10. If you invest $2000 at 6% compounded monthly, how long will it take the account to double in
value?
Answers
If I invest $2000 at 6% interest compounded monthly, it will take 11.58 years by the account to double in value.
What is compound interest?
The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It happens when interest is reinvested, added to the lent capital rather than paid out, or required to be paid by the borrower, resulting in interest being created the next period on the principal amount plus any accrued interest. Compound interest is a prominent concept in finance and economics.
The initial investment of $2000 at 6% compounded monthly.
Since, the interest rate of 6% is compounding monthly, then the effective annual interest rate will be
= (1+)−1i = (1+rm)m−1
Here, r = interest rate in decimals
= (1+0.0612)12−1i = (1+0.0612)12−1
= 0.061678i = 0.061678
= ×100 = 6.1678%
Now, we are using Rule 72 to calculate the doubling time
Time to double the initial amount = 72 /effective annual interest rate
Time to double the initial amount = 11.58 years
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Related Questions
Determine the real number x and y if (x-yj)(3+5j) is the conjugate of -6-24j
Answers
The values of the variables x and y such that the conjugate of - 6 - j 24 is found are 3 and 3, respectively.
How to find the value of two variables associated with the conjugate of a complex number
Let α + i β be a complex number, whose conjugate is the complex number α - i β. In this problem we find the values of the variables x and y such that:
(x + i y) · (3 + i 5) = - 6 + i 24
3 · x + i 3 · y + i 5 · x + i² 5 · y = - 6 + i 24
(3 · x - 5 · y) + i (5 · x + 3 · y) = - 6 + i 24
Then, we need to solve the following system of linear equations:
3 · x - 5 · y = - 6
5 · x + 3 · y = 24
Now we proceed to solve the system algebraically. Clear x in the first equation:
x = (- 6 + 5 · y) / 3
x = - 2 + (5 / 3) · y
Substitute x on the second equation and clear y:
5 · [- 2 + (5 / 3) · y] + 3 · y = 24
- 10 + (25 / 3) · y + 3 · y = 24
34 / 3 · y = 34
(1 / 3) · y = 1
y = 3
Finally, we substitute on y in the first equation:
x = - 2 + (5 / 3) · 3
x = - 2 + 5
x = 3
The values of the variables x and y are 3 and 3, respectively.
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what is 2 3/24 simplified
Answers
2 3/24
Multiply the denominator by the whole number and add the numerator to obtain the new numerator. the denominator stays the same.
(2x24)+3 /24 = 48+3 /24 = 51/24
simplify by 3
17/8
Please help me solve. I also need help on what ratios to put in the two boxes before the answer. Do I just choose any of them?
Answers
Explanation
By metric conversion
[tex]\begin{gathered} 1\text{ mile =}1.61km \\ 1\text{ hour = 60 mins} \end{gathered}[/tex]Therefore;
[tex]\frac{57mi}{1hr}\times\frac{1.61}{1}\times\frac{1}{60}=1.5295\frac{km}{\min }[/tex]Answer:
[tex]\begin{gathered} \text{Box 1= }\frac{\text{1.61}}{1} \\ \text{Box 2=}\frac{1}{60} \\ \text{Box 3=}1.53 \end{gathered}[/tex]Factor 9x^4-18x^3+36x^2
Answers
Given the expression:
[tex]9x^4-18x^3+36x^2[/tex]You can factor it by following these steps:
1. Find the Greatest Common Factors (GCF) of the terms:
- The Greatest Common Factor (GCF) of the coefficients can be found by decomposing each coefficient into their Prime Factors:
[tex]\begin{gathered} 9=3\cdot3 \\ 18=2\cdot3\cdot3 \\ 36=2\cdot2\cdot3\cdot3 \end{gathered}[/tex]Notice that all the coefficients have:
[tex]3\cdot3=9[/tex]Therefore, that is the Greatest Common Factor (GCF) of the coefficients.
- The Greatest Common Factor (GCF) of the variables is the variable with the lowest exponent:
[tex]x^2[/tex]Hence:
[tex]GCF=9x^2[/tex]2. Now you can factor it out:
[tex]=9x^2(x^2-2x+4)[/tex]Hence, the answer is:
[tex]9x^2(x^2-2x+4)[/tex]Renta scored 409 points in a video game. This was 223 more points than Sadia score (s). Which equation does not represent this situation? And why?
A) 223 = 409 - s
B) s = 409 - 223
C) s = 409 + 223
D) 223 + s = 409
Answers
Answer:C
Step-by-step explanation: S is equal to a number less than 409 and if you add 223 you go over 409
A company estimates that that sales will grow continuously at a rate given by the functions S’(t)=15e^t where S’(t) Is the rate at which cells are increasing, in dollars per day, on day t. find the sales from the 2nd day through the 6th day (this is the integral from one to six)
Answers
Given the function:
[tex]S^{\prime}(t)=15e^t[/tex]Where S’(t) Is the rate at which sales are increasing (in dollars per day). To find the sales from the second day through the 6th day, we need to integrate this function from t = 1 to t = 6:
[tex]\int_1^6S^{\prime}(t)dt=\int_1^615e^tdt=15\int_1^6e^tdt[/tex]We know that:
[tex]\int e^tdt=e^t+C[/tex]Then:
[tex]15\int_1^6e^tdt=15(e^6-e^1)\approx\text{\$}6010.66[/tex]The sales from the 2nd day through the 6th day are $6,010.66
b. Function h will begin to exceed f and g around x = [. (Round up to the nearest whole number.)
Answers
If we evaluate x = 10 on all the functions, we have:
[tex]\begin{gathered} h(10)=1.31^{10}=14.88 \\ f(10)=1.25(10)=12.5 \\ g(10)=0.1562(10)^2=15.625 \end{gathered}[/tex]and then, evaluating x = 11, we get:
[tex]\begin{gathered} h(11)=1.13^{11}=19.49 \\ f(11)=1.25(11)=13.75 \\ g(11)=0.15625(11)^2=18.9 \end{gathered}[/tex]notice that on x = 10, h(x) does not exceed g(x), but on x = 11, h(x) exceeds the other functions. Therefore, h will begin exceed f and g around 11
how many ones equal 4 tens
Answers
We have to find the number of ones in 4 tens.
As we know that, there are 10 ones in a 10.
Therefore, in 4 tens, the total number of ones would be 1 x 4 x 10 = 40
7. Find the slope of a line which passes through the origin and point (2,4).A 0.5B -0.5C 2D 4
Answers
Answer:
C
Step-by-step explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
in our case here we are going e.g. from the origin (0, 0) to (2, 4).
so, x changes by +2 (from 0 to 2).
y changes by +4 (from 0 to 4).
therefore, the slope is
+4/+2 = 2
FYI - the direction is not important. it works the same way in the other direction. but what is important : once you pick a direction for one coordinate, you have to use the same direction for the second one. you cannot go e.g. for x in one direction and for y in the other.
The pyramid has a square base with side
length 2 cm and height 3 cm. What is the
volume of the chocolate to the nearest
tenth?
A 12 cm
B 6 cm3
C 4 cm
D 2 cm
E 1.3 cm3
Answers
The radius of cylinder is r = 3 in.
The height of cylinder is h = 10 in.
The formula for the volume of cylinder is,
[tex]V=\pi\cdot(r)^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cylinder.
[tex]\begin{gathered} V=\pi\cdot(3)^2\cdot10 \\ =282.743 \\ \approx282.7 \end{gathered}[/tex]So volume of cylinder is 282.7 in^3.
Option H is correct.
Given rectangle BCDE below. If BF = 22, find EF.
Answers
Okay, here we have this:
Considering the provided graph, we are going to find the requested measure, so we obtain the following:
Let us remember that a rectangle besides having the properties of a parallelogram also stands out because it has congruent diagonals. So considering this we have:
BD=EC
EF=BF
EF=22
Finally we obtain that EF is equal to 22 units.
Hello! I think the answer is 398. Would you mind guiding me?
Answers
Given -
Total Personal Videos Players = 400
Video Players with no defects = 398
Number of Video Players sent = 2000
To Find -
The number of Video Players with no defects =?
Step-by-Step Explanation -
Total Personal Videos Players = 400
Video Players with no defects = 398
So,
Two video players in every 400 are defected
So,
2000 = 5 × 400
So,
Total number of Video Players with defects = 5 × 2 = 10
Hence,
The number of Video Players with no defects = 2000 - 10 = 1990
Final Answer -
The number of Video Players with no defects = 1990
Hi hope you are well!!I have a question: When Debbie baby-sits she charges $5 to go the house plus $8 for every hour she is there. The expression 5+8h gives the amount in dollars she charges. How much will she charge to baby-sit for 5 hours? Please help me with this questionHave a nice day,Thanks
Answers
5 + 8h
h= number of hours
Replace h by 5 and solve
5 + 8(5)
5 +40
45
She will charge $45
Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that thisbatting average will stay the same this year, answer the following questions,What is the probabilitythat his first hit willoccur within his first 5at-bats? Answer choice. 0.654. 0.765. 0.821. 0.876
Answers
The probability of a successful batting is 0.341; we need to find the probability of at least 1 hit within the first 5 at-bats; thus,
[tex]P(Hit)=1-P(NoHit)[/tex]Therefore, we need to calculate the probability of not hitting the ball within the first 5 at-bats.
The binomial distribution states that
[tex]\begin{gathered} P(X=k)=(nBinomialk)p^k(1-p)^{n-k} \\ n\rightarrow\text{ total number of trials} \\ k\rightarrow\text{ number of successful trials} \\ p\rightarrow\text{ probability of a successful trial} \end{gathered}[/tex]Thus, in our case,
[tex]P(k=0)=(5Binomial0)(0.341)^0(0.659)^5=1*1*0.124287...[/tex]Then,
[tex]P(Hit)=1-0.124287...\approx0.876[/tex]Therefore, the answer is 0.876Leila triples her recipe that calls for 2/5 of a cup of flour. Leila has 1 cup of flour. Does she have enough to triple her recipe?
no
yes
Answers
Answer:
No
Step-by-step explanation:
3 × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex] cups required to triple her recipe
she only has 1 cup
so does not have enough to triple her recipe
Answer:
No
Step-by-step explanation:
If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.
Use the Quotient Rule to find the derivative of the function.f(x) = x/(x − 6)f'(x)=
Answers
ANSWER
[tex]\frac{-6}{(x-6)^2}[/tex]EXPLANATION
We want to find the derivative of the function:
[tex]f(x)=\frac{x}{x-6}[/tex]The quotient rule states that:
[tex]f^{\prime}(x)=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}[/tex]where u = the numerator of the function
v = the denominator of the function
From the function, we have that:
[tex]\begin{gathered} u=x \\ v=x-6 \end{gathered}[/tex]Now, we have to differentiate both u and v:
[tex]\begin{gathered} \frac{du}{dx}=1 \\ \frac{dv}{dx}=1 \end{gathered}[/tex]Therefore, the derivative of the function is:
[tex]\begin{gathered} f^{\prime}(x)=\frac{(x-6)(1)-(x)(1)}{(x-6)^2} \\ f^{\prime}(x)=\frac{x-6-x}{(x-6)^2} \\ f^{\prime}(x)=\frac{-6}{(x-6)^2} \end{gathered}[/tex]write each percent as a decimal 1%
Answers
You have the following percentage:
24.1%
In order to determine the associated decimal to this fraction you proceed as follow:
What is 2 2/3 - 3/5? 7/154 4/152 1/15 1 2/5
Answers
Hi, can you help me to solve this exercise please, it’s about Function Evaluation & Applications!
Answers
Given
[tex]f(x)=\lvert x\rvert+4[/tex]Part A
[tex]\begin{gathered} we\text{ want to find f(4)} \\ we\text{ only n}eed\text{ to substitute the value of 4 to x in the given function} \\ f(4)=\lvert4\rvert+4 \\ f(4)=4+4_{} \\ f(4)=8 \end{gathered}[/tex]Part B
[tex]\begin{gathered} we\text{ want to evaluate f(-4)} \\ \text{note that the absolute value returns postive values} \\ \text{thus, }\lvert-4\rvert=4 \\ f(-4)=\lvert-4\rvert+4 \\ f(-4)=4+4 \\ f(-4)=8 \end{gathered}[/tex]Part C
[tex]\begin{gathered} To\text{ find f(t), we only n}eed\text{ to replace t with x} \\ f(t)=\lvert t\rvert+4 \end{gathered}[/tex]Drag each tile to the correct box. Not all tiles will be used. Arrange the steps to solve the equation x + 3 − 2 x − 1 = - 2 . Simplify to obtain the final radical term on one side of the equation. Raise both sides of the equation to the power of 2. Apply the Zero Product Rule. Use the quadratic formula to find the values of x. Simplify to get a quadratic equation. Raise both sides of the equation to the power of 2 again.
Answers
The value of x = 16 + 4[tex]\sqrt{15}[/tex]
Given,
To solve the equations :
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Solve by the given steps :
Now, According to the question:
Step 1: Simplify to obtain the radical form on one side of the equation:
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Step 2: Raise both sides of the equation to the power of 2
[tex](\sqrt{x+3} - \sqrt{x -1})^2 = (-2)^2[/tex]
x + 3 + 2x - 1 -2 [tex]\sqrt{(x+3)(2x -1)}[/tex] = 4
3x - 2 = 2 [tex]\sqrt{(x+3)(2x -1)}[/tex]
[tex](3x - 2)^2 = [2\sqrt{(x+3)(2x -1)}]^2[/tex]
9[tex]x^{2}[/tex] - 12x + 4 = 4 (2[tex]x^{2}[/tex] + 5x -3)
Step 3: Apply the zero product rule, Simplify to get a quadratic equation :
[tex]x^{2}[/tex] - 32x +16 = 0
Step 4: Use the quadratic formula to find the values of x :
[tex]x^{2}[/tex] - 32x + 16 =0
x = 16 + 4[tex]\sqrt{15}[/tex] and x = 16 - 4[tex]\sqrt{15}[/tex]
x = 16 - 4[tex]\sqrt{15}[/tex] (It is rejected)
So, the value of x = 16 + 4[tex]\sqrt{15}[/tex]
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Answer: Raise both sides of the equation to the power of 2
simplify to obtain the final radical term on one side of the equation
raise both sides of the equation to the power of 2 again
simplify to get a quadratic equation
use the quadratic formula to find the xvalues
Step-by-step explanation:
Is P(A and B) ≠ 0? Explain.
A.) No. P(A and B) = 0.
B.) Yes. Even if P(A) = 0 or P(B) = 0, P(A and B) will always be non-zero.
C.) No. Because both P(A) and P(B) are not equal to 0, P(A and B) = 0.
D.) Yes. Because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0. (b)
Answers
The right option is D as P(A and B) ≠ 0 only for the independent probability events for A and B.
What is an independent event in probability?Two events say A and B are said to be independent if the probability of the intersection of A and B is equal to the product of their respective probability, But same events are said to be mutually exclusive if the probability of the intersection of A and B is equal to zero(0).
In the given question, P(A and B) ≠ 0 can only be true if A and B are independent event and P(A) and P(B) are not equal to zero such that
P(A and B)=P(A)× P(B)≠ 0.
Hence, we can deduce from the axiom of independent events of probability that because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0.
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Which can be the first step in finding the equation of the line that passes through the points (5,-4) and (-1,8) in slope-intercept form?8-(-4) 12-12--2Calculate -1-5Calculate 8-(-4) 12-1-5 -6Find that the point at which the line intersects with the line y = 0 is (3,0).Find that the point at which the line intersects with the line X=Y is (2, 2).
Answers
The first step to finding the equation of the line in the slope-intercept form is to find the slope.
So, to find the slope we can use the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are points of the line.
Therefore, if we replace (x1, y1) by (5, -4) and (x2, y2) by (-1, 8), we get that the first step is to calculated:
y2 - y1 = 8 - (-4) = 8 + 4 = 12
x2 - x1 = -1 - 5 = -6
Answer: Calculate 8 - ( - 4 ) = 12
Calculate - 1 - 5 = -6
ind the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
Answers
ANSWER
x = 10.2
EXPLANATION
In this problem, we are given a right triangle: one of its non-right interior angles measures 22°. We know that the length of the hypotenuse is 11 units long and we have to find the length of the side adjacent to the given angle, x.
With the given information, we can use the cosine of the angle to find the missing value,
[tex]\cos\theta=\frac{adjacent\text{ }leg}{hypotenuse}[/tex]In this problem,
[tex]\cos22\degree=\frac{x}{11}[/tex]Solving for x,
[tex]x=11\cdot\cos22\degree\approx10.2[/tex]Hence, the value of x is 10.2, rounded to the nearest tenth.
Write an equation of a circle with diameter AB.A(1,1), B(11,11)Choose the correct answer below.A. (X-6)2 + (y-6)2 = 11C. (x-6)2 – (y+6)2 = 50E. (X+6)2 + (y-6)2 = 50G. (X+6)2 – (y + 6)2 = 50
Answers
The question asks us to find the equation of a circle with diameter AB with coordinates:
A = (1, 1), B = (11, 11)
In order to solve this, we need to know the general form of the equation of a circle.
The general form of the equation of a circle is given by:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where,} \\ (a,b)=\text{ coordinates of the center of the circle} \\ r=\text{radius of the circle} \end{gathered}[/tex]We have been given the coordinates of the diameter. This means that finding the midpoint of the diameter
will give us the center coordinates of the circle, which is (a, b).
The formula for finding the midpoint of a line is given below:
[tex]\begin{gathered} (x,y)=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ \text{where,} \\ x_2,y_2=\text{ second coordinate} \\ x_1,y_1=\text{first coordinate} \end{gathered}[/tex]For better understanding, a sketch is made below:
Therefore, let us find the coordinates of the center of the circle using the midpoint formula given above:
[tex]\begin{gathered} a,b=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ x_2=11,y_2=11 \\ x_1=1,y_1=1 \\ \\ \therefore(a,b)=\frac{11+1}{2},\frac{11+1}{2} \\ \\ (a,b)=6,6 \\ Thus, \\ a=6,b=6 \end{gathered}[/tex]Now that we have the coordinates of the center, we now need to find the value of the radius of the circle.
This is done by finding the length from the center of the circle to any side of the diameter.
Let us use from point (6,6) which is the center to the point (11, 11) which is one side of the diameter.
The formula for finding the distance between two points is given by:
[tex]\begin{gathered} |\text{distance}|^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ \text{where,} \\ x_2,y_2=\text{second point} \\ x_1,y_1=\text{first point} \end{gathered}[/tex]hence, we can now find the square of the radius as:
[tex]\begin{gathered} r^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ x_2,y_2=11,11_{} \\ x_1,y_1=6,6 \\ \\ \therefore r^2=(11-6)^2+(11-6)^2 \\ r^2=5^2+5^2 \\ r^2=25+25 \\ \therefore r^2=50 \end{gathered}[/tex]Now that we have the radius, we can now compute the equation of the circle as:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ a=6,b=6,r^2=50 \\ \\ \therefore(x-6)^2+(y-6)^2=50\text{ (Option B)} \end{gathered}[/tex]A graph of the circle is given below:
Solve the following/3x=7-3/x
Answers
Value of x is 8.46 for equation 3x=7-3/x
What is Equation?Two or more expressions with an Equal sign is called as Equation
The given equation is 3x=7-3/x
3x+3/x=7
3x²+3=7x
3x²-7x+3=0
Use quadratic equation formula
a=3, b=-7, c=3
x=-b±√b²-4ac/2a
x=7±√49-4(3)(3)/2(3)
x=7±√49-36/6
x=7±√13/6
x=7±√2.16
x=7+1.46
x=8.46
Hence value of x is 8.46 for equation 3x=7-3/x
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What is the low end value, high end value, and does it have an outlier
Answers
Solution;
Given the results:
From the above data:
A) The low-end value is
[tex]0[/tex]B) The high end value is
[tex]95[/tex]C) Does this data set have outlier?
[tex]Yes[/tex]D) Outlier:
[tex]95[/tex]In terms of trigonometry ratios for triangle BCE what is the length of line CE. Insert text on the triangle to show the length of line CE.When you are done using the formula for the triangle area Area equals 1/2 times base times height write an expression for the area of triangle ABC Base your answer on the work you did above
Answers
CE can be written as:
[tex]\frac{BE}{CE}=\frac{CE}{AE}[/tex]Solve for CE:
[tex]\begin{gathered} CE^2=BE\cdot AE \\ CE=\sqrt[]{BE\cdot AE} \end{gathered}[/tex]The area is:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ _{\text{ }}where\colon \\ _{\text{ }}b=AB \\ h=CE=\sqrt[]{BE\cdot AE} \\ so\colon \\ A=\frac{AB\cdot\sqrt[]{BE\cdot AE}}{2} \end{gathered}[/tex]1+——>1/12 write. Fraction to make each number sentence true, answer I got is 1/1
Answers
c) Set x to be the number we need to find; therefore, the inequality to be solved is
[tex]\begin{gathered} 1+x>1\frac{1}{2}=1+\frac{1}{2}=\frac{3}{2} \\ \Rightarrow1+x>\frac{3}{2} \\ \Rightarrow-1+1+x>-1+\frac{3}{2} \\ \Rightarrow x>\frac{1}{2} \end{gathered}[/tex]Therefore, any number greater than 1/2 (greater, not equal to) satisfies the inequality; particularly 1/1=1>1/2. Thus, 1/1 is a possible answer
^3square root of 1000
Answers
Given the following question:
[tex]\sqrt[3]{1000}[/tex][tex]\begin{gathered} \sqrt[3]{1000} \\ \sqrt[3]{1000}=\sqrt[3]{10^3} \\ 10^3=1000 \\ \sqrt[3]{10^3} \\ \sqrt[n]{a^n}=a \\ \sqrt[3]{10^3}=10 \\ =10 \end{gathered}[/tex]Your answer is 10.
What is the average rate of change from g(1) to g(3)?Type the numerical value for your answer as a whole number, decimal or fractionMake sure answers are completely simplified
Answers
The average rate of change from g(1) to g(3)
[tex]\frac{g(x)_3-g(x)_1}{X_3-X_1}_{}[/tex]where
[tex]g(x)_3=-20,g(x)_1=-8,x_3=3,x_1=\text{ 1}[/tex][tex]\begin{gathered} =\frac{-20\text{ --8}}{3-1}\text{ = }\frac{-20\text{ +8}}{2} \\ =\frac{-12}{2} \\ -6 \end{gathered}[/tex]Hence the average rate of change is -6
