Joey opens a bank account with $675. The account pays 3.9% annual interest compounded continuously. How long will it take for Joey to double his money? (Round answer to 2 decimal places)
Answers
It will take approximately 17.77 years for Joey to double his money with an account that pays interest compounded continuously.
What is the time taken to double the accrued amount?The compounded interest formula is expressed as;
\(A = P\ *\ e^{(rt)}\)
Where A is accrued amount, P is the principal, r is the interest rate and t is time.
Given that:
Principal amount P = $675
Final amount P = double = 2($675) = $1,350.00
Interest rate I = 3.9%
Time t (in years) = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 3.9/100
r = 0.039
Plug these values into the above formula:
\(A = P\ *\ e^{(rt)}\\\\t = \frac{In(\frac{A}{P} )}{r} \\\\t = \frac{In(\frac{1350}{675} )}{0.039}\\\\t = 17.77\ years\)
Therefore, the time taken is approximately 17.77 years.
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Related Questions
Is the relation a function?
{(1,12), (3, 14), (14, 3), (5, 12)}
Answers
Answer:
many-to-one
Step-by-step explanation:
1 and 5 have same co-domain which is 12
while 3 and 14 each have difference co domain which is 14 and 3 respectively
Can someone help me asap? It’s due tomorrow. Select all that apply
Answers
The valid generalizations are:
There are no oranges in the fruit salad
Pieces of pear make up a majority of fruit salad
Pieces of pineapple make up about 10% of fruit salad
Determining the valid generalization about the composition of the fruit saladFrom the question we are to determine the valid generalization about the composition of the fruit salad.
From the given information,
The fruit salad is made up of 15 blueberries, 55 pieces of pear, 20 pieces of apple, and 10 pieces of pineapple.
The total is
15 + 55 + 20 + 10 = 100
Half of a fruit salad is made up of pieces of appleThis statement is not correct because the composition of apple in the fruit salad is about 20%
There are no oranges in the fruit saladThis statement is correct because there are actually no oranges in the fruit salad
Pieces of pear make up a majority of fruit saladThis statement is correct because the composition of pear in the fruit salad is 55%. Thus, pieces of pear make up a majority of fruit salad
Pieces of pineapple make up about 10% of fruit saladThis statement is correct because the composition of pineapple in the fruit salad is 10%
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What’s the volume of the rectangular prism ?
Answers
Hey there!
Option answer: \(12 \frac{1}{4} \: cubic \: inches\)
volume of cuboid: length * breadth * height {formula}
=> \((3 \frac{1}{2} )\)× (2) × \((1 \frac{3}{4} )\)
=> \( \frac{7}{2} \times 2 \times \frac{7}{4} \)
=> \( \frac{49}{4} inches\)
=> \(12 \frac{1}{4} \: cubic \: inches\)
Use the Root Test to determine whether the series convergent or divergent. [infinity] n2 + 2 7n2 + 5 n n = 1 Identify an. Evaluate the following limit. lim n → [infinity] n |an| Since lim n → [infinity] n |an| ? 1, ---Select--- .
Answers
By using the Root Test on the series "∑n" , we found that the series is Divergent and diverges to infinity .
The Root Test states that, if the limit of nth root of the absolute value of the nth term of a series is less than 1, then the series converges. and
If the limit is greater than or equal to 1, the test is inconclusive.
In the series ∑n , the nth term of the series is "n" ,
So, the nth root of the absolute value of nth term is the nth root of |n|, which is = n^(1/n).
we see that as n approaches infinity, the nth root : n^(1/n) approaches 1, So, the limit of the nth root of the absolute value of the nth term is equal to 1. Which means that the Root Test is inconclusive for this series.
Therefore , the series ∑n diverges, it is a known series called as Harmonic series, which diverges to infinity.
The given question is incomplete , the complete question is
Use the Root Test to determine whether the series convergent or divergent. ∑n , where n is from 1 to infinity .
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the color to match on the left is represented by the binary rgb values 11011011 01101110 11001100. convert each color component into decimal in order to match the color.
Answers
The decimal values for the RGB color components are 219, 110, and 204, respectively, to match the given color.
To convert the binary RGB values to decimal, we need to consider each 8-bit component separately. The first component, 11011011, represents 219 in decimal. The second component, 01101110, represents 110 in decimal.
Finally, the third component, 11001100, represents 204 in decimal. Thus, the decimal values for the RGB color components are 219, 110, and 204, respectively, to match the given color.
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Sasha uses a recipe for orange preserve. She uses 750 g oranges and 1.5 kg sugar. What is the ratio of oranges to suger
Answers
The ratio of the quantity of oranges to sugar is 1:2.
Given that, Sasha used 750 g oranges and 1.5 kg sugar to prepare orange preserve.
We need to find the ratio of oranges to sugar.
What is the ratio?The ratio is a term that is used to compare two or more numbers. It is used to show how large or small a quantity is when compared to another.
Convert 1.5 kg into grams. That is 1.5 kg=1.5×1000=1500 g (∵1 kg=1000 grams)
Now, the ratio of oranges to sugar = oranges:Sugar=750:1500
=75:150=1:2
Hence, the ratio of the quantity of oranges to sugar is 1:2.
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Can somebody help me solve this with an explanation?
Answers
Answer:
x=1
Step-by-step explanation:
10/x+2/x = 12
Combine like terms
12/x = 12
Multiply each side by x
12/x * x = 12 *x
12 = 12x
Divide by 12
12/12 = 12x/12
1 =x
Answer:
x = 1
Step-by-step explanation:
Combine the two fractions, which is easily done because the denominators are the same:
12
--- = 12, which can also be written as 12 = 12x. Then x = 1
x
Triangle ABC with vertices A(9, 13), B(12, 11), and C(8,7);
scale factor: k = 2, center of dilation: (11, 14) (help please)
Answers
When a triangle is dilated, the size of the triangle changes.
The image of \(\triangle A'B'C'\) are:
\(A' = (7,12)\)
\(B' = (13,8)\)
\(C' =(5,0)\)
We have:
\(A = (9,13)\)
\(B = (12,11)\)
\(C = (8,7)\)
\(k = 2\)
Start by multiplying the scale factor by the coordinates of \(\triangle ABC\)
\(A = (9,13) \times 2\)
\(A = (18,26)\)
\(B = (12,11) \times 2\)
\(B = (24,22)\)
\(C =(8,7) \times 2\)
\(C =(16,14)\)
Subtract the center of dilation from the above coordinates
\(A' = (18,26) - (11,14)\)
\(A' = (18-11,26-14)\)
\(A' = (7,12)\)
\(B' = (24,22) - (11,14)\)
\(B' = (24-11,22-14)\)
\(B' = (13,8)\)
\(C' =(16,14) - (11,14)\)
\(C' =(16 - 11,14 - 14)\)
\(C' =(5,0)\)
Hence, the image of \(\triangle A'B'C'\) are:
\(A' = (7,12)\)
\(B' = (13,8)\)
\(C' =(5,0)\)
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Divide (6x2 + 12x) by 3x
Answers
Answer:
choice 1) 2x+4
Step-by-step explanation:
(6x²+12x)/3x = 2x+4
which statement about 307° is correct?
a. sin 307° > 0
b. cos 307° < 0
c. tan 307°<0
Answers
Answer: C. tan 307°<0
Step-by-step explanation: Quizzed
1. Jatan works twice as many hours per week as Hrishik. One week, they work 39 hours together. How many hours did each one work?
Answers
Hrishik worked 13 hours and Jatan worked 26 hours in the given week.
Assume that Hrishik puts in x hours per week at his job. The issue states that because Jatan works two times as many hours as Hrishik does each week.
If they both put in 39 hours a week, we can construct the following equation:
x + 2x = 39
combining comparable phrases
3x = 39
by 3 and dividing both sides:
x = 13
As a result, Hrishik puts in 13 hours per week while Jatan puts in twice that amount, or 2 x 13 = 26 hours per week. As a result, throughout the specified week, Hrishik worked 13 hours and Jatan 26.
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4x³ - 4x + 3 is divided by (2x-1)
Answers
Complete question:
4x³ - 4x + 3 is divided by (2x - 1). Find the quotient and the remainder
Answer:
The quotient = 2x² + x - ³/₂ and the remainder = ³/₂
Step-by-step explanation:
Given function;
4x³ - 4x + 3 divided by (2x-1)
Use long division method to obtain the remainder and the quotient.
2x² + x - ³/₂
-----------------------
2x - 1 √4x³ - 4x + 3
- (4x³ - 2x²)
----------------------------
2x² - 4x + 3
- ( 2x² - x)
-----------------------------
-3x + 3
-(-3x + ³/₂)
----------------------------
³/₂
Therefore, the quotient = 2x² + x - ³/₂ and the remainder = ³/₂
determine the total and lateral surface area of the square pyramid
the lengths=12.8 cm 12 cm and 9 cm
Answers
The total surface area of the square pyramid is 394.24 cm², and the lateral surface area is 230.4 cm².
To determine the total and lateral surface area of a square pyramid, we need to use the given measurements: the lengths of the base and the height of the pyramid.
In this case, the base of the square pyramid has sides of length 12.8 cm, and the height is 9 cm.
To calculate the lateral surface area of a square pyramid, we need to find the area of the four triangular faces that surround the pyramid.
Each triangular face is an isosceles triangle with two equal sides and a height equal to the height of the pyramid.
The area of an isosceles triangle can be calculated using the formula: area = 0.5 \(\times\) base \(\times\) height.
Since the base of each triangular face is equal to the length of the square base (12.8 cm), and the height is equal to the height of the pyramid (9 cm), we can calculate the area of one triangular face as follows:
Area of one triangular face \(= 0.5 \times 12.8 cm \times 9 cm = 57.6 cm ^{2} .\)
Since there are four triangular faces in total, the lateral surface area of the square pyramid is 4 times the area of one triangular face:
Lateral surface area = 4 * 57.6 cm² = 230.4 cm².
To calculate the total surface area of the square pyramid, we also need to consider the area of the square base.
The area of a square can be calculated by squaring one side length.
Area of the square base = (12.8 cm)² = 163.84 cm².
The total surface area is the sum of the lateral surface area and the area of the square base:
Total surface area = Lateral surface area + Area of the square base
= 230.4 cm² + 163.84 cm²
= 394.24 cm².
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Which inequality represents all the solutions of -2(3x + 6) ≥ 4(x + 7)?
Answers
The inequality that represents all the solutions of -2(3x + 6) ≥ 4(x + 7) is x ≤ -4
How to determine the solution of the inequality?From the question, we have the following parameters that can be used in our computation:
-2(3x + 6) ≥ 4(x + 7)
Divide both sides of the inequality by -2
So, we have the following representation
3x + 6 ≤ -2(x + 7)
Open the brackets
This gives
3x + 6 ≤ -2x - 14
Add 2x to both sides of the inequality
So, we have the following representations
5x + 6 ≤ -14
Subtract 6 from both sides of the inequality
So, we have the following representations
5x ≤ -20
Divide both side of the inequality
x ≤ -4
Hence, the solution is x ≤ -4
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NEED HELP WITH NUMBER 4! GIVING BRAINLIEST AND 20 POINTS TO BEST ANSWER. GIVE MODELS IF U CAN! THANKS! YOU CAN DO IT! :D
Answers
Answer:
10/21
Step-by-step explanation:
5
7
+
2
3
=
5 × 3
7 × 3
+
2 × 7
3 × 7
=
15
21
+
14
21
=
15 + 14
21
=
29
21
=
1 8
21
\(Hello\) \(There!\)
Let's do this step-by-step explanantion!
\(\frac{5}7}\) × \(\frac{2}{3}\)
Apply the fraction rule:
\(\frac{5x2}{7 x 3}\)
Multiply the numbers: \(5\) × \(2=10\)
\(=\frac{10}{7 x 3}\)
Again, Multiply the numbers: \(7\) × \(3=21\)
\(=\frac{10}{21}\)
Answer:
\(\frac{10}{21}\)
Also, sorry. I wasn't able to give you a model.
Hopefully, this helps you!!
\(OwoSokka\)
When a random representative sample is drawn from a population, the procedure is deemed to be what type of sample?
Answers
The procedure which is deemed to be the type of sample in discuss is; representative sample are free of bias.
What is a random sampling?Representative sampling and random sampling are two techniques used to help ensure data is free of bias. A representative sample on the other hand is a group or set chosen from a larger statistical population according to specified characteristics. A random sample is a group or set chosen in a random manner from a larger population.
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why is the square root of 70 irrational?
Answers
Answer:
The sqrt(70) is irrational because there isn't a rational product of any 2 same rational numbers that equal 70.
Step-by-step explanation:
Anne creates necklaces and rings to sell. It takes her 3 hours to make a necklace and 1 hour to make a ring. If she makes 10 items in 2 standard 8-hour work days, how many necklaces and rings did Anne make during those 16 hours?
Answers
3 individual hours to make a necklace, and 1 hour to make a ring. according to the problem, she made 10 items in 16 hours. this problem will most likely be trial and error. let’s try one first guess.
my first guess will be, maybe she will make 6 rings and 4 necklaces. 6 times 1 is 6, which takes 6 hours for the rings. 4 times 3 is equal to 12. 6 + 12 is too high! let’s try again.
what about 6 rings and 2 necklaces? 6 times 1 is 6, so that’s 6 hours. 2 times 3 is 6 hours! 6 plus 6 is 12, which is close, but not quite there!
let’s try 7 rings and 3 necklaces! 7 times 1 is 7 hours. 3 times 3 is equal to 9 hours! total that together, 7 plus 9, is equal to 16 hours spent!
so, the answer would be, “Anne made 7 rings and 3 necklaces within 16 hours.” hope this helped!:)
An oven is priced at $745.75. There is an 8% sales tax rate.
What is the sales tax for the oven in dollars and cents?
a) $93.22
b) $59.66
c) $652.53
d) $686.09
Answers
you do 745.75*0.08 which gives you the answer
Answer:
B. 59.66
Step-by-step explanation:
In order to solve this youd have to multiply 745.75 by 8% in order to find it
First you'd need to turn 8% into a decimal
8%/100 = 0.08
0.08 x 745.75 =59.66
So the sales tax rate for this price is 59.66
The cross section of a prism is an n sided polygon.
Circle the number of edges that the prism has.
2n
n+2
n+ 3
3n
Answers
The number of edges that the prism has is
n + 2What does a prism's cross section look like?When a plane intersects a prism, the shape formed is known as the cross section. The cross section of the prism will have the same form as the base if it is divided by a plane that runs horizontally and parallel to the base.
A prism is a 3-dimensional object with two congruent and parallel bases (which are polyggonal) connected by rectangular lateral faces. The number of edges of a prism is equal to the sum of the number of edges of the two bases and the number of lateral faces.
Each base of the prism has n edges, so the two bases together have 2n edges. The number of lateral faces of the prism is equal to the number of edges of one of its bases, so there are n lateral faces. Each lateral face has 4 edges, so the total number of edges of the lateral faces is 4n.
Therefore, the total number of edges of the prism is equal to the sum of the number of edges of the two bases (2n) and the number of lateral faces (4n), which is 2n + 4n = 6n.
In conclusion, the cross section of a prism is an n-sided polygon and the prism has n + 2 edges.
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Rewrite the expression in the form a^n. (a^2/3)^-1
Answers
Answer:
a^(-2/3)
Step-by-step explanation:
(a^2/3)^-1
We know x^y^z = x^(y*z)
a^(2/3*-1)
a^(-2/3)
Troy started at the fire station. He walked to the library and then rode his bike to the post office. If Troy only traveled along the grid lines and took the shortest route, how far did he travel? please helllllllppppppppppppppp my last one
Answers
Answer:
14 blocks
Step-by-step explanation:
next time plz add a grid :(
Kristin wants to buy a pair of jeans that cost $25. she gets a 20% discount since she works at the store. she must pay 6% sales tax. How much will she pay for the jeans
Answers
Kristin will pay 21.20 for the jeans after the discount and sales tax are applied.
The first step is to calculate the discount Kristin will receive:
Discount = 20% of 25 = 0.20 x 25 = 5
Now subtract the discount from the original price to find the sale price:
Sale price = 25 - 5 = 20
Next, calculate the amount of sales tax Kristin will have to pay on the sale price:
Sales tax = 6% of 20 = 0.06 x 20 = 1.20
Finally, add the sale price and sales tax to find the total cost:
Total cost = 20 + 1.20 = 21.20
Therefore, Kristin will pay 21.20 for the jeans after the discount and sales tax are applied.
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a length of black steel pipe is 21'-0" long. how much if the length remains of two pieces 7'-9 5/8" are cut from the length?
Answers
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 9 5/8, where 9 is the quotient and 5 is the remainder.
Remain length = 13.2' = 13' 2 2/5 ".
What is a mixed fraction?The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognized fraction.Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction's value doesn't change. We can assert that the actual mixed number and the simplified mixed number are fractions of the same size.Length of black steel pipe is 21'-0".
7' 9 5/8" =7.8 '
Remain length = 13.2' = 13' 2 2/5 ".
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I need to find the area of this parallelogram
Answers
Answer:
Step-by-step explanation:
Describe fully the single transformation that takes shape A to shape B.
It is a ......
angle ...... degress clockwise
about the point.....
Answers
Answer: It is a Rotation Angle 90 Degrees clockwise about the point (3,4)
Step-by-step explanation:
Mark the point (3,4) with your finger and turn your phone once to the right Your old shape is where your new shape your be now. That’s rotation.
What is the slope of the line that passes through (-2,7) and (4, 9)?
Answers
Answer:
Step-by-step explanation:
(9 - 7)/(4 + 2) = 2/6 = 1/3 is the slope of the line
I dont understand? Can someone plz help
Answers
Answer:
2/5; 1/2; 2/3; 14/10; 2/6
Step-by-step explanation:
When finding equivalent fractions, multiply or divide both the numerator and denominator by the same number.
4/10 = 2/5 because 4÷2=2 and 10÷2=5
The same thing has been done to both the numerator and denominator (in this case they have both been divided by 2)
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞)
Answers
The correct statement is that F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
What is value?Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.
This can be seen by looking at the function's minimum and maximum values and its points of intersection with the x- and y-axes. The minimum value of (1.9, negative 5.7) is to the left of the x-axis, indicating that the function is negative over the interval (-0.7, 0.76). The maximum value of (0, 2) is above the x-axis, indicating that the function is negative over the interval (2.5, ∞).
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Find the inverse of each function.
Answers
The inverse of the function (1/2)^x/3
Given function,
y = 3\(log_{1/2}\) x
Now,
y = 3\(log_{1/2}\) x
Let y = f(x)
then,
x = \(f^{-1} (y)\)
Now put \(f^{-1} (y)\) in the place of x,
y = 3\(log_{1/2}\) \(f^{-1} (y)\)
Simplifying,
y/3 = \(log_{1/2} f^{-1} (y)\)
\(f^{-1} (y) = 1/2^{y/3}\\\)
Replace y variable with x,
\(f^{-1} (x)\) = \((1/2)^{x/3}\)
Hence the inverse of function is \((1/2)^{x/3}\) .
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