Aiden invested $43,000 in an account paying an interest rate of 9 1/4 % compounded monthly. Hailey invested $43,000 in an account paying an interest rate of 8 7/8% compounded continuously. To the nearest dollar, how much money would Aiden have in his account when Hailey's money has doubled in value?
first off let's change the mixed fractions to improper fractions, and let's Hailey's account first.
[tex]\stackrel{mixed}{9\frac{1}{4}}\implies \cfrac{9\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{37}{4}} ~\hfill \stackrel{mixed}{8\frac{7}{8}}\implies \cfrac{8\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{71}{8}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &\stackrel{43000(2)}{\$86000}\\ P=\textit{original amount deposited}\dotfill & \$43000\\ r=rate\to \frac{71}{8}\%\to \frac{~~ \frac{71}{8}~~}{100}\dotfill &0.08875\\ t=years \end{cases} \\\\\\ 86000=43000e^{0.08875\cdot t}\implies \cfrac{86000}{43000}=e^{0.08875t}\implies 2=e^{0.08875t}[/tex]
[tex]\ln(2)=\ln(e^{0.08875t})\implies \log_e(2)=\log_e(e^{0.08875t})\implies \ln(2)=0.08875t \\\\\\ \cfrac{\ln(2)}{0.08875}=t\implies 7.81\approx t[/tex]
ok, now we know how long it takes for Hailey's money to double, how much money does Aiden have by then?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$43000\\ r=rate\to \frac{37}{4}\%\to \frac{~~ \frac{37}{4}~~}{100}\dotfill &0.0925\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &\frac{\ln(2)}{0.08875} \end{cases}[/tex]
[tex]A=43000\left(1+\frac{0.0925}{12}\right)^{12\cdot \frac{\ln(2)}{0.08875}}\implies A=43000\left( \frac{4837}{4800} \right)^{\frac{12\ln(2)}{0.08875}}\implies \boxed{A\approx 88311}[/tex]
notice, in Hailey's amount we used the logarithmic value for "t", just to avoid any rounding issues.
Write an equation in slope-intercept form of the line that passed through (-3,4) and (1, 4).
Show work
Answer:
y = 4
Step-by-step explanation:
Use slope intercpet form: y = mx + b
Classify each of the following angles as acute, obtuse, right,straight, or reflex.
Answer:
1. Acute, because it is less than 90 degrees or less than a right angle.
2. that is obtuse because it is bigger than 90 degrees
3. acute, because it is less than 90 degrees.
Answer:
1. Acute 2. Obtuse 3. Acute
Step-by-step explanation:
1 and 3's angles are smaller than 90 degrees. 2 is obtuse because its angle is larger than 90 degrees.
Compute x/y if
x + 1/y = 4 and
y + 1/x = 1/4
Please explain the process on how to solve it- I'll give brainliest!
Let first consider the equations one by one and will be solving one by one ;
[tex]{:\implies \quad \sf x+\dfrac{1}{y}=4}[/tex]
Multiplying both sides by y will lead ;
[tex]{:\implies \quad \sf xy+1=4y}[/tex]
[tex]{:\implies \quad \boxed{\sf xy=4y-1\quad \cdots \cdots(i)}}[/tex]
Now, consider the second equation which is ;
[tex]{:\implies \quad \sf y+\dfrac{1}{x}=\dfrac14}[/tex]
Multiplying both sides by x will yield
[tex]{:\implies \quad \sf xy+1=\dfrac{x}{4}}[/tex]
[tex]{:\implies \quad \sf xy=\dfrac{x}{4}-1}[/tex]
[tex]{:\implies \quad \boxed{\sf xy=\dfrac{x-4}{4}\quad \cdots \cdots(ii)}}[/tex]
As LHS of both equations (i) and (ii) are same, so equating both will yield;
[tex]{:\implies \quad \sf 4y-1=\dfrac{x-4}{4}}[/tex]
Multiplying both sides by 4 will yield
[tex]{:\implies \quad \sf 16y-4=x-4}[/tex]
[tex]{:\implies \quad \sf 16y=x}[/tex]
Dividing both sides by y will yield :
[tex]{:\implies \quad \boxed{\bf{\dfrac{x}{y}=16}}}[/tex]
Hence, the required answer is 16
The copy machine at the library made a copy of Leslie's 3-page essay in just 1/10 of a minute. What is the speed of the copy machine?
Answer:
30 pages
Step-by-step explanation:
https://brainly.com/question/17253194
Speed is the change in distance of a body with respect to time.
Speed = Distance/Time
If the library made a copy of leslie's 3 page essay in just 1/10 of a minute, this means that she made 3 pages in (1/10 * 60)secs i.e 6secs
To get the speed, we need to calculate the amount of page of essay that are produced in a minute (60secs).
If 3 page essay = 6secs
x page essay = 60 secs
cross multiply
3*60 = 6x
180 = 6x
x = 180/6
x = 30
This shows that 30 page essays are produced in just a minute. Hence the speed of the copy machine is 30page essay/min.
only question 6 and 7 please answer fast I need it now ty
Answer:
6. $62.74 7.$331
Step-by-step explanation:
6. The original cost= $119.5
After 30% of discount = (70/100)× 119.5
= $83.65
After 25% discount = (75/100)× 83.65
= $62.74
7. Original cost= 679
Price after 35% discount = (65/100)×679=$441.35
Price after 25% discount = (75/100)× 441.35
=$331
So the final price will be = $331
Use substitution to solve the system.
Y=2x+11 5x+2y=-14
X=
y=
Answer:
x = -4, y = 3
Step-by-step explanation:
1. Substitute 2x + 11 for y:
5x + 2(2x + 11) = -14
2. Simplify:
2(2x) = 4x
4x + 5x = 9x, 2(11) = 22
so,
9x + 22 = -14
3. Isolate x:
9x + 22-22 = -14-22 = 9x -36
9x/9 = -36/9
x = -4
4. Plug in the value of x in to solve for y:
y = 2(-4) + 11
y = 3
hope this helps!
Solve the following inequality for s. Write your answer in simplest form.
-10 + 5(78 + 8) < - 4s +3 - 8
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - 10 + 5(78 + 8) < - 4s + 3 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \: - 10 + 5(86) < - 4s - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: - 10 +430 < - 4s - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: 420 + 5 < - 4s [/tex]
[tex]\qquad \sf \dashrightarrow \: 42 5 < - 4s [/tex]
[tex]\qquad \sf \dashrightarrow \: 42 5 \div 4 < - s [/tex]
[tex]\qquad \sf \dashrightarrow \: 106.25 < - s [/tex]
Inequalities change when it is multiplied by -ve number
[tex]\qquad \sf \dashrightarrow \: - 106.25 > s [/tex]
what is 1/4x-6=-10 step by step please help me
Answer:
x = -16
Step-by-step explanation:
[tex]\frac{1}{4}x-6=-10 < ==add\ 6\ to\ both\ sides\\ \ \ \ \ \ \ \ \ +6 \ \ \ \ \ \ \ \ +6\\\\\frac{1}{4}x=-4 < ==multiply\ both\ sides\ by\ 4\\4(\frac{1}{4}x=-4)\\\\x=-16 < ==final\ answer[/tex]
Hope this helps!
Find the volume of the following. Show your work
Answer:
the #1 one is about 307.88 & the #2 on is 100.53
Step-by-step explanation:
Answer:
308 in³, 101 in³ (from left to right)
Step-by-step explanation:
Volume of cylinder= πr²h, where r is the radius and h is the height.
Cylinder on left
radius= 7 in
height= 2 in
Volume
= π(7²)(2)
= 98π
= 308 in³ (3 s.f.)
Cylinder of right
radius= 4 in
height= 2 in
Volume
= π(4²)(2)
= 32π
= 101 in³ (3 s.f.)
if a quadratic in x is greater than zero for all values of x, then can it have real roots?
Answer:
There's no real roots
Answer:
No.
Step-by-step explanation:
The graph will not cut the x-axis.
Isaac made 2 quarts and 1 cup of cupcake batter. If 6 ounces of butter make one cupcake, And Isaac is making 10 cupcakes,How much batter will be left over.
Answer:
The Answer is 1 cup and 4 oz, I'm sorry if incorrect..>~<
Answer:
The Answer is 1 cup and 4 oz.
Step-by-step explanation:
2qts + 1cup equals 72 oz. 6oz x 10=60oz.
72 oz - 60 oz = 12 oz. 1 cup and 4 oz.
The area of the figure is
square units?
Answer:
8 squared units
Sorry if this answer is not correct, if it is or is not, please tell me in the comments!
Step-by-step explanation:
Rectangle:
To find the area of the rectangle, we need to mutiply the base and the height. 3 units(base) x 2 units(height) = 6 squared units
Triangle:
To find the area of the triangle is very similar to finding the area of the rectangle. We need to multiply the base and the height and divide it by 2.
Base= 2 units(since it is a rectangle, the opposite side is the same length)
Height = 2 units
Next, we plug it in to this formula: 1/2 bh (b = base and h = height)
multiplying by one half is the same as dividing by 2
The area of the triangle is 2 x 2 = 4
4 divided by 2 = 2 squared units
For the final step, we add the areas together. (6+2 = 8) the label is very important (squared units)
Which of these could be the lengths of right triangle abc
A) 4,3,7
B) 5,7,12
C) 6,8,10
D) 7,8,15
Answer: C
Step-by-step explanation:
This is a Pythagorean triple.
The area of the Atlantic Ocean is 2.9638 x 107 mi? . The area of the
Pacific Ocean is 6.0061 x 107 mi? How much greater is the area of the
Pacific Ocean than the area of the Atlantic Ocean?
A 3.0423 x 10° mi?
B 3.0423 x 104 mi?
C 3.0423 x 106 mi?
D 3.0423 x 10? mi?
Answer:
Answer not in the listed options....did you enter all of the info correctly ?
Step-by-step explanation:
6.0061 / 2.9638 = 2.026 times bigger
i really need the help with this multiple choice question for geometry.
Answer:
A. 50°
Step-by-step explanation:
The external angle ACB created by tangents CA and CB is the supplement of arc AB it intercepts.
∠ACB = 180° -AB
∠ACB = 180° -130°
∠ACB = 50°
Richard worked 14 hours this week. He also got a bonus of $50. If he made a total of 232, how much does he get paid per hour.
Arianna paid $144 in simple interest on a $2000 loan that she repaid in 2 years. what interest rate did ariana pay on the loan
Ariana paid a 3.6% interest rate on the loan.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
We have been given data as:
Principal (P) = $2000
Simple interest = $144
Time (T) = 2 years
⇒ Simple interest = P × R × T
Substitute the value of P and T in the above formula,
⇒ 144 = 2000 × R × 2
⇒ 144 = 4000 × R
⇒ R = 144/4000
Apply the division operation, and we get
⇒ R = 0.036
⇒ R = 3.6 %
Therefore, Ariana paid a 3.6% interest rate on the loan.
Learn more about the simple interest here:
brainly.com/question/22621039
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Two drums have their radii in the ratio of 2:3, if the height of the first drum is 1.5m, what is the height of the second drum, if the two contain same amount of water?
Answer:
0.6
Step-by-step explanation:
apply the volume of cylinder and equal both of them because both contain same amount of water.
see the picture for full solution
Compare learning about functions to learning a new language. How are they similar?
Answer:
Similarities
They both follow strict laws (typically stricter for math).
Practice makes perfect: both can be learned to points of practical perfection.
The brain must first attribute meaning or value to elements of either in order to build a learning pattern.
Differences:
Math is learned under assumptions of perfection (2 + 2 = 4 ALWAYS); whereas, language is learned under assumptions of reality (2 + 2 may be 5 for significantly larger values of 2). In other words, 2 average sized men plus 2 average sized Texans would more likely equal 5 or more average sized men.
Math is logical and language is largely artistic.
There is only one solution (or specific set of solutions) to every math problem. On the other hand, there are at least 100 different ways to express the same idea using language.
Step-by-step explanation:
Answer:
Language rules could be compared to syntax rules that govern the writing and scripting of a function. Language-based rules could be compared to syntax rules when writing functions, such that when the guiding syntax is correctly displayed, the function is clear and easy to read.
2. The cost to rent a paddleboat at the city park includes an initial fee of $7.00, plus $3.50 per hour.
Which equation models the relationship between the total cost, y, and the number of hours, x,
,
that the paddleboat is rented?
(2015)
A. y=3.5x+7 B. y=7x +3.5 C. y=+3.5 D. y + 7
Answer:
The answer would be y=3.5x+7
Step-by-step explanation:
This is because there is a one-time fee of $7, meaning there is no x attached with it. 3.5 has an x with it because it is 3.5 per hour, and not just one time. Hope this helps! :)
In experimental studies, we follow a logical method to arrive at a conclusion. Arrange the given steps in the correct sequence.
Answer:
state the problem
ask relevant questions
perform an experiment to collect data
compare with the baseline value of the control group
arrive at a logical conclusion
make a hypothesis
identify the equation of the graph.
2x+3y=6
2x-3y=6
2x-3y=-6
2x+3y=-6
What is the Evaluate 5^3+6x3
Answer:
33 Is your answer :)
Step-by-step explanation:
Always do P.E.M.D.A.S ( always go in order it gives you) parenthesis, exponets, multiply/divide, and add/subtract
5^3+6*3=
15+18= 33
HELP please! I need Help. Pre-calc. I'm not sure how to solve this. 50 Points! Please It will be appreciated.
An elliptical mirror has an eccentricity of 0.8. The mirror is surrounded by a 2-inch wide golden frame and is 34 inches tall including the frame. If a replacement mirror is being cut from a rectangular sheet of glass, what is the minimum dimensions needed for the sheet of glass?
Group of answer choices
A. 17 inches by 9 inches
B. 17 inches by 8 inches
C. 15 inches by 8 inches
D. 15 inches by 9 inches
[tex]\large{\mathcal{QUESTION:}}[/tex]
An elliptical mirror has an eccentricity of 0.8. The mirror is surrounded by a 2-inch wide golden frame and is 34 inches tall including the frame. If a replacement mirror is being cut from a rectangular sheet of glass, what is the minimum dimensions needed for the sheet of glass?
[tex]\large{\mathcal{ANSWER:}}[/tex]
B. 17 inches by 8 inches
The minimum dimensions needed for the sheet of glass are B. 17 inches by 8 inches
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We are given that elliptical mirror has an eccentricity of 0.8.
Since the mirror is surrounded by a 2-inch wide golden frame and is 34 inches tall including the frame. If a replacement mirror is being cut from a rectangular sheet of glass,
We can conclude that the minimum dimensions needed for the sheet of glass could be;
17 inches by 8 inches
Learn more about the area;
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The first three and last terms of an arithmetic sequence are 7, 13, 19,..., 1357.
(a) Find the common difference.
Answer:
6
Step-by-step explanation:
common difference = (n + 1) - nth term = 13 - 7 =6
Answer:
subtract 6 every time
Step-by-step explanation:
you subtract first term from second term
Which is the largest ratio?
StartFraction 5 Over 36 EndFraction, 2:9, 3 to 18, 1:3
Answer:
Convert these ratios into fractions and then into their actual values.
(This is just one way of solving this, there are other plentiful ways you could use to solve this.)
2 : 9
Will become
2/9
Which will result in
0.222...
3 : 18
Will become
3/18
Which will result in
0.1666...
1 : 3
Will become
1/3
Which will result in
0.333...
Now, compare these numbers:-
0.222..., 0.1666..., and 0.333...
And out of these three numbers, 0.333... is by far the greatest number out of all of these ratios.
Therefore, the ratio 1:3 is the largest ratio.
3. Erin is an architect who is currently constructing a new building. She is looking at the building's new blueprints. a) Erin needs to find the distance around the patio in order to finish construction soon and build a fence. What is the distance around the patio? Show your steps. b) Erin now needs to find the area of this part of the building in order to buy tiles for the floor plan, which is shown on the blueprints. What is the area of the floor plan? Show your steps
Answer:
a is when you need to go from 12 to 5 so is this flvs?
Step-by-step explanation:
Answer:
a)
first you need to find the missing lengths the first one would be
12-7=5
and the second one you will need to find the circumference
π*4*2=8π
and now you add
12+7+5+5+3+8π=32+8π
so the perimeter is 32+8π
b)
so lets make some sections
one of the sections will be a rectangle that is 8 in length and 7 in width
8*7=56units^2
and another reactangle that is 3 in length and 5 in width
3*5=15units^2
and then we need to find the area for the semicircle with a raidius of 4
π*4^2=16πunits^2
them divide by 2
(16π)/2=8pi
so the area would be 71+8π
Step-by-step explanation:
13
3. It's About Time, in Langley, British
Columbia, is Canada's largest custom clock
manufacturer. They have a grandfather
clock that, on the hours, chimes the
number of times that corresponds to the
time of day. For example, at 4:00 p.m., it
chimes 4 times. How many times does the
clock chime in a 24-h period?
9. A training program requires a pilot to fly
Using an arithmetic sequence, it is found that the clock chimes 132 times in a 24-h period.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In this problem, as the day is divided in two 12-hours period, the total will be twice the sum of the 12 elements of the following sequence:
{0, 1, 2, 3, ..., 11}
In which [tex]a_1 = 0, a_11 = 11, n = 12[/tex].
Then:
[tex]T = 2\frac{12(0 + 11)}{2} = 12 \times 11 = 132[/tex]
The clock chimes 132 times in a 24-h period.
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
Is 2x + 6x equivalent to 9x when x=0?
Answer:
Yes
Step-by-step explanation:
Anything muliplied by zero end up equalling zero. So with this in mind we can put 0 in for x and find out what each eqautian equals.
2(0) + 6(0) = 0; Once we multiply both sides we end up adding 0 and 0, so it equals 0
9(0) = 0
Since, 0 = 0 they are both equal.
Hope this helps!
