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3 years ago

How much would $500 invested at 9% interest compounded annually be

Mathematics

2 answers:

dalvyx [7]3 years ago

8 0

Answer:

$705.79.

Step-by-step explanation:

The formula is

Amount = P(1 + r/100) ^ t so

Amount = 500 (1 + 9/100)^4

= $705.79.

makvit [3.9K]3 years ago

5 0

Answer: $705.79

Step-by-step explanation:

The concept of compound interest is that interest is added back to the principal sum so that interest is gained on that already-accumulated interest during the next compounding period.

Interest can be compounded on any given frequency schedule, from continuous to daily to annually. When incorporating multiple compounds per period (monthly compounding or quarterly compounding, etc), the general formula looks like this:

$\boxed{A = P(1 +\frac{r}{n})^{n*t}}$

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = number of times interest is compounded per unit "t"

t = the time the money is invested or borrowed for

<h3>(Using the data provided in the question)</h3>

P = $500

r = 9/100 = 0.09

n = 1 (compounded annually)

t = 4 years 

$A = 500(1 +\frac{0.09}{1})^{1*4}$

A = $500(1 + 0.09)⁴ = $500(1.09)⁴ = $500(1.4115816) = $705.79

Answer: $705.79

$\textit{\textbf{Spymore}}$

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There are 550 people at the school carnival.

Svet_ta [14]

Answer:

70% of the people at the fair are students

165 people are on the ride

Step-by-step explanation:

In order to find a percentage, take the fraction given, 385/550, and divide the numerator, 385, and divide it by the denominator, 550. Once completing this, we get 0.7

Next, we multiply the result by 100, and get 70, thus, 385 is 70% of 550.

To find how many people 30% of 550 is, we take the percentage and put it in a fraction with the denominator being 100(changes with size of fraction like a decimal, 300 would be over a denominator of 1000)

With 30/100, we then multiply by 550 with the equation looking like this:

30/100*550/1

Once we finish multiplying(typically using a calculator, although you can do it manually) we get 165, the value of how many people are on rides out of the total 550.

4 0

3 years ago

WILL GIVE BRAINLIEST

tiny-mole [99]

The expressions for each of the given statements are

a. 6 + z

b. 20 - x

c. x/6 - 8

d. x + 5/4

<h3>Writing an expression </h3>

From the question, we are to write an expression for each of the given statement

a. the sum of 6 and z

That is,

6 + z

b. the difference between 20 and x

That is,

20 - x

c. 8 less than the quotient of x divided by 6

That is,

x/6 - 8

d. x increased by 5 divided by 4

That is,

x + 5/4

Hence, the expressions for each of the given statements are

a. 6 + z

b. 20 - x

c. x/6 - 8

d. x + 5/4

Learn more on Writing an expression here: brainly.com/question/17651563

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4 0

1 year ago

Help please!!!!!!!!!!!!

matrenka [14]

Answer:

your answer is as follows

Step-by-step explanation:

5x+20=3x+60

2x=40

x=20

(equating the slopes)

8 0

2 years ago

A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. (a) What must be true

valentina_108 [34]

Answer:

(a) The distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b) The value of $P(\bar X$ is 0.7642.

Step-by-step explanation:

A random sample of size n = 10 is selected from a population.

Let the population be made up of the random variable X.

The mean and standard deviation of X are:

$\mu=68\\\sigma=15$

(a)

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. n = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

Then, the mean of the distribution of the sample mean is given by,

$\mu_{\bar x}=\mu=68$

And the standard deviation of the distribution of the sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{10}}=4.74$

Thus, the distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b)

Compute the value of $P(\bar X$ as follows:

$P(\bar X$

$=P(Z$

*Use a z-table for the probability.

Thus, the value of $P(\bar X$ is 0.7642.

(c)

Compute the value of $P(\bar X\geq 69.1)$ as follows:

Apply continuity correction as follows:

$P(\bar X\geq 69.1)=P(\bar X> 69.1+0.5)$

$=P(\bar X>69.6)$

$=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{69.6-68}{4.74})$

$=P(Z>0.34)\\=1-P(Z$

Thus, the value of $P(\bar X\geq 69.1)$ is 0.3670.

7 0

3 years ago

the volume v of a right circular cylinder of radius r and heigh h is V = pi r^2 h 1. how is dV/dt related to dr/dt if h is const

laiz [17]

In general, the volume

$V=\pi r^2h$

has total derivative

$\dfrac{\mathrm dV}{\mathrm dt}=\pi\left(2rh\dfrac{\mathrm dr}{\mathrm dt}+r^2\dfrac{\mathrm dh}{\mathrm dt}\right)$

If the cylinder's height is kept constant, then $\dfrac{\mathrm dh}{\mathrm dt}=0$ and we have

$\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dt}{\mathrm dt}$

which is to say, $\dfrac{\mathrm dV}{\mathrm dt}$ and $\dfrac{\mathrm dr}{\mathrm dt}$ are directly proportional by a factor equivalent to the lateral surface area of the cylinder ( $2\pi r h$ ).

Meanwhile, if the cylinder's radius is kept fixed, then

$\dfrac{\mathrm dV}{\mathrm dt}=\pi r^2\dfrac{\mathrm dh}{\mathrm dt}$

since $\dfrac{\mathrm dr}{\mathrm dt}=0$ . In other words, $\dfrac{\mathrm dV}{\mathrm dt}$ and $\dfrac{\mathrm dh}{\mathrm dt}$ are directly proportional by a factor of the surface area of the cylinder's circular face ( $\pi r^2$ ).

Finally, the general case ( $r$ and $h$ not constant), you can see from the total derivative that $\dfrac{\mathrm dV}{\mathrm dt}$ is affected by both $\dfrac{\mathrm dh}{\mathrm dt}$ and $\dfrac{\mathrm dr}{\mathrm dt}$ in combination.

8 0

3 years ago