Suppose that between the ages of 22 and 40, you contribute $3000 per year to a 401(k) and your employer contributes $1500 per year on your behalf. The interest rate is 8.3% compounded annually.
a.) What is the value of the 401(k) rounded to the nearest dollar after 18 years?
b.)Suppose that after 18 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the 401(k). How much money to the nearest dollar, will you have in the plan when you reach 65?
c.) What is the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan?

Answer:

[tex]5y - 20 = 0 \\ 5y = 20 \\ y = \frac{20}{5} = 4[/tex]

Answer: LN=29

Step-by-step explanation:

LN=LM+MN

KM=KL+LM

KM-KL=KL-KL+LM

LM=KM-KL

LN=KM-KL+MN

LN=8-3+24

LN=5+24

LN=29

The lifeguard walks around the perimeter which is 637.50 feet.

Perimeter is defined as the measure of sum all sides of a 2 dimensional figure. To calculate the perimeter we add all the individual sides of a polygon. The perimeter of a square is the sum of all four sides.

Since a triangle has three sides, the perimeter of a triangle is calculated by adding the sum of all the three sides of the triangle.

In the given figure we can see that the triangle is isosceles and the measure of the sides of the triangle are 216.75 feet , 216.75 feet and 204 feet.

Now the lifeguard walks around the perimeter of the triangular lazy-river ride.

Therefore perimeter = 216.75 +216.75 + 204 = 637.50 feet

Hence the lifeguard walks the perimeter which is  637.50 feet.

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What the given equation m = ((C + 200y) - 8000))/12y represents is as follows;

m is the amount of each monthly payment

C is the cost of the car

y is the length of loan in years

(C + 200y) - 8000) is the total amount she will repay

12y is the number of payments that she will make

We know that the formula to get the compound interest is;

A = P(1 + r/100)ⁿ

Where;

A is Amount.

P is Principal

r is Rate of interest

n is time in years

Now, when we compare that to our formula given as;

m = ((C + 200y) - 8000))/12y

we can say that;

m is the amount of each monthly payment

C is the cost of the car

y is the length of loan in years

(C + 200y) - 8000) is the total amount she will repay

12y is the number of payments that she will make

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Answer:

V(x) = -1600x + 21,000

x (number of years)

Step-by-step explanation:

"advised "

(a). if x = 4 (replace x with 4)

Using the formula above

V(4) = -1600(4) + 21,000

= -6400 + 21,000

= $14600

Value of the car after four years is $14600.

(b). if x = 8 (replace x with 8)

Using the formula

V(8) = -1600(8) + 21000

= -12800 + 21000

= $8200.

Value of the car after eight years is $8200.

(c). V(10) = 5000

This is the value of the car after 10 years

Check.

V(10) = -1600(10) + 21,000

= -16000+21,000

= $5000.

Value of the car after 10 years is $5000.

Hope this helps >>>>

Answer:

39 hours

Step-by-step explanation:

52 × 45 = 2340

2340 mins into hours = 39 hours

hope this helps :)

Answer:

468

Step-by-step explanation:

use the smallest digit in the hundreds place , that is 4

use the next smallest digit in the tens place, that is 6

use the next smallest digit in the units place, that is 8

smallest 3- digit number is 468

Answer: 468

Step-by-step explanation:

Numbers are= 9,6,4,8

Now, rearrange all numbers according to weight,

4<6<8<9

The smallest possible 3-digit number will be 468

Answer: IK=14

Step-by-step explanation:

IK=IJ+JK

IL=IJ+JL

IL-JL=IJ+JL-JL

IJ=IL-JL

IK=IL-JL+JK

IK=31-25+8

IK=6+8

IK=14

Answer: The answer would be 3x+4y=-17

Step-by-step explanation: The reason why that would be the answer is because when you substitute the coordinates into the equation you get -17 and their asking if it is parallel and they are!

Hope this helps :P

The standard form of the given equation f(x) = 6x² − x + 1 is:

[tex]f(x)=6\left(x-\frac{1}{12}\right)^2-\frac{23}{24}[/tex]

So, f(x) = 6x² − x + 1:

We must convert this to standard form, which is provided by:

Where x² is the co-efficient of the leading term and (h, k) is the curve's vertex (minimum and maximum point).

The formula h = -b/2a can be used to calculate h.

We can find k by determining f(h), as k=f (h).

[tex]\begin{aligned}&k=f\left(\frac{1}{12}\right)=6\left(\frac{1}{12}\right)^2-\frac{1}{12}+1 \\&k=\left(6 \times \frac{1}{141}\right)-\frac{1}{12}+1 \\&k=\frac{1}{24}-\frac{1}{12}+1 \\&k=\frac{1-2+24}{24}=\frac{23}{24}\end{aligned}[/tex]

Therefore, the standard form of the given equation f(x) = 6x² − x + 1 is:

[tex]f(x)=6\left(x-\frac{1}{12}\right)^2-\frac{23}{24}[/tex]

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The correct question is given below:

Write the quadratic function in standard form.

f(x) = 6x² − x + 1

The number of digits attached to the number is irrelevant as long as we considering the first non-identical integer. For example:

[tex]6.32215 > 6.32214 \\ since \: 5 > 4[/tex]

Additionally some numbers are written with two decimals only, implying that there an infinite amount of unnecessary zeros attached at the end. For example:

[tex]6.32 = 6.320000000000000000...[/tex]

Now a more clear approach would be to compare these two numbers after attaching these zeros.

[tex]6.3200000000... \\ 6.2350000000...[/tex]

Comparing the first three digits,

[tex]320 > 235 \\ 6.32 > 6.235[/tex]

Answer:

10362

I found it from somewhere

Answer:

When faced with this question as multiple choice, you can either try to verify that one of the answers is true, or you can try to solve for the answer and compare to the choices. Your challenge during a multiple choice test is to identify the fastest possibility so that you can go on to the next problem.

In this case neither choice takes any significant amount of time. You can verify which equation is satisfied by any two points in the table very quickly.

Or you can notice that the equations are all linear and then take two points and solve for the equation of the line between them.

In either case, answer C quickly reveals itself as correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First choice

to find x intercept, substitute y = 0.

where it cuts the y axis is -55

similarly, where it cuts the x-axis is 25

anser is x-int (-55,0) u - int (x,25)

Answer:

f(1) = 1

f(4) = -2

f(0) = 2

Step-by-step explanation:

y = f(x)

The original garden was 6 feet long on each side. The original garden's footprint measured 36 feet.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

Using the information provided,

(x-1)²=25

(x-1)=5

x=6

6x6=36 feet²

The original garden had six sides that were the same length.

The original garden covered 36 feet of space.

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Answer:

6 ft & 36ft

Step-by-step explanation:

Answer:

3:1 = 6:2 = 12:4

Hope this helps :)

Answer:

3.1=12.4

Step-by-step explanation:

12.4

12/12+4=12/16=3/4.

so 3.1=12.4

The floor and ceiling functions of 71.999 returns ⌈x⌉ = 71 and ⌊x⌋ = 72.

By definition, the ceiling function returns the smallest nearest integer which is greater than or equal to the specified number whereas the floor function returns the largest nearest integer which is less than or equal to a specified value.

Thus, the Floor function ⌊x⌋ of 71.999 returns 71 which is less than 71.999. Meanwhile, the ceiling function  ⌈x⌉ of 71.999 returns 72 which is greater than 71.999.

Thus, we conclude that the floor and ceiling functions of 71.999 returns ⌈x⌉ = 71 and ⌊x⌋ = 72.

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By subtracting the taxes from the gross pay we can see that Carlos' net pay is $1,500.30

We know that the gross pay is $1,800, now we need to subtract the social security and taxes.

First, there is a 6.2% and 19% in taxes, adding that we get:

6.2% + 9% = 15.2%

Then we need to subtract a 15.2% of the gross pay, this will give:

P = $1,800*(1 - 15.2%/100%) =  $1,800*(0.848) = $1,526.40

And now we also need to subtract the Medicare, which is $26.10, it gives:

$1,526.40 - $26.10 = $1,500.30

We conclude that Carlos' net pay is $1,500.30

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In the figure, m ∠ 7 = 100 °. The measure of angle 8 is 80°

An angle is a figure in the Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by the two rays are in the plane where the rays are located. The meeting of the two planes also creates angles. We refer to these as the dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of the intersecting curves.

Angle can also refer to length of a rotation or an angle. This metric represents relationship between a circular arc's length and radius. The arc is centered at the vertex and defined by sides in the case of a geometric angle. When there is a rotation, the arc is defined by any other point and rotation's image, and it is centered at the rotation's center.

Given,

∠7 = 100°

According to the given figure,

∠7+∠8= 180°

100°+ ∠8= 180°

∠8= 180°- 100° = 80°

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According to the empirical rule, there are a answers of the given statement.

According to the statement

We have to find that the answers of the given statement.

So, For this purpose, we know that the

The empirical rule is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

From the given information:

The mean of 340 grams and a standard deviation of 35 grams.

Then

a) About 68% of organs weight between:

According to the empirical rule:

68% of the information values lie within 1 variance of the mean

95% of the info values lie within 2 variance of the mean

99.7% of the information values lie within 3 variance of the mean

Thus, 68% of the information values consist the range: Mean - 1 variance to Mean + 1 variance.

Using the values of Mean and variance, we get:

Mean - 1 variance = 320 - 20 = 300 grams

Mean + 1 variance = 320 + 20 = 340 grams

This means 68% of the organs will weigh between 300 and 340 grams.

And

b) In order to search out what percentage of organs weight between the given range, we'd like to seek out what proportion far these values are from the mean.

Since, mean is 320 and 280 is 40 but mean, we will write:

280 = 320 - 40

280 = 320 - 2(2)

280 = 320 - 2 Standard Deviations

Similarly,

360 = 320 + 40

360 = 320 + 2 Standard Deviations

So, we've got to inform what percentage of values lie within 2 variance of the mean. in step with the empirical law, this amount is 95%.

So, 95% of the organs weigh between 280 grams and 360 grams.

And

c) From the previous part we all know that 95% of the organs weight between 280 grams and 360 grams.

It is on condition that the distribution is bell shaped. the full percentage under a bell shaped distribution is 100%. So so as to calculate what proportion percentage of values are below 280 and above 360, we'd like to subtract the proportion of values that are between 280 and 360 from 100% i.e.

Percentage valuable outside the range = 100% - Percentage of values inside the range

So,

Percentage of organs weighs but 280 grams or over 360 grams = 100 - Percentage of organs that weigh between 280 grams and 360 grams

Percentage of organs weighs but 280 grams or quite 360 grams = 100% - 95% = 5%

So, 5% of the organs weigh but 280 grams or over 360 grams.

And

D) 300 is 1 variance below the mean and 360 is 2 standard deviations above the mean.

Previously it's been established that, 68% of the info values lie within 1 variance of the mean i.e

From 1 variance below the mean to 1 variance above the mean, the share of values is 68%. Since the distribution is bell shaped and bell shaped distribution is symmetric about the mean, therefore the percentage of values below the mean and above the mean must be the identical.

So, from 68% of the information values that are within 1 variance from the mean, 1/2 them i.e. 34% are 1 variance below the mean and 34% are 1 variance above the mean. Thus, percentage of values from 300 to 320 is 34%

Likewise, data within 2 standard deviations of the mean is 95%. From this half the information i.e. 47.5% is 2 standard deviations below the mean and 47.5% is 2 standard deviations above the mean. Thus, percentage of values between 320 and 360 grams is 47.5%

So,The total percentage of values from 300 grams to 360 grams = 34% + 47.5% = 81.5%

Therefore, 81.5% of organs weigh between 300 grams and 360 grams.

So, According to the empirical rule, there are a answers of the given statement.

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Considering the greatest common divisor, you obtain:

The greatest common divisor is the largest number that exactly divides two or more numbers at the same time. That is, it is the largest number by which two or more numbers can be divided, resulting in a whole number.

A method to calculate the greatest common factor must follow the following steps:

To find the greatest number of gift bags the party planner can make, you find the greatest common divisor.

To do this, decompose the numbers 96, 36 and 24:

The common factors with the smallest exponent are: 2² and 3

So, the greatest common divisor between 96, 26 and 24 is calculated as: 2²×3= 4×3= 12

This means that the greatest number of gift bags that the party planner can make is 12.

To calculate the number of each item present in each bag, you divide the quantity of each item by the quantity of gift bags:

Finally, the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.

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Answer:

Step-by-step explanation:

f(x) = 1/x

Answer:  its  correct

Step-by-step explanation:

The rate of commission for a commission of $5040 on total sales of $180700 nearest to tenth percent will be 2.8 %.

What is commission rate ?

The commission rate is the percentage or fixed payment associated with a certain amount of sale.

It is given that , Myrtle Gould's total sales last month were of $180700. And the commission she got for the sales was $5040.

Here , the sale is above the criteria to get the commission which is $50000.

The rate of commission can be calculated as follows :

Rate of commission (R) = (5040 × 100)  / 180700

or

R = 504000 / 180700

or

R = 2.8 %

or

Rate of commission will be 2.8 %.

Therefore , the rate of commission nearest to tenth percent will be 2.8 %.

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