4. Meagan invests $1,200 each year in an IRA for 12 years in an account that earned 5%
compounded annually. At the end of 12 years, she stopped making payments to the
account, but continued to invest her accumulated amount at 5% compounded annually for
the next 11 years.
a. What was the value of the Ira at the end of 12 years?
b. What was the value of the investment at the end of the next 11 years?
c. How much interest did she earn?

Answers

Answer 1

part A)

[tex]\bf \qquad \qquad \textit{Future Value of an ordinary annuity}\\ \left. \qquad \qquad \right.(\textit{payments at the end of the period}) \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right][/tex]

[tex]\bf \qquad \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array} \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &1200\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &12 \end{cases}[/tex]

[tex]\bf A=1200\left[ \cfrac{\left( 1+\frac{0.05}{1} \right)^{1\cdot 12}-1}{\frac{0.05}{1}} \right]\implies A\approx 19100.55[/tex]

part B)

so, for the next 11 years, she didn't make any deposits on it and simple let it sit and collect interest, compounded annually at 5%.

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \ \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$19100.55\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &11 \end{cases} \\\\\\ A=19100.55\left(1+\frac{0.05}{1}\right)^{1\cdot 11}\implies A\approx 32668.42[/tex]

part C)

well, for 12 years she deposited 1200 bucks, that means 12 * 1200, or 14,400.

now, here she is, 12+11, or 23 years later, and she's got 32,668.42 bucks?

all that came out of her pocket was 14,400, so 32,668.42 - 14,400, is how much she earned in interest.

Answer 2

a. The value of the Ira at the end of 12 years is $19,100.55.

b. The value of the investment at the end of the next 11 years is $32,668.43.

c. Interest earn is $18,288.43.

a. Using this formula to determine the value of the Ira at the end of 12 years

A=Pmt [(1+r)^n-1]/r

Let plug in the formula

A=1,200[(1+0.05)^12-1]/0.05

A=1,200[(1.05)^12-1]/0.05

A=$1,200(0.795856)/0.05

A=$955.02759/0.05

A=$19,100.55

b. The value of the Ira at the end of 11 years is:

$19,100.55(1+0.05)^11

=$19,100.55(1.05)^11

=$19,100.55(1.710339358)

=$32,668.43

c. Interest earn

Total investment=1200(12)

Total investment= $14,400

Now let calculate the interest earned

Interest earned = $32,668.43 - $14,400

Interest earned= $18,288.43

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Related Questions

Knowing that this number, the Golden Ratio, is present not just in mathematics, but may also be present within your own brain and body (at the atomic or subatomic level), what do you think it means? Is this number evidence of a grand design, a massive freak coincidence or something else?

Answers

The Golden Ratio is a mathematical relationship that exists in art, shapes, nature and the human body. The golden ratio can be present in your body, from the length of your arms and legs when compared to your torso. Fingers is another example because the length of our fingers, each section from the tip of the base to the wrist is larger than the preceding.

The measurement of the human navel to the floor and to the top of the head to the navel is also the Golden ratio. Plastic surgeons and dental surgeons use it to reconstruct the human face. It also appears in everything around us like in the nature and science. It appears on in flower petals because it is believed that each petal is placed to so that each petal gets the best exposure to sunlight. Dolphins, starfish, sea urchins and honeybees also exhibit the proportion like humans. DNA molecules measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral, these two number are successive numbers. I think that the Golden Ratio is just a freak coincidence that happened.

The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse

Answers

check the picture below

you can pretty much get the values for "a" and "b" from the grid.

1. Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
2. Divide all terms in the equation by a.
3. Subtract the constant (the term without an x) from both sides.
4. Add a constant (in terms of a and b) that will complete the square.
5. Take the square root of both sides of the equation.
6. Solve for x.

Answers

We are given that:

a x^2 + b x + c = 0

Divide all terms with c/ a:

x^2 + (b / a) x + (c / a) = 0

Subtract c from both sides:

x^2 + (b / a) x + (c / a) – c / a = 0 – c / a

x^2 + (b / a) x = - c / a

Add a constant k to complete the square:

where k = ((b / a) / 2)^2 = (b /2a)^2

x^2 + (b / a) x + k = - c / a + k

x^2 + (b / a) x + (b/2a)^2 = - c / a + (b /2a)^2

So the perfect square trinomial is:

(x + b/2a)^2 = - c / a + (b /2a)^2

Taking the square root of both sides:

x + b/2a = sqrt [- c / a + (b /2a)^2]

x = sqrt [(-c/a) + (b /2a)^2] – (b/2a)

Answer:

My equation is 3x^2 + 12x + 24 = 0. When I divide all of the terms by 3, the equation becomes x^2 + 4x + 8 = 0. When I subtract both sides by the constant, 8, the equation is x^2 + 4x = -8. When I add a constant to create the perfect square, the equation now becomes x^2 + 12x + 36 = 28. Finally, the equation simplified equals (x + 6)= the square root of 28.

Step-by-step explanation:

In mathematics, the distance between one point (a) and another point (b), each with coordinates (x,y), can be computed by taking the differences of their x coordinates and their y coordinates and then squaring those differences. the squares are added and the square root of the resulting sum is taken and... voila! the distance. given two variables, p1 and p2 that are of type point -- a structured type with two fields, x and y, both of type double-- write an expression whose value is the distance between the two points represented by p1 and p

Answers

Final answer:

The distance between two points can be found using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2).

Explanation:

The distance between two points can be found using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2). To find the distance between the two points represented by p1 and p2, we substitute the x and y coordinates of p1 and p2 into the formula:

distance = sqrt((p2.x - p1.x)^2 + (p2.y - p1.y)^2).

What is next number after 2 7 8 3 12 9

Answers

2+5=77+1=88-5=33+9=1212-3=9Can someone help me and tell me why i can not figure this out?

Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.

Answers

directly proportional ? (but what's mt?)

Answer:

Joint variation.

Step-by-step explanation:

There are four types of variation,

Direct variation : When a variable varies directly as another variable,

Example : y varies directly with x ⇒ y = kx,

Where, k is the constant of variation,

Inverse variation : When a variable varies inversely as another variable,

Example : y varies inversely with x ⇒ [tex]y=k\frac{1}{x}[/tex]

Joint variation : When a variable varies directly with two or more than two variables,

Example : y varies directly with both x and z ⇒ y = kxz

Combined variation : When a variable varies both directly and indirectly as another variables,

Example : y varies directly with x and inversely with z ⇒ [tex]y=k\frac{x}{z}[/tex]

Now, here the given expression,

y = 4mt,

Where, y, m and t are variables and 4 is the constant of variation,

⇒ y varies directly as both m and t,

⇒ y = 4mt is an example of joint variation.

A radio telescope has a parabolic surface, as shown below.
If the telescope is 1 m deep and 12 m wide, how far is the focus from the vertex? (5 points)

Answers

check the picture below.

so.. "p" is the distance from the vertex to either, the focus point or the directrix.

thus the focus is "p" units from the vertex.

now, if we set the parabola at the origin, like in the picture, and then use another point on the parabola, let's say we'll use (6,1), then

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=0\\ k=0 \end{cases}\implies (x-0)^2=4p(y-0)\implies x^2=4py \\\\\\ \begin{cases} x=6\\ y=1 \end{cases}\implies (6)^2=4p(1)\implies \cfrac{6^2}{4}=p\implies \cfrac{36}{4}=p\implies 9=p[/tex]

Final answer:

For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.

Explanation:

For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.

Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.

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The slope of a vertical line is zero. true or false

Answers

it is true because the y and x will always be the same number and a vertical line has no slope thus equaling 0,0

The solution is False

The slope of a vertical line is given by the equation Slope m = undefined

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the line be represented as A

Now , the line A is a vertical line

So , the equation of line will be represented as y = mx + c

where m is the slope of the line

And , Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of a vertical line is infinite or undefined as it has no y-intercept

Because , the change is x is 0

So , the denominator of the fraction is 0 and division by 0 is undefined

Slope m = ( y₂ - y₁ ) / 0

Hence , the slope m is undefined

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What is the derivative of this function?

Answers

[tex]\bf y=\sqrt{x}-\left( \frac{1}{2} \right)^x\implies y=x^{\frac{1}{2}}-\left( \frac{1}{2} \right)^x\implies \cfrac{dy}{dx}=\frac{1}{2}x^{\frac{1}{2}-1}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right) \\\\\\ \cfrac{dy}{dx}=\frac{1}{2}x^{-\frac{1}{2}}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)\implies \cfrac{dy}{dx}=\cfrac{1}{2\sqrt{x}}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)[/tex]

in 2000 you weighed 175 pounds. in 2001 you weighed 62 pounds, and in 2002 you weighed 154 pounds. how many pounds did you lose from 2000 to 2002.

Answers

You should get the answer 154 afte u subtract and at that school be your answer

Nate rides his bike to school every day. From his home he rides 2.5 miles north, and then six miles west. If a straight line is drawn from Nate's house to the school, find the distance between these two locations.

Answers

use Pythagorean Theorem

2.5^2 + 6^2 = x^2

6.25 +36 = 42.25

x= sqrt(42.25) = 6.5 miles

By the Pythagorean Theorem, the length of the hypotenuse of a right triangle is equal to the sum of the side lengths squared, mathematically:

h^2=x^2+y^2

h^2=6^2+2.5^2

h^2=36+6.25

h^2=42.25

h=√(42.25) miles

h=6.5 miles

Which expression is equivalent to 3(8 + 7)? 24 + 7 24 + 21 11 + 10 11 + 7

Answers

Multiply 3&8 and 3&7, this expands it to 24 + 21.

3(8 + 7) = 3(8) + 3(7)...distributive property
= 24 + 21

answer is
24 + 21

find the coefficient of x^6 in the binomial expression of (2x+3)^9

Answers

Its 2 bc its in front of the variable

By the Binomial Theorem:
(a + b)^n = sum(k=0 to n) [C(n, k) * a^(n - k) * b^k].

By letting a = 2x, b = 3, and n = 9
(2x + 3)^9 = sum(k=0 to 9) [C(9, k) * (2x)^(9 - k) * 3^k].
As you can see, the power of x is 9 - k. Since we want the x^6 term:
9 - k = 6 ==> k = 3
Thus, letting k = 3 yields the term containing x^6 to be:
C(9, 6) * (2x)^(9 - 3) * 3^4 = 435456x^6.
.

The sun produces 3.9 x 10^33 ergs of radiant energy per second. how many ergs of radiant energy does the sun produce in 3.25 x 10^3 seconds?

Answers

Answer:

1.2675 x 10^37

Step-by-step explanation:

you would have to first multiply 3.9 x 3.25 =12.675. It is not in scientific notation so you would have to change the decimal 1.2675 x 10^37

The ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]

The rate of energy is given as:

[tex]Rate = 3.9 * 10^{33}\[/tex] radiant energy per second

The time is given as:

[tex]Time = 3.25 * 10^3[/tex] seconds

The amount of radiant energy produced in this time is:

[tex]Energy = Rate * Time[/tex]

So, we have:

[tex]Energy = 3.9 * 10^{33} * 3.25 * 10^3[/tex]

Multiply

[tex]Energy = 12.675* 10^{36}[/tex]

Rewrite as:

[tex]Energy = 1.2675* 10^{37}[/tex]

Approximate

[tex]Energy = 1.3* 10^{37}[/tex]

Hence, the ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]

Answers

Without using the trigonometry ratio, we can find the distance between the ship and the buoy by:

the distance between City and Lemont SUBTRACT the vertical distance between City and the point parallel to the Ship

The distance between the City and Lemont can be worked out using the Sin rule
[tex] \frac{57.8}{sin(36)}= \frac{City-Lemont}{sin(92)} [/tex]
[tex]City-Lemont= \frac{57.9sin(92)}{sin(36)} = 98.27.....[/tex]≈98.3

The vertical distance between the City and the point parallel to the ship can be worked out using the Pythagoras theorem
[tex] \sqrt{57.8^{2}- 44.6^{2} } =36.765... [/tex]≈36.8

The distance between the ship and the Buoy is given:
[tex]98.3-36.8=61.5 [/tex] miles

On Saturday, a local hamburger shop sold a combined total of 273 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?

Answers

Final answer:

To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.

Explanation:

The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.

Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.

in the final event of a track meet, 6 runners run a 100 meter dash. A) How many possible arrangements are there for the medal winners (gold, silver and bronze)? B) state whether it is a combination or permutation

Answers

6 runners, 3 medals, how many ways to give them? well, runner say 2 could get gold or not, bronze or not and silver or not, and so can any other runnner, and the order "does matter", it makes a distinction, thus, is a Permutation

[tex]\bf _nP_r=\cfrac{n!}{(n-r)!}\qquad \qquad _6P_3=\cfrac{6!}{(6-3)!}[/tex]

Answer:

120 possible arrangements.

It is a permutation

Step-by-step explanation:

Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.

Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:

N= Total number possibilities:

[tex]N=6*5*4=120[/tex]

This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.

The permutation can be learnt by the formula:

[tex]N=\frac{p!}{(p-n)!}[/tex]

where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:

[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]

What are the solutions to the quadratic equation (5y + 6)2 = 24? y = and y = y = and y = y = and y = y = and y =

Answers

For this case we have the following quadratic expression:

[tex] (5y + 6) ^ 2 = 24
[/tex]

From here, we must clear the value of y.

For this, we follow the following steps:

1) We clear the square term:

[tex] (5y + 6) =+/-\sqrt{24} [/tex]

[tex] (5y + 6) =+/-2\sqrt{6} [/tex]

2) Pass the value of 6 by subtracting:

[tex] 5y =-6+/-2\sqrt{6} [/tex]

3) Pass the value of 5 to divide:

[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]

Answer:

The solutions to the quadratic equation are:

[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]

[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]

There are 36 girls and 40 boys at a summer camp. The campers will be divided into equal-sized groups. Each group will have the same number of girls and the same number of boys. What is the greatest number of groups that can be formed?

Answers

The maximum number groups would be 4, which contain 9 girls and 10 boys in each group.
Hope it helps.

The question asks you to split these numbers into smaller ones.
This is called the prime factorization of a number:
Lets do this for 36 first, can it be diveded by the smallest prime? (2) Yes, 36/2=18 can 18 still be dived by 2? Yes, 18/2=9 . Can 9 be divided by 2? No, so we move up in primes. Can it be divieded by 3, yes 9/3=3 and 3 is a prime so we can stop.
What we concluded is that 36=2*2*3*3
Lets do this with 40 too, 40/2=20, 20/2=10, 10/2=5 and that is a prime so we can stop.
40=2*2*2*5

Now will you figure out how does this help you?

What is an open map?

Answers

The term open map is used in topology, field in the Mathematics which focuses on the properties of space, dimension and transformation. The open map is a function which maps open sets (set that doesn't contain any of its boundary points); to open sets. This term and concept helps two points in the topology to be distinguished.

How do you rename 5400

Answers

Answer: "Fifty-four hundred" .
__________________________________________________

Henry recorded the number of miles he biked each day for a week. His miles were 25, 40, 35, 25, 40, 60, and 75. Enter the data into the statistics calculator. What is the standard deviation of the miles Henry biked to the nearest tenth?

Answers

The standard deviation of the miles Henry biked to the nearest tenth is 17.1. The standard deviation is calculated following the steps below.

Calculation of standard deviation

First calculate the mean of the numbers that where given which is = 25 + 40 + 35 + 25 + 40 + 60+ 75/7

= 300/7

= 42.9

Then for each number, subtract the Mean and square the result.

(25 - 42.9)² = −17.9² = 320.41

(40-42.9)² = -2.9²= 8.42

(35-42.9)² = -7.9² = 62.41

(25-42.9)² = −17.9² = 320.41

(40-42.9)² = -2.9²= 8.42

(60-42.9)² = 17.1²= 292.41

(75-42.9)² = 32.1²= 1030.41

Then work out the mean of those squared differences. That is,

320.41+ 8.42+62.41+320.41+8.42+292.41+1030.41/7

= 2042.89/7

= 291.8

Take the square root of 291.8 which is,

√291.8 = 17.08215443

= 17.1 to the nearest tenth.

Therefore, the standard deviation of the miles Henry biked to the nearest tenth is = 17.1

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Answer:

17.1

Step-by-step explanation:

got it right

What is the ratio of the two values and what new value do they produce? 4m in 2 min

Answers

the ratio is 2:1. They could be resaigned to 8 meters and 4 meters.

Answer:

2:1

Step-by-step explanation:

The ratio is 2:1 and the new value can also be 8/4= 2/1

subtract one- fifth from seven times w

Answers

We can write one fifth as [tex] \frac{1}{5} [/tex]

7 times of w , we can write as = 7w

Now we have to subtract one fifth from seven times of w.

So we can write it in algebraic expression as

[tex]7w - \frac{1}{5} [/tex]

last year, Carmen opened an investment account with $7400. At the end of the year, the amount in the account had decrease buy 26.5%. How much is this decrease in dollars? How much money was in her account at the end of the year?

Answers

The account decreased by
7,400×0.265=1,961

The account at the end of the year
7,400−1,961=5,439

Final answer:

The decrease in Carmen's account was $1961, which is 26.5% of her original investment of $7400. Hence, by subtracting this decrease from the original investment, we find that Carmen had $5439 left at the end of the year.

Explanation:

The decrease in Carmen's account over the year is 26.5% of the original investment of $7400. In mathematical terms, we can calculate this value by multiplying the original investment by the percentage decrease, using the formula: Decrease = Original Amount * Percentage Decrease.

In Carmen's case, this would be $7400 * 0.265 (converted from 26.5%). Upon calculating, we find that the decrease is $1961.

Now, to find how much money Carmen had at the end of the year, we subtract this decrease from the original amount invested. Again, using the formula: Final Amount = Original Amount - Decrease, we plug in the numbers to get $7400 - $1961, which equals $5439. This is how much Carmen had left in her account at the end of the year after the decrease.

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Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the paraboloid z = 7x2 + y2 and the parabolic cylinder y = 3x2

Answers

Letting [tex]x=t[/tex], we get [tex]y=3x^2=3t^2[/tex] and [tex]z=7x^2+y^2=7t^2+(3t^2)^2=7t^2+9t^4[/tex], so we can parameterize the intersection by

[tex]\mathbf r(t)=\langle t,3t^2,7t^2+9t^4\rangle[/tex]

where [tex]-\infty<t<\infty[/tex].

Image attached.

Final answer:

The vector function r(t) representing the curve of intersection of the surfaces z = 7x² + y² and y = 3x² is r(t) = it + 3t²j + (7t² + 9t´)k.

Explanation:

Finding a Vector Function for a Curve of Intersection

To find the vector function r(t) that represents the curve of intersection of the surfaces z = 7x² + y² and y = 3x², we can parameterize the variables using a suitable parameter, commonly denoted as t. We can set x = t, which imminently provides y as y = 3t² by substituting t into the equation of the parabolic cylinder. Then, substituting both x and y into the equation of the paraboloid gives us z = 7t² + (3t²)² = 7t² + 9t´. Therefore, the vector function is:

r(t) = it + j3t² + k(7t² + 9t´).

This function r(t) represents all points (x, y, z) on the curve where the two surfaces intersect. Since the curve lies on both surfaces simultaneously, z must be equal for both equations when x and y from the curve are substituted into them.

Which set of numbers does 8 2/3 belong to

Answers

real and rational numbers

805 tens in standard form

Answers

805 tens = 805 x 10 = 8,050

To write 8,050 in standard form, we have
[tex]805\ tens=8,050=8.05\times10^3[/tex]

Felicia invested money at an interest rate of 4%. After six months, she had earned $90.00 interest. How much money did Felicia invest?

Answers

The formula is
I=prt
I interest earned 90
P amount invested?
R interest rate 0.04
T time 6/12
Solve the formula for p
P=I÷rt
P=90÷(0.04×(6÷12))
P=4,500 ....answer

Answer:

the answer is 4500 i got it right

Step-by-step explanation:

The vertex form of the equation of a parabola is y = (x - 4)2 + 22. What is the standard form of the equation?

Answers

First foil (x-4)^2 into x^2-8x+16. You now have y=x^2-8x+16+22. Add 16+22 to get the final equation of y=x^2-8x+38.

The equation in standard form is y = x^2 - 8x + 38

How to write the equation in standard form?

The vertex form of the equation is given as':

y = (x - 4)^2 + 22

Expand the equation

y = x^2 - 8x + 16 + 22

Evaluate the sum

y = x^2 - 8x + 38

Hence, the equation in standard form is y = x^2 - 8x + 38

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