Please help me with this question

Answer:

The total amount of pollution discharged during the first 7 years of operation is 1.955 tons

Step-by-step explanation:

Given

[tex]r(t) = \frac{t}{t^2 + 1}[/tex]

Required

The total amount in the first 7 years

This implies that:

[tex]r(t) = \frac{t}{t^2 + 1}; [0,7][/tex]

The total amount is calculated by integrating r(t) i.e.

[tex]v = \int\limits^a_b {r(t)} \, dt[/tex]

So:

[tex]v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt[/tex]

--------------------------------------------------------------

We have:

[tex]t^2 + 1[/tex]

Differentiate

[tex]d(t^2 + 1) = 2t[/tex]

Rewrite as:

[tex]2t = d(t^2 + 1)[/tex]

Solve for t

[tex]t = \frac{1}{2}d(t^2 + 1)[/tex]

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So:

Make t the subject

[tex]v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt[/tex]

[tex]v = \int\limits^7_0\frac{1}{2}* {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt[/tex]

[tex]v = \frac{1}{2}\int\limits^7_0 {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt[/tex]

Integrate

[tex]v = \frac{1}{2}\ln(t^2 +1)|\limits^7_0[/tex]

Expand

[tex]v = \frac{1}{2}[\ln(7^2 +1) - \ln(0^2 +1)][/tex]

[tex]v = \frac{1}{2}[\ln(50) - \ln(1)][/tex]

[tex]v = \frac{1}{2}[3.91 - 0][/tex]

[tex]v = \frac{1}{2}[3.91][/tex]

[tex]v = 1.955[/tex]

Answer:

1/2

Step-by-step explanation:

Given the equation

6/12 = x/8

We are to find the proportion

Cross multiply

12 * x  = 8 * 6

12x = 48

x = 48/12

x = 4

Hencethe value of x is 4

Substitute into the expression to get the proportion

6/12 = 4/8

In its lowest term;

6/12 = 4/8 = 1/2

Hence the required proportion is 1/2

Answer:

plot ur x,y coordinates as (0,-8) (1,-8)

Answer:

The first and third set

Step-by-step explanation:

Because no two inputs can have different outputs

Answer:

p = 4

Step-by-step explanation:

Given the expression x ^ 2-px + 3 = 0

If x = 0 is a solution

Substitute into the expression

0² - 0p + 3  = 0

-0p = -3

p = 3/0

p cannot be determined for this root

If x = 1

1² - 1p + 3 =0

1 - p + 3 = 0

-p+4 = 0

-p = -4

p = 4

Hence the va;ue of p is 4

Find 7% of 5000 students ?

Answer :

[tex]5000 \times \frac{7}{100} = 350[/tex]

So, 7% of 5000 students is 350 students.

Answer:

42.05 HRS

Step-by-step explanation:

D = R x T ..... D=765 MILES R= 95 MILES/HR WE HAVE TO SOLVE FOR T BECAUSE THE QUESTIONS ASKS "HOW LONG.." T = D/R AND THEN SUBSTITUTE THE DISTANCE AND RATE ;)

Answer:

0.273 = 27.3% probability that she was late on Thursday.

Step-by-step explanation:

On time on Monday, late on Thursday:

Possible outcomes (tuesday-wednesday-thursday).

on time(0.7 probability) - on time(0.7 probability) - late(0.3 probability)

on time(0.7 probability) - late(0.3 probability) - late(0.2 probability)

late(0.3 probability) - on time(0.8 probability) - late(0.3 probability)

late(0.3 probability) - late(0.2 probability) - late(0.2 probability).

What is the probability she was late on Thursday?

Sum of these four outcomes. So

[tex]p = 0.7*0.7*0.3 + 0.7*0.3*0.2 + 0.3*0.8*0.3+0.3*0.2*0.2 = 0.273[/tex]

0.273 = 27.3% probability that she was late on Thursday.

Answer: The range for the distribution = 30

Step-by-step explanation:

The range of the distribution is computed as :

Range = Highest data value - Lowest data value

Given, the IQs of all students at a certain prep school were obtained. The highest was 135, and the lowest was 105.

Thus, Range = 135-105  (difference between highest and lowest value)

Range = 30

Therefore,  the range for the distribution = 30

Answer:

Solution given:

The opposite of -1.5 is 1.5

note:

Just multiply by - or change its sigh .

Step-by-step explanation:

Insufficient information!

however, volume will remain same in both of these figures!

Answer:

18o rotational symetry  

Step-by-step explanation:

Answer: Volume is 4308.1 in³

Step-by-step explanation: Volume is  pii· r²·h = 3.14 · (14 in)²·7 in

Answer:

<V = 40

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

20x = 60+7x+5

Combine like terms

20x = 7x+65

Subtract 7x from each side

20x -7x = 7x+65-7x

13x = 65

Divide each side by 13

13x/13 = 65/13

x = 5

<v = 7x+5 = 7*5+5 = 35+5 = 40

Answer:

C. g(x) + (-3x + 1)2

Step-by-step explanation:

did the test for it

Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100......

Step-by-step explanation:

This is a list of perfect squares.

1 is the square of 1. ( 1 x 1 = 2)

4 is the square of 2. (2 x 2 = 4)

9 is the square of 3. (3 x 3 = 9)

So, the next number would be the square of 4 which is 16 ( 4 x 4)

And so on.

Answer:

The line of best fit will look like this (see attatchement):

The total amount of money earned in tips after working 12 hours is $120.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given coordinate points are (8, 80) and (2, 20).

Here, slope (m) = (20-80)/(2-8)

= 10

Substitute m=10 and (x, y)=(8, 80) in y=mx+c, we get

80=10×8+c

c=0

So, the equation of a line is y=10x

Here, x=12

Then, y=120

Therefore, the total amount of money earned in tips after working 12 hours is $120.

To learn more about the equation of a line visit:

https://brainly.com/question/2564656.

#SPJ7

Answer: 2n^2 + 16n + 32

Step-by-step explanation:

Distribute 2 to all the terms inside parentheses.

2 (n^2 + 8n + 16)

2n^2 + 16n + 32

Hope this helped!

Answer:

f(g(2)) = 44

Step-by-step explanation:

g(2) = 3(2) + 1 = 7

Plug 7 into f(x) since g(2) = 7

f(7) = 7² - 5 = 44

f(g(2)) = 44

Answer:

[tex]21^{\circ}[/tex]

Step-by-step explanation:

The Law of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex] and works for every triangle.

Substituting given values, we have the following equation:

[tex]\frac{\sin 68^{\circ}}{18}=\frac{\sin C}{7}, \\\\\sin C=\frac{7\sin 68^{\circ}}{18},\\\\C=\sin^{-1}(0.36057149899),\\\\C\approx \boxed{21^{\circ}}[/tex]

*Note that because [tex]\sin \theta=\sin(180-\theta)[/tex], when solving for an angle with the Law of Sines, there may be two answers. However, since the problem designates angle C as an acute angle, the other angle is negligible.

Answer:

2x+30 = 90

Step-by-step explanation:

The two angles are complementary so they add to 90 degrees

2x+30 = 90

Answer:

2x+30 = 90° is the required equation.

Step-by-step explanation:

We see that, the angle formed in the image is 90°, so by adding in the angles inside it, we get 90

hope it helps :)

mEDF = 124°

Steps

360 = 146 + 90 + x

360 = 236 + x

-236 -236

124 = x

Answer:

m(EDF) = 214°

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

SOLUTION :-

According to the figure given in question ; in the orange circle ,

m(minor FE) + m(minor DE) + m(minor FD) = 360°

⇒ 146° + 90° + m(minor FD) = 360°

⇒ m(minor FD) = 360° - 236° = 124°

∴ m(major FE) [or] m(EDF) = m(minor DE) + m(minor FD) = 90° + 124° = 214°

Answer:

Step-by-step explanation:

2

Answer:

a)  P (COO)  = 0,135

b) P ( SISI) = 0,00015

Step-by-step explanation:

a) the probability of an ion channel in open position is 50 %   0,5

   the probability of an ion channel in close position is 50 %   0,5

probability for the following sequence of states COO

to be closed   0,5    (C)

from (C) to pass to open  0,3  (O)

and to stay O  is 0,9

Then the probability of the sequence of states COO is

P (COO)  = 0,5 * 0,3 * 0,9  

P (COO)  = 0,135

b) If people are either infected or susceptible, then

Probability of an individual infected is  0,5

Probability of an individual susceptible  is 0,5

to pass from susceptible to infected is 0,05

to pass from infected to susceptible is 0,12

then

P ( SISI) = 0,5 * 0,05*0,12*0,05

P ( SISI) = 0,00015

probability for the following sequence of states COO

9514 1404 393

Answer:

  coterminal angle: 98°

  reference angle: 82°

Step-by-step explanation:

Adding 360° × 3 = 1080° brings the angle into the range 0-360°.

The coterminal angle is -982 +1080° = 98°

This is a 2nd-quadrant angle. The reference angle is 180° -98° = 82°.

I'm going to refer to the two separate triangles in this problem by their missing angles. So the smaller triangle is triangle 1, and the larger triangle is triangle 2.

Let's work on triangle 1 first.

We can easily find the supplementary angle to the 115 degree angle in the middle there, which is in triangle 1.

180 - 115 = 65

Now that we know two of the angles in the triangle, and we know that the sum of the interior angles in a triangle is 180, we can find our missing angle 1.

80 + 65 + <1 = 180

145 + <1 = 180

<1 = 35 degrees

Now let's go ahead and move on to triangle 2.

We can again find the supplementary angle to the 115 degree angle in the middle there, which is in triangle 2 also.

180 - 115 = 65

Then, we can use the same principle as we did with triangle 1 to find our missing angle 2 in triangle 2.

85 + 65 + <2 = 180

150 + <2 = 180

<2 = 30 degrees

Hope this helps!! :)

Answer:

6 x 32 = 192 divided by 6 = 34

Step-by-step explanation:

Answer:

20 plus 20 is equla to 5000