Rachel deposited $6,449.82 into a savings account with an interest of 6.9% compounded annually. About how long will it take for the accout to be worth $8,000?
Answers
Answer:
3 years and 3 months.
Step-by-step explanation:
Since, the amount formula in compound interest,
[tex]A= P(1+\frac{r}{100})^t[/tex]
Where,
P = principal amount,
r = rate per period,
t = number of periods,
Here, A = $ 8,000, r = 6.9%, P = $6,449.82,
By substituting the values,
[tex]8000 = 6449.82(1+\frac{6.9}{100})^t[/tex]
[tex]\frac{8000}{6449.82}=(1+\frac{6.9}{100})^t[/tex]
[tex]\ln (\frac{8000}{6449.82})=t\ln(1.069)[/tex]
[tex]\implies t = \frac{\ln (\frac{8000}{6449.82})}{\ln(1.069)}=3.228[/tex]
Hence, it would be take 3.228 years or 3 years and 3 months.
Related Questions
Write an equation for a rational function that has a vertical asymptote at x=1 and a hole at x=3
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--------
(x-3)(x-1) aka x^2 - 4x+ 3
How many times larger is a 10-pound dog than a hamster weighing 5/8 pound?
Answers
n = mass of the dog / mass of the hamster
Substituting the known value,
n = 10 lb/ 5/8 lb
n = 16
ANSWER: 16 times
How to do a math probem of two people working together?
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Help pleaseeeeeee!!!!!
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Then, for each case we consider the probabilities of the kit being accurate or not.
we are interested in the branch Oil---Kit accurate---
Since P(Oil)=0.45, and P(Kit accurate)=0.8, the probability of there being oil and the Kit showing it correctly is:
0.45*0.8=0.36.
Answer: C) 0.36
The table gives the numbers of teachers and students in grades 6 to 8 at Earhart Middle School. Grade Teachers Students 6 1 25 7 2 50 8 3 75 Which teacher-to-student ratio maintains the proportional relationship described in the table?
Answers
Grade Teachers Students
6 1 25
7 2 50
8 3 75
Grade 6 to 8 all maintained the same proportional relationship because for every one teacher, there's 25 students
find the perimeter of a ruler that measures 12 inches by 7/8 inch.
Answers
24+7/8+7/8
24+1+6/8
25+3/4
25 3/4 inches
Solve these Multi-Step Equations (include work): 6-8, 9 & 10 (is the equation right? if not please help)
Answers
8t+16-3t+12=6t-42+8
8t-6t=-42+8-16-12
2t=-62
t=-62/2
t=-31
What is the remainder when 4x4 − 10x3 + 14x2 + 7x − 19 is divided by 2x − 1
Answers
___________________
2x-1 | 4x^4-10x³+14x²+7x-19
Next, we divide the first term of 2x-1 by the first term of 4x^4-10x³+14x²+7x-19 to get 4x^4/2x=2x³ (since 4/2=2 and to divide exponents you subtract the denominator from the numerator). Next, we put our 2x³ on the top and multiply (2x-1) by that. With the result of (2x-1) and 2x³, we multiply that by -1 and add it to 4x^4-10x³+14x²+7x-19, looking like
2x³
___________________
2x-1 | 4x^4-10x³+14x²+7x-19
- (4x^4-2x³)
____________________
-8x³+14x²+7x-19. Repeating the process, we get
2x³-4x²+5x+6
___________________
2x-1 | 4x^4-10x³+14x²+7x-19
- (4x^4-2x³)
____________________
-8x³+14x²+7x-19.
-(-8x³+4x²)
______________________
10x²+7x-19
-(10x²-5x)
__________
12x-19
-(12x-6)
_________
-13 as our remainder
The remainder when [tex]4x^4 - 10x^3 + 14x^2 + 7x - 19[/tex] is divided by 2x − 1 is -13.
The given expressions are [tex]4x^4 - 10x^3 + 14x^2 + 7x - 19[/tex] and 2x-1.
What is the remainder?The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.
The division of the given expressions are given below:
2x³-4x²+5x+6
___________________
2x-1 | [tex]4x^4 - 10x^3 + 14x^2 + 7x - 19[/tex]
- ([tex]4x^4-2x^3[/tex])
____________________
-8x³+14x²+7x-19.
-(-8x³+4x²)
______________________
10x²+7x-19
-(10x²-5x)
__________
12x-19
-(12x-6)
_________
-13
Therefore, the remainder when [tex]4x^4 - 10x^3 + 14x^2 + 7x - 19[/tex] is divided by 2x − 1 is -13.
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A total of 697 tickets were sold for the school play. They were either adult tickets or student tickets. There were 53 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
Let x-53 = number of student tickets sold
x + x -53 = 697
2x - 53 = 697.
Add 53 to both sides to get:
2x = 750
Divide both sides by 2 to get:
x = 375
375 adult tickets were sold.
What is the value of x?
Enter your answer in the box.
x =
°
Triangle A B C with angle A measuring thirty degrees, angle B measuring seventy degrees and angle C marked x
Answers
Answer: In a triangle, the sum of the 3 angles is always equal to 180°
Then if the angle A is equal to 30°, the angle B is equal to 70°, what is the angle C?
if x is the angle C, and using the first statement, we got:
30° + 70° + x = 180°
100° + x = 180°
x = 180° - 100° = 80°
So the angle of C is equal to 80°.
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 75 miles per hour. The westbound train travels at 65 miles per hour. How long will it take for the two trains to be 196 miles apart?
Answers
196/140=1.4 hrs, or 84 minutes
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When developing a plan for a geometric proof, which of the following is not important?
A.) evaluate the given statement(s)
B.)determine the number of steps needed
C.)look carefully at the figure
D.)create a plan for the proof
Answers
Answer: B.)determine the number of steps needed
Step-by-step explanation:
A geometric proof of a geometric statement includes the following steps :-
a) Evaluate the given statement.
b) Look carefully at the figure related to the geometric statement .
c) Create a plan to express the proof.
d)Then use definitions, given axioms, postulates and previously proved theorems to write a logical explanation approaches to the conclusion.
Hence, the step is not important to develop a plan for a geometric proof: is "determine the number of steps needed" .
Which shape has congruent diagonals? Question options:
a rectangle
a parallelogram
a trapezoid
Answers
Because some angles are more out than others in Parallelograms and trapezoids, their diagonals aren't congruent.
A car travels 252 miles in 5 hours and 15 minutes. how many miles does it travel per hour?
Answers
Answer:
48 miles per hour
Step-by-step explanation:
5hrs and 15minutes = 315minutes
If 252 = 315
x = 60
By cross multiplication
315x = 60 * 252
315x = 15,120
x = 15120/315
x = 48 miles per hour
HELP ASAP 115 points please hurry...
help asap please hurry...15 points.
Clara estimates that the length of a hiking trail is 10 km. She later learns that its actual length is 12 km.
What is the percent error in Clara's estimate?
.002%
8.0%
0.2%
11.5%
Answers
Experimental value = 10 km
accepted value = 12 km
Step 1: Deduct the accepted value from the experimental value.
10 km – 12km = -2 km
Step 2: Take the absolute value of step 1
|--2km| = 2km
Step 3: Divide that answer by the accepted value. 2km/10km = 0.2%
On a given blueprint, 1 inch=12 feet. if the dimensiopns of a recreation room on the blueprint are 2 onches x 1.75 inches. what are its actual measurements
Answers
Unit conversion is the conversion of one unit to another unit with its standard conversion.
The actual dimension of the recreation room is 24 feet x 21 feet.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
1m = 100 cm
1 hour - 60 minutes
We have,
Recreation room dimension on the blueprint:
= 2 inches x 1.75 inches ______(A)
Scale factor:
1 inch = 12 feet
The actual dimension of the recreational room:
1 inch = 12 feet
Multiply 2 on both sides.
2 inches = 24 feet _____(1)
1 inch = 12 feet
Multiply 1.75 on both sides.
1.75 inches = 1.75 x 12 feet
1.75 inches = 21 feet ______(2)
From (1) and (2) and (A) we get,
= 2 inches x 1.75 inches
= 24 feet x 21 feet
Thus,
The actual dimension of the recreation room is 24 feet x 21 feet.
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The price of an item has been reduced by 55% . The original price was $80 . What is the price of the item now?
Answers
=$36
the price of the item is $36 now
The area of a rectangle is 45 square inches. The rectangle is 9 inches long. How wide is the rectangle?
A. 5 inches
B. 36 inches
C. 27 inches
D. 3 inches
Answers
Final answer:
To find the width of a rectangle with an area of 45 square inches and a length of 9 inches, divide the area by the length, resulting in a width of 5 inches (Option A).
Explanation:
The area of a rectangle can be calculated by multiplying its length by its width. In this case, we know the area is 45 square inches and the length is 9 inches. To find the width, we divide the area by the length.
Width = Area ÷ Length = 45 sq in ÷ 9 in = 5 in
Therefore, the width of the rectangle is 5 inches, which corresponds to option A.
You can use a minus sign to make a negative number like -2. what happens if you put a plus sign before a number? what about 2++2?
Answers
Final answer:
A plus sign before a number does not change its value. In the expression 2++2, the two plus signs next to each other are interpreted as a positive number followed by another positive number.
Explanation:
When you put a plus sign before a number, it doesn't change the value of the number.
The plus sign is just a symbol to indicate that the number is positive.
In the expression 2++2, the two plus signs next to each other are not a valid mathematical operation.
Instead, it is interpreted as a positive number followed by another positive number.
So, 2++2 is equal to 2+2, which is 4.
what is thirty five percent of two hundred
Answers
2 * 35 =
70
Which statement correctly describes the relationship between △RST and △R’S’T?
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What is the sum of the solution of 2lx-1l-4=-2
Answers
Please help thank you!
Answers
2 is
9x - 18 = 3x
6x - 18 = 0
6x = 18
x = 3
3 is 9(3) - 18 = 27 - 18 = 9
Identify the slope and y intercept in this statement "it takes 45 minutes to paint 2 rooms. you have all ready painted for 45 minutes.
Answers
The y-intercept is (0,42)
I need help with 13 please ASAP
Answers
338.50 - 45 = 293.50 was spent on tolls
293.50 / 14 = 20.96
so 21 tolls
Find a) the GCM (Greatest Common Multiple) and b) the LCM (lowest common multiple:
x²- 3x + 2; x²- 4x + 4
Answers
To do both parts, you need ot factor the polynomials.
x^2 - 3x + 2 = (x - 2)(x - 1)
x^2 - 4x + 4 = (x - 2)(x - 2) = (x - 2)^2
(a) GCF: use only common factors with lower exponent.
The GCF is x - 2
(b) LCM: use common and not common factors with the larger exponent.
The LCM is (x - 2)^2(x - 1)
Given that BC = 7, AB = 17.89, and C is between A and B, what is the length of ?
Answers
then you have
AB = 17.89 ..... this is the length of the whole line
BC is a part of the line = 7
therefore the length of the other part = 17.89 - 7
= 10.89
You know that the distance from A to b is 17.89 and the distance from b to c is 7. So the length from a to c is the whole distance(a to b) subtracted by a portion of the distance(b to c) giving us 10.89
Which equation could be used to solve the problem?
Mr. Guzman drove his car 1080 miles in 6 weeks.
If he drove the same distance every week, which equation shows how far he drove each week (d)?
A.
d = 6 ÷ 1080
B.
d = 1080 – 6
C.
d = 1080 • 6
D.
d = 1080 ÷ 6
Answers
All you have to do is take the distance she drove and divide it by how many weeks it took.
Mr. Guzman drove 1080 miles in 6 weeks. To find the distance driven each week, use the equation d = 1080 ÷ 6, which equals 180 miles per week. Therefore, the correct equation is option D.
Mr. Guzman drove 1080 miles in 6 weeks. We need to find out how far he drove each week if he drove the same distance every week.
Identify the Total Distance Driven: 1080 milesIdentify the Total Time Period: 6 weeksSet Up the Equation: Since Mr. Guzman drove the same distance every week, we use the formula:
d = Total Distance / Total Time.Substitute Known Values:
d = 1080 ÷ 6Calculate the Result:
d = 180 miles per weekThe correct equation that shows how far Mr. Guzman drove each week is d = 1080 ÷ 6, which corresponds to option D.
While catching fireflies, you and a friend decide to have a competition. After mm minutes, you have (3m+13)(3m+13) fireflies and your friend has (4m+6)(4m+6) fireflies.
a. How many fireflies are caught each minute during the competition?1m+7 fireflies are caught per minute.
b. How many fireflies are caught before the competition starts? fireflies are caught before the competition starts.
Answers
Answer: the equation is 7m + 19
Step-by-step explanation:
Is an equation that has 0 for a solution the same as an equation with no solution?