The ways that you can maximize a tax-sheltered retirement program include:
1. when the contributions made by the employer are not taxable
2. when the employee has started making contributions early in life,
What is a tax-sheltered retirement?A tax-sheltered is a retirement savings plan that enables self-employed individuals and workers of tax-exempt organizations to invest pretax money to create retirement income. A dependable source of income in retirement, tax-sheltered annuities are made to pay out consistently throughout time.
The fact that employer contributions are tax-free is one of the best features of retirement programs. Only when an employee takes money out of their retirement accounts do taxes need to be paid. If the employee starts making contributions early in life, the plans also allow the employee the chance to maximize returns, which is another benefit that the employee can get from them.
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Graph the circle with center (2, −3) that passes through (2, 0). Find the area in terms of π and to the nearest tenth. Use 3.14 for π.
Circle with center (2,-3) that passes through (2,0) has an area of 9π units² in terms of π and 28.3 units² (nearest tenth).
As given in the question,
Circle with center C(2, -3)
Passes through point A(2,0)
Graph of the circle attached.
Radius of the circle 'r'
r =CA
CA = √(2-2)² +(0+3)²
= √9
= 3
Area of the circle = πr²
= π (3)²
= 9π units² (in terms of π)
= 9 ×3.14
= 28.26
= 28.3 units²
Therefore, circle with center (2,-3) that passes through (2,0) has an area of 9π units² in terms of π and 28.3 units² (nearest tenth).
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which equation represents the standard form of the equation y=(x+3)^2-4
A. y = x^2 + 3x - 4
B. y = x^2+ 6x - 4
C. y = x^2 + 3x + 5
D. y = x^2 + 6x + 5
Answer: y=x^2+6x+5 ==> D
Step-by-step explanation:
y=(x+3)^2-4
y=(x+3)(x+3)-4
y=x*x+3*x+3*x+3*3-4
y=x^2+3x+3x+9-4
y=x^2+6x+5 ==> D
4. Write an equation of the line that passes through (1,3) and has a slope of 5/4
5. Write two equivalent equations for a line with x-intercept (3,0) and y-intercept (0, 2).
The equation of the first line is y = -1/3x - 4, while the equivalent equations of the second line are y = -2/3(x - 3) and y = -2/3x + 2
How to determine the equation of the line?The given parameters are
Slope, m = 5/4
Point, (x1, y1) = (1, 3)
A linear equation is represented as
y = m(x - x1) + y1
So, we have
y = 5/4(x - 1) + 3
This gives
y = 5/4x + 7/4
Hence. the linear equation is y = 5/4x + 7/4
The equivalent equationsHere, we have
(x, y) = (3, 0) and (0, 2)
A linear equation is represented as
y = m(x - x1) + y1
Where
m = (y2 - y1)/(x2 - x1)
So, we have
m = (2 - 0)/(0 - 3)
m = -2/3
So, we have
y = -2/3(x - 3)
The above equation can be rewritten as
y = -2/3x + 2
Hence, the equations are y = -2/3(x - 3) and y = -2/3x + 2
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if a= 4 and b=b : 5a - b =
Answer:
20 - b
Step-by-step explanation:
5a - b
substitute a for 4 because a = 4
5(4) - b
20 - b
Solve a³ = 11.
Solve c² = 27.
Answer: A: A = 2.2240 B: C = 3
Hope this helped! :)
Can you please help me? Thank you!
The volume of the figure shown in the reference attachment, provided hereby with the question statement will be 6786 ft³.
As per the question statement and the reference attachment, we are provided with a figure and its dimensions.
We are required to calculate the volume of the concerned figure using the dimensional values provided.
To solve this question, we need to calculate the volumes of the bottom cuboidal part, and the top pyramidal part separately, and then add these volumes, to obtain our final desired answer.
Given, the dimensions of the bottom cuboidal part is (21ft by 18ft by 13ft).
We know that, volume of a cuboid = (length * breadth * height).
Therefore, volume of our concerned bottom cuboidal part
= (21 * 18 * 13) ft³
= 4914 ft³.
Also given, the dimensions of the top pyramidal part are as follows,
Base of the triangle = 18 ft,
Altitude of the triangle = 16 ft,
and length of the pyramid = 13 ft.
Therefore, Volume of the concerned pyramid
= [(1/2) * base * altitude * length]
= [(1/2) * 18 * 16 * 13] ft³
= (9 * 16 * 13) ft³
= 1872 ft³.
Therefore, Total volume of the concerned figure shown in the reference attachment, provided hereby with the question statement will be
(4914 + 1872) ft³ = 6786 ft³
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Events A and B are mutually exclusive. Suppose event A occurs with probability 0.23 and event B occurs with probability 0.21.
a. Compute the probability that A occurs but B does not occur.
b. Compute the probability that either A occurs without B occurring or B occurs without A occurring.
Using it's concept, the probabilities for this problem are given as follows:
a) A occurs and B does not: 0.1817 = 18.17%.
b) Either occurs: 0.3434 = 34.34%.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
In the context of this problem, we have two mutually exclusive events, meaning that they cannot happen together.
For item a, we have that:
The probability of A occurring is 0.23.The probability of B not occurring is of 1 - 0.21 = 0.79.The events are mutually exclusive, hence we can multiply the probabilities as follows:
p = 0.23 x 0.79 = 0.1817 = 18.17%.
For item b, we add the probability in item with the probability of B occurring and A not, found as follows:
The probability of B occurring is 0.21.The probability of A not occurring is of 1 - 0.23 = 0.77.Hence:
p = 0.1817 + 0.21 x 0.77 = 0.3434 = 34.34%.
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two carts, a and b, are connected by a rope 39 ft long that passes over a pulley p. the point q is on the floor 12 ft directly beneath p and between the carts. cart a is being pulled away from q at a speed of 2 ft/s. how fast (in ft/s) is cart b moving toward q at the instant when cart a is 5 ft from q? (round your answer to two decimal places.)
The velocity of the cart b is found as 20/23 ft/s over the pulley.
What is defined as the rate of change?The momentum of a variable is represented by the rate of change, which is used to mathematically define the percentage change in value over such a defined period of time.For the given data in the question.
q's velocity is 2 feet per second.
Rope length is 39 feet.
Assume x is the distance between A and Q. (refer the image).
Assume y is the distance between Q and B. (refer the image).
As a result of the image,
x² + 12² = L²
Now, with respect to time t, differentiate the above equation.
2x(dx/dt) + 0 = 2L.(dL/dt)
For x = 5 ft and L = 13 ft
dL/dt = (5×2)/13 = 10/13
In the case of B,
y² + 12² = (39 - L)² ; from diagram.
Differentiating now,
2y(dy/dt) + 0 = -2(39 - L).(dL/dt)
At x = 5 ft and y = 23 ft.
dy/dy = -20/23
(A negative sign indicates the opposite direction)
Thus, the velocity of cart b is found as 20/23 ft/s.
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The equation shown has a missing value.
-2(2x - _) + 1 = 17 - 4x
For what missing value(s), if any, does the equation have exactly one solution?
There is no value for which the missing place should be filled in order to have exactly one solution.
A Linear equation may be defined as the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Since the equation only has one variable that is x then the linear equation will be rightly called as linear equation in one variable. We are given the equation -2(2x - _) + 1 = 17 - 4x. We solve the equation further which results as
-4x - _ + 1 = 17 - 4x
As we can see that there is -4 in both the right-hand side as well as the left-hand side both of them gets cancelled out.
- _ +1 = 17
As we can see that there is no variable left in order to find the value so any value of missing space will not be able to give any solution.
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A statement is given below:
"The number of square units in the area of a square is greater than or equal to the number of units in the perimeter of the
square
Which side length of a square provides a counterexample to the given statement?
o 10 units
O 2 units
o 6 units
Previos
The side length of the square that provides a counterexample to the statement square units in the area of a square is greater than or equal to the number of units in the perimeter is 2 Units.
What is a square?A square is a kind of a 2D figure in which all the sides are equal.
We know that the absolute perimeter of a square is the sum of the lengths of all the total sides and as we see the area of a square is (side)².
Assuming that the whole square has four units completed for each side.
The square's circumference can be calculated as is 4 sides plus 4 fours, or as seen as 16 units.
Now the area of the square will be calculated as (4) ² = 16 sq units.
Now assuming that the total side length of the square about is 2 units.
The square's perimeter is calculated as (24) = 8 units, while its total area is calculated as (22) = 4 units.
∴ 2 units make up the side length that serves as a counterexample.
Basically, herein we have to determine the absolute numbers that when are multiplied by 4 are seen to be greater than it's square such numbers are 1, 2, 3.
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Trigonometry please help
Radius = 12 cm
Central angle = 30°
Length of circular arc = 2πr(θ/360)
⇒ Length of circular arc = 2π x 12 (30/360)
⇒ Length of circular arc = 2π x 1
⇒ Length of circular arc = 2π = 2 x 3.14 = 6.283 cm
What is a Circular arc?A section of curvature or a circle is referred to as an arc in mathematics. The chord of the circle is the line that forms the connection between the arc's ends. A semicircular is exactly half the length of the circle.If the two points are not exactly opposite one another, the major arc will subtend an angle larger than radians at the circle's center whereas the minor arc will subtend an angle less than radians (180 degrees).Plotting two lines from the arc's ends to the circle's center, measuring the angle at which the two lines intersect, and solving for L by cross-multiplying the resulting statement are useful methods for calculating an arc's length.To learn more about Circular arcs, refer to:
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Suppose PQ has one endpoint at P (4, 6) and a midpoint coordinate of (-5, 9).
The coordinate for Point Q is
Answer:
(-14,12)
Step-by-step explanation:
Way 1: (little more complicated)
we know two things,
The two halves of the line have the same slope, and that the length from the endpoint to the midpoint is equal to the length from the midpoint to the other end point.
The slope is equal to: (6-9)/(4-(-5)) = -3/9 = -1/3
The length is equal to (using the Pythagorean theorem):
height = delta y = 9 - 6 = 3
length = delta x = 4 - (-5) = 9
3^2+9^2=hypotenuse^2
9+81 = h^2
h = sqrt(90)
So, the let's say point Q has the coordinate (a, b).
The formula of the slope would give us (b-9)/(a-(-5)) = -1/3
The formula of the hypotenuse would give us (b-9)^2+(a-(-5))^2 = 90
solving the system of equations, we would get that a = -14 and b = 12, so the point is (-14,12)
Make sure to be careful, however, because you will get two points with this system of equations. Only one works
Way 2:
since from point P to the midpoint we went to the left by 9 and up by 3, from the midpoint to point Q, we would go left by 9, and up by 3.
from the midpoint (-5,9), go left by 9, so x decreases by 9 to get (-14, 9).
go up by 3, so y increases by 3 to get (-14,12). This agrees with our other answer
Can Someone please help!!
1) The slope of line that goes through the points (12, 13) and (-8, 8) is; 5/28
2) Using the point (12, 13) and the slope 5/28, the equation of the line is;
y - 13 = (5/28)(x - 12)
3) The equation of the line in slope intercept form is; y = (5/28)x - 76/7
Write the equation of the Line in slope intercept form?We are told that a line goes through the points; (12, 13) and (-8, 8)
1) The slope is gotten from the formula;
m = (y2 - y1)/(x2 - x1)
m = (8 - 13)/(-8 - 20)
m = -5/-28
m = 5/28
2) Using the point (12, 13) and the slope 5/28, the equation of the line is;
y - 13 = (5/28)(x - 12)
3) Expanding the equation in answer 2 above, we have;
y - 13 = (5/28)x - (60/28)
y - 13 = (5/28)x - 15/7
y = (5/28)x - 15/7 + 13
y = (5/28)x - 76/7
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Please help! Write without using rational exponents.
[tex](m^3n^5)^\frac{1}{4}[/tex]
Please show all work.
I will give brainliest!!!
The expression without the rational exponents is ⁴√(m^3n^5)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to rewrite the expression?The expression is given as
(m^3n^5)^1/4
The exponents of the above expression cannot be simplified
This means that, we simply rewrite the expression using the fourth root expression
So, we have
(m^3n^5)^1/4 = ⁴√(m^3n^5)
Hence. the equivalent expression is ⁴√(m^3n^5)
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Draw the graph and find the equation of the hyperbola if the asymptotes are y=0.5x and y = −4−0.5x, and one of the vertices is (−4, 0).
The equation of the hyperbola is -(1/16) (x +4)² + (1/4) (y +2)² = 1
What is Hyperbola?
A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows. These two sections are known as connected components or branches.
The intersection of the two asymptotes is where the hyperbola's center is located. This is the key idea (-4,-2)
We have y orientation because the vertex at (-4,0) is above this location. The equation will take the form as a result.
-a (x + 4)
2 + b (y + 2)
In the case of certain a and b, 2 Equals 1.
Inputting (-4,0) reveals that b = 1/4.
Finally, requiring that y = x/2 be an asymptote reveals that a = 1/16.
-(1/16) (x +4)² + (1/4) (y +2)² = 1
Hence, The equation of hyperbola is -(1/16) (x +4)² + (1/4) (y +2)² = 1
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Parallel lines are in the same ____? , but they do not____?
Answer: parallel lines are in the same slope? , but they do not intersect.
Step-by-step explanation:
because
Answer: slope, intersect
Step-by-step explanation:
As parallel lines never intersect
Drag and drop the range of each data set into the boxes.
PLS HELP! ITZ MY LAST QUESTION
Answer:
Team 1 is 7, team 2 is 6
Step-by-step explanation:
Upper Extreme-Lower Extreme
2) Ashton left his house and ran 4 miles east and then 3 miles north. He then took the diagnol path back home. If he burned 105 calories every mile that he ran, how many total calories did he burn on his run? (just type in the number value and units)
1,470
Step-by-step explanation:
because if he 4 miles and than 3 miles you would add them and get 7. you would take that 7 and double the 7 and multiply it by 105 cause that's how many calories he burnt each miles he ran then you would get the total of 1470 calories
the volume of a cylinder closed at one end is 2136cm³.. if its height is 14cm, find its diameter
diameter = 13.93771776cm
Find the equation of the line.
Use exact numbers.
y=____x+
Answer:
y= 1/2 x - 3
Step-by-step explanation:
because -3 is the y-intercept, it is where the graph crosses the y-axis
the line is increasing at a rate of 1 unit up, and 2 units to the right. meaning that the slope is 1/2
HELP ASAP I NEED THIS DONE BEFORE TONIGHT
PARALLEL LINES HAVE EQUAL GRADIENTS...MEANING THE GRADIENT OF THE NEW LINE IS ALSO
[tex] \frac{5}{6} [/tex]
I WILL USE THE GIVEN POINTS RO FIND THE VALUE OF c
[tex] 6= \frac{5}{6} ( - 1) + c \\ 6 = - \frac{5}{6} + c \\ c = 6 + \frac{5}{6} \\ c = \frac{41}{6} [/tex]
The equation now is
[tex]y = \frac{5}{6} x + \frac{41}{6} [/tex]
ATTACHED IS THE SOLUTION
Hello!
A line that is parallel to another line:
⇒ has the same slope
Thus the line: has a slope of 5/6
However, the line passes through (-1, 6):
==> let's set up the equation in point-slope form
[tex]y - y_1=m(x-x_1)[/tex]
m: slope(x₁, y₁): point on the line[tex]y - 6 = \dfrac{5}{6} (x -(-1))\\\\y -6 = \dfrac{5}{6} x + \dfrac{5}{6} \\\\y = \dfrac{5}{6} x +\dfrac{5}{6}+6\\\\ y=\dfrac{5}{6} x + \dfrac{5}{6} +\dfrac{36}{6} \\\\y=\dfrac{5}{6} x + \dfrac{41}{6}[/tex]<== Answer:
Hope that helps!
Mell is twice as old as jerrey. if you subtract 16 from mells age, and 16 is added to jerreys age, their ages will be equal. what are their present ages
Answer: 32 year
Step-by-step explanation:
Let Jerrey age is 'y' year
Mell age = 2y
Now,
2y – 16 = y + 16
y = 32
∴ Mells age = 64 year
& Jerrey age = 32 year
50-100 points + brainliest
Construct a perpendicular bisector to AB
Step-by-step explanation:
In order to construct a perpendicular from a point to a given line segment: Draw two arcs crossing the line segment. Make two more arcs which intersect. Join the point where the arcs intersect to the original point.
Solve the equation.
-7(x-2)-28 - 14
(Simplify your answer.)
Answer:
[tex]-7x-28[/tex]
Step-by-step explanation
[tex]-7(x-2)-28-14[/tex]
To solve this, we must first solve what is inside the parenthesis by the distributive property. We will multiply -7 by x and -2.
[tex]-7(x)=-7x\\-7(-2)=14[/tex]
So then we have:
[tex]-7x+14-28-14[/tex]
From here, we combine like terms.
7x does not have any like terms, so we just combine 14, -28, and -14.
[tex]14+(-28)+(-14)\\=-28[/tex]
So, the final answer would be:
[tex]-7x-28[/tex]
If you have any questions, please feel free to ask!
is the sum rational or irrational drag the labels
The rational sums are:
√16 + (-21/5)
√4 + 5
√36 + ∛27
The irrational sums are:
π + 24
√8 + π
3/4 + √27
What are rational and irrational numbers?Irrational numbers cannot be stated as a fraction, although rational numbers can be expressed as ratios (such as P/Q and Q≠0). Additionally, an irrational number's decimal expansion neither repeats nor terminates. Terminating and repeating decimals are rational numbers.√16 + (-21/5)
= 4 + (-21/5)
= 4 - (21/5)
= (20 - 21) / 5
= - 1/5
= -0.2
Hence, the sum can be expressed as p/q so it is a rational number.
π + 24
= 3.1428571429 + 24
= 27.1428571429
The sum is non-terminating, so it is an irrational number.
√8 + π
= 2.82842712 + 3.1428571429
= 5.97128426
The sum is non-terminating, so it is an irrational number.
√4 + 5
= 2 + 5
= 7
The sum is an integer so it is a rational number.
√36 + ∛27
= 6 + 3
= 9
The sum is an integer so it is a rational number.
3/4 + √27
= 3/4 + 5.1961524227
= 0.75 + 5.1961524227
= 5.9461524227
The sum is non-repeating so it is an irrational number.
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The complete question is: "The table has a set of expressions representing the sums of rational and irrational numbers. Find each sum, and indicate whether the sum is rational or irrational. Drag the labels to the correct locations on the table. Each label can be used more than once."
the area of lake Okeechobee is 7.3 * 10 to the second power square miles. how many square miles is the area of lake Okeechobee?
Lake Okeechobee has a surface area of 5329 square miles, as determined by solving the given values.
How do you compute a square mile?The area of a square unit, such as a square mile, is calculated by multiplying two lengths. Each length in the case of square miles is measured in miles.
Given: The Okeechobee lake is 7.3 * 10 to the second power square miles in area.
We need to figure out how many square miles Lake Okeechobee covers.
Area covered in square miles = (7.3 × 10)²
= 73²
= 5329 square miles
Therefore, Lake Okeechobee covers an area of 5329 square miles which was calculated by solving the given values.
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Order the following numbers from least to greatest.
√19 3√64 4.2
Answer: 4.2; √19; 3√64
Step-by-step explanation: 4.2; 4.35889894354; 24
Write a paragraph proof to prove that if P, Q, R, and S are collinear, PQRS, and O is the midpoint of PR, then R is the midpoint
of QS.
Because PQ RS and congruent segments have ___ lengths, PQ = ___ Because Q is the midpoint of PR, ___ so R is the midpoint of QS. PQ ___ By the Select Choice Property of Equality. QR
The Addition of AnglesABD + DBC = ABC, according to the postulate formula, if D is within of ABC.The formula is applicable to adjacent angles' angle measurements.The greater angle that the two adjacent angles combine to generate will equal the total of the two adjacent angles.
Write a paragraph proof to prove that if P, Q, R, and S are collinear, PQRS, and O is the midpoint of PR, then R is the midpointof QS.
demonstrating PR = QS
Given: Q is PR's halfway point.
A segment's midpoint:
PQ = QR
Given: QS's midpoint is R.
A segment's midpoint:
PQ = QR
The equality's addition property is: QR + RS = PQ + QR.
Consequently, PR = QS.
The seven seven-statement proof below provides evidence that "PQO" and "RSO" are true.
I have provided the triangles image since it is missing.
The following is a step-by-step statement proof that "PQO" and "RSO" are true:
First statement; P R
the first; given
2. O is the midway of PR and QS
second; provided
Indicator 3; PO OR ; QO OS
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Consider the following expression.
5a+3+4b
Select all of the true statements below.
5a+3+4b is written as a product of three factors.
3 is a constant.
4 is a coefficient.
4b and 3 are like terms.
5a+3+4b is written as a sum of three terms.
None of these are true.
3 is a constant, 4 is the coefficient, 5a+3+4b is written as a sum of three terms are the true statements.
What is addition?The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. Mathematicians employ the action of addition to combine numbers. The sum of the given numbers is the outcome of addition, or the total of the inputted numbers.
Given that,
5a+3+4b
Select all of the true statements below.
5a+3+4b is written as a product of three factors.
3 is a constant.
4 is a coefficient.
4b and 3 are like terms.
5a+3+4b is written as a sum of three terms.
Therefore, 3 is a constant, 4 is the coefficient, 5a+3+4b is written as a sum of three terms are the true statements.
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Maxim raised $290.44 for charity. He divided the amount equally among his ten favorite
charities. How much did each charity receive (round to the nearest cent)?
Answer:
$29
Step-by-step explanation:
First you divide 290.44 by 10 which would equal 29.044, then you would round both 4's down to 0 which would get you $29.