PLEASE HELP
If p(-3) = 18, how would you represent this as an ordered pair?

Answer:

1) x  =  [ - (12/1000)*  e∧ ( - 15/1000)*t  + 12/1000 ] /e∧ - (15/1000)*t

2) x =  - 0,012 * ( e ∧ 0.18 + 0,012 ) / e∧-0,18

Step-by-step explanation:

1.-Quantity of salt in the tank after t minutes

The rate  of change of the quantity of salt in the tank is:

dx(t) /dt   =  original quantity (0) + input quantity - output quantity  (1)

quantity = concentration* rate   Then

input quantity   =  0.04 Kg/lt * 5 Lt/min + 0.06 Kg/lt * 10Lt/min  =  0.2 Kg/min

+ 0.6  Kg/min  =  0,8 Kg/lt

output quantity =  Output concentration * rate of draining

rate of draining = 15 Lt/min

The input quantity and the output quantity occur at the same rate therefore the volume in the tank is constant  1000Lt.

output quantity = (x/1000 )*15

Plugging these values in equation (1) we get.

dx/dt  =  0,8  -  ( x/1000)* 15

The last one is a differential first-order equation like

x´ +  P(t)*x = q(t)

and the solution is:

x*μ   =  ∫ q(t)*μ*dt  + C

where    μ  is the integration factor   e ∧ ∫p(t)*dt

let´s call  b = -15/1000

μ = e ∧ ∫p(t)*dt  =  e∧∫ b*dt  =  e∧ b*t = e∧ ( -15/1000)*t

μ  =  e∧ - (15/1000)*t

Then  x*μ    =   x *  e∧ - (15/1000)*t

∫ q(t)*μ*dt  = ∫  0.8 * e∧ - (15/1000)*t*dt  =  0.8 * ∫ e∧bt * dt  

 ∫ q(t)*μ*dt  = 0.8 * ( 1/b ) e∧bt  = - 0,8 *( 15/1000) * e∧ ( - 15/1000)*t

∫ q(t)*μ*dt  = - (12/1000)*  e∧ ( - 15/1000)*t

x *  e∧ - (15/1000)*t  =   - (12/1000)*  e∧ ( - 15/1000)*t + C

Initial condition  t = 0  x = 0

0  =  - (12 / 1000 )* e⁰ = C

C = 12/1000

x *  e∧ - (15/1000)*t  =   - (12/1000)*  e∧ ( - 15/1000)*t  + 12/1000

x  =  [ - (12/1000)*  e∧ ( - 15/1000)*t  + 12/1000 ] /e∧ - (15/1000)*t

When t = 60 min

x =   [ - (12/1000)*  e∧ ( - 15/1000)*12 + 12/1000 ] / e∧ - (15/1000) * 12

x =  - 0,012 * ( e ∧ 0.18 + 0,012 ) / e∧-0,18

Answer:

(D) is equal to 8 so that means that u have to divide and multiply all in one

Answer:

Reflection

Step-by-step explanation:

Mean = 24.47

Variance = 108.31

Standard deviation = 10.41

The probability distribution table has been attached to this response.

(1) To calculate the mean (m)

(a) First multiply each of the values of x by their corresponding probability values.

This is shown in the third column of the table.

(b) The sum of the results in the third column gives the mean of the distribution. i.e

m = ∑xP(x) = 11.52 + 9.36 + 3.15 + 0.44

m = 24.47

(2) To calculate the variance (σ²).

(a) First find the square of the difference between the values of x and the mean (m) calculated in (1b) above. i.e

(x - m)²

The result is shown in the fourth column of the table.

(b) Next, multiply each of the results in the fourth column (x - m)², by their corresponding probability values P(X = x). i.e

(x - m)²(P(X = x))

The result is shown in the fifth column of the table.

(c) Now find the variance (σ²) which is the sum of the results in the fifth column. i.e

σ² = ∑(x - m)²(P(X = x)) = 42.5411 + 0.8427 + 18.8330 + 46.0923

σ² = 108.3091

σ² = 108.31      [to 2 decimal places]

(3) To calculate the standard deviation (σ)

The standard deviation is the square root of the variance of the distribution. Calculate this by finding the square root of the result in (2c) above.

σ = √σ²

σ = [tex]\sqrt{108.31}[/tex]

σ = 10.4072

σ = 10.41        [to 2 decimal places]

Answer:

sqrt(1^2 + 2^2)

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

75.7m^2

Step-by-step explanation:

[tex] \frac{30}{360} \times \pi {r}^{2} \\ \frac{30}{360} \times \frac{22}{7} \times {17}^{2} \\ \frac{1}{12} \times \frac{22}{7} \times 289 \\ 75.6904761905 = 75.7[/tex]

9514 1404 393

Answer:

  (c)  10 -N = 8 +N

Step-by-step explanation:

The difference between 10 and a number is (10 -N).

The sum of 8 and a number is (8 +N).

In this context, "is" means "equals," so we have ...

  10 -N = 8 +N

Answer:

π/2 + n*π

Step-by-step explanation:

All real numbers except π/2 + n*π

Answer:

Step-by-step explanation:

For some problems, stating the domain actually means to identify what x CANNOT be as opposed to what x IS. This occurs with tangent and cotangent functions along with rational functions.

As far as the tangent function goes, look at your unit circle. Your unit circle gives you 2 values for each angle, the first value reflects the cosine of the angle and the second value reflects the sine of the angle. This is because cosine is directly related to the x values and sine is directly related to the y values; cos goes into the "x" position and sin goes into the "y" position inside the brackets just like x and y go into parenthesis for coordinates. Anyway, a ratio is undefined if the denominator equals 0, right? And since tangent is the same as sin/cos, tangent is undefined when cos is 0. This occurs at [tex]\frac{\pi}{2}+k\pi[/tex] . That means that tangent does NOT exist at pi over 2 and every integer of pi you add in after. Let's look at a couple of examples of how that domain "works". Adding in an integer means adding in 1, 2, 3, etc. If the domain of tangent is undefined at [tex]\frac{\pi}{2}+k\pi[/tex], then let's let k = 1, and

[tex]\frac{\pi}{2}+1\pi=\frac{\pi}{2}+\frac{2\pi}{2}=\frac{3\pi}{2}[/tex] . Now let k = 2:

[tex]\frac{\pi}{2}+2\pi=\frac{\pi}{2}+\frac{4\pi}{2}=\frac{5\pi}{2}[/tex]. Now let k = 3:

[tex]\frac{\pi}{2}+ 3\pi=\frac{\pi}{2}+\frac{6\pi}{2}=\frac{7\pi}{2}[/tex]. And it continues like that.

You can see when you graph the tangent function in radian mode on your calculator that these values where tangent is undefined show up as asymptotes. Use your unit circle and your graphs to determine the domain of trig functions.

Answer:

-24 feet

Step-by-step explanation:

Boat is 4 feet above sea level => +4 feet

She descends 28 feet => -28 feet

Position = +4-28 = -24 feet

Therefore,

Gemma is 24 feet below the sea level

Answer:

-24 feet

Step-by-step explanation:

Because she is 4 feet above sea level, she can descend 4 feet to be at sea level. Now she only has to descend 24 feet below sea level, which is -24 feet.

Answer:

1.14male studying biology

Answer:

2 1/2

Step-by-step explanation:

4 7/8= 39/8

2 2/8= 19/8

39/8 - 19/8 = 20/8 = 2 4/8 = 2 1/2

Answer:

32

Step-by-step explanation:

40 = 100%

how many are 80% ?

well, 80% = 80× 1%

1% = 100% / 100

so, in our case

80% = 80×40/100 = 8×4 = 32

as a shortcut you consider a percentage x as a ratio factor of x/100 you multiply the 100% number with.

in our case

80% = 40 × 80/100 = 32

Answer:

The answer is

[tex]2 {x}^{2} + 3x - 1 = 0[/tex]

Why? Below I explain

Step-by-step explanation:

That formula has three variables a, b and c.

So, a = 2, b = 3 and c = -1

Because the formula is written like

[tex] \frac{ - b + - \sqrt{ {b}^{2} - 4 \times a \times c} }{2 \times a} [/tex]

Answer: Fran's speed while swimming​ upstream = 1.4 km/h

Step-by-step explanation:

Given: Fran's swimming speed = 2.1 ​km/h

Speed of river = 0.7 km/h

The direction against the stream is called upstream.

Speed in Upstream = Fran's swimming speed - Speed of river

= 2.1-0.7  km/h

= 1.4 km/h

hence, Fran's speed while swimming​ upstream = 1.4 km/h

Answer:

SAS

Step-by-step explanation:

AC ≅ EC (Given), ∠ACB ≅∠ECD ( Vertical Angles), and BC ≅ DC

Answer:

it says round to the nearest 10th so it wouldn't be 81, it would be 81.8%

Answer:

The plane travelled for [tex]\text{$2$ hours}[/tex] at an average of speed [tex]120\; \rm mph[/tex] and [tex]\text{$3$ hours}[/tex] at an average speed of [tex]130\; \rm mph[/tex].

Step-by-step explanation:

Let [tex]x[/tex] denote the number of hours that the plane travelled at an average speed of [tex]120\; \rm mph[/tex].

Given that the trip is [tex]5\; \text{hours}[/tex] long in total, the plane would have travelled at an average speed of [tex]130\; \rm mph[/tex] for [tex](5 - x)\; \text{hours}[/tex].

The plane would have travelled [tex]120\, x[/tex] miles after [tex]x\; \text{hours}[/tex] at an average speed of [tex]120\; \rm mph[/tex]. Likewise, the plane would have travelled [tex]130\, (5 - x)\; \text{miles}[/tex] after [tex](5 - x)\; \text{hours}[/tex] at an average of [tex]130\; \text{mph}[/tex].

The plane has travelled [tex]630\; \text{miles}[/tex] in total. In other words:

[tex]120\, x + 130\, (5 - x) = 630[/tex].

Solve this equation for [tex]x[/tex]: [tex]x = 2[/tex].

In other words, the plane has travelled for [tex]\text{$2$ hours}[/tex] at an average of speed [tex]120\; \text{mph}[/tex]. It would have travelled for [tex](5 - x)\; \text{hours} = (5 - 2)\; \text{hours} = 3 \; \text{hours}[/tex] for the other part of the trip (at an average speed of [tex]130\; \text{mph}[/tex].)

closer to, shorter, longer.  (T=A^1.5

just took the assigniment.

Answer:

So, their orbital periods are than Earth's orbit. The further a planet is from the sun, the its orbit is.

Step-by-step explanation:

Even though Venus is farther from the sun than mercury, Venus's surface is hotter than Mercury's because Venus has a carbon dioxide atmosphere that traps the sun's heat.

Answer:

B. √2^5

Step-by-step explanation:

(2^½. 2^¾)²

= 2¹ . 2^(1½)

= 2^(2½)

= 2^(5/2)

=√2^5

Answer:

m(arc CD) = 112°

Step-by-step explanation:

Use the property of intersecting chords and angles between these chords,

m∠CED = [tex]\frac{1}{2}(\text{arc CD}+\text{arc}AB)[/tex]

m∠CED + m∠AED = 180°

80° + m∠CED = 180°

m∠CED = 100°

Now substitute the measure of angle CED and arc AB in the expression,

100° = [tex]\frac{1}{2}(88^{\circ}+\text{arc CD})[/tex]

200° = 88° + m(arc CD)

m(arc CD) = 112°

Answer:

x = -3

Step-by-step explanation:

2x – 3(x + 8) = -21

Distribute

2x - 3x - 24 = -21

Combine like terms

-x - 24 = -21

Add 24 to both sides

-x = 3

Multiply both sides by -1

x = -3

Given:-

To find:-

Answer:-

Mass defect arises when the mass of the atom differs from the sum of masses of nucleons . As we know that the nucleus of an atom is made up of neutrons(n) and protons (p) , and the total mass of a atom is the mass of nucleons ( protons and neutrons ) as electrons have mass very low as compared to that of n or p .

If we denote mass number by [tex]\green{A}[/tex] , then ;

[tex]\implies A = n_{\rm neutrons} + n_{\rm protons} [/tex]

Let [tex] Z[/tex] be the atomic number, then ;

[tex]\implies n_p = Z [/tex]

So, the number of neutrons will be;

[tex]\implies n_n = (A-Z) [/tex]

Therefore total mass would be ;

[tex]\implies M = m_pZ +m_n (A-Z) [/tex]

Then the mass defect would be ,

[tex]\implies\underline{\underline{\green{ \Delta M = [Zm_p + (A-Z)m_n - M ] }}} [/tex]

where ,

_______________________________________

Now we know that the Atomic number of Nitrogen is 7(Z) and its mass number is 14(A) .

Now substitute the respective values,

[tex]\implies \Delta M = 7(1.007825) + (14-7)1.008665 - 14.0031 \\ [/tex]

[tex]\implies \Delta M = 7.054775 + 7(1.008665) - 14.00 31 [/tex]

[tex]\implies \Delta M = 7.054775 + 7.060655 - 14.0031 [/tex]

[tex]\implies \Delta M = 14.11543 - 14.0031 [/tex]

[tex]\implies \underline{\underline{\green{ \Delta M = 0.11233 \ u }}}[/tex]

Hence the mass defect is 0.11233 u .

Also this mass defect appears as energy which is responsible for the binding of nucleons together.

and we are done!

Answer:

The answer is D. 22 square feet

Answer:

D

Step-by-step explanation:

3(2) + 8(2) = 22 sq ft

Answer:

3q + 2p =

Step-by-step explanation:

Perimeter refers to the outside lines only so hence, 3q + 2p =

Answer:

17

Step-by-step explanation:

_____________ Hair color

Eye color ___ Brown ___ Black ___ total

Green _____ 22 ________ 15 ____ 37

Blue _______ 18 ________ 19 ____ 37

Total _______40 ________34 ____ 74

Calculate the expected frequency of Blue Eyes and Black Hair?

The expected frequency Count ;

(row total * column total) / total number of observations

Expected frequency ;

Blue eye n black hair = (37 * 34) / 74

Expected frequency count = 1258 / 74 = 17

Expected count = 17

Answer:

The row total of blue eyes is 18 + 19 = 37.

The column total of black hair is 15 + 19 = 34.

The total of the whole table is 22 + 15 + 18 +19 = 74.

Step-by-step explanation:

E=(37)(34)/74=1258/74=17

=====================================================

Explanation:

Set the expression equal to 100 and get everything to one side

[tex]d^2 - 12d + 45 = 100\\\\d^2 - 12d + 45 - 100 = 0\\\\d^2 - 12d - 55 = 0\\\\[/tex]

Now use the quadratic formula. We'll plug in a = 1, b = -12, c = -55.

[tex]\ d = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\ d = \frac{-(-12)\pm\sqrt{(-12)^2-4(1)(-55)}}{2(1)}\\\\\ d = \frac{12\pm\sqrt{364}}{2}\\\\\ d \approx \frac{12\pm19.07878403}{2}\\\\\ d \approx \frac{12+19.07878403}{2}\ \text{ or } \ d \approx \frac{12-19.07878403}{2}\\\\\ d \approx \frac{31.07878403}{2}\ \text{ or } \ d \approx \frac{-7.07878401}{2}\\\\\ d \approx 15.53939201\ \text{ or } \ d \approx -3.53939201\\\\d \approx 15.54 \ \text{ or } \ d \approx -3.54[/tex]

We'll ignore the negative d value as we can't have a negative number of days.

This means d = 15.54 is the only approximate solution we'll consider.

If we plugged in d = 15, then,

d^2 - 12d + 45

(15)^2 - 12(15) + 45

90

This tells us that 90 masks were sold on day d = 15.

Now try d = 16

d^2 - 12d + 45

(16)^2 - 12(16) + 45

109

We see that 109 masks were sold on day d = 16. Somewhere between those days, 100 masks were sold. At the end of the 15th day, we got to 90. So in the middle of day 16 is when we reach the exact 100 mark we're after.

In short, we would round d = 15.54 up to d = 16 so that we clear the hurdle.

In other words, if you rounded d = 15.54 to d = 15, then you'd be 10 masks short of the goal. Besides, 15.54 rounds to 16 when rounding to the nearest whole number.

Answer:

g(-1 )=-1 and g(2)+g(1)=7

Step-by-step explanation:

If g(x) = x^3+x^2-x-2 find g(-1)

if we find g(-1)

we substitute all the x's in the function with -1

-1^3+-1^2-(-1)-2

-1^3 = -1

-1^2 = 1

-1+1+1-2

(two minuses make a plus)

-1+1 = 0

0+1 = 1

1-2 = -1

if x=-1, g(-1) is -1

g(2)+g(1)

substitute the x's in the function with 2 and 1 and add your results

2^3+2^2-2-2

2^3 = 8, 2^2 = 4

8+4-2-2

8+4= 12, 12-2 = 10, 10-2 = 8

g(2)=8

g(1) now

1^3 + 1^2-1-2

1^3=1, 1^2 = 1

1+1-1-2

1+1 = 2, 2-1 = 1, 1-2 = -1

g(3) = -1

g(2) (which equals 8) + g(3) (which equals -1) =

8+(-1) = 7

g(2)+g(3)=7

Answer:

26=x

Step-by-step explanation:

-15 from both sides

3x=78 /:3

x=26

Answer:

It depends on what shape you have. Here are some formulas for different shapes.

Step-by-step explanation:

Rectangular prism: 2lw + 2lh + 2wh

Cylinder: 2 pi r² + 2 pi rh

Sphere: 4 pi r²

Cone: pi r² + pi rl

Square-based pyrimid: 1/2lp +B

I hope this helps!

Answer:

y = -4x + 14

Step-by-step explanation:

using the slope intercept form of a line

y = mx + c

Given points

slope (m) =

[tex] = \frac{y2 - y1}{x2 - x1} \\ = \frac{2 - 10}{3 - 1} \\ = \frac{ - 8}{2} \\ = - 4[/tex]

taking one point as for filling x and y and finding the y intercept (c)

y =mx + c

10 = (-4) × 1 + c

10 + 4 = c

14 = c

therefore the equation is

y = -4x + 14

Answer:

2y + 8x = 28

Step-by-step explanation:

Hi there

So we are going to solve this together

m = y - y1/y2- y1 =x - x1/x2 - x1

y - 10/ 2- 10 =x - 1/ 3 -1

y -10/-8 =x - 1/2

cross multiply

2(y - 10) =-8(x -1)

2y - 20= -8x + 8

Collect terms

2y +8x = 8 +20

ANSWER = 2y + 8x = 28

Hope this helps you!

Bye , have a nice day :-)