Answer:
[tex] - \sin( \beta ) \times - \sin( \beta ) \\ = ( { \sin}^{2} \beta ) \\ = \sqrt{1 - { \cos }^{2} \beta } [/tex]
Need help with my final it’s my final grade
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?
In scenerio 1, the money in the retirement account at 62 years old is $1,267,250.76
In scenerio 2, the money in the retirement account at 62 years old is $ 633,625.38.
How do we calculate future value of an ordinary annuity?Scenerio 1:
a) 6% of salary = Salary * 6% = $6,100 * 6% = $366
b) Total amount the company paid monthly = 6% of salary = Salary * 6% = $6,100 * 6% = $366
c) The money in the retirement account at 62 years old can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity given as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where:
FV = Future value = Money in the retirement account at 62 years old = ?
M = Monthly payment = Contribution you + Contribution by the employer = $366 + $366 = $732
r = Monthly interest rate = Annual interest rate / 12 = 6.28% / 12 = 0.0628 / 12 = 0.0052
n = number of months = Number years * Number of months in a year = (Retirement age – Age when hired) * 12 = (62 - 25) * 12 = 37 * 12 = 444
Substituting all the values into equation (1), we have:
FV = $732 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $1,267,250.76
d) Amount of money you put into the account = 6% of salary * number of months = $366 * 444 = $162,504
e) Amount of money your employer put into your account = Amount of money you put into the account = $162,504
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $1,267,250.76 – ($162,504 + $162,504) = $942,242.76
Scenario 2:
a) 3% of salary = Salary * 3% = $6,100 * 3% = $183
b) Total amount the company paid monthly = 3% of salary = Salary * 3% = $6,100 * 3% = $183
c) Using equation (1), we have:
M = Monthly payment = Contribution you + Contribution by the employer = $183 + $183 = $366
Substituting all the values into equation (1), we have:
FV = $366 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $633,625.38
d) Amount of money you put into the account = 3% of salary * number of months = $183 * 444 = $81,252.00
e) Amount of money your employer put into your account = Amount of money you put into the account = $81,252
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $633,625.38 – ($81,252 + $81,252) = $471,121.38
The difference in the amount of money at age 62 between scenarios 1 and 2 = Money in the retirement account at 62 years old in scenarios 1 + Money in the retirement account at 62 years old in scenarios 2 = $1,267,250.76 - $633,625.38 = $633,625.38
Difference in the amounts of money you put into retirement between scenarios 1 and 2 = $366 - $183 = $183
Amount got from your employer in scenario 1 than 2 = $366 - $183 = $183
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Which equation represents the situation shown in the bar diagram?
A bar diagram with 15 across the top row and 4 n's and a 2 across the bottom row.
n + 2 = 15
4n + 2 = 15
4(n + 2) = 15
4n – 2 = 15
Answer:
try that it should help you with you question
Step-by-step explanation:
https://www.khanacademy.org/math/cc-2nd-grade-math/x3184e0ec:data/cc-2nd-bar-graphs/v/creating-bar-charts-1
Is gram mole equal to mole?
No, one mole is not equal to one gram. For an object, the mole and gram numerical values differ.
1 gram, what is it?
One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.
The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.
A mole's relationship to a gram is
The product of the number of Moles of an object to its atomic weight equals one gram.
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find the area of the figure below:
Answer:
104 ft^2
Step-by-step explanation:
Answer:
104 ft²
Step-by-step explanation:
you can solve this multiple ways, one way is: find the area of the big rectangle and subtract from it the area of the small rectangle
big rectangle
A big = 8 * (5+6+5)= 8 * 16 = 128 ft²
small rectangle
Asmall = 4*6 = 24 ft²
area of the shape
Abig -Asmall = 128-24 = 104 ft²
Karen has a square rug that covers 76.5 ft^2 of her living room floor. Which measurement is closest to the side length of this rug in feet?
A. 8 ft
B. 9 ft
C. 19 ft
D. 20 ft
E. 38 ft
F. None of the above
A club consisting of 11 men and 12 women needs to choose a committee from among its members so that the number of women on the committee is one more than the number of men on the committee. The committee could have from 1 to 23 members. How many committees can be formed
The total number of such committees that may be created, divided by the prime numbers that divide N, is 81.
What is the prime numbers that divide N?In the scenario presented in this question, a club with 11 men and 12 women must elect a committee from among its members in order for there to be one more woman on the committee than males.
The committee might consist of only 1 person or up to 23 people.
Let N represent the maximum possible number of such committees.
The total number of prime numbers that divide N must be determined.
The number of ladies chosen will be m.
The number of guys who were not chosen would thus be:
11 - (m - 1) = 12 - m
Each pairing of men who were not chosen and women who were chosen represents a committee choice.
Since selecting 12 people from a total of 23 would result in m women and 12 - m males, the committee chose:
making use of a combination formula
N = 23C12
N = 23!/12!(23 - 12)!
N = 1352078
These are the main components of 1352078: 2, 7, 13, 17, 19, and 23.
Consequently, the prime number total would be,
2 + 7 + 13 + 17 + 19 + 23 = 81
The total of the prime numbers is thus 81.
The complete question is:
A club consisting of 11 men and 12 women needs to choose a committee from among its members so that the number of women on the committee is one more than the number of men on the committee. The committee could have as few as 1 member or as many as 23 members. Let N be the number of such committees that can be formed. Find the sum of the prime numbers that divide N.
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help
A certain television is advertised as a 38-inch TV (the diagonal length). If the width of the TV is 29 inches, how tall is the TV? Round to the nearest tenth of an inch.
Answer:
24.6
You are welcome
Step-by-step explanation:
11. - a? - 2bc - Icl
if a = -2, b = 3,
and c = -3
problem in the photo
algebra
The value of expression - a² - 2bc - |c| if a = -2, b = 3, and c = -3, is 11.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
- a² - 2bc - |c|, a = -2, b = 3, and c = -3,
Plug the values of a, b, and c as shown below,
- a² - 2bc - |c| = -(-2)² - 2 × (3) × (-3) - |-3|
- a² - 2bc - |c| = - 4 - 6 × (-3) - 3
- a² - 2bc - |c| = -4 + 18 - 3
- a² - 2bc - |c| = 18 - 7
- a² - 2bc - |c| = 11
Thus, the value of the expression is 11.
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Which equation, together with y = -1.5x + 3, makes a system with one solution?
Y= -1.5x + 6
Y= -1.5x
2Y= -3x + 6
2Y + 3x = 6
Y= -2x + 3
Answer:
2y + 3x = 6 is answer correct
if the perimeter of the rectangle was known to be 90 in what would the value of x be in order for this to be true
Answer:
x = 30 in
Step-by-step explanation:
length of rectangle is (2/3)x + 10; width is (1/3)x + 5;
perimeter is 90 in; find x:
P = 90 in = 2(2/3)x + 2(10) + 2(1/3)x + 2(5), or
90 in = (6/3)x + 30 in
Solving for x, we get (2)x = 60 in, or x = 30 in
Kendra and Haley are each saving money. Kendra starts with $100 in his savings
account and adds $5 per week. Haley starts with $10 in her savings account and adds
$20 each week. After how many weeks will Haley have at least the same amount of
money as Kendra?
OX26
Ox>6
O x 216
Ox< 16
That means after 6 weeks will Haley have at least the same amount of
money as Kendra
Kendra and Haley are each saving money. Kendra starts with $100 in his savings account and adds $5 per week. Haley starts with $10 in her savings account and adds $20 each week. After how many weeks will Haley have at least the same amount of money as Kendra?
Kendra and Haley are each saving money.
Kendra starts with $100 in his savings
account and adds $5 per week.
After 6 week 6* 5 = 30
Total amount in After 6 week in Kendra savings
account = $100 + $30
= $130
Haley starts with $10 in her savings account and
adds $20 each week.
After 6 week 6* 20 =120
Total amount in After 6 week in Haley savings
account = $10 + $120
= $130
That means after 6 weeks will Haley have at least the same amount of
money as Kendra
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If 2/3x-1=4,then x=?
Answer:
a
Step-by-step explanation:
Edwin got 95% of the questions right on a quiz. If there were 20 questions on the quiz, how many questions did he miss??
Answer:
He got a 19 out of 20, great job Edwin ;)
Step-by-step explanation:
Hope this helps :)
Edwin missed 1 question on the quiz.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
If Edwin got 95% of the questions right on a quiz and there were 20 questions in total, we can calculate the number of questions he missed by finding 5% of the total number of questions.
First, let's find 5% of 20:
= 5% of 20
= (5/100) x 20
= 1 x 20 / 100
= 20 / 100
= 0.2
Since we can't have a fraction of a question, we round the decimal up to the nearest whole number.
In this case, 0.2 rounds up to 1.
Therefore, Edwin missed 1 question on the quiz.
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Jared’s monthly income is 4500 Jared spend 11%of his income on grocies
Answer:
Jared's groceries = 495
Step-by-step explanation:
We calculate 11% from Jared monthly income:
11% x 4500 = 495
Jared's groceries = 495
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write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation
(-2,3); y=1/2x - 1
Answer:
y = -2x - 1
Step-by-step explanation:
y = -2x + b
3 = -2(-2) + b
3 = 4 + b
-1 = b
y = -2x - 1
While Mike was visiting his sister in Arlington, he bought an aquarium that was marked down 60% from an original price of $100. If the sales tax in Arlington is 5%, what was the total cost of the aquarium?
Answer:
$42
Step-by-step explanation:
100 - 60% * 100 = $40
Since tax is 5%, therefore:
40 + 5% of 40 = $42
Thenks and mark me brainliest :))
Answer:
The answer is $42 but give the other guy brainliest.
Step-by-step explanation:
The ratio of blueberries to strawberries is 1:7 if there are 210 strawberries how many blueberries are there.
Answer:
30 blueberries
Step-by-step explanation:
1: blueberry
7: strawberries
?: blueberries
210: strawberries
[tex] \frac{1}{7} = \frac{?}{210} [/tex]
210÷7=30
1×30=30
Davis earns a 4% commission for all furniture he sells. If David receives $7509 in commission this year , what is the dollar amount of his sales?
Answer:
187,725
Step-by-step explanation:
7,509/.04=187,725
50 POINTS NEED HELP ASAP!!! What is the arc length of an arc with a central angle of 23π radians in a circle with a radius of 18 cm?
Enter your answer to the nearest whole centimeter in the box.
__cm
Answer:
38 cmStep-by-step explanation:
Arc length is:
s = rθ, where r- radius and θ - central angle in radianss = 18*(2/3)π ≈ 38 cmUse the general formula
L=rØL=2/3π(18)L=2(6)πL=12πL=38cmThe roof on a house is 6 metres wide peaks at at a height of 3 metres above the top of the walls. Find the length of the sloping side of the roof.
I don't get this, please help me.
Answer:
Ok
Step-by-step explanation:
Answer:
rate of change is 1
Step-by-step explanation:
She grew one inch per month
Please Help ASAP!!!!
Will mark branliest if correct.
Solve this system of equation by elimination. 2x-5y=8 3x+5y=-13
Answer:
x=-1, y=-2. (-1, -2).
Step-by-step explanation:
2x-5y=8
3x+5y=-13
----------------
5x=-5
x=-5/5
x=-1
2(-1)-5y=8
-2-5y=8
5y=-2-8
5y=-10
y=-10/5
y=-2
The price of a video game was orginally $60. There was a $15 discount. By what percentage was the price of the video game reduced?
Answer$84:
Step-by-step explanation:
Answer: 25%
Step-by-step explanation:
What are the properties of directed line segment?
The equation of the line segment is written in the form y = mx + b, where m is the slope and b is the y-intercept. Finally, a directed line segment is two-dimensional.
1. It has a definite starting point and a definite ending point.
2. It has a definite length.
3. It has a definite direction.
4. It has a slope and equation.
5. It divides the plane into two parts.
6. It is symmetric about its mid-point.
7. It is two-dimensional.
A directed line segment is a line segment that has a definite starting point and a definite ending point. Its length is the distance between the two points and it has a direction, given by the vector from the starting point to the ending point. The line segment divides the plane into two parts. It is symmetric about its mid-point, which is the point halfway between the two endpoints. It has a slope and an equation. The slope is the ratio of the change in y-coordinates to the change in x-coordinates. The equation of the line segment is written in the form y = mx + b, where m is the slope and b is the y-intercept. Finally, a directed line segment is two-dimensional.
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A coefficient indicates the number of times a term has been a. added b. subtracted c. multiplied d. divided
Answer:
C. Multiplied
Step-by-step explanation:
A coefficient is a quantity placed before a variable to indicate how many times it has been multiplied.
How much of a radioactive kind of barium will be left after 39 days if you start with 52,256 grams and the half-life is 13 days?
Answer:
Step-by-step explanation:
Answer:
6,532
Step-by-step explanation:
ixl
Find the area of the shaded region.
Answer:
i think 132. but I could be wrong.
Step-by-step explanation:
Leo's bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively. The balances form a geometric sequence.
What will Leo's balance be after 8 months?
Leo's bank balance will be $
after 8 months.
Leo's balance after 8 months is $1725.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16 is a geometric sequence.
We have,
1500, 1530, and 1560 is a geometric sequence.
First term.
a = 1500
Common ratio.
r = 1.02
The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].
Now,
For n = 8,
8th term.
= 1500 x [tex]1.02^7[/tex]
= 1500 x 1.15
= 1725
Thus,
The balance after 8 months is $1725.
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