Answer:
No, I believe the solution is (2/3, 11/3)
Step-by-step explanation:
Nathaniel invested $37,000 in an account paying an interest rate of 5.7% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $70,900?
Answer:
11
Step-by-step explanation:
\text{Compounded Daily:}
Compounded Daily:
A=P\left(1+\frac{r}{n}\right)^{nt}
A=P(1+
n
r
)
nt
Compound interest formula
A=70900\hspace{35px}P=37000\hspace{35px}r=0.057\hspace{35px}n=365
A=70900P=37000r=0.057n=365
Given values
70900=
70900=
\,\,37000\left(1+\frac{0.057}{365}\right)^{365t}
37000(1+
365
0.057
)
365t
Plug in values
70900=
70900=
\,\,37000(1.0001562)^{365t}
37000(1.0001562)
365t
Simplify
\frac{70900}{37000}=
37000
70900
=
\,\,\frac{37000(1.0001562)^{365t}}{37000}
37000
37000(1.0001562)
365t
Divide by 37000
1.9162162=
1.9162162=
\,\,1.0001562^{365t}
1.0001562
365t
\log\left(1.9162162\right)=
log(1.9162162)=
\,\,\log\left(1.0001562^{\color{blue}{365t}}\right)
log(1.0001562
365t
)
Take the log of both sides
\log\left(1.9162162\right)=
log(1.9162162)=
\,\,\color{blue}{365t}\log\left(1.0001562\right)
365tlog(1.0001562)
Bring exponent to the front
\frac{\log\left(1.9162162\right)}{\log\left(1.0001562\right)}=
log(1.0001562)
log(1.9162162)
=
\,\,\frac{365t\log\left(1.0001562\right)}{\log\left(1.0001562\right)}
log(1.0001562)
365tlog(1.0001562)
Divide both sides by log(1.0001562)
4164.8632402=
4164.8632402=
\,\,365t
365t
Use calculator
\frac{4164.8632402}{365}=
365
4164.8632402
=
\,\,\frac{365t}{365}
365
365t
Divide by 365
11.4105842=
11.4105842=
\,\,t
t
t\approx
t≈
\,\,11
11
Using compound interest, it is found that it would take 11 years for the value of the account to reach $70,900.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.Hence, the parameters are given as follows:
[tex]A(t) = 70900, P = 37000, n = 365, r = 0.057[/tex]
We have to solve for t, then:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]70900 = 37000\left(1 + \frac{0.057}{365}\right)^{365t}[/tex]
[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = \frac{70900}{37000}[/tex]
[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = 1.91621622[/tex]
[tex](1.00015616)^{365t} = 1.91621622[/tex]
[tex]\log{(1.00015616)^{365t}} = \log{1.91621622}[/tex]
[tex]365t\log{1.00015616} = \log{1.91621622}[/tex]
[tex]t = \frac{\log{1.91621622}}{365\log{1.00015616}}[/tex]
t = 11.41
Rounding to the nearest year, it would take 11 years for the value of the account to reach $70,900.
More can be learned about compound interest at https://brainly.com/question/25781328
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DO Y'ALL KNOW THE ANSWER?
Answer:
C
Step-by-step explanation:
12000 feet equals about 2 miles.
5280 is about half of 12000 so it is about 1 mile.
Which graph has a slope of 4/5 ?
Answer:
quadratic
Step-by-step explanation:
maybe you can try searching in google
Solve for the missing angle measures
Answer:
Set 1 angles a and c are 62
Set 2 angles b and d are 120
Step-by-step explanation:
angle a = angle c = 62
angle b = angle d = 120
19 - 4x + 15x.
Please Help And Explain How To Do This.
Answer:
Step-by-step explanation:
19-4x+15x combine like terms
19+11x
It cost me $46,80 to fill my 13-gallon gas tank. What was the price of gas
per gallon?
Compare the two statements below and decide if the phrase: "In a plane," needs to be included in order to make a true statement.
1. In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
versus
2. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
answer choices:
A) It does not need to be included. By leaving it out of the statement, the reader considers three dimensions not just the xy-plane. The two parallel lines would determine a plane. However, the transversal could intersect only one of the lines. This would allow the proof to use the Corresponding Angles Theorem.
B) It does not need to be included. By leaving it out of the statement, the reader considers three dimensions not just the xy-plane. The two parallel lines would determine a plane. However, the transversal could intersect only one of the lines. This would allow the proof to use the Angle Bisector Theorem.
C) It needs to be included as it forces the reader to consider only two dimensions, like the xy-plane. The two parallel lines would determine the plane and the transversal would intersect both lines. This would allow the proof to use the Corresponding Angles Theorem.
D) It needs to be included as it forces the reader to consider only two dimensions, like the xy-plane. The two parallel lines would determine the plane and the transversal would intersect both lines. This would allow the proof to use the Angle Bisector Theorem.
by any chance do you go to a higl school in Conroe bc I’m taking that exact test on canvas
Step-by-step explanation:
Please Answer if you're a smarty pants in Algebra!
[tex]\huge\text{B. $\boxed{7x-2y=39}$}[/tex]
Hey there! We can use point-slope form to start off the equation, then change that to standard form.
[tex]\begin{array}{c|l}\textbf{Solving}&\textbf{Reasoning}\\\cline{1-2}\\y-y_1=m(x-x_1)&\text{Start with point-slope form.}\\\\y-(-2)=\dfrac{7}{2}(x-5)&\text{Substitute in the known values.}\\\\y+2=\dfrac{7}{2}(x-5)&x-(-y)=x+y\\\\y+2=\dfrac{7}{2}x-\dfrac{35}{2}&\text{Use the distributive property.}\\\\-\dfrac{7}{2}x+y=-\dfrac{39}{2}&\text{Move the variables to the left.}\\\\\boxed{7x-2y=39}&\text{Multiply everything by $-2$.}\end{aligned}[/tex]
Find the value of x.
Answer:
x=3
Step-by-step explanation:
BRAINLIEST plzzzzzzzzzzzzzzzzzz
Is this congruent by SSS, SAS, AAS, ASA??
Answer:
sss
Step-by-step explanation:
Please help me nobody will help me with this please
Answer:
[tex]24[/tex]
Step-by-step explanation:
Each bottle of water costs $2 so we multipy 12 by 2.
[tex]12[/tex]×[tex]2=24[/tex]
Victor has 1 and a half hours before he has to leave. He starts watching a movie that runs for 107 minutes. How many minutes of the movie will he miss?
Evaluate x + 2y when x = 3.5 and y = -1.7
Answer:
0.1
Step-by-step explanation:
x + 2y
3.5 + 2(-1.7)
3.5 + (-3.4)
3.5 - 3.4
0.1
LOOK AT PICURE, THEN ANWSER QUESTION, I WILL MARK BRAINIEST WHOEVER HAS CORRECT ANWSER
Answer:
A is correct
Step-by-step explanation:
Answer:
it is letter A
What pair of factors of -45 has a
sum of 4?
Answer:
9 and -5
Step-by-step explanation:
9*-5=-45
9+-5=4
The pair of factors is 9 and -5.
What is a factor?
The factor of a number is another number that can divide the first number without any remainder.
Let, one of the factors is x.
Then, the other factor is = -45/x.
Given,
x + (- 45/x) = 4
⇒ x - 45/x = 4
⇒ x - 45/x - 4 = 0
⇒ x² - 45 - 4x = 0
⇒ x² - 4x - 45 = 0
⇒ x² - 9x + 5x - 45 = 0
⇒ x(x-9) + 5(x-9) = 0
⇒ (x-9) (x+5) = 0
Hence, x = 9, -5.
Learn more about factors here: https://brainly.com/question/16603643
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What is the equation of the line in the graph?
Answer:
Step-by-step explanation:
SOLVE FOR X. HELP ME NOW PLEASE!
Answer:
For number 2, its A. For number 1, its C.
Step-by-step explanation:
For both equations, you just set it equal to to each other because alternate interior angles are equivalent.
2) The equation would be
7x+3=6x+12
Then solve.
1) The equation would be
14x-3=95
Then solve.
I love geometry! If you have questions, just comment.
Charlotte wants to know which website gains more new subscribers per amount of content. 1) Charlotte thought of two different ways to define this quantity. Identify these two definitions among the following options. Choose 2 answers: Choose 2 answers: (Choice A) A Number of new subscribers divided by number of writers (Choice B) B Number of new subscribers divided by number of likes (Choice C) C Number of new subscribers divided by number of posts (Choice D) D Number of new subscribers divided by number of words 2) Determine which website gains more new subscribers per amount of content according to the two definitions. Did you get the same result for both definitions? Choose 1 answer: Choose 1 answer: (Choice A) A Yes. According to both definitions, website A gains more subscribers per amount of content. (Choice B) B Yes. According to both definitions, website B gains more subscribers per amount of content. (Choice C) C No. The definitions have opposite results.
Answer:
1)
Number of new subscribers divided by number of posts.
Number of new subscribers divided by number of words.
2)
No. The definition have opposite results
Step-by-step explanation:
Khan academy said it was right tehee
Answer:
Step-by-step explanation:
number of new subscribers divided by posts
number of new subscribers divided by the number of words
no the definitions have opposite results.
look at the pic below
answer quick please I need this asap
i will mark thx, star you & mark brainliest
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex] \cos( \frac{5\pi}{12} ) = \cos( \frac{6\pi}{12} - \frac{\pi}{12} ) = \\ [/tex]
[tex] \cos( \frac{\pi}{2} - \frac{\pi}{12} ) = \sin( \frac{\pi}{12} ) \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Also we have :
[tex] \sin( \frac{5\pi}{12} ) = \cos( \frac{\pi}{12} ) \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
So :
[tex] \cos( \frac{\pi}{12} ). \sin( \frac{\pi}{12} ) + \sin( \frac{\pi}{12} ) . \cos( \frac{\pi}{12} ) = \\ [/tex]
[tex]2 \sin( \frac{\pi}{12} ) . \cos( \frac{\pi}{12} ) \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Hint :
[tex] \sin(2 \alpha ) = 2 \sin( \alpha ) . \cos( \alpha ) [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
So ;
[tex]2 \sin( \frac{\pi}{12} ) . \cos( \frac{\pi}{12} ) = \\ [/tex]
[tex] \sin(2 \times \frac{\pi}{12} ) = \sin( \frac{\pi}{6} ) \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex] \sin( \frac{\pi}{6} ) = \cos( - \frac{\pi}{3} ) \\ [/tex]
Thus the correct answer is the first option.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
What is greater 11/12 or 2 1/3
Answer:
2 1/3
Step-by-step explanation:
Chau has bought 30 pounds of dog food. He feeds his dog 3/5 pounds for each meal. For how many meals will the food last?
Answer:
50 meals.
Step-by-step explanation:
30 divided by 3/5= 50
Paige ran 3 miles on Monday, walked 8 miles Tuesday
and ran a combined 11 miles on Wednesday and
Thursday. How many total miles did Paige exercise in
four days?
Answer:
22
Step-by-step explanation:
add 11 + 8+ 3
True or False
If an acute angle is 80o then we add the obtuse angle of 110o to equal 180o?
Answer:
true
Step-by-step explanation:
A = p + prt solve for t
Answer:
t = [tex]\frac{A - p}{pr}[/tex]
Step-by-step explanation:
A = p + prt
A - p = p - p + prt
A - p = 0 + prt
A - p = prt
[tex]\frac{A - p}{pr}[/tex] = [tex]\frac{prt}{pr}[/tex]
[tex]\frac{A - P}{pr}[/tex] = t
5 and 4/5 as an improper fraction!
ANSWER ASAP! * 10 points *
Answer:
29/5
Step-by-step explanation:
5 4/5=(25+4)/5
29/5
Hope I helped! Please mark Brainliest!!!
Answer: The answer is [tex]\frac{29}{5}.[/tex]
Step-by-step explanation: Here are the 3 steps in order to convert the mixed number fraction to an improper fraction:
Step 1. First, let's multiply the denominator by the whole fraction that looks like this: [tex]5*5=25.[/tex]
Step 2. Then, we add the answer with the numerator from step 1 that looks like this: [tex]25+4=29.[/tex]
Step 3. Finally, we write the answer from step 2 over the denominator that looks in the improper fraction like this: [tex]\frac{29}{5}.[/tex]
Conclusion Step-By-Step Explanation:
Here's the conclusion for how to convert the mixed number fraction into an improper fraction given the equation [tex]\frac{29}{5},[/tex] that looks like this in the simplified solution: [tex]\frac{5*5+4}{5}=\frac{29}{5}.[/tex]
I hope that my full answer with the full step-by-step explanation is very helpful to your question about how to convert the mixed number fraction into an improper fraction and have a great rest of the day! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
Given: PQRS is a parallelogram; S, P, and T are collinear. Prove: ∠1 ≅ ∠4.
Answer:
∠1 ≅ ∠4 because yeah
Step-by-step explanation:
Brainliest! Correct! Fast!
Answer:
c or the third one
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
PLEASE HELP!!! GIVING BRAINLIST
If x + 2y = 8 and x/2 -y= 10, then x = ?
A)-3
B) 0
C) 10
D) 14
Answer:
D. 14
make y the subject of the formula in equation 1 and then substitute it in equation 2
how do u find the slope of this lol
Answer:
y=3x+6
Step-by-step explanation:
3 is the slope
6 is the y intercept
remember rise/run
•first find VISIBLE points and count squares up and then right or down and left depending on if its negative slope or not
Which shows the equation below written in the from ax^2 + bx + c = 0? x + 9 = 2(x - 1) ^2
Answer:
i may be wrong but i thinks its A
Step-by-step explanation: