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My name is Ann [436]

3 years ago

7

You invest $2500 in an account to save for college. Account 1 pays 6%annual interest compounded quarterly. Account 2 pays 4% ann

ual interest compounded continuously. Which account should you choose to obtain the greater amount in 10 years?
Account 1
Or
Account 2

1 answer:

pentagon [3]3 years ago

6 0

Account 1 I presume

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Please show full solutions! WIll Mark Brainliest for the best answer. <br><br> SERIOUS ANSWERS ONLY

Ierofanga [76]

Answer:

vertical scaling by a factor of 1/3 (compression)
reflection over the y-axis
horizontal scaling by a factor of 3 (expansion)
translation left 1 unit
translation up 3 units

Step-by-step explanation:

These are the transformations of interest:

g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k

g(x) = f(x) +k . . . . vertical translation by k units (upward)

g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis

g(x) = f(x-k) . . . . . horizontal translation to the right by k units

__

Here, we have ...

g(x) = 1/3f(-1/3(x+1)) +3

The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:

vertical scaling by a factor of 1/3 (compression) . . . 1/3f(x)
reflection over the y-axis . . . 1/3f(-x)
horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
translation left 1 unit . . . 1/3f(-1/3(x+1))
translation up 3 units . . . 1/3f(-1/3(x+1)) +3

_____

<em>Additional comment</em>

The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.

The horizontal transformations could also be described as ...

translation right 1/3 unit . . . f(x -1/3)
reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)

The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.

8 0

2 years ago

A taxi charges a flat rate of R10, and an additional cost of 30 cents per kilometer. If you have

Maslowich

Step-by-step explanation:

so, just by getting into the taxi we have to pay R10.

that leaves us 22 - 10 = R12 for the actual trip.

30 cents per kilometer.

so, how many units of 30 cents are there in R12 ? that is the number of kilometers we can go.

R12 = 1200 cent (right ?)

1200 / 30 = 120 / 3 = 40

so, we can travel 40 kilometers for that money.

8 0

3 years ago

Mr.Ward runs a lot. He ran 45 minutes each day, 5 days each week , for 16 weeks . In that time, he ran 450 miles. What was his a

Savatey [412]

Answer:

7.5 miles per hour.

Step-by-step explanation:

We have been given that Mr. Ward runs a lot. He ran 45 minutes each day, 5 days each week, for 16 weeks.

First of all, we will find time for that Mr. Ward ran in 16 weeks.

We will multiply 5 by 16 to find number of days for that Mr. Ward ran and then we will multiply the result by 45 minutes to find the time.

$\text{Time for that Mr. Ward ran in 16 weeks}=16\times 5\times 45\text{ minutes}$

$\text{Time for that Mr. Ward ran in 16 weeks}=3600\text{ minutes}$

Now, we will divide 3600 minutes by 60 minutes to convert time into hours as:

$\text{Hours}=\frac{3600}{60}=60$

Now, we will divide 450 miles by 60 hours to find Mr. Ward's average speed as:

$\text{Mr. Ward's average speed}=\frac{450\text{ miles}}{\text{60 hours}}$

$\text{Mr. Ward's average speed}=\frac{7.5\text{ miles}}{\text{ Hour}}$

Therefore, Mr. Ward's average speed in 7.5 miles per hour.

7 0

3 years ago

nickel has an approximate diameter of 20 mm and an approximate thickness of 2 mm what is the approximate volume of a stack of 40

ziro4ka [17]

Answer:

The approximate volume of a stack of 40 nickels is 25132.741 cubic milimeters.

Step-by-step explanation:

A nickel can be modelled by the formula of a right cylinder, the approximate volume of the stack of nickels ( $V_{net}$ ), measured in cubic milimeters, is the product of the number of elements ( $n$ ), no unit, and the volume of each element ( $V$ ), measured in cubic milimeters. That is:

$V_{net} = n\cdot V$ (1)

By volume equation of right cylinder, we have the following formula:

$V_{net} = \frac{\pi}{4}\cdot n \cdot D^{2}\cdot h$ (2)

Where:

$n$ - Amount of nickels, no unit.

$D$ - Diameter of nickel, measured in milimeters.

$h$ - Thickness of nickel, measured in milimeters.

If we know that $n = 40$ , $D = 20\,mm$ and $h = 2\,mm$ , then the net volume of the stack of nickels is:

$V_{net} = \frac{\pi}{4}\cdot (40)\cdot (20\,mm)^{2}\cdot (2\,mm)$

$V_{net} \approx 25132.741\,mm^{3}$

The approximate volume of a stack of 40 nickels is 25132.741 cubic milimeters.

8 0

3 years ago

Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan. Th

Alisiya [41]

Answer:

s ≈ 105

Step-by-step explanation:

<u>Given:</u>

The data set: 700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750

<u>To find:</u>

The standard deviation of the data

<u>Steps:</u>

To find the standard deviation, first write the computational formula for the standard deviation of the sample.

${s}= \sqrt{\frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n - 1}}$

Take the square root of the answer found in step 7 above. This number is the standard deviation of the sample. It is symbolized by $s$ . Here, we round the standard deviation to the nearest whole number.

${s} = \sqrt{10987.878787879} = 104.8231$

Rounding to the nearest whole number:

s ≈ 105

6 0

2 years ago