Kenneth started saving for retirement at age 40 with plans to retire at age 70. He invested an average of $400 per month in various securities, with an average annual return of 7% adjusted for inflation. Assuming monthly compounding, how much has Kenneth saved at the start of retirement.
A. $487,988.40

B. $720,421.84

C. $37,784.31

D. $556,559.8​

the value of |x-2| lies between 0 and 1 then λ also lies between 0 and 1. Then λ belongs to (0,1).

In the given question, if λ∈R and the domain of f(x) = [tex]\sqrt{\frac{log_{\lambda}|x-2|}{|x|}}[/tex] is [1,2)∪(2,3], then λ belong to

The given function is

f(x) = [tex]\sqrt{\frac{log_{\lambda}|x-2|}{|x|}}[/tex]

The function is belong in between [1,2)∪(2,3]. So

|x-2| ≠ 0  and  |x| > 0

x ≠ 2       and  x > 0

Since the value of x can not be equal to 2 and x value is always greater than 0. So

[tex]log_{\lambda}|x-2|\geqslant 0[/tex]

The value of |x-2| should be lies between 0 and 1 because x cannot be equal to 2 and greater than 1.

So 0< |x-2| < 1

If the value of |x-2| lies between 0 and 1 then λ also lies between 0 and 1.

Hence, 0 < λ < 1.

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A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.

For a triangle the circumcentre is a point equidistant from each of the three vertices. Every non-degenerate triangle has such a point. This result can be generalised to cyclic polygons: the circumcentre is equidistant from each of the vertices. Likewise, the incentre of a triangle or any other tangential polygon is equidistant from the points of tangency of the polygon's sides with the circle.

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The total mileage on Joe's shoes after the 21 weeks is 2,457 miles.

The total mileage of Joe's shoes is the sum of all the distance travelled by Joe within the given time of period of 21 weeks.

The distance travelled by Joe in 1 week is calculated as follows;

distance travelled by Joe in 1 week = 1 mile/day  x  7 days = 7 miles

The distance travelled by Joe in 21 weeks is calculated as follows;

distance travelled in 21 weeks = ( 7 miles / week ) x ( 21 weeks )

distance travelled in 21 weeks = 147 miles

the number of additional mile added each week = 110 mile

for 21 weeks = 21 x 110 mile = 2,310 miles

The total mileage on Joe's shoes after the 21 weeks is calculated as follows;

total mileage = 2,310 miles  +  147 miles

total mileage = 2,457 miles

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The equation of the line that passes through the given points in the slope-intercept form is y = (-5/2)x - 1

From the question, we are to determine the equation of the line that passes through the given points

We will pick two value pairs from the table

Picking (-4, 9) and (-2, 4)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Then,

(y - 9) / (x - (-4)) = (4 - 9) / (-2 - (-4))

Simplify

(y - 9)/(x + 4) = -5/(-2 + 4)

(y - 9)/(x + 4) = -5/2

Cross multiply

2(y - 9) = -5(x + 4)

2y - 18 = -5x - 20

2y = -5x -20 + 18

2y = -5x - 2

Divide through by 2

y = (-5/2)x - 1

Hence, the equation is y = (-5/2)x - 1

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We need 6 cans of paint are needed to cover an area of 2 200 square units.

In this question we need to find the number of cans of paint needed to cover an area of 2 200 square units.

We have been given one can of paint covers an area of 400 square units.

Let x cans of paint are needed to cover an area of 2200 square units..

1 can = 400 square units

x cans = 2200 square units

Bu Unitary method,

x = 2200/400

x = 22/4

x = 11/2

x = 5.5

x ≈ 6

Therefore, six cans of paint are needed to cover an area of 2 200 square units.

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A complete question is:

How many cans of paint are needed to cover an area of 2 200 square units if one can of paint covers an area of 400 square units?

The coefficient of the variable x squared is number 5.

The coefficients are the numbers on the left side or before each variable.

Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In this problem we have an expression given by:

5x²y

And we want to know what is the coefficient of x²

5 is the coefficient

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Answer:

  (c)  The range of the function is all real numbers less than or equal to 0

Step-by-step explanation:

You want the true statement describing the domain or range of f(x) = -√x.

The domain of the function is the set of values x for which the function is defined. The square root is only defined for non-negative arguments:

  x ≥ 0 . . . . . . not an answer choice

The range is of the function is the set of values f(x) that the function can produce. The square root function can produce any non-negative value, so the opposite of the square root function will produce any non-positive value:

  f(x) ≤ 0 . . . . . the range is real numbers less than or equal to zero

The probability that the shipment will be rejected is 0.724.

Given :

Since we have given that

n = 125

p' = 8 % = 0.08

p = 10 % = 0.10

Test statistic value :

z = p' - p / [tex]\sqrt{p(1-p)/n}[/tex]

= 0.08 - 0.10 / [tex]\sqrt{0.10 * 0.90 / 125}[/tex]

= -0.75

p value at z = -0.75

p = 0.226

What is probability ?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Probability of shipment will be rejected = 1 - 0.226

= 0.724

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The distance the 12 centimeters minute hand moves in 20 minutes obtained by converting the angular motion to translational motion is about 25.133 centimeters

Angular motion is the circular motion of an object around a point or location.

The complete 360° rotation of the minute hand = 60 minutes

Therefore;

60 minutes is equivalent to 360°

1 minute is equivalent to 360°/60 = 6°

20 minutes is equivalent to 20 × 6° = 120°

The circular path motion following an angular rotation of angle theta = Radius × Theta

Where, theta is in radians

The radius of the minute hand = 12 centimeters

360° = 2•π radians

120° = 360°/3 = (2•π/3) radians

The distance moved by the the minute hand = 12 cm × (2•π/3) radians = 8•π cm

8•π cm ≈ 25.133 cm

The distance the minute hand moves in 20 minutes is about 25.133 cm

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The theoretical and experimental probabilities are equal.

Probability determines the likelihood of a random event occurring. The ratio of the number of favorable outcomes to the total number of possible outcomes is known as theoretical probability.

Theoretical probability = number of odd sides/ die sides

Here given that the numbers that are odd comes 6

So,

6/20 = 3/10 theoretical probability

The outcome of an experiment that has been repeated multiple times is used to calculate experimental probability.

Experimental probability = number of times Tani landed on a odd number  divided by the number of times the experiment was performed

6/ 20= 3/10.

Therefore here , both experimental and theoretical probabilities are equal.

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In the figure, the angles m∠ 1 and m∠ 2 are corresponding angles

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

In the question given, m∠ 1 and m∠ 2 are corresponding angles with each other.

This also implies that they are equal with one another using corresponding angle theorem.

Corresponding angle theorem states that : All corresponding angles are equal to one another.

Therefore, m∠ 1 and m∠ 5 are corresponding angles and are equal to one another.

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Children who are 4 years old frequently count up to 1,0and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

In order to calculate the size of a set, or the number of items in a finite set, one must count. Calculating the amount or total number of items in a collection or group is what is meant when we say we are counting in arithmetic. To count, then, is to speak numbers in sequence while giving each item in a group a value based on a one-to-one correlation. Objects are counted using counting numbers.

Children who are eight years old frequently count up to 1,000 and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

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The graph of y² 4x is a parabola with vertex (0,0) and x- and y-intercepts (0,0). The graph opens downward and can be written as y=4x².

The graph of y² 4x is a parabola in the shape of a "U" that opens downward. This parabola can be written in the standard form of y=a(x-h)²+k. In this case, a=4, h=0, and k=0. This means that the equation for the graph of y² 4x is y=4x².

To calculate the graph, we must first determine the vertex, which is the point of the parabola that has the maximum or minimum value. To do this, we use the formula for the vertex of a parabola, which is (h,k)=(-b/2a,f(h)). With a=4 and b=0, the vertex of the parabola is (0,0).

We can then calculate the x-intercepts, which are the points at which the graph of y² 4x crosses the x-axis. To do this, we set y=0 in the equation y=4x² and solve for x. This gives us x=±√(0/4) or x=0. This means that the x-intercepts of the graph of y² 4x are (0,0).

Finally, we can calculate the y-intercept, which is the point at which the graph of y² 4x crosses the y-axis. To do this, we set x=0 in the equation y=4x² and solve for y. This gives us y=0. This means that the y-intercept of the graph of y² 4x is (0,0).

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Answer:

$1.41

Step-by-step explanation:

0.20 * 5.8 ounces = $1.16

0.25 * 1.16 = $1.41

The mail  weighing 6.8 ounces cost 145 cents

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given here, the first ounce cost 25 cents and all subsequent ounces or parts of an ounce cost 20 cents each

therefore cost of the first ounce = 25

        and cost of 5.8 ounces = 20× 6

                                                = 120 cents

thus total cost is 120+25 =145 cents

Hence, the  total cost to mail a package is 145 cents

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Two triangles are congruent because the sides of two triangles and angles are congruent and the transformation applied to map triangle EBD onto triangle CBA is rotation of 90 degrees.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

There are two triangles in the coordinate plane.

Triangle ABC and triangle EBD are in plane.

We need to find the transformation applied to EBD onto triangle CBA.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

The triangle EBD undergoes a rotation of 90 degrees in clockwise direction to get triangle CBA.

The two triangles are congruent because the sides of two triangles and angles are congruent. So we conclude that the two triangles are congruent.

Hence, rotation of 90 degrees is the transformation (s) could be applied to map triangle EBD onto triangle CBA.

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The equation y= 2x-15 can be used to estimate how many minutes will pass after 4:00 pm until she reaches her destination.

The following equation can be used to estimate how many minutes after 4:00 p.m. the pilot will reach her destination:

y = 2x - 15

This equation represents the number of minutes after 4:00 p.m. the pilot will arrive at her destination. The variable x represents the time, in minutes, of her original flight, and y represents the number of minutes after 4:00 p.m. she will arrive at her destination. The expression "2x" represents the time the pilot will arrive at her destination if she had traveled at twice her original speed, and the "-15" represents the delay caused by air traffic.

To solve this equation, you would substitute the value of x into the equation and solve for y. For example, if the pilot's original flight time was 60 minutes, the equation would be:

y = 2(60) - 15

= 120 - 15

= 105

This means that the pilot will arrive 105 minutes after 4:00 p.m., or at 5:45 p.m.

The complete question is:-

A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 15 minutes. Air traffic control approved a new flight plan that

will allow her to arrive two times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation

that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.

y = 2x + 15

©y=-*x+15

y = x-15

y = 2x - 15

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There are countless possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable. If we try to solve an equation and receive a variable or a number equal to itself, there are infinitely many solutions to the equation.

Single-solution equations:

Some equations only have one precise solution. The variable in these equations can only take on one value in order for the equation to be true. When you solve an equation and the result is a variable equal to a number, you know that the equation only has one solution.

Example: For x, find the solution to the equation 6x-3=21.

6x \s= 24

To both sides, add 3.

x \s= 4

Subtract 6 from both sides.

For a single value of the variable, x=4, the equation is true. Consequently, there is only one solution to the equation 6x-3=21

Non-solvable equations:

There are certain equations with no answers. These equations don't have a value for the variable that would make them true. If you attempt to solve an equation and the result is false, the problem has no solutions.

Example: Solve the equation 4x+12=2x+12+2x.

4x+12

= 2x+12+2x

4x+12

= 4x+12 Combine like terms 2x and 2x.

12

= 12 Subtract 4x from both sides.

Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.

Equations that have infinitely many solutions:

The number of solutions to some equations is limitless. When a variable is used in these equations, any value makes the equation true. If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions.

Solve the equation 4x+12=2x+12+2x.

4x+12

= 2x+12+2x

4x+12

= 4x+12 Combine like terms 2x and 2x.

12

= 12 Subtract 4x from both sides

Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.

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The factors of x³ 2x² 5x 6 are two binomials. The first binomial is x² + 2, and the second binomial is x + 3. These two binomials can be multiplied together to get the original equation, x³ 2x² 5x 6.

To find the factors of x³ 2x² 5x 6, we need to use the factorization process. This involves breaking down the equation into its prime factors. First, we need to factor out the greatest common factor (GCF) from the equation. The greatest common factor of x³ 2x² 5x 6 is x, so we can factor out x to get x² 2x 5 6. Now, we can use the difference of squares formula to factor out the remaining terms. The difference of squares is (a + b)(a - b). We can use this formula with 2x and 5 to get (2x + 5)(2x - 5). This leaves us with the two binomials (x² + 2)(x + 3). These two binomials can be multiplied together to get the original equation, x³ 2x² 5x 6.

x³ 2x² 5x 6 = (x)(x² 2x 5 6)

= (x)(2x + 5)(2x - 5)

= (x)(x² + 2)(x + 3)

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The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.

The common denominator needed to subtract the given fractions is 42.

Given that,

5/6 - 2/7

The denominator is the number that is placed below the horizontal line of a fraction. It is the bottom number of a fraction that shows the total number of equal parts an object is divided into.

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators the same first and then subtract them.

Here, the LCM of denominators 6 and 7 is 42.

Now, 35/42 - 12/42

= 23/42

So, the common denominator is 42.

Hence, the common denominator needed to subtract the given fractions is 42.

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The quantity written below a fraction's horizontal line is known as the denominator. The total number of equally spaced sections into which an object is divided is indicated by the bottom number of a fraction.

When subtracting fractions, it's possible to use either the same or distinct denominators for two or more of the fractions. While unlike fractions must first have their denominators made the same before being subtracted, like fractions can be done so immediately.

The LCM of denominators 6 and 7 in this case is 42.

Now, 35/42 - 12/42

= 23/42

Therefore, 42 is the common denominator.

Consequently, 42 is the common denominator required to remove the provided fractions.

FA is the corresponding side to SU

AR is the corresponding side to UN

RF is the corresponding side to NS

What are Corresponding Sides ?

Corresponding sides are the sides that are in the same position in any different 2-dimensional shapes. For any two polygons to be congruent, they must have exactly the same shape and size. This means that all their interior angles and their corresponding sides must be the same measure. For any two polygons to be similar, the ratios of the lengths of each pair of corresponding sides must be equal.

In the below-given images, the two triangles are congruent and their corresponding sides are color-coded.

In the above two triangles ABC and XYZ,

AB is the corresponding side to XY

BC is the corresponding side to YZ

CA is the corresponding side to ZX

Similarly , if ΔFAR is similar to ΔSUN

then ,

FA is the corresponding side to SU

AR is the corresponding side to UN

RF is the corresponding side to NS

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The value of "i" squared results in:

(-1) = i²

Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.

Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.

In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:

(-1) = i²

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Answer:

m = 3

Step-by-step explanation:

rise over run

Answer:

Hope it helps you ...........

There is major 3 types of expression. Numerical expression, algebraic expression and fractional expression.

This expression contains only two or more numbers along with symbols or operator. There is no variable present.

such as 226÷113+2×22-11

or (44÷88) ×100%

the above sign is percentage sign we can determine a percent value

or∛ (64)

the above sign represents a cubic root

we get the value 4

The expression having two or more fractional terms along with symbols are called fractional expression. There are numerator and denominator from which we need to determine a common denominator to obtain a result.

such as, 4/5+3/4

we have 2 different denominators 5 and 4. we need to find a common denominator by multiplying both. 5x4

                                                           20

In the next, common denominator is divided by each denominator and the result is multiplied with each numerator.

                 (4×4+3×5)/20

       hence, the result is 31/20

The expression contains both variables and numbers along with symbols are called algebraic expression. The algebraic expression having equal sign are termed as equation. Tha main purpose of using equation is to determine unknown value.

Algebraic expression are different types such as linear expression

2x+3-4y

2 and 4 are coefficient, 3 is constant

Polynomial expression as example 2x²-3y+4

Besides, we have other algebraic expression such as 3y+4 or x/4+y/3

and so on.

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Answer:

h = 1.25m

Step-by-step explanation:

a=20m, b= 30m

Area = (½) (a+b) (h)

375= ½ (20+30) h

375= 300h

300h = 375

h= 375÷300

= 1.25m

Answer:

c.)    a = (2(x-b-vy))/t^2

Step-by-step explanation:

Manipulate the given equation to isolate a on the left side:

x=b+vy+(1/2)at^2

x=b+vy+(1/2)at^2

(1/2)at^2 = x-b-vy

at^2 = 2(x-b-vy)

a = (2(x-b-vy))/t^2

Answer:

Neither

Step-by-step explanation:

It is not opposite to each other (perpendicular) or the same slope (parallel)

The frequency of oscillation for the spring with the constant value of 2.5×10⁴ is 0.0012

The term frequency is defined as the number of waves that pass a fixed point in unit time and it is also known as the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.

Here we have given the following values,

Spring constant = 2.5 × 10⁴

And the weight of the cart = 1.4 kg

Now, we have calculated the value of the frequency of oscillation as,

=> v = 1/T

Here T refers the time period.

Where it can be rewritten as,

=> 1/2π x √(k/m)

Now, we have to apply the values on it then we get

=> 1/2π  x √(1.4/2.5 x 10⁴)

=> 0.1592 x 0.0074

=> 0.0012

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The theorem that is a valid triangle congruence theorem is the: ASA

A triangle congruence theorem is a set of conditions that must be met by a set of triangles before both triangles can be said to be congruent to each other.

Some of the valid triangle congruence theorem are:

Therefore, from the option given, the only valid triangle congruence theorem is: ASA.

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Complete Question:

Which of the following is a valid triangle congruence theorem?

AAA

SSA

ASA

none of the above