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3 years ago

You have 65 movies on your Netflix queue. In how many ways can you order them?

1 answer:

4 0

Ok so permuations
slot method basically
first slot is 65 options
2nd slot is 64 options
3rd slot is 63
...
65th slot is 1 option

basically the answer is 65! or 65 factorial which is about 8,247,650,592,082,470,666,723,170,306,785,496,252,186,258,551,345,437,492,922,123,134,388,955,774,976,000,000,000,000,000 or about 8<span> trigintillion</span> or in scientific notiotion, $(8.247)(10^{93})$

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A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha

8_murik_8 [283]

To model this situation, we are going to use the decay formula: $A=Pe^{rt}$
where
$A$ is the final pupolation
$P$ is the initial population
$e$ is the Euler's constant
$r$ is the decay rate
$t$ is the time in years

A. We know for our problem that the initial population is 1,250, so $P=1250$ ; we also know that after a year the population is 1000, so $A=1000$ and $t=1$ . Lets replace those values in our formula to find $r$ :
$A=Pe^{rt}$
$1000=1250e^{r}$
$e^{r}= \frac{1000}{1250}$
$e^{r}= \frac{4}{5}$
$ln(e^{r})=ln( \frac{4}{5} )$
$r=ln( \frac{4}{5} )$
$r=-02231$

Now that we have $r$ , we can write a function to model this scenario:
$A(t)=1250e^{-0.2231t}$ .

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C.
- The function is decreasing
- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0:
$A(0)=1250e^{(-0.2231)(0)$
$A_{0}=1250e^{0}$
$A_{0}=1250$
- Over the interval [0,10], the function will have a minimum at t=10:
$A(10)=1250e^{(-0.2231)(10)$
$A_{10}=134.28$

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: $m= \frac{A(0)-A(10)}{10-0}$
where
$m$ is the rate of change
$A(10)$ is the function evaluated at 10
$A(0)$ is the function evaluated at 0
We know from previous calculations that $A(10)=134.28$ and $A(0)=1250$ , so lets replace those values in our formula to find $m$ :
$m= \frac{134.28-1250}{10-0}$
$m= \frac{-1115.72}{10}$
$m=-111.572$
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

7 0

3 years ago

Find the value of x in the picture please

nika2105 [10]

The answer is B-40.

It is an acute angle so it can not be 155 but the angle does not look like it is close to being 90 degrees so the answer has to be 40!

Hope this helps(can I get brainliest)

8 0

3 years ago

Can someone please help me with this i don't know

Liula [17]

50.2/3divided by 8/7
it will equal 1 5/16 which is C

7 0

3 years ago

Enter the phrase as an algebraic expression.

zysi [14]

Answer:

I believe the answer is p over 5, it won't let me type it out but it put the p on top of the 5

3 0

3 years ago

How do I solve this problem?

jekas [21]

<span>Future Value: $227,016.59
Total Deposits: $186,000.00
Interest Earned: </span>$41,016.59

A = P ( 1 + r / n ) ^nt

A = value after t periods

P = principal amount (initial investment)

r = annual nominal interest rate (not reflecting the compounding)

n = number of times the interest is compounded per year

t = number of years the money is borrowed for

8 0

3 years ago