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3 years ago

3x^2 - 4x + 7 (Find the domain of the expression)

Mathematics

1 answer:

Jobisdone [24]3 years ago

3 0

x1 = −(−4) − √ (−4)2 − 4×3×7 2×3 = 4 − 2 × √ 17 i 6 ≈ 0.666667 − 1.374369ix2 = −(−4) + √ (−4)2 − 4×3×7 2×3 = 4 + 2 × √ 17 i 6 ≈ 0.666667 + 1.374369i

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You want to be able to withdraw $25,000 from your account each year for 20 years after you retire.

Nina [5.8K]

Answer:

When using formulas in application, or memorizing them for tests, it is helpful to note the similarities and differences in the formulas so you don’t mix them up. Compare the formulas for savings annuities vs payout annuities.

Savings Annuity Payout Annuity

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)

−

)

(

)

(

−

(

)

−

)

(

)

PAYOUT ANNUITY FORMULA

(

−

(

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−

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(

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P0 is the balance in the account at the beginning (starting amount, or principal).

d is the regular withdrawal (the amount you take out each year, each month, etc.)

r is the annual interest rate (in decimal form. Example: 5% = 0.05)

k is the number of compounding periods in one year.

N is the number of years we plan to take withdrawals

3 0

3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

3 years ago

The cost per minute for a conference phone call originally 2.60 increased by 30% what is the new price?

harkovskaia [24]

c.) $3.38

Original price = $2.60
* It is the basis of increase thus, 100%
* The increase is 30%, thus, 100% + 30% = 130%

To get the new price, simply multiply the original price to 130%

$2.60 * 130% = $3.38

Another way of solving the problem is getting the equivalent of 30% and adding it to the original price.

$2.60 * 30% = $0.78
$2.60 + $0.78 = $3.38

6 0

3 years ago

Read 2 more answers

Question: What is the number of the parking space covered by the car?

sukhopar [10]

Answer:

Step-by-step explanation:

7 0

2 years ago

Is 4 a solution of 3x+8=4 ? complete the statement

nordsb [41]

I think it would have to equal a fraction being -4/3

4 0

3 years ago