Find the principal amount invested if the amount in a monthly compounded account with a 5.1% interest rate is $9,996.32 after 54 months.

Answers

Answer 1

again, there are 12 months in a year, so 54 months is 54/12 years

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$9996\\ P=\textit{original amount deposited}\\ r=rate\to 5.1\%\to \frac{5.1}{100}\to &0.051\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to \frac{54}{12}\to &\frac{9}{2} \end{cases}[/tex]

[tex]\bf 9996=P\left(1+\frac{0.051}{12}\right)^{12\cdot \frac{9}{2}}\implies \cfrac{9996}{\left(1+\frac{0.051}{12}\right)^{12\cdot \frac{9}{2}}}=P[/tex]

Related Questions

If m = 4 and n = 4, then m = n What property is this?

Answers

Definition of symmetric property

prove that triangle with side lengths of x^2-1, 2x, x^2+1 is a right triangle.

pls include full proof tysm!!

Answers

Right triangles must follow the pythagorean theorem, so a^2+b^2=c^2.

Let's find a^2 and b^2 by squaring the first 2 side lengths.

(x^2-1)^2= x^4-2x^2+1
(2x)^2= 4x^2

Then add the two to find c^2
x^4+ 2x^2 +1= c^2

Root both sides
x^2+1=c

Since the side lengths can be plugged into the pythagorean theorem, the side lengths must represent a right triangle.
Hope this helps!

Final answer:

A triangle with sides of lengths x^2-1, 2x, and x^2+1 is a right triangle as confirmed by the Pythagorean theorem. By squaring these lengths and simplifying the resulting equation, it's shown that the squares of the lengths of the two shorter sides sum up to the square of the length of the longest side.

Explanation:

To prove that a triangle with sides of lengths x^2-1, 2x, and x^2+1 is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, if x^2-1 and 2x are two sides of the triangle and x^2+1 is the hypotenuse, then the equation becomes:

(x^2-1)^2 + (2x)^2 = (x^2+1)^2

If this equation is true, then we have a right triangle. Let's simplify the equation:

x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1

After simplifying, we get that 2x^2 equals 2x^2, which confirms that we indeed have a right triangle.

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The elevator of a high-rise office building provides access to all floors. if each floor is 5 meters high and the elevator travels at a rate of 7.5 meters per second, approximately how long will it take to travel from the first floor to the sixty-eighth floor?

Answers

Final answer:

It will take approximately 44.67 seconds for the elevator to travel from the first floor to the sixty-eighth floor, assuming it travels at a constant speed of 7.5 meters per second throughout the journey.

Explanation:

To determine how long it takes for the elevator to travel from the first floor to the sixty-eighth floor, we must first calculate the total distance traveled and then use the speed of the elevator to find the time.

Since each floor is 5 meters high, the total distance for 67 floors (from the first to the sixty-eighth) is 67 floors × 5 meters/floor = 335 meters.

Given that the elevator travels at a rate of 7.5 meters per second, the time taken to travel this distance can be calculated using the formula:

time = distance/speed

Substituting the values, we get:

time = 335 meters / 7.5 meters/second

time ≈ 44.67 seconds

Therefore, it will take approximately 44.67 seconds for the elevator to travel from the first floor to the sixty-eighth floor, assuming it travels at a constant speed throughout the journey.

Flip a fair coin 25 times. what is the size of the sample space? that is, how many different sequences of heads and tails are possible? what is the probability of each one of those possible outcomes?

Answers

There are 50% chance's that it would land on heads or tails. there could be many different outcomes like (H) for heads and (T) for tails many times like this H, T, H, T, H, T.

you have exactly $120 to spend on new school clothes, including 6% sales tax. What is the most that the clothes themselves can cost?

Answers

120 multiplied by .06 is 7.2
120 subtracted by 7.2 is 112.8

The most the clothes themselves can cost is $112.80.

Hope this helps!

Sove each problem and write your answers in scientific notation. 1. (6.0 x 10^5) x (3.0 x 10^4) =

Answers

Evaluate using scientific notation.
1.848*10^6

If you wanna convert it to SN then, Move the decimal so there is one non-ZERO DIGIT to the left of the DECIMAL POINT. The number of decimal places you move will be the EXPONENT on the 10. If the decimal is being moved to the right, the EXPONENT will be negative. If the decimal is being moved to the left, the EXPONENT wil be positive. Again, ANSWER IS 1.848*10^6.

Hope this helped! :D

What is the length of AB?

Answers

Thanks for your question!

Because the angles are the same, the sides are the same.
So:

6x = 3x + 9
3x = 9
x = 3

But this problem isn't over yet. We need to find AB not x.

6(3) = 18

Hope this helps!

As you can see from the diagram, this is an isosceles triangle (triangle where 2 sides are equal and angles opposite are also equal).

Since there are two 65 degree angles, the sides opposite them are also equal. So we can write:

[tex]6x=3x+9[/tex]

Solving for x:

[tex]6x=3x+9\\6x-3x=9\\3x=9\\x=\frac{9}{3}\\x=3[/tex]

Now, we want to know side length of AB, which is 6x. Plugging in x = 3 into that, we get:

[tex]AB=6(3)\\AB=18[/tex]

Answer choice D is right.

ANSWER: D

Counting significant digits when measurements are multiplied or divided calculator

Answers

When using significant digits for multiplication and division, it is the smallest value of significant digits that is kept when finishing the calculation. E.g 2.21/1.0 you would keep two significant digits. In 1000x3.04343, you would keep 1 significant digit.

Suppose you flip a penny and a dime. Use the following table to display all possible outcomes. If each single outcome is equally likely, you can use the table to help calculate probabilities. What is the probability of getting one head and one tail, on either coin?

Answers

50% can I see the table but pretty sure it's 50% or 25%

Answer:

50%

Step-by-step explanation:

The next table display all possible outcomes.

penny | dime

head | head

head | tail

tail | head

tail | tail

If each single outcome is equally likely and there are 4 options , then all outcomes has a probability of 1/4 = 0.25 or 25%. The probability of getting one head and one tail is 50% because it's obtained by two outcomes.

How do you solve this?

Answers

Alright, so 9^(-1/2) would mean that we have 1/(9^(1/2)). Since 9^(1/2) is the square root of 9 (1/3 would be the cube root, etc.), we have 1/sqrt(9)=1/3. For 3/(1/3), we have (3/1)/(1/3), which is (3/1)*(3/1)=9. Squaring 9, we get the cube root of 81 which is around 4.3

Solve the system using elimination. 5x = –25 + 5y 10y = 42 + 2x

Answers

5x = –25 + 5y ---> 5x - 5y = -25 (1)
10y = 42 + 2x ---> 2x - 10y = -42 (2)
divide equation (2) by 2
so
x - 5y = -21

now you have
5x - 5y = -25
x - 5y = -21
-----------------subtract
4x = -4
x = -1

substitute x = -1 into 5x - 5y = -25
5x - 5y = -25
5(-1) - 5y = -25
-5 - 5y = -25
-5y = -20
y = 4

answer
(-1 , 4)

Final answer:

To solve the given system of equations using elimination, multiply the first equation by 2 to make the coefficients of 'x' the same in both equations. Then solve for 'x' and substitute the value into the first equation to solve for 'y'. The solution is x = -8 and y = -11.

Explanation:

To solve the given system of equations using elimination, first multiply the first equation by 2 to make the coefficients of 'x' the same in both equations.

10x = -50 + 10y

Next, subtract the equation obtained in step 1 from the second equation.

10y = 42 + 2x - (-50 + 10y)

Simplify the equation and solve for 'x'.

x = -8

Substitute the value of 'x' into the first equation to solve for 'y'.

5(-8) = -25 + 5y

y = -11

Therefore, the solution to the system of equations is x = -8 and y = -11.

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If point a is located at (-12,6) on a coordinate plane, and point b is located at (4,6) what is the distance between the two points

Answers

Final answer:

The distance between point A at (-12, 6) and point B at (4, 6) is 16 units according to the distance formula for a coordinate plane.

Explanation:

The question is asking for the distance between two points on a coordinate plane. To solve this, we use the distance formula for a coordinate plane which is D = sqrt((X2-X1)^2 + (Y2-Y1)^2), where X1, Y1 and X2, Y2 are the coordinates of the two points. In this case, both Y coordinates are the same (6), which makes the calculation simpler.

In this case, point A is at (-12, 6) and point B is at (4, 6). Subtracting the x-coordinates of A and B, (-12 - 4), we get -16, but we square this to get a positive result, which gives us 256. Since the y-coordinates are the same, the part of the equation dealing with them results in 0. So, the distance D is then the square root of 256, which is 16 units.

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23X67 Estimate then find the prouduct

Answers

To estimate, you would usually round to a significant figure
so, 20* 70=1400

The actual answer is 1521, so we know we are close

Prove that the eigenvalues of a matrix squared are greater than the matrix eigenvalues

Answers

yes it issssgvrttvnrtbt

If a trend line has a slope of -3, what is true about the data? Select all that apply.

Both sets of data are increasing.

One set of data is increasing, while one is decreasing.

The data is going up from left to right.

The data is going down from left to right.

Answers

Answer: Choice B and choice D

--------------------------------------------------------

A negative slope indicates that the line moves downward as you move from left to right. As x increases, y decreases (and vice versa). There's this opposite relationship going on.

The standard deviation is the average distance of each score in a distribution from the

Answers

The answer is the mean. In statistics, the standard deviation is a measure that is used to compute the amount of variation or distribution of a set of data values. In other words, standard deviation (also variance) are measures of the spread of the data around the mean. They summarize how near each observed data value is to the mean value. A low standard deviation indicates that the data points tend to be close to the mean (otherwise known as the expected value) of the set, while a high standard deviation indicates that the data points are vast over a wider range of values.

A tennis ball has a radius of 3.4 cm. What volume of this cylinder is empty?

Answers

check the picture below.

so, now, we simply get the volume of the cylinder, and then volume of the 3 balls, and subtract the volume of the balls from the cylinders, effectively making a hole in the volume of the cylinder, and what's leftover, is the empty area.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~ \begin{cases} r=3.4\\ h=20.4 \end{cases}\implies V=\pi \cdot 3.4^2\cdot 20.4\implies V=235.824\pi \\\\ -------------------------------\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad r=3.4\implies V=\cfrac{4\cdot \pi \cdot 3.4^3}{3}\implies V=\cfrac{157.216\pi }{3}[/tex]

[tex]\bf \textit{volume of the \underline{3 balls}}\quad 3\cdot \cfrac{157.216\pi }{3}\implies 157.216\pi \\\\ -------------------------------\\\\ \stackrel{\textit{volume of the cylinder}}{235.824\pi }-\stackrel{\textit{volume of the balls}}{157.216\pi }\implies 78.608\pi [/tex]

Answer:

Thanks to point

ok nerd

The store sold fewer blue jeans after the new pants became popular
Month Sales
1 7360
2 3680
3 1840
4 920
5 ?
Predict the number of sales in month 5

Answers

7360/3680 = 2

3680/1840 = 2

920/2= 460

month 5 sales will be 460

Write any Quetion of the line and soap intercept form that passes through (-2,4) and has a slope of 4

Answers

Plug the values into point slope and simplify

y-4= 4(x-(-2))
y-4= 4x+8
y= 4x+12

Final answer: y=4x+12

What is the first step in solving 4x -3 = 9

Answers

The first step is to add 3 to both sides.

Our goal is to isolate x and we first want to make sure that the term with x is the only one on its side of the equation. From there, you can determine the value of 1x by dividing all terms by 4

Simplify.
73+3(23−13)2

Answers

23-13=10
73+3(10)2
3(10)=30
73+30 x 2
30 x 2 = 60
60 +73 = 133

The value of the given expression is 133.

What is simplification?

Simplification involves taking complicated mathematical expressions and simplifying them. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression 73+3(23−13)2 is termed as E and will be solved as below:-

Use the concept of PEMDAS. Here, the PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

E = 73+3(23−13)2

E = 73 + 3 ( 10 ) 2

E = 73 + 6 ( 10 )

E = 73 + 60

E = 133

Therefore, the value of the given expression is 133.

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The product of 9 and a number t

Answers

Work : product of 9 and t
Answer: 9t

Simplify x + 15 - 4.

Answers

Answer:

[tex]x+11[/tex]

Step-by-step explanation:

In order to simplify this:

[tex]x+15-4[/tex]

You just need to substract like terms:

[tex]15-4=11[/tex]

Hence, the simplified is expression is:

[tex]x+11[/tex]

This represents a line which intercepts with the y-axis at 11 and with the x-axis at -11. I attached you the graph.

The simplified form of the expression is x + 11.

How do we simplify the expression?

To simplify the expression "x + 15 - 4", you just need to do the addition and subtraction operation:

x + 15 - 4 = x + 11

Simplifying an expression means to make it as easy to understand as possible. This can involve combining like terms, removing unnecessary parentheses, and using the distributive property.

In the expression x + 15 - 4, the like terms are x and 15. These terms can be combined to give x + 11. The parentheses around the 15 are unnecessary, so they can be removed. The simplified expression is x + 11.

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What is the units digit of 8 to the 97th? (no using a calculator)

Answers

If you do long division right you get 97/8= 12.125

8 divided by 97 equals 0.082

I stopped after getting the 2, so not sure what the next number would've been

( I didn't use a calculator)

PLZ HELP!!!! WILL GIVE BRAINLIEST!!! @YOLOSWAGGS51 I REALLY NEED YOUR HELP!!!!

What is the value of x?

Answers

[2(x+10)] =
well we have to add first
x=1 + 10= 11 since there is parenthesis around the "11" it is times 11 x 2 = 22

we will just have to times this and put a - in front of the 90 (3x - 30) = -90

Hope I could help out.

Insert parentheses so that the expression has a value of 67: 3×5+6×2+1

Answers

Below is the expression with parentheses that is equivalent to: 67. The work is shown.

[tex][3(5+6)2]+ 1 [3(11)2] + 1 66 + 1 67[/tex]

What is the product? (X-3)(2x^2-5x+1)

Answers

Sent you a pic of the product of the expressions.

Answer:

[tex]2x^3-11x^2+16x-3[/tex]

Step-by-step explanation:

We have been given an expression [tex](x-3)(2x^2-5x+1)[/tex]. We are asked to find the product of our given expression.

Upon using distributive property, we will get:

[tex]x(2x^2-5x+1)-3(2x^2-5x+1)[/tex]

[tex]x*2x^2-x*5x+x*1-3*2x^2-3*-5x-3*1[/tex]

[tex]2x^3-5x^2+x-6x^2+15x-3[/tex]

Upon combining like terms, we will get:

[tex]2x^3-5x^2-6x^2+15x+x-3[/tex]

[tex]2x^3-11x^2+16x-3[/tex]

Therefore, the product of our given expression would be [tex]2x^3-11x^2+16x-3[/tex].

Victoria is 4 years older than her neighbor . The sum of their ages is no more than 14 years .

Answers

(x+4)+v<=14 is the equation
the neighboor's age is at most, 5 years
and victoria is 9 at most

the smallest child is 5

9/4x-1/2y=-3 in x and y intercepts

Answers

Answer: 4(y/2 - 3)/9

hope this helps

We know the equation:
y=mx + b
So
9/4x-1/2y=-3
-1/2y = -3 + 9/4x
-1/2y = 9/4x - 3
-1/2y * -2 = (9/4x - 3) * -2
y = -9/2x + 3
Therefore:
b = 3
and the slope is - 9/2

George wants to save money for a car. George invest 1300 and an account that is an interest rate of 7.5%

How many years will it take for that account 7,100?

Answers

According to the formula above
7100=1300 (1+0.075)^t
Solve for t
Divide both sides by 1300 to get
7100/1300=(1+0.075)^t
Take the log for both sides
Log (7100/1300)=t×log (1.075)
Divide both sides by log (1.075) to get
T=log(7,100÷1,300)÷log(1.075)
T=23.48 years round your answer to get 23 years

Hope it helps!

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