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Nat2105 [25]
3 years ago
8

The population of a school of fish increases at a rate of 12% per month. There are currently 500 fish in the school. Find the am

ount of fish there will be in the population after 3 months. Round to the nearest whole fish.
The yearly profits of a start-up company is $25,000. The profits have been decreasing by 6% per year. What will the company’s profits be in 8 years? Round to the nearest dollar.

Steps would also be great! I can't seem the grasp the concept of Exponential Growth and Decay
Mathematics
1 answer:
Jlenok [28]3 years ago
5 0

Answer:

702 fish

Step-by-step explanation:

You might be interested in
What is this solution of the equation 4w = 2/3
amid [387]
First, you need to isolate w. So you get w = 2/3 divided by 4.
I made the 2/3 a decimal, as it is easier to work with: 0.6666 divided by 4 is 0.167. 
0.167 is 1/6.
w = 1/6, or 0.167.
6 0
3 years ago
Read 2 more answers
Here is my question i need help answering it
ollegr [7]
Ur answer will be C… basically u make the equation equal to zero and then use the quadratic formula to find ur answers…. x = -3 and 9
5 0
2 years ago
Four darts are thrown at this dartboard. If all four darts hit the board, how many different point totals are possible. (Dartboa
jonny [76]

Answer:

Different point total are possible = 497

Step-by-step explanation:

Given - Four darts are thrown at this dartboard. Dartboard regions are  

             1, 4, 7, 10 points

To find - If all four darts hit the board, how many different point totals are

              possible.

Proof -

Are given there are 4 regions -

1st region - 1 point

2nd region - 4 points

3rd region - 7 points

4th region - 10 points

Case I :

If all the darts hit the different region -

Total points possible are - 1 + 4 + 7 + 10 = 22 points

Case II :

If all the darts hit the same region -

It means either they hit 1 region or 2nd region or 3rd region or 4th region

If they all 4 hit first region , points are - 1+1+1+1 = 4

If they all 4 hit second region , points are - 4+4+4+4= 16

If they all 4 hit third region , points are - 7+7+7+7 = 28

If they all 4 hit fourth region , points are - 10+10+10+10 = 40

So,

the Total points possible are - 4 + 16 + 28 + 40 = 88

Case III :

If 3 darts hit the same region -

Sub-case 1 :

If 1 dart hit 1st region, other 3 dart hit 2nd region

Points are - 1 + 4 + 4+ 4 = 13

Sub-case 2 :

If 1 dart hit 1st region , other 3 dart hit 3rd region

Points are - 1 + 7 + 7 + 7 = 22

Sub-case 3 :

If 1 dart hit 1st region , other 3 dart hit 4th region

Points are - 1 + 10 + 10 + 10 = 31

Sub-case 4 :

If 1 dart hit 2nd region , other 3 dart hit 1st region

Points are - 4 + 1 + 1 + 1 = 7

Sub-case 5 :

If 1 dart hit 2nd region , other 3 dart hit 3rd region

Points are - 4 + 7 + 7 + 7 = 25

Sub-case 6 :

If 1 dart hit 2nd region , other 3 dart hit 4th region

Points are - 4 + 10 + 10 + 10 = 34

Sub-case 7 :

If 1 dart hit 3rd region , other 3 dart hit 1st region

Points are - 7 + 1 + 1 + 1 = 10

Sub-case 8 :

If 1 dart hit 3rd region , other 3 dart hit 2nd region

Points are - 7 + 4 + 4 + 4 = 19

Sub-case 9 :

If 1 dart hit 3rd region , other 3 dart hit 4th region

Points are - 7 + 10 + 10 + 10 = 37

Sub-case 10 :

If 1 dart hit 4th region , other 3 dart hit 1st region

Points are - 10 + 1 + 1 + 1 = 13

Sub-case 11 :

If 1 dart hit 4th region , other 3 dart hit 2nd region

Points are - 10 + 4 + 4 + 4 = 22

Sub-case 12 :

If 1 dart hit 4th region , other 3 dart hit 3rd region

Points are - 10 + 7 + 7 + 7 = 31

So,

Total points possible are - 13+22+21+7+25+34+10+19+37+13+22+31 = 254

Case IV :

If 2 darts hit the same region -

Sub-case 1:

If 2 darts hits 1st region , other 2 darts hit 2nd region

Points are - 1 + 1 + 4 + 4 = 10

Sub-case 2:

If 2 darts hits 1st region , other 2 darts hit 3rd region

Points are - 1 + 1 + 7 + 7 = 16

Sub-case 3:

If 2 darts hits 1st region , other 2 darts hit 4th region

Points are - 1 + 1 + 10 + 10 = 23

Sub-case 4:

If 2 darts hits 2nd region , other 2 darts hit 3rd region

Points are - 4 + 4 + 7 + 7 = 22

Sub-case 5:

If 2 darts hits 2nd region , other 2 darts hit 4th region

Points are - 4 + 4 + 10 + 10 = 28

Sub-case 6:

If 2 darts hits 3rd region , other 2 darts hit 4th region

Points are - 7 + 7 + 10 + 10 = 34

So,

Total points possible are - 10 + 16 + 23 + 22 + 28 + 34 = 133

Case V :

If 1 darts hit the same region -

This case is include in the Case III.

∴ we get

Different point total are possible = Points in Case I +  II +  III +  IV

                                                       = 22 + 88 + 254 + 133

                                                       = 497

⇒Different point total are possible = 497

4 0
2 years ago
guse lagrange multipliers to find the maximum or minimum values of the function subject to the given constraint. (if an answer d
Novosadov [1.4K]

Therefore the maximum value of function f(x,y,z)=x^{2} y^{2} z^{2} =1/27

And the minimum value is 0

<h3>What is function?</h3>

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable) (the dependent variable) (the dependent variable). Mathematics uses functions frequently, and functions are essential for specifying physical relationships in the sciences.

Here,

The function is given as:

f(x,y,z)=x^{2} y^{2} z^{2}

x^{2} +y^{2}+ z^{2}=1

=>x^{2} +y^{2}+ z^{2}-1=0

Using Lagrange multiplies, we have:

L(x,y,z,λ)=f(x,y,z) +λ(0)

Substitute f(x,y,z)=x^{2} y^{2} z^{2}  and x^{2} +y^{2}+ z^{2}-1=0

Differentiate

L(x)=2xy^{2} z^{2}+2λx

L(y)=2yx^{2} z^{2}+2λy

L(z)=2zx^{2} y^{2}+2λz

L(λ)=x^{2} +y^{2}+ z^{2}-1

Equating to 0

2xy^{2} z^{2}+2λx =0

2yx^{2} z^{2}+2λy = 0

2zx^{2} y^{2}+2λz = 0

x^{2} +y^{2}+ z^{2}-1 = 0

Factorize the above expressions

2xy^{2} z^{2}+2λx =0

2x(y^{2} z^{2}+λ)=0

2x=0 and (y^{2} z^{2}+λ)=0

x=0 and  y^{2} z^{2}= -λ

2yx^{2} z^{2}+2λy = 0

2y(x^{2} z^{2}+λ)=0

2y=0 and (x^{2} z^{2}+λ)=0

y=0 and  x^{2} z^{2}= -λ

2zx^{2} y^{2}+2λz = 0

2z(y^{2} x^{2}+λ)=0

2z=0 and (x^{2} y^{2}+λ)=0

z=0 and  x^{2} y^{2}= -λ

So we have ,

x=0 and  y^{2} z^{2}= -λ

y=0 and  x^{2} z^{2}= -λ

z=0 and  x^{2} y^{2}= -λ

The above expression becomes

x=y=z=0

This means that,

x^{2} +y^{2}+ z^{2}=1

x^{2} +x^{2}+ x^{2} =1 \\3x^{2 } =1

x= ±1/\sqrt{3}

So,

y= ±1/\sqrt{3}

z= ±1/\sqrt{3}

The critic points are

x=y=z=±1/\sqrt{3}

x=y=z=0

Therefore the maximum value of function f(x,y,z)=x^{2} y^{2} z^{2} =1/27

And the minimum value is 0

To know  more about function , visit

brainly.com/question/12426369

#SPJ4

3 0
1 year ago
PLEASE HELP ME!!<br><br> BRAIINLIEST WILL BE GIVEN
PtichkaEL [24]
Your answer would be <em />answer choice C. The initial number of transactions is a dependent variable, because the number of transactions made are dependent on the number of hours that have passed.

Hope this helps,
<em>♥A.W.E.<u>S.W.A.N.</u>♥</em>
4 0
2 years ago
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