If you have 2500 to invest at 6 interest compounded quarterly. For how many years will the money need to be invested for that amount to triple?

Answers

Answer 1

For this case we have the following equation:
P (t) = P * (1 + r / n) ^ (n * t)
Where,
P: initial investment
r: interest rate
n: periods
Substituting values:
3 * 2500 = 2500 * (1 + 0.06 / 4) ^ (4 * t)
Rewriting:
3 = (1,015) ^ (4 * t)
Clearing t:
log1.015 (3) = log1.015 ((1.015) ^ (4 * t))
4 * t = log1.015 (3)
t = (1/4) * log1.015 (3)
t = 18.45 years
Answer:
the money will need to be invested 18.45 years for that amount to triple

Related Questions

fully expand the logarithm: log(x^3/z^5)

Answers

to expand this logarithm, we have to apply the rules. These rules are;

Log(A/B) = logA - LogB and Alogx=log(x∧A)

Log (x³/z∧5) = log (x³) - log z∧5
=3log x - 5log z

Using the following properties we can expand the given expression:

1) Quotient Rule of Logs:
Log(A/B) = Log A - Log B

2) Power Rule of Logs:
[tex]Log(a)^{b}=b*Log(a) [/tex]

[tex]log( \frac{ x^{3} }{ z^{5} } ) \\ \\ =log( x^{3})-log( z^{5}) \\ \\ =3logx-5logz[/tex]

Instructions:Select the correct answer from each drop-down menu. The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is

Answers

In order to find the rang, solve for the first inequality:

2x - 5< 7

2x <12

x < 6

Solve for the second inequality:

4x +10 > 6
4x > -4
x > -1

Graph these two inequalities on a number line to see that their union is the complete number line. Note that for any number of x can either be greater than negative 1 or less than 6 and can be both.

so the answer is:

range of negative infinity to infinity. required to use parenthesis

(-∞, ∞)

what is the surface area of a sphere with a radius of 3m

Answers

The area is 113.1m If you want to double check go on google and look up surface area of a sphere. A calculator will come up. Hope this helped.

Part A: Factor 2x2b2 + 5xb2 + 2b2. Show your work. (4 points) Part B: Factor x2 − 8x + 16. Show your work. (3 points) Part C: Factor x2 − 49. Show your work. (3 points)

Answers

[tex]2x^2b^2 + 5xb^2 + 2b^2 = b^2(2x^2 + 5x + 2) = b^2(2x + 1)(x + 2)[/tex]

[tex]x^2 - 8x + 16 = (x - 4) (x - 4) = (x-4)^2[/tex]

[tex]x^2 - 49 = x^2- 7^2 = (x - 7)(x + 7)[/tex]

PLZ HURRRY!!

Of the 12,000 votes cast in an election, 42% of the votes were for Mr.Jones. How many votes were cast for all the other candidates?

Answers

42/100 × 12000
= 5040
Therefore, Number of Voters left = 12000-5040
= 6960

6960 is the correct answer :)

y = x3 - 3x On which intervals is this function increasing?

Answers

The function is increasing on the intervals
x ∈ (-∞, -1) ∪ (1, ∞)

Polygon ABCDEF is the result of a translation of polygon GHIJKL . GL¯¯¯¯¯ is parallel to HI¯¯¯¯¯ in the pre-image. please help

Answers

Since GL and HI are parallel to each other, then in the translation this condition is going to be kept. So that, we can write in these gaps that AB and FE are parallel to each other.

GL parallel to HI in the pre-image ensures AB remains parallel to FE in the translation.

Given that GL and HI are parallel, we can infer that AB and FE will also remain parallel in the translation. The parallelism of lines GL and HI suggests that their corresponding sides, AB and FE, will exhibit the same parallel relationship during the translation process. This is a consequence of the consistent geometric transformation applied to all points on lines GL and HI. As each point on GL undergoes translation, its corresponding point on HI experiences the same displacement, preserving the parallelism.

Therefore, we can confidently state that AB and FE maintain their parallel orientation, aligning with the geometric properties of the translation that preserves parallel lines. The parallelism observed in the original configuration persists throughout the translation, ensuring that AB and FE remain parallel to each other.

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Jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. The expected value of the number of days per week that Jackson goes to the gym is 2.05. The probability that he goes 0 days is 0.1, the probability that he goes 2 days is , and the probability that he goes 3 days is .

Answers

So what's your question?

Alrighty, lets say he did this in a month. Probablity always equals one in this scenario. So:
1-.1=.9
He needs more time at 3 days so:
3 days > 2 days
The equality has to be bigger on three so It can be .46 or bigger. Yet we want concise, clear answers:
.1 (zero), .23 (two) .67 ( three)

What is the equation of the circle shown in the graph ? (Blank)^2 + (Blank)^2 = blank

Answers

check the picture below.

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{4}{ k})\qquad \qquad radius=\stackrel{6}{ r} \\\\\\\ [x-(-6)]^2+[y-4]^2=6^2\implies (x+6)^2+(y-4)^2=36[/tex]

The equation of the circle shown in the graph is equal to [tex](x + 6)^2 + (y - 4)^2 = 36[/tex]

Form the graph, we can deduce the following points:

The center of the circle is denoted by the black dot and we can see that the values are -6 and 4 respectively.

Center (h, k) = (-6, 4)

Also, the diameter of the circle is:

Diameter = 12 units

Radius = [tex]\frac{Diameter}{2} = \frac{12}{2} = 6 \;units[/tex]

Mathematically, the standard form of the equation of a circle is given by;

.....equation 1

Where;

h and k represents the coordinates at the center.r represents the radius of the circle.

Substituting the values into eqn 1, we have:

[tex](x - [-6])^2 + (y - 4)^2 = 6^2\\\\(x + 6)^2 + (y - 4)^2 = 36[/tex]

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The net asset value of stock in a mutual fund had increased by $20 per share when an investor decided to redeem them. The investor had purchased 100 shares of the stock for $2,316 and redeemed them for $4,301. What can you conclude about the fund? a. The fund is a no-load fund. b. The offer price of the fund was $0.15 less than the net asset value when purchased. c. The offer price of the fund was $0.15 more than the net asset value when purchased. d. The offer price of the fund was $0.15 more than the net asset value when sold.

Answers

The correct answer is letter c. The offer price of the fund was $0.15 more than the net asset value when purchased.

Formula for calculating NAV:

Net Asset Value (NAV) = (Assets - Debts) / (Number of Outstanding Units)

The Net Asset Value (NAV) is the price in which you pay to buy a unit of mutual fund scheme when you invest.

please help! i dont understand this.
a 25 gram sample substance that's used for drug research has a k-value of 0.1229. find the substances half-life, in days using the exponential decay formula. round your answer to the nearest tenth

Answers

With a k-value of 0.1229, the half-life is approximately 5.6 days.

The exponential decay formula is given by:

amount remaining = initial amount × e^-(k × t)

For a substance's half-life, the amount remaining is half of the initial amount. The formula to find the half-life (t1/2) is:

t1/2 = ln(2) / k

Here, ln(2) is approximately 0.693 and k is given as 0.1229. Substituting these values in:

t1/2 = 0.693 / 0.1229 ≈ 5.64 days

Rounding to the nearest tenth, the half-life of the substance is 5.6 days.

Terry uses 3 cups of pumpkin seeds to decorate the tops of 12 loaves if bread. She puts an equal amount of seeds on each loaf. How many cups of pumpkin seeds does she put on each loaf of bread?

Answers

There are 3 cups of pumpkin seeds used every 12 loaves of bread. To find how much she puts on each single loaf, divide 3 by 12 and get your answer, 0.25. So she uses 0.25 cups of pumpkin seeds per loaf.

Question 19 find the solution

Answers

y = 31 because 6x5 is 30 and if you add one it becomes 31.

y = 6x +1
x= 5

Using the value of x in first equation we can write:

y = 6(5) + 1

y = 30 + 1

y = 31

So, the solution is (5, 31)

Thus, option 2nd is the correct answer

A line has a slope of 2 and a y intercept of (0,-4) what is the value of y when x=6

Answers

First we set up an equation with the givens (slope and y intercept):
y = 2x -4
next plug in 6 for x.
y = (2x6) - 4
y = 12 - 4

And this will give us the value of y: 8.

Final answer:

The question is about finding the y-value of a line when the x-value is given, knowing the slope and the y-intercept. By plugging the given slope, y-intercept and the provided x-value into the formula y = mx + b, we find that y equals 8 when x equals 6.

Explanation:

If we know the slope (m) of a line and the y-intercept (b), we can use the formula y = mx + b to calculate the y-value for any x-value. In the given question, the slope (m) is 2 and the y-intercept (b) is -4. If we want to find the y-value when x = 6, we can substitute these values into the formula:

y = 2*6 - 4

So, y = 12 - 4 = 8. Therefore, when x = 6, the value of y is 8.

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PLZ HELP ASAP CIRCLES WILL GIVE BRANLIEST

Answers

From the given, it is obvious that angle I is the opposite angle of angle D. This means that the sum of the measures of these two should be equal to 180°.

If we are to look closely to the figure, angle I intercepted the arc BDR. Also, the angle D intercepted arc BIR. The sum of the measures these two arcs is 360°. Hence, the sum of the measures of the angles intercepting these arcs is 180°.

m∠I + m∠D = 180°
117° + m∠D = 180°

The measure of angle D is 63°.

Answer: 63°

fresh raspberry contain 80% water.Dried raspberry contain only 20%.how many pounds do you get from 36lb fresh berries

Answers

80% water = 36 lbs fresh berries

1 % water = 36 ÷ 80 = 0.45 lb

20% water = 0.45 x 20 = 9 lbs

Answer: You will get 9 lbs of raspberry.

The amount of fresh berries that contain 80% water is 7.2 pounds.

Amount of water in fresh raspberry = 80%

It means the amount of raspberry only in a fresh raspberry =20%

Amount of water in dry raspberry =20%

What is a percentage?

A percentage is a value per hundred.

So, the amount of raspberry only in 36 lbs fresh berries = 20% of 36

20% of 36 = (20/100)*36 = 7.2 lbs

So, the amount of raspberry only in 36 lbs of fresh berries = 7.2 lbs

Therefore, we get 7.2 lbs from 36lb fresh berries.

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coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3

The coordinate grid shows points A through K. Which points are solutions to the system of inequalities listed below?

2x + y ≤ 10
2x − 4y < 8

Answers

A graph shows points A, C, D, K are in the solution set.

_____
Doing all the calculations is fairly tedious, but can be done manually. (It works better, perhaps, to do it on a spreadsheet.) It is convenient to reduce the second equation by a factor of 2 to
x -2y < 4

point A(-5, 4) in the first equation: 2(-5)+(4) = -2 ≤ 10
point A(-5, 4) in the second (reduced) equation: (-5)-2(4) = -13 < 4

point H(-4, -4) in the first equation: 2(-4) +(-4) = -12 ≤ 10
point H(-4, -4) in the second equation: (-4) -2(-4) = 4 < 4 . . . FALSE

Which point best approximates the root of 45

Answers

To solve for √45 we shall proceed as follows:
We rewrite 45 as 3²×5
thus
√45=√(3²×5)
pulling terms out from under the radical we obtain
3√5
thus the exact answer form is:
3√5
or the decimal form is:
6.70820393

Adams sister want to watch her intake of fat per day.he estimate that the dinner will have 48grams of fat.what percentage of her total daily allowance of fat will the dinner be round your answer to a whole number.the recommended daily allowance of fat is70g

Answers

You have to figure out what 48 percent of 70 is.
Use the formula percent/of = x/100.
So, 48/70 and x/100 you cross multiply the numbers; 48*100 and 70*x and end up with 70x=4800.
Divide both sides by 70, which gives you 68.57.
Round the number up to 69 percent.

Given the least squares regression equation, = 1202 + 1,133x, when x = 4, what does equal?

Answers

The answer is 5734.
This can be done by substituting the value of x for 4 and multiplying it by 1,133 which will eventually give you the answer of 4532.
After this step, all you have to do it add 1202 to 4532, resulting in an answer of 5734.

Al and Bill each have two bullets. They fire alternately at a glass bottle. Al has hitting probability 1/3 and Bill 1/4. What is the probability that Al smashes the bottle if he is the one who fires the first shot? (Note: Al can smash the bottle even if he misses with his first shot.)

Answers

P(Al hits bottle first time) = 1/3
P(Al misses the first shot but hits on his second shot) =
P( Al misses and bill misses and Al hits) = 2/3 * 3/4 * 1/3 = 1/6

So required probability = 1/3 + 1/6 = 1/2

Can a chord also be classified as a radius? Explain your answer.

Answers

No
A chord is a straight sediment that joins two points of the circumference. The radius goes from the center of the circle, which is not on the radius.

y = |x| translated two units to the right.

Answers

If you want to translate y = |x| two units to the right, then you'll replace every x with x-2. This will move the xy axis 2 units to the left, giving the illusion that the V shape graph moves 2 units to the right.

So we go from y = |x| to y = |x-2|

how many times does 15 go into 46

Answers

15 goes into 46 3 times

The answer is 3.06666666667

What is the similarity ratio of the smaller to the larger similar pyramids? Enter your answer as a:b

Answers

the ratio will be 7:11

In the number 7,777.777, how does the 7 in the hundreds place compare to the 7 in the place to its left?
A.
The 7 in the hundreds place represents of what the 7 to its left represents.

B.
The 7 in the hundreds place represents 10 times what the 7 to its left represents.

C.
The 7 in the hundreds place represents of what the 7 to its left represents.

D.
The 7 in the hundreds place represents 100 times what the 7 to its left represents.

Answers

B is your answer!
hgfgjdhsghdfg

After a comparison of the number 7 which is at hundreds of places to the number 7 left off it, it is 10 times of what the 7 to its left represents. Hence, option B is correct

What are arithmetic Operations?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data provided in the question,

The given number is 7,777.777

Now, we have to compare the number 7 which is at the hundreds place with the 7 in the place left to it.

So, the 7 which is left to the 7 at the hundredth place will be 10 times it. Also, the 7 which is the second left to the 7 at the hundredth place is 100 times and so on it will increase like this.

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hey can you please help me posted picture of question

Answers

G(x) = x² is the parent square function.

It has its vertex at origin and opens upwards.

The given graph is obtained by shifting the graph of x² 2 units vertically down. This vertically translation can be expressed by subtracting 2 from the parent function.

So,

F(x) = G(x) - 2

F(x) = x² - 2

Thus the correct option is A

find the number of gallons in 6 liters of solution(1gal=3.79l)

Answers

Final answer:

To convert 6 liters of solution into gallons, given that 1 gallon is equivalent to 3.79 liters, you divide 6 by 3.79 which gives you 1.58 gallons of solution.

Explanation:

The question is asking to find the number of gallons in 6 liters of a solution, given that 1 gallon is equivalent to 3.79 liters. The conversion from liters to gallons is a basic concept in measurement conversion. Here is a step-by-step explanation to help you understand the process:

You have 6 liters of solution which you want to convert to gallons. We know that 1 gallon is equivalent to 3.79 liters. So, to convert liters to gallons, we divide the number of liters by 3.79. Therefore, you have 6 / 3.79 = 1.58 gallons (rounded to two decimal places) of solution.

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Greg has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs on it. What is \text{P(not a rap song})P(not a rap song)P, left parenthesis, n, o, t, space, a, space, r, a, p, space, s, o, n, g, right parenthesis?

Answers

We have been given that Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs.

Therefore, total number of songs are

[tex]666+777+999\\ =2442[/tex]

The formula for probability is given by

[tex]P(E)=\frac{n(E)}{n(s)}[/tex]

Let us first find the probability for rap song

[tex]P(\text{rap song})= \frac{999}{2442} \\ P(\text{rap song})= \frac{9}{22}[/tex]\\

Therefore, we have

[tex]P(\text{ not rap song})=1- P(\text{rap song})\\ \\ P(\text{ not rap song})=1-\frac{9}{22} \\ \\ P(\text{ not rap song})=\frac{13}{22} =0.59[/tex]

Hence, we have

P(not rap song)=0.59

2. An earthquake was felt throughout a circular area of 1,808.64 square miles. What was the radius of the circular area?

A. 24 miles B. 12 miles C. 576 miles D. 20 miles

Answers

Answer:

A. 24 miles

Step-by-step explanation:

Using 3.14 for π, we have ...

... Area = πr^2

... √(Area/π) = r = √(1808.64/3.14) = √576 = 24 . . . . miles

Answer:

its 24 miles so the correct answer would be A

Step-by-step explanation:

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