Jordan invested $97,000 in an account paying an interest rate of 1.6% compounded
monthly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $109,700?
Answer:
t≈ 8
Step-by-step explanation:
\text{Compounded Monthly:}
Compounded Monthly:
A=P\left(1+\frac{r}{n}\right)^{nt}
A=P(1+
n
r
)
nt
Compound interest formula
A=109700\hspace{35px}P=97000\hspace{35px}r=0.016\hspace{35px}n=12
A=109700P=97000r=0.016n=12
Given values
109700=
109700=
\,\,97000\left(1+\frac{0.016}{12}\right)^{12t}
97000(1+
12
0.016
)
12t
Plug in values
109700=
109700=
\,\,97000(1.0013333)^{12t}
97000(1.0013333)
12t
Simplify
\frac{109700}{97000}=
97000
109700
=
\,\,\frac{97000(1.0013333)^{12t}}{97000}
97000
97000(1.0013333)
12t
Divide by 97000
1.1309278=
1.1309278=
\,\,1.0013333^{12t}
1.0013333
12t
\log\left(1.1309278\right)=
log(1.1309278)=
\,\,\log\left(1.0013333^{\color{blue}{12t}}\right)
log(1.0013333
12t
)
Take the log of both sides
\log\left(1.1309278\right)=
log(1.1309278)=
\,\,\color{blue}{12t}\log\left(1.0013333\right)
12tlog(1.0013333)
Bring exponent to the front
\frac{\log\left(1.1309278\right)}{\log\left(1.0013333\right)}=
log(1.0013333)
log(1.1309278)
=
\,\,\frac{12t\log\left(1.0013333\right)}{\log\left(1.0013333\right)}
log(1.0013333)
12tlog(1.0013333)
Divide both sides by log(1.0013333)
92.3402971=
92.3402971=
\,\,12t
12t
Use calculator
\frac{92.3402971}{12}=
12
92.3402971
=
\,\,\frac{12t}{12}
12
12t
Divide by 12
7.6950248=
7.6950248=
\,\,t
t
What is the measure of angle x? 62" X
Answer:
c
Step-by-step explanation:
62+90=152
180-152=28
the sum of the interior angles must equal 180 degrees
Angle x measures 28°
What is triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Given,
In the figure, interior angles of triangle measures =
62°, right angle = 90°, x
Sum of interior angles of a triangle = 180°
⇒ 62° + 90° + x = 180°
⇒ 152° + x = 180°
⇒ x = 180° - 152°
⇒ x = 28°
Hence, 28° is the measure of angle x.
Learn more about triangle here:
https://brainly.com/question/2773823
#SPJ2
50 points plus Brainnlest for right answer
What is the equation?
What should you replace for each given variable?
What should you solve for?
Equations: 60x + 3000 = 3,000, 600 + 150y = 3000
X: 20
Y: 10
You should solve for x & y
Q1: 0, it's already filled up to the max of 3000 pounds.
Q2: 16, 60 times 10 is 600. 3000-600 = 2400. 2400/150 = 16
I hope this helped, ask if you need more help :)
help plz ive been stuck on this for a while now
Answer:1.20/5
Step-by-step explanation:
Answer:
9/10 or in decimal form 0.9
Step-by-step explanation:
The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time.
A'(t) =???
MARK AS BRAINLIST
Step-by-step explanation:
L = 6t+5
H = √t
A = L*H
= (6t+5) *√t = 6t√t + 5√t
A'(t) = 6t * 1/2*√t + √t * 6 + 5/2*√t
= 6t/2√t + 6√t + 5/2√t
Expression for the rate of change of the area with respect to time will be,
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex] cm per second
It's given in the question,
Length of a rectangle is given by the expression(6t + 5) cm
Width or height of the rectangle is given by the expression,[tex]\sqrt{t}[/tex] cm
Area of the rectangle is given by,
Area = Length × Height
A = (6t + 5)(√t)
A = [tex]6t^{\frac{3}{2}}+5t^\frac{1}{2}[/tex]
Now find the derivative of area (A) with respect to time (t).
[tex]\frac{dA}{dt}=\frac{d}{dt}(6t^{\frac{3}{2}}+5t^\frac{1}{2})[/tex]
A' = [tex](6\times \frac{3}{2})t^\frac{1}{2}+\frac{5}{2} t^{-\frac{1}{2}}[/tex]
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]
Therefore, expression for the rate of change of the area will be,
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]
Learn more,
https://brainly.com/question/12596049?
Please answer this.. please
SOME 1 HELP WITH 11 PLZZZZ
Answer: Tiffany got 45 questions right! Hope this helped.
Step-by-step explanation:
Total bill of four pairs of shoes came to $69.25 what is the average price for each pair of shoes
Answer:
Each pair is $17.31 average
Step-by-step explanation:
All you do is divide $69.25 by 4
Answer:17 or 18....17.31 that's what it gave me but if you rounded to the nearest number that could be your answer
Step-by-step explanation:
Melanie had 3 pounds of dried fruit. She packed the dried fruit into bags of 3/8 pound each. How many bags of dry fruit does she pack?
Answer: 8 bags
Step-by-step explanation:
From the question, we are informed that Melanie had 3 pounds of dried fruit and that she packed the dried fruit into bags of 3/8 pound each.
For us to get the number of bags of dry fruit does she will pack, we have to divide 3 pounds by 3/8 pounds. This will be:
= 3 ÷ (3/8)
= 3 × (8/3)
= 8
Therefore, she will pack 8 bags of dried fruit.
12. A worker can pack 72 boxes of oranges in 2 hours. At this rate, how many boxes of oranges can she pack
in 8 hours?
Beth has to choose which trail to hike. Trail A is 3 miles long, all uphill, with an elevation change of 900 feet. Trail B is 1 mile long, also uphill, with an elevation change of 700 feet.
1. Which trail do you think would be more difficult to hike up?
2. Explain your answer to question
help please i'll love you forever thanksssss . *btw i am going to post a lot of questions if you answer & explain I'll give you brainliest each time .*
Isabella noticed that when she doesn't study for a test, on average she makes a 45. Isabella also realizes that for every hour she studies, on average she scores an additional 7 points. Which of the following represents g, get average test score she studied for h hours?
a. 7-5h=g
b. 7+5h=g
c. 45+7h=g
d. 45-7h=g
Answer:
C. 45 + 7h = g
Step-by-step explanation:
This one would be correct because you have to add 7 points to the 45 points she would get on average without studying, without forgetting to multiply 7 by the number of hours that Isabella studied.
Example:
Let's say that Isabella studied for 3 hours. We could replace the h for the number of hours that she studied.
45 + 7(3) = g
Now you just have to solve the equation.
45 + 21 = g
Following the rules of PEMDAS, you would get rid of the parenthesis first by multiplying 7 times 3. Now you just have to add and you will have your answer for g.
g = 66
operaciones complejas raiz de -100
Answer:
Step-by-step explanation:
10 i
es esto
Please help me I got a bad grade and I need to redo them
Find the slope
Answer:
The first one has a slope of 4
The second one has a slope of 0.3 repeating
Step-by-step explanation:
You pick two points on the graph.
You find the x and y coordinates of each point.
You find the difference between the two x coordinates.
You find the difference between the two y coordinates.
Divide the difference in the y coordinates by the x coordinates.
If im wrong sorry owo im only in elementary school... <3
Answer:
4/6
Step-by-step explanation:
1) If the mean is 15.5 and the standard deviation is 2.5, Label b, c, d, e, and f
Answer:
I accidentally clicked I can’t click out
Step-by-step explanation:
Sorry
Ian purchased cans of soda for a party he was having. For every 12 cans of soda she payed $4.98. What is the cost per can of soda?
The cost of each can of soda is $
i need this quik and now
$.40
Step-by-step explanation:
if you want the full one it's .415
Multiply 2.89x 23.2 =
x2 + 45x = -200 Using the quadratic formual and the discirimnat
Answer:
Positive discriminant = 2 real solution
x= -5,-40
Step-by-step explanation:
The discriminant is used to see how many solutions an equation has. If it is negative, the equation has no real solutions, if =0 the equation has 1, and if it is positive, the equation has two real solutions.
The discriminant is the part of the quadratic formula inside the square root:
[tex]b^{2}-4ac[/tex]
Every quadratic formula has the structure:
[tex]ax^{2} +bx+c=0[/tex]
So first, in order to meet this structure we need to add 200 to both sides so the equation is equal to 0. This gives us:
[tex]x^{2} +45x+200=0[/tex]
Our a=1, b=45 and c=200
Now we can substitute these values into the discriminant:
[tex](45)^{2} -4(1)(200)[/tex]
Solve:
[tex]2025-800=1225[/tex]
The discriminant is a positive number which means this equation will have 2 real solution. Now we just need to plug in our values into the quadratic formula to solve this equation. Quadratic formula:
[tex]x=\frac{-+/-\sqrt{b^{2}-4ac} }{2a} \\x=\frac{-45+/-\sqrt{1225} }{2}[/tex]
(Same discriminant value)
[tex]x=\frac{-45+/-35}{2}[/tex]
Now to find the two solutions, we use both signs in the equation. Solution 1:
[tex]x=\frac{-45+35}{2}[/tex]
[tex]x=\frac{-10}{2}=-5[/tex]
Our first solution is -5, now for the second:
[tex]x=\frac{-45-35}{2}\\\\ x=\frac{-80}{2}=-40[/tex]
The two solution to this equation are -5 and -40.
Hope this helped!
Write a slope intercept equation for line with the given characteristics m=-3/5 passes through (4,-4)
Step-by-step explanation:
Hey there!
Given;
Slope (m) = -3/5
And passes through the point(4,-4).
Now; The equation of a line in slope intercept form is y= mx+b.
So, try to bring it in y= mx+b form.
Firstly let's use one-point formula.
[tex](y - y1) = m(x - x1)[/tex]
Now, keep all values.
[tex](y + 4) = \frac{ - 3}{5} (x - 4)[/tex]
Now, simplify to get answer.
[tex]5(y + 4) = - 3(x - 4)[/tex]
[tex]5y + 20 = - 3x + 12[/tex]
[tex]5y = - 3x + 12 - 20[/tex]
[tex]5y = - 3x - 8[/tex]
[tex]y = \frac{ - 3}{5} x - \frac{8}{5} [/tex]
Therefore the equation is y = -3/5x - 8/5.
Hope it helps...
I NEED HELP ITS URGENT!!! I WILL MARK BRAINLIST!! LOOK AT THE IMAGE ABOVE AND DO BOTH PROBLEMS BY SHOWING THE ENTIRE WORK!!
Do NOT answer if you DONT know. This could lead to serious consequences. Ex: “idk” could lead to the monitor marking you to loose points.
PLEASE HELP
Answer:
okay well all i can explain is the image on the far left, the answer would be x=112 and then for the one on the far right (im not sure ) i think its 17
explanation: so a straight line had 180 degress and the outside angle is 126 meaning that if you do 180-126 you can find the amount of the inside angle on the bottom right. When you do this you get 54 degress. Then remember that a triangle has a total of 180 degrees all added up so the final angle inside the triagle is 80 minus the sum of the other two angles. 58+54=112 and 180-112=68. remember that 68 is the angle on the INSIDE and x is clearly on the outside meaning that you would need to do 180-68. your final answer would be 112. (and im really sorry i couldn't answer the other ones they're too blurry :(
Make Sense and Persevere A submarine
descends to of its maximum depth. Then it
descends another of its maximum depth. If it
is now at 650 feet below sea level, what is its
maximum depth?
Workers have been down the street installing two blinking red lights in front of the fire station. The two lights are always turned on at the same time. Both lights blink as they are turned on. One lights blinks after every 8 seconds. The other light blinks every 22 seconds. After how many seconds will they blink together again?
Answer:
After 88 seconds, they will blink together.
Step-by-step explanation:
Time after which the first light blinks = 8 seconds
Time after which the second light blinks = 22 seconds
Initially, both the lights blink together.
To find:
The time at which they will blink together again.
Solution:
Let us have a look at the time after which each light will blink.
First light will blink after:
8 s, 16 s, 24 s, 32 s, 40 s, 48 s, 56 s, 64 s, 72 s, 80 s, 88 s, 96 s, 104 s, ......
Second light will blink after:
22 s, 44 s, 66 s, 88 s, 110 s, .....
It can be seen that common time is 88 second, at which the both will blink together.
So, the answer is 88 s.
This answer can also be computed by taking the LCM (Least Common Multiple) of both the numbers i.e. 8 and 22.
Using the factorization method:
[tex]8=\underline{2}\times 2\times 2[/tex]
[tex]22=\underline{2}\times 11[/tex]
Common is 2.
Therefore the LCM will be:
[tex]2\times 2\times2\times 11 = \bold{88}[/tex]
So, the answer is 88 s.
evaluate the expression when a=32 and b=7 a/4 +b
Which equation represents a line that passes through the 2 points in the table
Answer:
A
Step-by-step explanation:
I took the test
Which line is steeper Line A or Line D? EXPLAIN. PLEASE HELP I WILL MARK BRAILIEST!!
Answer:
line A is steeper.
Line A´s slope is 1, while line d´s slope is 2/5
RiDdLE oF ThE DaY: PaRt 2- Mr.White had been missing and the only evidence he left behind was a paper that said "The first of July, the fourth of January, the first of December and the eighth of February" the police questioned the people that were in the house at that time. Judy said she was at her parents house, Logan was Mr.Whites secretary said he was working on a report for his boss and haven't left his room and Rose, Mr. Whites daughter said she was having guest and never left the living room. Can you crack the case?
Answer:
Step-by-step explanation:
1st of July: J
4th of January: U
1st of December: D
8th of February: Y
Answer: JUDY!
Answer:
Child this has to be one the most hard riddles I ever did
Step-by-step explanation:
y = -5x– 1
y = -5x + 7
Answer:
see below
Step-by-step explanation:
y = -5x– 1
y = -5x + 7
Since they are both equal to y, we can set them equal to each other
-5x-1 = -5x+7
Add 5x to each side
-5x-1+5x= -5x+7+5x
-1 = 7
This is not true so there is no solution
The lines are parallel with different y intercepts
PLSS!!!! HELP!!! ME I WILL MARK U!!!!
Answer:
562
Step-by-step explanation:
Plug in the values of x, y, and z provided.
(5(5)-1)^2-2(7)
Solve.
(25-1)^2-14
(24)^2-14
576-14
562
Answer: 562
Step-by-step explanation:
(5x+y)^2-2z
first put in the known values. (5(5)+(-1))^2-2(7)
(25+-1)^2-14
Second, do 25+-1=24
(24)^2-14
Third, do 24 squared
576-14
Subtract
562
Help me plz!!!!!!!!!!!
Answer:
88%
Step-by-step explanation:
22/25 = .88 x 100= 88%
Answer:
88%
Step-by-step explanation:
First, you start with the bottom (denominator). You turn it into 100 since all percentages are over 100. So 25 times 4 is 100. Therefore, you also have to multiply the top with a 4, getting an 88 over 100. That is equal to 88%.
14. Craig jogs 12 km in 1 h. If he jogs at the
same rate, how long will it take him to jog
18 km?
Answer: 1:30 (one hour and thirty minutes)
Step-by-step explanation:
If he jogs 12 km in an hour, and he wants to jog 18 km, you divide 12 km from when he jogged for and hour by 2 and get 6. Add 12 km to 6 km, and get 18 km in one hour and thirty minutes. So, basically 6 km every 30 minutes.
Answer:
1.5 hours
Step-by-step explanation:
12/1 = 18/x
X = 18/12 = 1.5 hours