Simplify the following expression.



(3x−6)+(5x−5)
PLEASE I NEED HELP

Answer:

[tex](a)\ \frac{dP}{dt} = 0.078- 0.000857t[/tex]

[tex](b)\ P = 0.078t- 0.0004285t^2 + 7.02[/tex]

[tex](c)\ 9.37\ billion[/tex]

Step-by-step explanation:

Given

In 2012

[tex]P(t) = 7.02\ billion[/tex]

[tex]R_1 = 134\ million/year[/tex] --- Birth rate

[tex]R_2 = 56\ to\ 80[/tex] -- Death rate from '12 to '40

Solving (a): Equation for population from 2012

In 2012, we have the addition in population to be:

[tex]\triangle P= Birth - Death[/tex]

[tex]\triangle P= 134 - 56[/tex]

[tex]\triangle P = 78[/tex] million

From 2012 to 2040, we have the death rate per year to be:

[tex]Rate/yr = \frac{80 - 56}{2040 - 2012}[/tex]

[tex]Rate/yr = \frac{24}{28}[/tex]

[tex]Rate/yr = \frac{6}{7}[/tex] million/year

So, the differential equation is:

[tex]\frac{dP}{dt} = \triangle P - Rate/yr * t[/tex] where t represents time

[tex]\frac{dP}{dt} = 78 - \frac{6}{7} * t[/tex]

[tex]\frac{dP}{dt} = 78 - \frac{6t}{7}[/tex]

Express in millions

[tex]\frac{dP}{dt} = \frac{78}{1000} - \frac{6t}{7000}[/tex]

[tex]\frac{dP}{dt} = 0.078- 0.000857t[/tex]

Solving (b): The solution to the equation in (a)

[tex]\frac{dP}{dt} = 0.078- 0.000857t[/tex]

Make dP the subject

[tex]dP = (0.078- 0.000857t)dt[/tex]

Integrate both sides

[tex]\int dP = \int (0.078- 0.000857t)dt[/tex]

[tex]P = \int (0.078- 0.000857t)dt[/tex]

This gives:

[tex]P = 0.078t- \frac{0.000857t^2}{2} + c[/tex]

[tex]P = 0.078t- 0.0004285t^2 + c[/tex]

Solve for c.

When t = 0; P = 7.02

So, we have:

[tex]7.02 = 0.078*0- 0.0004285*0^2 + c[/tex]

[tex]7.02 =0-0 + c[/tex]

[tex]7.02 =c[/tex]

[tex]c = 7.02[/tex]

So:

[tex]P = 0.078t- 0.0004285t^2 + c[/tex]

[tex]P = 0.078t- 0.0004285t^2 + 7.02[/tex]

Solving (c): The population in 2050

We have:

[tex]P = 0.078t- 0.0004285t^2 + 7.02[/tex]

In 2050, the value of t is:

[tex]t = 2050 - 2012[/tex]

[tex]t = 38[/tex]

So, the expression becomes

[tex]P = 0.078*38- 0.0004285*38^2 + 7.02[/tex]

[tex]P \approx 9.37\ billion[/tex]

Answer:

1780.43

Step-by-step explanation:

Given:

P = 800

r = 10% or 0.1

t = 8

Work:

[tex]A=Pe^{rt}\\\\A=800e^{0.1*8}\\\\A=800e^{0.8}\\\\A=1780.43[/tex]

Answer:

slope=1/4

y-intercept=3

y=.25x+3

Step-by-step explanation:

slope=rise over run so

slope=1/4

y-intercept is the value of y where the line crosses the y axis..

y-intercept=3

In y=mx+b form m is slope and b is y-intercept so...

y=.25x+3

Answer:  58 .23

Step-by-step explanation:

Jets are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is

a 45% chance they'll win.

Answer:

90

Step-by-step explanation:

Answer:

13.89

Step-by-step explanation:

A^2+B^2=C^2

7^2+12^2=C^2

193 = C^2

193 square root = 13.89

Answer:

Step-by-step explanation:

Answer:

a

If they are vertical angles, they are equal.

5x - 24 = 3x + 24                      Add 24 to both sides

5x -24 +24 = 3x + 24 + 24       Combine

5x =   3x + 48                           Subtract 3x

5x - 3x = 3x-3x + 48                Combine

2x = 48                                    Divide by 2                                

x = 24

<A =5*24 - 24

<A = 96

Step-by-step explanation:

Answer:

10/30

Step-by-step explanation:

First, multiply the denominator by 10 to make 30.

Then, since we multiplied the denominator, we multiply the numerator. 1 x 10= 10

Therefore the answer is 10/30.

Answer:

c = 8.7 inches

Step-by-step explanation:

a^2 + b^2 = c^2

Substitute in the known values for a and b (the order doesn't matter):

(4.8)^2 + (7.3)^2 = c^2

multiply 4.8 times itself, 7.3 times itself:

23.04 + 53.29 = c^2

76.33 = c^2

Now find the square root of both sides of the equation (square root of c^2 = c):

8.736= c

It says round to the nearest tenth, so c = 8.7 inches

Answer:

search mo po sa goggle

Answer:

id k the first one

Simplify the expression (45y5y744y9)2 =

90[tex]y^{758}[/tex]

Answer:

y = 88

Step-by-step explanation:

y + 53 + 39 = 180

y + 92 = 180

y = 88

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

P=646

R=5%

T=2yrs

I=?

I=PRT/100

I= 646*5*2/100

I= 64.6

Step-by-step explanation:

Answer:

the answer is 100

Step-by-step explanation:

646 X 5 IS 3000

3000/5 is 600

and then round tenth so its 10

600/10 is 60

60 + 40 = 100 and there you go bravo

Answer:

[tex](3 \times 12) + (3 \times 3 \times 0.5)[/tex]

Step-by-step explanation:

answer is 40.5 . please like my answer and brainliest me HSHSSHSHS

Answer:

heyy guyss how r u all I'm Aditya from. India I've changed my server to Ireland is this Ireland

Step-by-step explanation:

and plss guyss fo llo w me

Answer:

12 more cleans

Step-by-step explanation:

You need to make each person have done work the same amount of time that is a multiple of 4 and 5. The closest is 20. So multiply 5 to 8 cleans for Ryan and 4 to 7 cleans for Issac. 40 cleans for Ryan - 28 cleans for Issac = 12 more cleans for RYAN, not Issac.

Answer:

42 multpliy by 6

Step-by-step explanation:

Sheldon bought 7 boxes of cookies if he spent $42 on cookies.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost of one box of cookies = $6.

And total amount spent by Sheldon on cookies = $42.

Let Sheldon bough x boxes of cookies.

To find the number of boxes of cookies x,

Use ratio property,

Cost of one box of cookies = $6

Cost of x boxes of cookies = $6x

Total price = 42

6x = 42

x = 7

The required number of boxes of cookies is 7.

To learn more about Ratio on :

https://brainly.com/question/13419413

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Answer:

0.5 or [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

1 taco is $4

Step-by-step explanation:

2t + 3d = 14              4t + 6d = 28

3t + 2d = 16              -9t -6d = -48

-5t = -20

t = 4

A tacos would cost $4.00.

Translating the word problem into an algebraic equation, we have;

[tex]2T \; + \; 3D = 14[/tex]   ......equation 1

[tex]3T \; + \; 2D = 16[/tex]   ......equation 2

To find how much a tacos cost, we would solve the above system of equations by using the substitution method.

From eqn 1, we would make D the subject of formula;

[tex]D = \frac {14 \; - 2T}{3}[/tex]  .....equation 3

Substituting eqn 3 into eqn 2, we have;

[tex]3T \; + \; 2(\frac {14 \; - 2T}{3}) = 16\\\\3T \; + \; \frac {28 \; - 4T}{3} = 16\\\\[/tex]

Lowest common multiple (LCM) = 3

[tex]\frac {9T \; + \; 28 \;- \; 4T}{3} = 16\\\\\\[/tex]

Cross-multiplying, we have;

[tex]9T \; + \; 28 \;- \; 4T = 16 \; * \; 3\\\\5T \; + 28 = 48\\\\5T = 48 \; - 28\\\\5T = 20\\\\T = \frac{20}{5} \\[/tex]

Tacos, T = $4.00

Therefore, the cost of a tacos is $4.00.

For more insight, visit: https://brainly.com/question/15257233

9514 1404 393

Answer:

  (a)  yes

Step-by-step explanation:

Put the numbers in for x and y and see if you get a true statement.

  5 ≤ 2(4) +1

  5 ≤ 9 . . . . . . true

The point is a solution.

Answer:

y=400(1.5)^4

Step-by-step explanation:

Answer:

3.24

Step-by-step explanation:

9 takes up 3.24 of 36%

Answer:

9 is 36% of 25

Step-by-step explanation:

36%×x=9

36/100×x=9

x=9×100/36

x=25

Answer:

The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.8}{2} = 0.1[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.1 = 0.9[/tex], so Z = 1.28.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.28\frac{1.5}{\sqrt{305}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 7.6 - 0.1 = 7.5

The upper end of the interval is the sample mean added to M. So it is 7.6 + 0.1 = 7.7

The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.

Answer:

140

Step-by-step explanation:

Here, we use BODMAS

12 x (3+2)² ÷ 2 - 10

12 x (5)² ÷ 2 - 10

12 x (5)² ÷ 2 - 10

12 × 25 ÷ 2 - 10

12 × 12.5 - 10

150 - 10 = 140

Thus, The answer is 140

-TheUnknownScientist

Answer:

5 seconds

Step-by-step explanation:

I did the same question a while ago.

Answer:

Step-by-step explanation:

28 : 50 and 15 : 30

14 : 25 and 1 : 2 are not equivalent