Answer:
a) F(x) = 28,000( 1.00575 )^12x + 12,000e^0.098x
b) F'(x ) = 28,000 ( In 1.071224 ) ( 1.071224 )^x + 1176 e^0.098x dollar per year
c) 3228.94 dollar/year, 3428.73 dollar/year
Step-by-step explanation:
Capital = $40,000
$28,000 = low-risk mutual fund
6.9% monthly compounded interest for the low risk mutual fund
$12,000 = high-risk yield bound fund
9.8% continuously compounded interest
A) Equation for total amount in two investments
F(x) = F1(x) + F2(x) ----- ( 1 )
where :
F1(x) ( future value for monthly compounded interest)
= 28,000( 1 + 0.069/12 )^12x = 28,000 ( 1.00575 )^12x
F2(x) ( future value for continuously compounded interest )
= ( 40,000 - 28,000 )e^0.098x = 12,000 e^0.098x
back to equation 1
F(x) = 28,000( 1.00575 )^12x + 12,000e^0.098x
B Rate of change equation
f'(x) = d/dx (28,000( 1.00575 )^12x) + d/dx ( 12,000e^0.098x )
∴ f'(x) = 28,000 d/dx (1.00575^12)^x + 12,000 d/dx(b^x)
= 28,000 ( In 1.071224 ) ( 1.071224 )^x + 12,000 ( In b ) ( b^x )
f'(x ) = 28,000 ( In 1.071224 ) ( 1.071224 )^x + 1176 e^0.098x dollar per year
C) Determine how rapidly the combined amount will grow after 6 months and after 15 months
i.e. x = 0.5 , x = 1.25 years
after 6 months
28,000 ( In 1.071224 ) ( 1.071224 )^(0.5) + 1176*e^((0.098(0.50))
= 1993.88 + 1235.06 = 3228.94 dollar/year
after 15 months
28,000 ( In 1.071224 ) ( 1.071224 )^(1.25) + 1176*e^((0.098(1.25 ))
= 2099.47 + 1329.26 = 3428.73 dollar/year
Help Help Help it's in khan academy
Answer:
Step 1 is wrong
Step-by-step explanation:
[tex] \frac{1}{4} r+ 2 = 10[/tex]
[tex] \frac{r}{4} + 2 = 10[/tex]
[tex] \frac{r}{4} = 10 - 2[/tex]
[tex] \frac{r}{4} = 8[/tex]
[tex]r = 8 \times 2[/tex]
[tex]r = 32[/tex]
Hope it is helpful...Can someone help ASAP
cosa \div tana = 1 - sin ^{2} a \div \sqrt{1 - cos ^{2} } acosa÷tana=1−sin
2
a÷
1−cos
2
a
Step-by-step explanation:
Hey there!
LHS
[tex] = \frac{ \cos(a) }{ \tan(a) } [/tex]
Use tan A = sin A/cosA
[tex] = \cos(a) \times \frac{ \cos(a) }{ \sin(a) } [/tex]
[tex] = \frac{ { \cos(a) }^{2} }{ \sin(a) } [/tex]
Then, Use formula cos²A = 1-sin²A and sinA = √(1-cos²A)
[tex] = \frac{1 - { \sin(a) }^{2} }{ \sqrt{ - { \cos(a) }^{2} } } [/tex]
Proved!
Hope it helps!
2. How many degrees has PRQ been rotated to make PRQ
Answer:
180 degree
Step-by-step explanation:
180 degee
......
......
.......
Zahraa made 4 pitchers of lemonade. Each pitcher holds ⅓ gallon. How many gallons of lemonade did she make? WHATS THE ANSWER??
Answer:
12 gallons
Step-by-step explanation:
If each pitcher can hold only a third of one of her makings. Think about it. Just pour the glasses in your mind. She fills it up a little bit, and then keeps doing it until 12 are full. or how else to explain it or really explain it at all.
2×(4×2-10)³ How do you simplify powers in this?
Answer:
Step-by-step explanation:
first work what's in the brackets { 4 x 2 -10}^3
{4 x 2-1000}
4 x -998
1. What must be added to 203 to get a number whose digits are reversed of the given number?
Please help solve this using L.C.M and explain the steps plz ty.
9514 1404 393
Answer:
(x, y) = (2, 3)
Step-by-step explanation:
The first step is to find the least common multiple of the denominators of each of the equations. If the denominators have no common factors, a reasonable choice is their product. Here, it works to start with the fractions that must be added, then compare the LCM found to the denominator on the right to see if any further factors must be included.
First equation:
LCM = 3×4 = 12
12(2x/3 -y/4) = 12(7/12) . . . . . multiply the equation by 12
8x -3y = 7 . . . . . . . . . simplify
Second equation:
LCM = 4×5 =20
20(3x/4 -2y/5) = 20(3/10) . . . . multiply equation by 20
15x -8y = 6 . . . . . . simplify
Solve by elimination
We can eliminate the y-variable by subtracting 3 times the second equation from 8 times the first:
8(8x -3y) -3(15x -8y) = 8(7) -3(6)
19x = 38 . . . . . simplify
x = 2 . . . . . . . divide by 19
Substituting into the first equation gives ...
8(2) -3y = 7
3y = 9 . . . . . . add 3y-7
y = 3 . . . . . divide by 3
The solution is ...
(x, y) = (2, 3)
_____
There are many ways to solve such a system of equations. Using the LCM to eliminate fractions is one way to start. You can also do the arithmetic with the fractions intact, though most folks don't care to. In addition to the elimination method used here, you can use matrix or graphical methods, substitution, or any of the variations of Cramer's Rule.
What is the slope of the line that contains the points (-1,-1) and (3, 15)?
O A.
1
4
B. 4
O C. -
4
D. -4
Answer:
its b
Step-by-step explanation:
ayuda ÷18=40 que número falta
Answer:
720
Step-by-step explanation:
x÷18=40
x=18•40
x=720
If the ratio of paintings to paintbrushes is 11:9, what percent of the items are paintbrushes. A.30% B. 35% C.40% D.45%
Answer:
D. 45%
Step-by-step explanation:
there are 11 paintings and 9 paintbrushes, added together you have a total of 20 items. There are 9 paintbrushes and 20 items in total which is 9/20. 9/20 as a percentage is 45%
Solve this equation 2n-9<25
Answer:
n < 17
Step-by-step explanation:
2n-9<25
Add 9 to each side
2n-9+9<25+9
2n < 34
Divide each side by 2
2n/2 < 34/2
n < 17
Answer:
n < 17
Step-by-step explanation:
Move the constant to the right -hand side and change its sign
2n<25+9
Then add the numbers
2n < 34
Divide both sides of the inequality by 2
so that would be n<17
The frequency table shows all but one score on a 5-point geography quiz. If the mode of the complete data set is 4, what is the unknown quiz score?
Answer:
(4)
Step-by-step explanation:
element =4
frequency=1
cumulative frequency-=1
relative frequency=1
cumulative relative frequency=1
A box is filled with several party favors. It contains 12 hats, 15 noisemakers, 10 finger traps, and 5 bags of confetti. Let H = the event of getting a hat. Let N = the event of getting a noisemaker. Let F = the event of getting a finger trap. Let C = the event of getting a bag of confetti. Find P(N).
Answer:
P(N) = 5/14
Step-by-step explanation:
Find P(N) by finding the probability of getting a noisemaker.
There are 42 items in total, and 15 are noisemakers. Find the probability by dividing 15 by 42:
15/42
Simplify:
5/14
So, P(N) = 5/14
Five schools are going to send their baseball teams to a tournament, in which each team must play each other team exactly once. How many games are required
Answer:
20 games are required to be play
The graph makes it appear that there are how many times as many students per teacher at North HS as there are at
West HS?
Student Teacher Ratios at Area High Schools
North RS
East HS
13
West HS
12
14
18
22
a.
b.
10
2 times
3 times
4 times
5 times
C.
d.
Answer:
5 times
Step-by-step explanation:
Using visual inspection, the bar of North HS is 5 times longer Than the bar of West HS.
The gtids are of equal size, West HS occupies one portion of the grid, while North HS occupies 5 portions of the grid
5 portions / 1 portion = 5
Hence, North HS according to the graph is 5 times West HS
Please help! Thank you!
Answer:
D: (2, -3)
Step-by-step explanation:
We have;
y = 3x - 9 - - - (1)
y = -2x + 1 - - - (2)
By substitution method, from eq 1, we see that: y = 3x - 9
Thus,let's put 3x - 9 for y in eq 2;
3x - 9 = -2x + 1
Rearranging to get;
3x + 2x = 9 + 1
5x = 10
x = 10/5
x = 2
Thus;
y = 3(2) - 9
y = 6 - 9
y = -3
Thus,the solution (x, y) = (2, - 3)
Which of the following represents the ratio of the given side to the
hypotenuse?
HELP if you’re good at GEOMETRY!!
You deposit $2000 in a retirement account that earns 5% annual interest. You repeat this deposit yearly for 30 years. How much money do you have in your account after you make your final deposit?
Answer:
$3000
Step-by-step explanation:
$2000×5/×30
$1000×3=$3000
What is the solution to -2(8x - 4) < 2x + 5?
Answer:
See image below:)
Step-by-step explanation:
Which graph represents the function (x) = -1x - 21 - 1?
Answer:
Given in the graph
Step-by-step explanation:
Alex was trying to determine how much money he owed the bank. Since his checking account has a balance of -155 dollars, he thinks that he can find the absolute value of -155 to determine that he owes the bank 155 dollars. Is Alex correct?
Answer:
Alex is correct.
Step-by-step explanation:
In order for Alex to get to $0, meaning he owes the bank nothing, he has to add 155 dollars to negative 155 dollars, because this means he has no debt left. The absolute value of -155 is 155 and if Alex pays the 155 dollars, he will not have to pay anything else to the bank.
A restaurent pays a water R18 per hour in one week he worked a shift from 12h00 to 23h00 Calculate the number of hours the water works per shift
Answer:
Number of hour work per shift = 11 hour per day
Amount paid for one shift = Rs 198
Step-by-step explanation:
Given:
Amount pay per hour = Rs 18
Shift time = 12 h to 23 h
Find;
Number of hour work per shift
Amount paid for one shift
Computation:
Number of hour work per shift = 23:00 - 12:00
Number of hour work per shift = 11 hour per day
Amount paid for one shift = Number of hour work per shift x Amount pay per hour
Amount paid for one shift = 11 x 18
Amount paid for one shift = Rs 198
In the figure below, which term best describes point R?
A. Orthocenter
B. Centroid
C. Incenter
D. Circumcenter
Orthocenter is the best term to describes point R in the triangle UVW.
What is orthocenter?" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."
According to the given figure,
In triangle UVW,
Ray VR perpendicular to UW
Ray UR perpendicular to VW
Ray WR perpendicular to UV
Altitudes of side ( UV , VW, and WU) of triangle UVW intersect at
point R.
As per the definition of orthocenter , point R represents orthocenter.
Hence, orthocenter is the best term to describes point R in the triangle UVW.
Learn more about orthocenter here
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Need help ASAP!!!!!!
Answer:
I dont know for sure, but maybe try B
Step-by-step explanation:
work out 8^1/3
^1/3 = power
Answer:
8/9 (decimal: 0.888889)
Answer:
[tex]2[/tex]
Two is the answer.
Step-by-step explanation:
simple explanation is; when you go through your two times table.. in order to arrive at eight, (8), you have to mention or go through 3 numbers
Or .... cube root of 8 is two..
PLEASE MARK ME BRAINIEST
Need the answer to number 4
Answer:
[tex]\sqrt{85}[/tex] /2
Step-by-step explanation:
lets find hypotenuse( longest side) first
let other two samller sides be a and b and hypotenuse be c
pythagorsd theorem
a^2 + b^2 =c^2
9^2 + 2^2 =c^2
81 + 4=c^2
85 =c^2
[tex]\sqrt{85}[/tex] =c
take theta as reference angle
cosec theta=hypotenuse/opposite
=[tex]\sqrt{85}[/tex] / 2
Answer:
Answer is B. CSC ∅ = √85 /2
Step-by-step explanation:
CSC = 1 / Sin ∅
So first find Sin ∅ = 2 / √ 85 and then substitute in the formula
And oh, in case you're wondering, √ 85 is the hypotenuse side which you find like this:
√ 9² + 2²
√ 81 + 4
√ 85
Anyone know this? Please help
Help (PLATO)
its Algebra
Answer: The answer is D
Step-by-step explanation:
You add z to the other side then it will cancel out which then it would be (w+z) and then you times it by 2 by both sides which would be 2(w+z) and then you would subtract x from both sides which will be 2(w+z)-x
Hopefully this helps
What is the perimeter of the trapezoid? In unit
Answer:
20 units
Step-by-step explanation:
the perimeter = 7+4+4+5 = 20 units
