629) and (0.12 , 334.50) the equation of line that can be formed it [tex]334.50x = 1629y - 0.47 = 0[/tex]
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
the provided coordinates are
(0.35 , 1629) and (0.12 , 334.50)
the equation of line that can be formed it
y1--y = m (x - x1)
1629y - 0.35 = 1(334.50x - 0.12)
334.50x = 1629y - 0.47 = 0
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the mean of 2,10,9 is what
Answer:
7.
Step-by-step explanation:
Mean = (2+10+9)/3
= 21/3
= 7.
Answer:
the mean is 7
Brief explanation:
To find the Mean of a set we add all the numbers first.
Remember that the Mean relies on a sum.
So we just add up 2 + 10 + 9 = 21
Then divide 21 by 3 (3 because there are 3 numbers in this set) :
21 : 3 = 7
so how do we find the Mean?We take all the numbers in the set, and divide by how many numbers we have in this set.
--
A student lifts up a spring scale attached to a block on a table. While the block is still resting on the table, compare the effort force to the force of gravity
The relation between effort force and the force of gravity can be represented as, Fₐ < Fₙ
What is Force ?The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.
Given that,
A student lifts up a spring scale attached to a block on a table
The block is still resting on the table
The relation between effort force to the force of gravity = ?
Suppose,
The effort force = Fₐ
The force of gravity = Fₙ
block is still resting on the table,
it means effort force is less than the force of gravity,
To move upward, it is required to apply more effort force,
but, here effort force is less
So, It can be written as,
Fₐ < Fₙ
Hence, the relation between both the forces is Fₐ < Fₙ
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I NEED HELP ON THIS PART
Because a cubic function is a polynomial function, which are continuous curves, the domain of a cubic function is all real numbers.
Do cubic functions possess three roots?All odd-degree polynomials have at least one real root; a cubic function has one to three real roots, which may or may not be distinct. A cubic function's graph always has one inflection point. It might have a local minimum and local maximum as its two critical points.
What are the cubic function's minimum and maximum?The cubic function [tex]f(x) = x^3 + x^2 + x + 1[/tex] has a local maximum at x = 1 and a local minimum at x = 1/3. A cubic function can also have two local extreme values (1 max and 1 min).
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5c - 4c + c; = 2, = 5, and =– 3
Answer: 0
Step-by-step explanation:
c2+2c−24=0
The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
Using the general depreciation calculation, y = A(1 - r)^t, the car will be worth $12528.15 after 4 years.
How to calculate the car's value in four yearsY = A(1 - r)^t, is the general depreciation formula, which is used to solve the car's worth.
Description of the variables
y is the current value and where =?
Original cost was $24,000,
rate of depreciation was 15%, and
time was measured in years. = 4 years
plugging in the values
current value, y = A(1 - r)^t
current value, y = 24000 * (1 - 0.15)^4
current value, y = $12528.15
The car has been depreciated to $12528.15
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complete question
The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years?
Evaluate The Following Integral If R [0, 1] X [0, 1]. 3yexy DA
Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].
What is integral ?
An integral is a mathematical concept that represents the area under a curve, or the accumulation of a quantity over a given interval. Integrals are a fundamental concept in calculus, which is the branch of mathematics that deals with the study of rates of change and accumulation. In other words, an integral can be thought of as the sum of an infinite number of infinitesimal "slices" of the quantity being measured, over a given interval. Integrals can be used to solve a wide variety of problems.
The integral is evaluated as follows,
∫[0,1]∫[0,1] 3yxy dydx
= 3∫[0,1] yxy dxdy
= 3 * (1/4) * ∫[0,1] x dxdy
= 3 * (1/4) * (1/2) * x^2 dy
= 3 * (1/4) * (1/2) * (1/3) = 3/24
Hence , Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].
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please help asap!! I'm doing a semester test! 16 points + brainly for correct answer!!
A regular-size box of cereal measures 3 1/2 inches by 8 1/2 inches by 15 inches. The manufacturer also sells an individual-size box that has a volume that is 1/10 of the volume of the regular-size box.
What is the volume of the individual-size box of cereal?
Enter your answer as a MIXED NUMBER IN SIMPLEST FORM by filling in the boxes.
Answer: 44 5/8
Step-by-step explanation:
Regular Volume: (3.5)(8.5)(15)= 446.25
Individual Volume (1/10 of regular): 446.25/10= 44.625
44.625 as Fraction: 44 5/8
jonah is playing a game with his frind rita.there using a spiner below for there game.If jonah spins the spinner twice ,which of these reprensents the possible outcomes of his spin
It all depends on how the spinner is set up, what symbols or numbers it contains and how it is marked.
What is symbol?Symbols are an important part of human communication. They are used to convey a specific meaning, feeling, or idea. Symbols can be visual, such as an object or gesture, or verbal, such as a word or phrase. Symbols are used to represent a concept or idea, often in a way that is easier or more efficient than using words.
The possible outcomes of Jonah's spin could be any of the following:
1. Two of the same numbers, e.g. both 7s or both 11s.
2. Two different numbers, e.g. 8 and 4.
3. One number and a symbol, e.g. 5 and the star.
4. Two symbols, e.g. the heart and the diamond.
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If the social security tax is 6.2% and the Medicare tax is 1.45% and Murr annual salary is 57,285.50 then what is murrs annual social security deduction
Answer: Murr's annual social security deduction is the amount of money he pays in social security taxes. Social security tax is 6.2% of Murr's annual salary. To find the annual social security deduction, we can multiply Murr's annual salary by the social security tax rate:
57,285.50 x 6.2% = 3,541.829
Murr's annual social security deduction is 3,541.829
Note that Medicare tax is 1.45% and it's calculated separately, if you want to calculate it you can use the same formula:
57,285.50 x 1.45% = 829.4078
So the total Social security and Medicare tax is 3,541.829 + 829.4078 = 4,371.2368
It's important to note that these are the federal Social Security and Medicare taxes, there might be additional state taxes or deductions that are not included.
Step-by-step explanation:
I need to know functions
An algorithm that converts one number into a different one is called a function.
What are the essentials of functions? A function is an algorithm that transforms one number into another.What the function receives as input is referred to as the independent variable or function's argument.The output of the function is referred to as dependent variables. Functions come in 4 different categories:the return values and arguments of functions.There are arguments and a value returned by this function:arguments-based functions without return values.functions that have both return values and no arguments.the absence of return values and arguments in functions.Chapter 1: Operation Function theory is not particularly difficult, yet students struggle because its fundamentals are unclear.Chapter 1 of Mathematics 2: Function .The human mind developed Function Theory to increase one's capacity for thought.To learn more about functions refer
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For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. {[ 6a-2c -5b-5c -6a+ 5b+ 2c -6a+ 2c]:a b c in R]
(a) A basis for a subspace is a set of linearly independent vectors that span the subspace. To find a basis for this subspace, we can use the following steps:
Write the given set of vectors as the rows of a matrix, with each vector as a row.
Use row-reduction (Gaussian elimination) to put the matrix in row-echelon form.
The non-zero rows of the row-echelon form matrix form a basis for the subspace.
So, we get the matrix:
| 6a - 2c | -5b - 5c | -6a + 5b + 2c | -6a + 2c |
Using row-reduction, we can simplify the matrix to:
| 1 - 1/3 | 0 | 1/3 | -1/3 |
The non-zero rows are {[ 1 - 1/3 0 1/3 -1/3 ]}
So, a basis for the subspace is:
{[ 1 - 1/3 0 1/3 -1/3 ]}
(b) The dimension of a subspace is the number of linearly independent vectors in a basis for the subspace. In this case, the basis for the subspace has only one vector, so the dimension of the subspace is 1.
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Short answers
a) For each matrix, describe the transformation that is
achieved.
b)
A further transformation matrix D is required which combines
the effects of matrices A and B. Explain why care must be
taken in the ordering of transformation matrices.
This could result in an unexpected transformation. Therefore, the order of the matrices must be taken into account when combining them.
What is matrix?Matrix is a mathematical entity composed of elements arranged in rows and columns. It is used to represent and manipulate various types of data and is commonly used in scientific and engineering applications. Matrices are useful for representing linear equations and transformations of vector spaces, such as scaling and rotation. They can also be used to store data and perform calculations on that data.
Matrix A is a scaling matrix which is used to change the size of an object. This transformation is achieved by multiplying each component of the vector by a value, resulting in a larger or smaller object.
Matrix B is a rotation matrix which is used to rotate an object. This transformation is achieved by multiplying each component of the vector by a coefficient which is then added to the other components, resulting in a rotated object.
Matrix D is a combination of matrices A and B, where the effects of matrix A are applied first and then the effects of matrix B are applied. Care must be taken when combining the two matrices because the order of the transformations matters; applying the effects of matrix B first would result in a different transformation than applying the effects of matrix A first. If matrix B is applied first, it will rotate the object before it is scaled, meaning that the scaling will be applied to the already-rotated object. This could result in an unexpected transformation. Therefore, the order of the matrices must be taken into account when combining them.
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