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
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
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?
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.
HELP ASAP I'M GIVING BRAINLIEST
Answer:
the picture is blurry is it only like that for me?
Leslie gained 5.54 pounds between her third and fourth birthdays. If she weighed 42.48 pounds when on her fourth birthday, how much did she weigh in pounds on her third birthday? Does this mean to add or subtract? Pick the correct operation and solve ONLY that one.
Answer:
We Subtract
Her weight on her third birthday = 36.94 pounds
Step-by-step explanation:
Does this mean to add or subtract? This means we add. The operation we are using is SUBTRACTION
Leslie GAINED 5.54 pounds between her third and fourth birthdays.
This means she added weight
She weighed 42.48 pounds on her Fourth birthday
Hence, Her weight in her third birthday is:
Third birthday + 5.54 pounds = 42.48
$42.48
Third birthday = 42.48 - 5.54
= 36.94 pounds
Her weight on her third birthday = 36.94 pounds.
Please answer this.. please
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 :)
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 :(
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
SOME 1 HELP WITH 11 PLZZZZ
Answer: Tiffany got 45 questions right! Hope this helped.
Step-by-step explanation:
A jet ski company charges a flat fee of $22.00 plus $3.00 per hour to rent a jet ski. Another company charges a fee of $17.50 plus $3.75 per hour to rent the same jet ski. Write a system of equations that can be used to determine when the cost will be the same, then solve your system.
Answer: The cost will be same for 6 hours.
Step-by-step explanation:
Given: A jet ski company charges a flat fee of $22.00 plus $3.00 per hour to rent a jet ski.
Another company charges a fee of $17.50 plus $3.75 per hour to rent the same jet ski.
Let x = Number of hours
y = Total cost
Then, Total cost (in $) for first company (y) = 22+3x
Total cost (in $) for second company (y) = 17.50+3.75x
So required system of equations :
y = 22+3x
y= 17.50+3.75x
When the cost will be the same,
22+3x = 17.50+3.75x
⇒ 3x - 3.75x = 17.50- 22
⇒ - 0.75x = -4.5
⇒ x =6 [Divide both sides by -0.75]
Hence, the cost will be same for 6 hours.
a
(
n
)
=
c
−
5
+
6
(
n
−
1
)
a
(
n
)
=
c
-
5
+
6
(
n
-
1
)
Answer:
what should we have to do here
I don't understand
PLS HELP WITH THIS QUESTION
Answer:
I think C
Step-by-step explanation:
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
Look at the angle shown below.
V.
Estimate the measure of the angle.
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.
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?
operaciones complejas raiz de -100
Answer:
Step-by-step explanation:
10 i
es esto
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:
Write an equation that relates the sale price, s, to the original price p.
Answer:
s= px
Step-by-step explanation:
3 + 15 + 3
- 4 2
I need help figuring this out
Answer:
3+15+3-42
=18+3-42
=21-42
=-21
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
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.
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The cost of a speeding ticket is a function of each mile per hour that exceeds the speed limit multiplied by a fixed rate of $2 plus a $40 processing fee.Write the function that represents this relationship.Then determine the cost of a speedingticket for a car that has gone 50 mph in a 35 mph zone
The cost of the speeding ticket for a car that has gone 50 mph in a 35 mph zone is $70.
Describe Function?In mathematics, a function is a relationship between two sets of numbers, known as the domain and the range, that assigns each element of the domain a unique element in the range. A function can be thought of as a machine that takes input from the domain and produces output in the range.
More formally, a function f from a set X to a set Y is denoted as f: X → Y
For example, the function f(x) = 2x assigns to each real number x a unique real number 2x. When x = 1, f(1) = 2; when x = -3, f(-3) = -6.
Functions can be represented in a variety of ways, including algebraic expressions, tables of values, and graphs. The graph of a function is a visual representation of the relationship between the input and output values, and can be used to analyze the behavior of the function.
Functions are important in many areas of mathematics, science, and engineering, and are used to model relationships between quantities, solve problems, and make predictions. They are also used in computer programming, where they are used to encapsulate behavior and modularize code.
The function that represents the relationship between the speed of a car and the cost of a speeding ticket can be expressed as:
C(x) = 2(x - L) + 40
where:
C(x) is the cost of the speeding ticket for a car traveling at speed x (in mph).
L is the speed limit (in mph).
(x - L) represents the number of miles per hour over the speed limit that the car was traveling.
The fixed rate is $2 per mile per hour over the limit, and there is a $40 processing fee added to every ticket.
To determine the cost of a speeding ticket for a car that has gone 50 mph in a 35 mph zone, we substitute the values for x and L into the formula above:
C(50) = 2(50 - 35) + 40
C(50) = 2(15) + 40
C(50) = 30 + 40
C(50) = $70
Therefore, the cost of the speeding ticket for a car that has gone 50 mph in a 35 mph zone is $70.
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if triangle ocd ≅ triangle JAL, then which of the following statements are true?
Answer:
I III and IV
Step-by-step explanation:
According to the SAS (Side Angle Side) postulate, the side OC is congruent to side JA, the angle COD is congruent to angle AJL, and the angle DCO is congruent to angle JAL.
Given :
Triangle OCD ≅ Triangle JAL
The given triangles can be similar through the ASA postulate. According to the Angle Side Angle postulate, two angles and included side of one triangle is congruent to the other two angles and included side of another triangle then both the triangles are congruent.
So according to the SAS (Side Angle Side) postulate, the side OC is congruent to side JA, the angle COD is congruent to angle AJL, and the angle DCO is congruent to angle JAL.
Therefore, the correct option is D).
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Plz help me I’ll give brainliest!!
Answer:
k = 1
Step-by-step explanation:
The equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (4, 1 )
with k = 1
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
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!
Denise runs a 10 kilometer race (6.2 miles). Her average time per mile is shown.
Answer:
Step-by-step explanation:
8.5*6.2=52.7
The required time taken by Denise to complete the race is 52.7 minutes.
Given that,
Denise runs a 10-kilometer race (6.2 miles). Her average time per mile is 8.5 minutes per mile.
Speed is defined as when an object is subjected to move, the distance covered by the object in a certain time interval is the speed of that object.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Denise runs a 10-kilometer race (6.2 miles).
Denise run 1 mile in 8.5 minutes
Time is taken by denis to run 6.2 miles = 6.2 * 8.5
= 52.7 minutes
Thus, the required time taken by Denise to complete the race is 52.7 minutes.
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