Answer:
A = $ 7,449.23
A = P + I where
P (principal) = $ 5,000.00
I (interest) = $ 2,449.23
Step-by-step explanation:
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Compound Interest Formulas and Calculations:
Calculate Accrued Amount (Principal + Interest)
A = P(1 + r/n)^nt
Calculate Principal Amount, solve for P
P = A / (1 + r/n)^nt
Calculate rate of interest in decimal, solve for r
r = n[(A/P)(^1/nt) - 1]
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]
Formulas where n = 1 (compounded once per period or unit t)
Calculate Accrued Amount (Principal + Interest)
A = P(1 + r)^t
Calculate Principal Amount, solve for P
P = A / (1 + r)^t
Calculate rate of interest in decimal, solve for r
r = (A/P)1/t - 1
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)
Continuous Compounding Formulas (n → ∞)
Calculate Accrued Amount (Principal + Interest)
A = Pe^rt
Calculate Principal Amount, solve for P
P = A / ert
Calculate rate of interest in decimal, solve for r
r = ln(A/P) / t
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = ln(A/P) / r
To calculate the future amount in the account after 5 years with compound interest, you can use the formula A = P(1 + r/n)^(nt). Plugging in the values, the amount in the account would be $6,803.85.
To calculate the future amount in the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
Plugging in the values, we get:
A = 5000(1 + 0.08/12)^(12*5)
Calculating this, we find that the amount in the account after 5 years would be $6,803.85.
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Answer:
0.085.
Step-by-step explanation:
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Answer:
0.085
Step-by-step explanation:
So, 8.5% means 8.5 per 100 or simply 8.5/100. If you divide 8.5 by 100, you get 0.085 (a decimal number).
Answer;
The above statement is true
Explanation;
-It is true that a parallelogram has symmetry with respect to the point of intersection of its diagonals.
-A parallelogram is a quadrilateral that has 2 pairs of parallel sides. The diagonals of a parallelogram bisect each other. Each diagonal of a parallelogram separates it into two congruent triangles.
4x2 + 22x + 31 = 0
x2 + 11x − 1 = 0
x2 + 11x + 31 = 0
Option c) x² + 11x - 1 = 0 is the correct quadratic equation that can be used to determine the thickness of the frame.
In this problem, Emily wants to hang a painting in a gallery, and she needs to determine the thickness of the frame, denoted by "x," surrounding the painting. The painting and frame together should have an area of 31 square feet. The dimensions of the painting are given as 5 feet in width and 6 feet in length. To find the equation that will help us determine the thickness of the frame, we need to set up a quadratic equation based on the given information.
Let's start by visualizing the problem. The painting is a rectangle, and the frame around it will also form a rectangle. So, we can find the area of the frame by subtracting the area of the painting from the total area of the painting and the frame.
The area of a rectangle can be calculated by multiplying its length and width. For the painting, we have:
Painting's area = Length * Width
= 6 feet * 5 feet
= 30 square feet
Now, we know that the total area of the painting and frame together is 31 square feet. So, we can set up the following equation:
Total area (painting + frame) = Painting's area + Frame's area
31 square feet = 30 square feet + Frame's area
Frame's area = 31 square feet - 30 square feet = 1 square foot
The frame's area is given by the product of its width (which is the thickness "x") and the length of the painting (6 feet):
Frame's area = x * 6 feet
Since the frame's area is equal to 1 square foot, we can write:
x * 6 = 1
Now, let's rearrange the equation to set it to zero on one side:
6x - 1 = 0
We have now derived the quadratic equation that represents the problem:
6x - 1 = 0
The correct answer is not directly provided among the options. However, let's manipulate the equation to put it in standard quadratic form (ax² + bx + c = 0):
Multiply the equation by -1 to change the sign of each term:
-6x + 1 = 0
Now, it matches option c) x² + 11x - 1 = 0.
Thus, option c) is the correct quadratic equation that can be used to determine the thickness of the frame, "x," for the given problem.
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The correct answer is 4x2 + 22x − 1 = 0
That's what you get when you (5 + 2x)(6 + 2x) = 31
And you get to expand that based on the data that is already provided in the question.
Answer:
see below
Step-by-step explanation:
This is a geomtric sequence
an = a1 r^(n-1)
a1 =1 and r=2
an = 2 ^(n-1)
A=a1 =1
B =a2 = 2^(2-1) =2
C =a3 = 2^(3-1) = 2^2 =4
D = a4 = 2^(4-1) = 2^3 = 8
E = a5 = 2^(5-1) = 2^4 = 16
F = a6 = 2^(6-1) = 2^5 = 32
G = a7 = 2^(7-1) = 2^6 = 64
H = a8 = 2^(8-1) = 2^7 = 128