The time required for the principal amount to double is 13 years 10 months and 10 days approx.
What is compound interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The term "compound" is crucial here.
CI Formula. C.I. = Principal (1 + Rate)^time − Principal.
Given, A sum of $5000 is invested at an interest rate of 5% per year.
hence, principle = 5000
Amount = 10000
rate = 5%
let's assume the time is x
Let's solve for time
A(t)= 10000 = 5000* e⁵ˣ/¹⁰⁰
2 = (e)^x/20
taking logs on both sides
ln 2 = x / 20
x = 20 ln2
time required = 20 ln2 = 20 * 0.69 = 13.86
Therefore, To make the amount double at the interest rate of 5% we need time approx 13 years 10 months, and 10 days.
Learn more about compound interest here:
https://brainly.com/question/29335425
#SPJ2
To make 112 dozen muffins, a recipe uses 312 cups of flour.
How many cups of flour are needed for every dozen muffins made?
Solve the system by elimination
2x+6y= -12
5x-5y= -10
A plane is traveling at a speed of 400 miles per hour.How far will the plane travel in 5 hours?
Answer:
Step-by-step explanation:
The perimeter of a church window is 80 inches. If the window is in the shape of a square.what is the length of each side of the window?
The length of each side of the church window is 20 inches.
Explanation:To find the length of each side, we need to determine the perimeter of the square. The perimeter is the sum of all four sides of the square. In this case, it is given that the perimeter is 80 inches. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of each side. So, each side of the church window will be 80 inches divided by 4, which is 20 inches.
Learn more about Square perimeter here:https://brainly.com/question/29192128
#SPJ12
If 40% is equal to the fraction x/30, what is the value of X?
The value of x is 12 and this can be determined by using the arithmetic operations and the given data.
Given :
40% is equal to the fraction x/30.
The following steps can be used in order to determine the value of 'x':
Step 1 - The arithmetic operations can be used in order to determine the value of 'x'.
Step 2 - According to the given data, the 40% is equal to the fraction x/30.
Step 3 - So, the value of X is calculated as:
[tex]\dfrac{40}{100}=\dfrac{x}{30}[/tex]
Step 4 - Simplify the above expression.
x = 12
For more information, refer to the link given below:
https://brainly.com/question/25834626
What is the unit rate for 4543.08 km in 52.4 h? Enter your answer, as a decimal, in the box. km/h
Final answer:
The unit rate, or average speed, for traveling 4543.08 km in 52.4 hours is calculated by dividing the distance by the time, resulting in an average speed of 86.70 km/h.
Explanation:
The question asks for the unit rate of 4543.08 km traveled in 52.4 hours, which is essentially asking for the average speed in kilometers per hour (km/h). To find this, you would divide the total distance traveled by the total time taken.
Mathematically, this is expressed as:
Distance (km) / Time (h) = Speed (km/h)Substituting the given values:
4543.08 km / 52.4 h = 86.70 km/hTherefore, the unit rate or average speed is 86.70 km/h. It's important to note that when calculating such problems, it's essential to maintain consistency in the units (in this case, km for distance and hours for time) to ensure the accuracy of your result.
What radius of a circle is required to inscribe an equilateral triangle with an area of 35.074 in2 and an altitude of 7.794 in? (round to nearest tenth)
Answer:
[tex]r[/tex]≈[tex]5.2 in[/tex]
Step-by-step explanation:
It is given that a circle is required to inscribe an equilateral triangle with an area of [tex]35.074 in^2[/tex] and an altitude of [tex]7.794 in[/tex],
Also, we know that the centroid divides the altitude into 2:1 form, thus
[tex]r=\frac{2}{3}(h)[/tex]
Substituting the value of an altitude, we have
[tex]r=\frac{2}{3}(7.794)[/tex]
[tex]r=5.196 in[/tex]
[tex]r[/tex]≈[tex]5.2 in[/tex]
Therefore, the radius of the circle is [tex]5.2 inches[/tex].
help asap need answer
Ryan earned $376 by working for 4 days. If he earned the same amount each day, how much could he earn working 5 days?
A theatre contains 441 seats and the ticket prices for a recent play were $60 for adults and $16 for children. If the total proceeds were $14,800 for a sold-out matinee, how many of each type of ticket were sold?
Anyone know how to do B? Help please do!
An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour.
Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt.
Answer:
its A
Step-by-step explanation:
Maryam had to sail 4 2⁄3 miles to reach her destination. At the end of the day, she had sailed 3 1⁄3 miles. How far was she from her destination?
subtract the distance she traveled from the total distance she has to go
4 2/3 - 3 1/3 = 1 1/3 miles to go
If f(x) = 9 cos2(x), compute its differential df. df = (−18cos(x)sin(x))dx correct: your answer is correct. approximate the change in f when x changes from x = π 6 to x = π 6 + 0.1. (round your answer to three decimal places.) δf = .738 incorrect: your answer is incorrect. approximate the relative change in f as x undergoes this change. (round your answer to three decimal places.)
Given: f(x) = 9 cos (2x)
The differential equation is df = - 18 sin(2x) dx
When x contrasts from π/6 to π/6 + 01, then dx = 0.1.
The variation in f is δf = - 18 sin(π/3) *(0.1) = -1.5588 ≈ -1.559
The computation in the change in f directly:
f(π/6) = 9 cos(π/3) = 4.5
f(π/6 + 0.1) = 9 cos(π/3 + 0.2) = 2.6818
δf = 2.6818- 4.5 = -1.6382 ≈ -1.638
Direct computation of δf is near to the real value but in error.
The two outcomes will be closer as dx gets smaller.
Answer would be:
δf = -1.559 (correct answer)
δf = -1.638 (approximate answer)
Answer:
a
Step-by-step explanation:
what is equivalent to the square root of -27
HELPPPPPPPPP STATTTSSSSS
What is y-10=9(x+8) written in standard form?
Answer:
-9x+y=82
Step-by-step explanation:
hope this helped!
The equation y-10=9(x+8) can be transformed into standard form by distributing, simplifying, and rearranging terms to get 9x - y = -82.
Explanation:The given equation is y-10=9(x+8), and we're asked to change this slope-intercept form into the standard form. First, we'll start by distributing the 9 to both x and 8 which will result in y-10 = 9x + 72. Then, we'll bring terms involving x and y to one side of the equation, leading to -9x + y = 82. This is almost in standard form, but typically we want the leading coefficient (the coefficient of x) to be positive, so we'll multiply the equation by -1. This gives us 9x - y = -82, which is the equation in standard form.
Learn more about Algebra here:https://brainly.com/question/32436021
Jimmy ran 3 miles west and then 4 miles north. How far is he from his starting point if he went in a straight line? (It makes a right triangle.)
the straight line would be 3^2 + 4^2 = X^2
9+16 = x^2
25 = x^2
x = sqrt(25)
x = 5
it is 5 miles
Which step could be used to solve x + 3.6 = -1.7 for x in one step? Check all that apply.
[ ] add 3.6 to both sides
[ ] add -3.6 to both sides
[ ] add 1.7 to both sides
[ ] add -1.7 to both sides
[ ] subtract 3.6 from both sides
[ ] subtract 1.7 from both sides
Answer: Option (2) and (5) are the correct options.
Step-by-step explanation:
Since, the given expression, x+3.6= -1.7
If we add -3.6 in both sides then we get x+3.6+(-3.6)=1.7-3.6⇒x= -1.9
while,
If we subtract 3.6 from both sides then we get x+3.6-3.6=1.7-3.6⇒x= -1.9
Thus, In the above by adding -3.6 and by subtracting 3.6 we get the value of x in one step.(because after this only x remains in LHS of the given expression)
Therefore, Option (2) and (5) are correct.
Note: Except these two options we can not get x in one step. (we can not get single x in LHS of the given expression by the other options.)
Answer:
b e
Step-by-step explanation:
A chicken soup recipe calls for
9
cups of chicken stock. How much is this in quarts?
Ronald is saving money to buy a bicycle. He has $37.80 in his savings account and saves 20% of his paper route
If $16,400 is deposited into a CD paying 5.1% annually, how much will be in the account after 20 years? Enter your answer rounded to the nearest cent.
16,400 x (1 + 0.051)^20 =
16400 x (1.051)^20 =
16400 x 2.70429659 =
$44,350.46
A recipe uses 6 cups of cheese to serve 30 people. How much cheese is needed for 50 people
Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles. Suppose a star is 13.6 light-years from Earth. In scientific notation, how many miles away is it?
Answer:
The distance traveled in 13.6 light year is [tex]7.9968\times 10^{13}\text{ miles}[/tex]
Step-by-step explanation:
Given : Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles. Suppose a star is 13.6 light-years from Earth.
To find : In scientific notation, how many miles away is it?
Solution :
According to question,
The distance can travel in 1 light year is
[tex]1 \text{ light year} = 5,880,000,000,000 \text{ miles}[/tex]
We have to find the distance traveled in 13.6 light-years.
[tex]13.6 \text{ light year} =13.6\times 5,880,000,000,000 \text{ miles}[/tex]
[tex]13.6 \text{ light year} =79,968,000,000,000 \text{ miles}[/tex]
In scientific notation,
[tex]13.6 \text{ light year} =7.9968\times 10^{13}\text{ miles}[/tex]
Therefore, The distance traveled in 13.6 light year is [tex]7.9968\times 10^{13}\text{ miles}[/tex]
if f(x)=-x+8 and g(x)= x^4 what is (g°f)(2)?
it takes Joaquin 1/3 hours to walk to the library 3/4 miles away what is his walking pace in miles per hour
find x when y= 14, if y=7 when x=8
Answer: The required value of x is 16.
Step-by-step explanation: Given that the value of y is 7 when the value of x is 8.
We are to find the value of x when y is 14.
The ratio of y to x is given by
[tex]y:x=7:8.[/tex]
Therefore, when y = 14, we must have
[tex]14:x=7:8\\\\\\\Rightarrow \dfrac{14}{x}=\dfrac{7}{8}\\\\\\\Rightarrow x=\dfrac{14\times8}{7}\\\\\Rightarrow x=16.[/tex]
Thus, the required value of x is 16.
What is the probability that two people have a birthday on the same day of the same month?
How many lines can be drawn through points j and k?
Graph the system of equations below on a piece of paper. What is the solution?
y = x – 1
y = 3x + 1

A. (2, 1)

B. (1, –2)

C. (–1, –1)

D. (–1, –2)
Answer:
Option D is correct
Solution = (-1, -2)
Step-by-step explanation:
Given the equation:
y = x – 1 ....[1]
y = 3x + 1 ....[2]
Equate equation [1] and [2] to solve for x.
[tex]x-1=3x+1[/tex]
Subtract x from both sides we have;
[tex]-1=2x+1[/tex]
Subtract 1 from both sides we have;
[tex]-2=2x[/tex]
Divide both sides by 2 we have;
x = -1
Substitute the value of x = -1 in [1] we have;
y=-1-1 = -2
Graphically:
Graph the system of equations as shown below.
The intersection point of these lines is the solution for the given system of equation
⇒ (-1, -2)
Therefore, the solution for the given system of equation is, (-1, -2)