The continuous compound interest of a $3,000 deposit with an annual rate of 28% over 5 years would be approximately $9,156.58.
Explanation:The question pertains to continuous compound interest, which is represented by the formula A = P imes ert, where A is the final amount, P the principal amount, r is the interest rate (written in decimal), t is the time in years, and e is the base of natural logarithms.
Given that P=$3,000, r=28/100=0.28 and t=5 years, you would substitute these values into the formula to get A = $3000 imes e(0.28 imes 5).
Computing this, gives:
A = $3000 imes e1.4 = $3000 imes 4.0552 (approximately).
So, A = $12156.58 (rounded to the nearest cent).
The interest earned would therefore be: A - P.
Thus, the interest would be $12156.58 - $3000 = $9156.58.
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To find out how much interest a deposit of $3,000 would earn over 5 years with an interest rate of 28% compounded continuously, we would need to use the formula for continuously compounded interest, which is A = P*e^(rt).
Here,
A represents the total amount of money accumulated after n years including interest,
P is the principal amount, which is the initial amount of money,
r refers to the annual interest rate expressed in decimal form, and
t is the time the money is invested for in years.
Given in the problem we have P = $3000, r = 28% = 0.28, and t = 5 years.
Substituting these values into the formula we get:
A = 3000 * e^(0.28*5)
Solving this would yield the total amount accumulated after 5 years.
Next, we would need to calculate the accrued interest. This is done by subtracting the principal amount (the initial deposit) from the total amount.
So, the interest earned would be calculated as:
Interest Earned = Total Amount - Initial Deposit.
The numerical calculation of these formulas provides us the result that the total amount after 5 years would be approximately $12,165.60 and the interest earned would be approximately $9,165.60.
Thus, a deposit of $3000, with an interest rate of 28% compounded continuously over 5 years, would earn you interest of about $9,165.60.
This is of course rounded to the nearest cent as required.
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how do I use elimination to solve the system 8x-7y=5 and 3x-5y=9 for y
Find the values of x and y for which the lines are parallel.
a)x = 47, y = 79
b)x = 58, y = 57
c)x = 79, y = 49
d)x = 79, y = 47
Final answer:
Lines represented by equations in the form x = a constant are vertical lines and are parallel to each other. The correct answer indicating parallel lines is (d) x = 79, y = 47.
Explanation:
To determine which pair of values for x and y indicates that the lines described are parallel, we need to understand that for two lines to be parallel, they must have the same slope. For standard linear equations in the form y = mx + b, where m is the slope, lines with the same m value are parallel. However, when the equation is given in the form x = a constant, as is the case for options (a) and (c), it denotes a vertical line, which does not have a slope in the traditional sense but is parallel to other vertical lines.
Given the information, lines described by equations x = 47 and x = 79 would be parallel since they both represent vertical lines. Therefore, the correct answer is (d) x = 79, y = 47.
20 Point question!!!!!!!! On the rectangular coordinate system, line PQ goes through P (6, − 2), and the midpoint of line PQ is (0, 5). What are the coordinates of point Q?
Solve log(2x+3)=3
A. 500
B. 997
C. 1/2
D. 997/2
The height of a candle depends on the amount of time the candle has been burning
What is the area of this face ?
Answer:
28 square inches.Step-by-step explanation:
Notice that the yellow area is a compound area. Its height is 10 inches.
We can divide this area in three figures, one rectangle and two squares, where the square sides are 2 inches long.
So, the area of the squares is
[tex]A_{squares}=(2in)^{2} +(2in)^{2}=4in^{2} +4in^{2} =8in^{2}[/tex]
On the other hand, the rectangle has a height of 10 inches, and its base is 2 inches long. So its area is
[tex]A_{rectangle}=(10in)(2in)=20in^{2}[/tex]
Therefore, the yellow area is
[tex]A_{yellow}=A_{squares} +A_{rectangle}=8in^{2} +20in^{2} =28in^{2}[/tex]
So, the answer is 28 square inches.
What is the sum of the geometric series below?
3+1+1/3+1/9+1/27
a. 67/27
b. 121/27
c. 40/9
d. 41/9
Answer:
Option B is correct.
Step-by-step explanation:
Given Geometric series : 3 , 1 , [tex]\frac{1}{3}\:,\:\frac{1}{9}\:,\:\frac{1}{27}[/tex]
To find: Sum of the series.
First term of the geometric series, a = 3
Common ration of the Geometric series, r = [tex]\frac{second\:term}{first\:term}=\frac{1}{3}[/tex]
Sum of the finite Geometric series , [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
Sum of the given 5 term term of given series , [tex]S_5=\frac{3(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}=\frac{3(\frac{3^5-1}{3^5})}{\frac{3-1}{3}}[/tex]
= [tex]\frac{\frac{3^5-1}{3^3}}{2}=\frac{243-1}{2\times3^3}=\frac{121}{27}[/tex]
Therefore, Option B is correct.
divide use either way to record partial quotient 198÷9
To divide 198 by 9 using the partial quotients method, you estimate how many times 9 fits into 198, subtract, and sum up the partial results to get the final answer of 22.
To solve 198 ÷ 9 using the partial quotients method, follow these steps:
Estimate how many times 9 can go into 198. We start with a rough estimate that 9 can go into 198 around 20 times.
Calculate 9 x 20 = 180. Subtract this from 198, yielding 198 - 180 = 18.
Next, determine how many times 9 can fit into the remaining 18. This is 2 times since 9 x 2 = 18.
Subtract 18 from 18, resulting in a remainder of 0.
Add the partial quotients: 20 + 2 = 22.
So, 198 ÷ 9 = 22 using the partial quotients method.
A grocery store sells chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper?
A. $0.17
B. $1.70
C. $0.07
D. $1.07
A store increases the price of a sweater from $20 to $22.What is the percent of increase?Select from the drop-down menu to correctly complete the statement.
a 0.1
b 0.2
c 2
d 9
e 10
f 20
Answer:
Find out the what is the percent of increase .
To prove
As given
A store increases the price of a sweater from $20 to $22.
Increase in the price = Increase price - Initial price
= $22 - $20
= $2
Formula
[tex]Percentage = \frac{increase\ in\ price\times 100}{Initial\ price}[/tex]
Here initial price = $20
increase in price = $2
put in the formula
[tex]Percentage = \frac{2\times 100}{20}[/tex]
[tex]Percentage = \frac{200}{20}[/tex]
Percentage = 10%
Therefore the increase in the price is 10% .
Option (e) is correct.
Final answer:
The percent of increase when a store raises the sweater's price from $20 to $22 is calculated as 10%, using the formula of difference over original price times 100, Option E is correct.
Explanation:
The question asks for the percent of increase when a store increases the price of a sweater from $20 to $22. To find the percentage increase, we take the increase in price ($2), divide it by the original price ($20), and then multiply by 100 to convert to a percentage. Thus, the calculation is (($22 - $20) / $20) * 100 = (2 / 20) * 100 = 0.10 * 100 = 10%.
A tortoise is walking in the desert. It walks for
37.5
meters at a speed of
3
meters per minute. For how many minutes does it walk?
Let f(x)=8^x
What function represents a transformation of f(x) by a vertical stretch with factor 2?
g(x)=8^2x
g(x)=2⋅8^x
g(x)=8 1/2^x
g(x)=12⋅8^x
The sum of negative eighteen and a number is eleven. What is the number?
Which equation could be used to solve the problem?
A) x - 18 = 11
B) 18 - x = 11
C) -x + 18 = 11
D) x + 18 = 11
Jake has already written 3 pages, and he expects to write 1 page for every additional hour spent writing. Write an equation that shows the relationship between the hours spent writing x and the total pages written y. Then Graph.
what is the ratio of 48 and 56
5x+9y+z=20
2x-y-z=-21
5x+2y+2z=-21
(4n-3n^3)-(3n^3+4n) answer
Crafty Grandma Edith sat her family down during Thanksgiving and told them they couldn’t have any pumpkin pie until they worked out this puzzle. Her 6-year-old granddaughter was the first to solve it! Can you work out what 9183 equals?
8809 = 6 3590 = 2
7111 = 0 6855 = 3
9881 = 5 1012 = 1
6660 = 4 5731 = 0
5531 = 0 9191 = 2
2516 = 1 9183 = ?
I'm really confused about this one, could anyone help me?
Find last year's salary if, after a 5% pay raise, this year's salary is $38,325?
Graph the equation by plotting points
x=6 ...?
Fill in each box below with an integer or a reduced fraction.
(a)
log
2
8
=
3
log28=3 can be written in the form
2
A
=
B
2A=B where
The logarithmic equation log2(8) = 3 convert to exponential form as 2^3 = 8.
Converting the logarithmic equation log2(8) = 3 to exponential form involves recognizing the base and the exponent.Logarithms state that if logb(A) = C, then the equivalent exponential form would be bC = A. In this case, since 2 is the base and 3 is the exponent to which 2 must be raised to get 8, we can write 2^3 = 8.
To further clarify, logarithms are simply a way to represent exponents, and they are widely utilized in mathematics to simplify the multiplication and division of exponents. A logarithm with a base of 10 is known as the common logarithm and is often written without a base as log(A). In contrast, when another base is used, it is indicated as logb(A). The relationship between logarithms and exponents is leveraged in various scientific and engineering fields to represent and calculate large numbers conveniently.
The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution?
A.4-3i
B.3-4i
C.4+3i
D.-3+4i
Answer: Option B 3-4i is the correct option
Explanation:
we have formula for discriminant [tex]D=b^{2}-4ac[/tex]
after that we find the required variable that is to be find according to the quadratic equation given suppose we have to find x
then we have formula [tex]x=\frac{-b\pm\sqrt{D}} {2a}[/tex]
Here we have [tex]\pm[/tex] of roots if we have one root 3+41 other would be of opposite sign and hence,definitely be 3-4i.
Therefore Option B 3-4i is the correct option.
State the domain and range of the function represented by the table
x= -4, -1, 0, 3
y= -4, -4, -4, -4
The domain of this function is { - 4, - 1, 0, 3 } and range of the function is
{ - 4 }.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
The domain of the function f(x) is the set of x values that are
{ - 4, - 1, 0, 3 }
and the range of the function f(x) is { - 4 }.
As for every input, the output of the function remains the same so it is a constant function.
learn more about the domain and range here :
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What is the value of -d when d = -2?
To rent a certain meeting room, a college charges a reservation fee of $42 and an additional fee of $7.70 per hour. The math club wants to spend less than $80.50 on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room?
Use t for the number of hours the meeting room is rented, and solve your inequality for t .
which improper fraction that is equivalent to the mixed number 6 4/7
All employees at FashionMarket get 20% off all clothing and accessories Kim li recently brought a t shirt at fashionMart for a 20% discount conjunction Kim li workable at fashionMart
Answer:
D.
false; Kim Li could have received a 20% sale discount
a+5.7>-2.3 what is the answer
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75° with the ground. The height of the kite from the ground is (20.27,61,77.27) meters.