You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2?

Answer:

6

Step-by-step explanation:

The prime factorization of 12x is 3*2*2x. The prime factorization of 18 is 2*3*3. The same thing that appears in both prime factorizations is 3*2, or 6.

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Answer: c=23

Step-by-step explanation: Honest guess

Answer: We start by distributing the -6 to the terms inside the parentheses:

8f - 6(-5) - 6(7f)

Then we simplify each term inside the parentheses:

8f + 30 + 42f

Now we combine like terms:

8f + 30 + 42f = 50f + 30

So the simplified expression is 50f + 30

Step-by-step explanation:

[tex]\displaystyle\\Answer:\ none \ of\ these\ (m=-\frac{5}{3} );\ isosceles,\ right[/tex]

Step-by-step explanation:

1.

a) find the midpoint G of the side DE:

[tex]x_D=-2\ \ \ \ x_E=3\ \ \ \ y_D=-2\ \ \ \ y_E=1[/tex]

[tex]\displaystyle\\x_G=\frac{x_D+x_E}{2} \\\\x_G=\frac{-2+3}{2}\\\\x_G=\frac{1}{2}\\\\x_G=0.5[/tex]

[tex]\displaystyle\\y_G=\frac{y_D+y_E}{2}\\\\y_G=\frac{-2+1}{2} \\\\y_G=\frac{-1}{2} \\\\y_G=-0.5\\\\Thus,\ G(0.5,-0.5)[/tex]

b) find the midpoint I of the side DF:

[tex]x_D=-2\ \ \ \ x_F=6\ \ \ \ y_D=-2\ \ \ \ y_F=-4[/tex]

[tex]\displaystyle\\x_I=\frac{x_D+x_F}{2} \\\\x_I=\frac{-2+6}{2} \\\\x_I=\frac{4}{2} \\\\x_I=2[/tex]

[tex]\displaystyle\\y_I=\frac{y_D+y_F}{2}\\\\y_I=\frac{-2+(-4)}{2}\\\\y_I=\frac{-6}{2} \\\\y_I=-3\\\\Thus,\ I(2,-3)[/tex]

c) the slope of GI:

[tex]x_G=0.5\ \ \ \ x_I=2\ \ \ \ y_G=-0.5\ \ \ \ y_I=-3[/tex]

[tex]\displaystyle\\m_{GI}=\frac{y_I-y_G}{x_I-x_G} \\\\m_{GI}=\frac{-3-(-0.5)}{2-0.5} \\\\m_{GI}=\frac{-3+0.5}{1.5} \\\\m_{GI}=\frac{-2.5}{1.5} \\\\m_{GI}=\frac{-2.5(2)}{1.5(2)} \\\\m_{GI}=-\frac{5}{3}[/tex]

2.

Type of Δ DEF:

a) find the length of the side DE:

[tex]|DE|=\sqrt{(3-(-2)^2+(1-(-2)^2}\\\\|DE|=\sqrt{(3+2)^2+(1+2)^2} \\\\|DE|=\sqrt{5^2+3^2}\\\\|DE|=\sqrt{25+9} \\\\|DE|=\sqrt{34} \ units[/tex]

b) find the length of the side EF:

[tex]|EF|=\sqrt{(6-3)^2+(-4-1)^2}\\\\|EF|=\sqrt{3^2+(-5)^2}\\\\ |EF|=\sqrt{9+25} \\\\|EF|=\sqrt{34}\ units[/tex]

Hence, DE=EF

c)  find the m∠DEF:

[tex]\displaystyle\\cos \angle E=\frac{\overrightarrow {DE}+\overrightarrow {EF}}{|DE|*|EF|} \\\\[/tex]

Find the coordinates of the vector by the coordinates of its beginning and end points:

[tex]\displaystyle\\\overrightarrow {DE}=(x_E-x_D,y_E-y_D)\\\\\overrightarrow {DE}=(3-(-2),1-(-2))\\\\\overrightarrow {DE}=(5,3)\\\\\overrightarrow {EF}=(x_F-x_E,y_F-y_E)\\\\\overrightarrow {EF}=(6-3),-5-1)\\\\\overrightarrow {EF}=(3,-5)\\Hence,\\\\cos\angle E=\frac{5*3+3*(-5)}{\sqrt{34}*\sqrt{34} } \\\\cos\angle E=\frac{15-15}{34 }\\\\cos\angle E=\frac{0}{34 }\\\\cos\angle E=0\\\\m\angle E=90^0[/tex]

Answer: 8 miles

Step-by-step explanation:

1.25m+6=2m

--1.25m. -1.25m

6=.75

6/.75m=8 mile

s

The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

What is a peripheral coordinate?

A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.

To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:

[tex]r=\sqrt{(x^2 + y^2 + z^2)} = \sqrt{((-2)^2 + (2\sqrt3)^2 + 4^2)} = \sqrt{(4 + 12 + 16)} = \sqrt32 = 4\sqrt2[/tex]

θ = [tex]tan^{-1}(y/x) = tan^{-1}(2\sqrt3/(-2)) = tan^{-1}((-\sqrt3)/1) = -60^o[/tex]

φ = [tex]cos^{-1}(z/r) = cos^{-1}(4/4\sqrt2) = cos^{-1}(1/\sqrt2) = \degree 45 ^o[/tex]

So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

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The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

What is a peripheral coordinate?

A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.

To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:

[tex]r=\sqrt{x^2+y^2+z^2} = \sqrt{(-2)^2+(2\sqrt{3})^2+4^2}=4\sqrt{2}[/tex]

θ = [tex]tan^{-1}(y/x)=tan^{-1}(2\sqrt{3}/(-2))=60^o[/tex]

φ = [tex]cos^{-1}(z/r)=tan^{-1}(4/4\sqrt{4})=45^o[/tex]

So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

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Answer:

D. 8

Step-by-step explanation:

8*3=24

8*5=40

8*4=32

The solution to the system of linear equations is (-8, -2).

NOTE: The problem that is solved here is, 'What is the solution to this system of linear equations? Y - x = 6, Y + x = -10'

The equations with two variables and the largest exponent order of 1 each have one, zero, or an infinite number of solutions, and are referred to as linear equations.

A linear equation with two variables has the conventional form ax + by + c = 0, where x and y are the variables.

Additionally, the answers can be expressed as ordered pairs, like as (x, y). The system of linear equations in two variables is graphically represented by two straight lines, which may intersect, be parallel, or be coincident.

y - x = 6 ----> y = x + 6

y + x = -10 -----> y = - x - 10

As both the equations in terms of y, we get

x + 6 = - x - 10

By further calculation

x + x = - 10 - 6

2x = - 16

Dividing both sides by 2

x = -8

Substituting the value of x in either of the equations

y - x = 6

y - (-8) = 6

So we get

y + 8 = 6

y = 6 - 8

y = - 2

Therefore, the solution to the system of linear equations is (-8, -2).

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Therefore , the solution of the given problem of equation comes out to be  the error range for x is [1250, 1350].

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Given: Some material has a length of 8.3 meters

We have provided a number, x, that has been rounded to two significant numbers with the supplied error.

Next, we must determine the x error interval.

​It is necessary for x to have a value that is both bigger than or equal to 1250 and less than or equal to 1300.

i.e.,1250 ≤ x ≤ 1300 ---(1)

2. The value of x is more than 1300 but not equal to 1350.

1300  ≤ x ≤ 1350--- (2)

When (1) and (2) are combined, we obtain

1250≤ x ≤ 1350

As a result, 1350 is not part of the error-interval for x.

As a result, the interval notation is [1250, 1350].

As a result, the error range for x is [1250, 1350].

Therefore , the solution of the given problem of equation comes out to be  the error range for x is [1250, 1350].

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The solution to the inequality expression is x > -84

From the question, we have the following parameters that can be used in our computation:

x +96 > 12

Subtract 96 from both sides of the inequality expression

So, we have the following representation

- 96 + x +96 > 12 - 96

Evaluate the like terms

x > -84

Hence, the solution is x > -84

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Answer:

Step-by-step explanation:

To calculate 7⋅VN−→3⋅MT−→, we need to perform scalar multiplication on the two vectors. Scalar multiplication is simply multiplying each of the components of the vector by the scalar value.

So for the first vector, we have: 7⋅VN−→ = {7⋅(-8); 7⋅3} = {-56; 21}.

For the second vector, we have: 3⋅MT−→ = {3⋅2; 3⋅10} = {6; 30}.

Then to add the two vectors, we simply add the corresponding components: {-56; 21} + {6; 30} = {-50; 51}.

Therefore, the final result is {-50; 51}.

Time taken to travel from North Carolina to Florida driving an average speed of 70 mph is 7 hours.

Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.

Given,

Time taken to travel = 9hours

average speed =55 mph

distance between North Carolina to Florida = speed x distance

distance= 55 x 9

distance= 495 miles

if driving at speed of 70 mph

time taken = distance/speed

time taken=495/70

time taken=7 hours

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By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

Expressions are polynomials, but expressions that equal zero are polynomial equations.

A polynomial may be written as the sum of a finite number of terms, where each term is the product of one or more variables raised to a positive integer exponent and a constant coefficient (or power).

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

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The correct comparison of solutions for the expression is x < 2

From the question, we have the following parameters that can be used in our computation:

2(5-x) > 6 and 22 > 2(9+x)

Rewrite the expression properly

So, we have the following representation

2(5 - x) > 6 and 22 > 2(9 + x)

Divide both sides of the expressions by 2

So, we have the following representation

5 - x > 2 and 11 > 9 + x

Subtract both sides of the expression by the constant term

This gives

-x > -3 and 2 > x

Rewrite as

x < 3 and 2 > x

So, we have

x < 3 and x < 2

When combined, we have

x < 2

Hence, the solution is x < 2

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A customer purchased 1/4 pound of ham, 1 1/2 pounds of turkey, 1 pound of roast beef, and 3/4 pound of bologna. Therefore, the customer pay for the purchase before sales tax is $22.

Sales tax:

A sales tax is a tax paid to a governing body on the sale of certain goods and services. Laws generally allow sellers to collect taxes from consumers at the time of purchase. When a tax on goods or services is paid by consumers directly to the governing body, it is usually called a use tax. Laws often provide excise and use tax exemptions for certain goods or services, such as: food, education, medicine, etc. Value Added Tax (VAT) charged on goods and services is related to sales tax.

For Example:

I am shopping at The Clothing Boutique and would like to estimate the total after tax before checking out. After counting the total price of the items in the cart, the total is $100. Sales tax in this county is 9.5%, so you charge 9.5% (100 x 0.095) of $100.

According to the question:

The purchase before sales tax:

                   = 1/4 × $5.99 + 1 1/2 × $4.99 + 1 × $6.99 + 3/4 ×2.99

                   = $1.5 + $7.5 + $6.99 + $5.24

                   = $21.23 ≈ $22

Therefore,  the customer pay for the purchase before sales tax is $22.

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Answer:

p(r(-3)) = 114

Step-by-step explanation:

I assume you want help with just #4:

[tex]r(x)=5r+2\\r(-3)=5(-3)+2=-15+2=-13\\\\p(x)=x^2+4x-3\\p(r(-3))=p(-13)=(-13)^2+4(-13)-3=169-52-3=117-3=114[/tex]

Answer:

Step-by-step explanation:

there is 1 dime and 12 quarters

What is the image of ( 12 , − 4 ) after a dilation by a scale factor of 1/4 centered at the origin is (3, -1)

Transformation is the movement of a point in the coordinate plane. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease of a figure by a scale factor k. If the value of k > 1, then it is an enlargement but if k < 1, it is a reduction.

The point (12, -4) is dilated by a scale factor of 1/4 using the rule (x, y) ⇒ (x/4, y/4). The new point is (4, -1)

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The given sequence represents the sales of a product over time. The sum of the first 6 terms is 693.75, which is calculated by multiplying each term in the sequence by its respective exponent.

The sum of the first 6 terms of the geometric sequence is calculated as follows:

[tex]a_1 = 125 \left(\frac{1}{5}\right)^{1-1} = 125 \\[/tex]

[tex]a_2 = 125 \left(\frac{1}{5}\right)^{2-1} = 25 \\[/tex]

[tex]a_3 = 125 \left(\frac{1}{5}\right)^{3-1} = 5 \\a_4 = 125 \left(\frac{1}{5}\right)^{4-1} = 1 \\a_5 = 125 \left(\frac{1}{5}\right)^{5-1} = \frac{1}{5} \\a_6 = 125 \left(\frac{1}{5}\right)^{6-1} = \frac{1}{25} \\[/tex]

Total sum = 125 + 25 + 5 + 1 +[tex]\frac{1}{5} + \frac{1}{25}[/tex] = 693.75

The geometric sequence a_n=12[tex]5\left(\frac{1}{5}\right)^{n-1}[/tex]represents the sales of a product over time, where n is the number of years after its release. The sum of the first 6 terms is calculated by multiplying each term in the sequence by its respective exponent. This gives us the following 6 terms: a_1 = 125, a_2 = 25, a_3 = 5, a_4 = 1, a_5 = 1/5, and a_6 = 1/25. The sum of these 6 terms is 693.75.

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Since starting balance is $922.36 and she deposits $256.71 and then debits $1317.24. Ending Balance will be 922.36+256.71-1317.24=$138.17 in debt.

You make a deposit when you add money to your bank account. To build savings and earn interest, you should put money in a bank. For money you can withdraw at any time, a demand deposit is made. A time deposit is an investment for the long term. When you take out a loan, you might also pay a deposit as collateral.

In double-entry bookkeeping, debits and credits are entries made in account ledgers to record value changes brought on by business transactions. A credit entry represents a value transfer from the account, whereas a debit entry represents a transfer of value to the account.

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Answer:

625

Step-by-step explanation:

1.25.625

125 = 5³

625 = 5⁴

prime factor 5 , number 125 is 3 number 625 is 4 LCM is 4

LCM = 5⁴

so the LCM is 625

Answer:

65.6488549618 %

Step-by-step explanation:

total left = 131

left who have artistic ability = 86

proportion of left who have artistic ability = number of favorable outcomes/total outcomes = 86/131 = 0.65648854961

mutliply by 100 to convert to a percent

65.6488549618 %

"20" is the Pythagorean triplet of 12 and 16.

A set of three integers that can be the lengths of the sides of a right triangle is called a Pythagorean triple, it also defines the positive integers a,b, and c such that a right triangle exists with legs a,b, and hypotenuse c.

By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying  a²+b²=c²

The simplest Pythagorean triple is the set “3,4,5.”

Now, substitute the values in the above equation:

=) x² = 12² + 16²

=) x² = 144 + 256

=) x² = 400

=) x = √(400)

=) x = 20.

Therefore, (12,16,20) is a Pythagorean triplet.

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The area for 2 pounds of fertilizer is 400 square feet

How to determine the amount of fertilizer for 2 pounds?

From the question, we have the following parameters that can be used in our computation:

seven pounds of fertilizer can cover 1400 square feet

This means that

7 pounds of fertilizer = 1400 square feet

Divide both sides of the equation by 7

So, we have the following representation

1 pounds of fertilizer = 200 square feet

Multiply both sides of the equation by 2

So, we have the following representation

2 pounds of fertilizer = 400 square feet

Hence, the area is 400 square feet

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Answer:

x = 60 , y = 85

Step-by-step explanation:

assuming the figure is a trapezoid

• each lower base angle is supplementary to the upper base angle on the same side.

x + 2x = 180

3x = 180 ( divide both sides by 3 )

x = 60

and

y + y + 10 = 180

2y + 10 = 180 ( subtract 10 from both sides )

2y = 170 ( divide both sides by 2 )

y = 85

No, three 4 5 triangles are not always right triangles.

A right triangle is a triangle in which one of the angles is a right angle (90°). Therefore, in order to be a right triangle, the following criteria must be met: a^2 + b^2 = c^2, where c is the longest side and a, b are the other two sides. In a 3 4 5 triangle, the longest side is 5, so a^2 + b^2 = c^2 becomes 3^2 + 4^2 = 5^2. Using simple algebra, this equation becomes 9 + 16 = 25, which is true. Therefore, a 3 4 5 triangle is a right triangle. However, if one of the sides is different, for example a 3 4 6 triangle, the equation becomes 9 + 16 = 36, which is not true. Therefore, a 3 4 6 triangle is not a right triangle. To summarize,3 4 5 triangles are right triangles, but three 4 6 triangles are not.

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The polynomial in terms of its simplest factors is (x + 3)(x − 6)

From the question, we have the following parameters that can be used in our computation:

x2 − 3x − 18.

Rewrite as

x² − 3x − 18

Expand

x² − 3x − 18 = x² − 6x + 3x − 18

Factorize the expression

This gives

x² − 3x − 18 = x(x − 6) + 3(x − 6)

Factor out x - 6

x² − 3x − 18 = (x + 3)(x − 6)

Hence, the expression is (x + 3)(x − 6)

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The ratio of the new area to the old area is 16:1. The correct option is the second option

From the question, we are to determine the statement that is true about the area of the circle.

First, we will determine the old area

Using the formula for calculating the area of a circle

A = πr²

Where A is the area

and r is the radius

From the given diagram,

r = 6 ft

Thus,

Old area = π × 6²

Old area = 36π ft²

Now,

If the radius is quadrupled

That is,

r = 4 × 6 ft

r = 24 ft

The new area will be

A = π × 24²

A = 576π ft²

The ratio of the new area to the old area is

576π ft² / 36π ft²

16 /1

= 16 : 1

Hence, the ratio is 16:1

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