The value of x that will make L and M

Answer:

b = -4

Step-by-step explanation:

Well we already have m which is slope which is -1.

And if we start at (-2,-2) and go down using the slope we get -4 as the y intercept or b.

Thus,

-4 is the y intercept or b.

Hope this helps :)

Answer:

b = -4.

Step-by-step explanation:

In this case, y = -2, m = -1, and x = -2.

-2 = (-1) * (-2) + b

-2 = 2 + b

b + 2 = -2

b = -4

Hope this helps!

Answer:

  a) -900 L/min

  b) 63000 L

  c) v = -900t +63000

  d) 7200 L

Step-by-step explanation:

a) You are given two points on the curve of volume vs. time:

  (t, v) = (20, 45000) and (70, 0)

The rate of change is ...

  Δv/Δt = (0 -45000)/(70 -20) = -45000/50 = -900 . . . . liters per minute

__

b) In the first 20 minutes, the change in volume was ...

  (20 min)(-900 L/min) = -18000 L

So, the initial volume was ...

  initial volume -18000 = 45000

  initial volume = 63,000 . . . . liters

__

c) Since we have the slope and the intercept, we can write the equation in slope-intercept form:

  v = -900t +63000

__

d) Put the number in the equation and do the arithmetic.

When t=62, the amount remaining is ...

  v = -900(62) +63000 = -55800 +63000 = 7200

7200 L remain after 62 minutes.

The correct answer is B. 40,320

Explanation:

In mathematics, a permutation refers to all the possible ways of arranging objects or elements in a set, while still considering an order. For example, you can calculate all the possible ways 5 athletes can end in a race as one athlete cannot have both the first and third place. The expression [tex]{8}[/tex][tex]P_{7}[/tex] shows a permutation because the P indicates the expression refers to a permutation. Additionally, this can be solved by using the formula [tex]{n}[/tex][tex]P_{r}[/tex]  =[tex]\frac{n!}{(n-r)!}[/tex]. This means, in the expression presented n = 8 while r = 7. Also, the symbol (!) indicates the number should be multiplied using all whole numbers minor to the given number until you get to 1, which is known as factorial functions. The process is shown below:

[tex]{8}[/tex][tex]P_{7}[/tex] = [tex]\frac{8 x 7 x 6 x 5 x 4 x 3 x 2 x 1}{1}[/tex]   or  8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 1

[tex]{8}[/tex][tex]P_{7}[/tex] = 40320

Answer:

24 ways.

Step-by-step explanation:

In this case, you just need a factorial.

For the first seat, you have 4 students you can place.

For the second seat, you have 3 students.

For the third, you have 2.

For the fourth, you have 1.

So, you can arrange the students by doing 4 * 3 * 2 * 1 = 12 * 2 = 24 ways.

Hope this helps!

Answer:

Explantation:

First seat: 4 seats

Second seat: 3 seats

Third: 2 seats

Fourth seat: 1 seat remaining

4 * 3 * 2 * 1 = 12 * 2 * 1 = 24 * 1 = 24

Answer:

Celcius=( farenheit -32)*5/9

Celcius temperature is= 428.3333°

Step-by-step explanation:

To convert for farenheit to celcius

Celcius=( farenheit -32)*5/9

To calculate a temperature from celcius to farenheit we multiply by 9/5 and then add 32.

Let x be the celcius temperature

X(9/5) + 32 = 803°

X(9/5) = 803-32

X(9/5) = 771

X=( 771*5)/9

X= 3885/9

X= 428.3333

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Answer: cross-sectional study

Step-by-step explanation:

Here, A research company uses a device to record the viewing habits of about 2500 ​households (that includes different persons such as adults , children and seniors )

The data collected today(at a single point in time).

If it is used to determine the proportion of households tuned to a particular children's children's program.

The type of observational study is described in the problem​ statement : "cross-sectional"

Answer:

Step-by-step explanation:

Let

T = number of trees

A = number of acorns

Given:

A =  18T + 4 ...........................(1)

A = 20T -4 .........................(2)

Equate A from (1) and (2)

20T-4 = 18T+4

simplify and solve for T

20T - 18T = 4+4

2T = 8

T = 4 trees

A = 18T + 4 = 72+4 = 76 acorns, or

A = 20T - 4 = 80 - 4 = 76 acorns.

Answer:

I. 60%

II. 75.4 kg

Step-by-step explanation:

We will use the z-scores and the standard normal distribution to answer this questions.

We have a normal distribution with mean 69 kg and variance 25 kg^2 (therefore, standard deviation of 5 kg).

I. What percentage of adult male in Boston weigh more than 72 kg?

We calculate the z-score for 72 kg and then calculate the associated probability:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{72-69}{5}=\dfrac{3}{5}=0.6\\\\\\P(X>72)=P(z>0.6)=0.274[/tex]

II.  What must an adult male weigh in order to be among the heaviest 10% of the population?

We have to calculate tha z-score that satisfies:

[tex]P(z>z^*)=0.1[/tex]

This happens for z=1.28 (see attachment).

Then, we can calculate the weight using this transformation:

[tex]X=\mu+z^*\cdot\sigma=69+1.28\cdot 5=69+6.4=75.4[/tex]

Answer:

1/5 if a kilometer

Step-by-step explanation:

Since it was 1/60 of a kilometer which is 0.0166 of the kilometer.

So In 12 minutes he would cover 0.2 of the kilometer which is 1/5

The distance Olivia swims in 2 minutes is 1/30 km.

Given,

It takes Olivia one minute to swim 1/60 of a kilometer.

We need to find out how far can she swim in 12 minutes.

Suppose if we have,

3 items cost = $9

Cost of one item = $9 / 3 = $3

If in 5 minutes one can walk for 1km

In 10 minutes one can walk:

= (10/5 x 1) km

= 2 km

Find the distance Olivia swims in one minute.

= 1/60 km

Find the distance Olivia swims in 2 minutes.

We have,

1 minute = 1/60 km

Multiply both sides by 2.

2 x 1 minute = 2 x 1/60 km  

2 minutes = 1/30 km

Thus the distance Olivia swims in 2 minutes is 1/30 km.

Learn more about how to find out how much time will it take to skate thirty laps here:

https://brainly.com/question/11339718

#SPJ2

Answer:

4.5 ×1000 =4500m

Step-by-step explanation:

450/1000=0.45km

Answer: 10 : 1

Step-by-step explanation: Now first let’s convert this to the same units, for instance, the SI unit for length meters. 4.5 x 1000 = 4500m. Then put the ratio 4500m : 450m. You can divide 4500 by 450 as it is divisible so you get 10 as the answer.

Even if you have converted them to kilometers before, nevermind, still 4.5 divide by 0.45 is 10 and there the answer is 10 : 1 or shortly the ratio is just 10.

Answer:

work is shown and pictured

Answer:

A) P(A|B) = 0.01966

B) P(A'|B') = 0.99944

Step-by-step explanation:

A) We are told that A is the event "the person is infected" and B is the event "the person tests positive".

Thus, using bayes theorem, the probability that the person is infected is; P(A|B)

From bayes theorem,

P(A|B) = [P(A) × P(B|A)]/[(P(A) x P(B|A)) + (P(A') x P(B|A'))]

Now, from the question,

P(A) = 1/400

P(A') = 399/400

P(B|A) = 0.8

P(B|A') = 0.1

Thus;

P(A|B) = [(1/400) × 0.8)]/[((1/400) x 0.8) + ((399/400) x (0.1))]

P(A|B) = 0.01966

B) we want to find the probability that when a person tests negative, the person is not infected. This is;

P(A'|B') = P(Not infected|negative) = P(not infected and negative) / P(negative) = [(399/400) × 0.9)]/[((399/400) x 0.9) + ((1/400) x (0.2))] = 0.99944

Answer:

-1.946 ; C

Step-by-step explanation:

Here, we want to identify the value of the z-statistic

Mathematically;

z = (x -mean)/SD/√n

Thus we have ;

Z = (11.58-12)/1.93/√80

z = -1.946

Answer:

((23GM)

Step-by-step explanation:

it goes for this because 23gm = 40pm

Answer:

45 min

Step-by-step explanation:

Here,

the we take the work as W and Alan's speed as A and Zack's speed as Z.

A = 2Z

W = 30 ( A+Z)

if the time for Alan to done cleaning alone is t then t = W ÷ A

t = ( 30 (A+(A÷2)))÷ A

t = 45 min

I am done .

Answer:

the dimensions that will minimize the cost of constructing the box is:

a = 5.8481  in ;   b = 5.848 in  ; c = 10.234 in

Step-by-step explanation:

From the information given :

Let a be the base if the rectangular box

b to be the height and c to be the  other side of the rectangular box.

Then ;

the area of the base is ac

area for the front of the box is ab

area for the remaining other sides   ab + 2cb

The base of the box is made from a material costing 8 ac

The front of the box must be decorated, and will cost 10 ab

The remainder of the sides will cost 4 (ab + 2cb)

Thus ; the total cost  C is:

C = 8 ac + 10 ab + 4(ab + 2cb)

C = 8 ac + 10 ab + 4ab + 8cb

C = 8 ac + 14 ab + 8cb   ---- (1)

However; the volume of the rectangular box is V = abc = 350 in³

If abc = 350

Then b = [tex]\dfrac{350}{ac}[/tex]

replacing the value for c in the above equation (1); we have :

[tex]C = 8 ac + 14 a(\dfrac{350}{ac}) + 8c(\dfrac{350}{ac})[/tex]

[tex]C = 8 ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]

Differentiating C with respect to a and c; we have:

[tex]C_a = 8c - \dfrac{2800}{a^2}[/tex]

[tex]C_c = 8a - \dfrac{4900}{c^2}[/tex]

[tex]8c - \dfrac{2800}{a^2}=0[/tex] --- (2)

[tex]8a - \dfrac{4900}{c^2}=0[/tex]   ---(3)

From (2)

[tex]8c =\dfrac{2800}{a^2}[/tex]

[tex]c =\dfrac{2800}{8a^2}[/tex] ----- (4)

From (3)

[tex]8a =\dfrac{4900}{c^2}[/tex]

[tex]a =\dfrac{4900}{8c^2}[/tex]   -----(5)

Replacing the value of a in 5 into equation (4)

[tex]c = \dfrac{2800}{8*(\dfrac{4900}{8c^2})^2} \\ \\ \\ c = \dfrac{2800}{\dfrac{8*24010000}{64c^4}} \\ \\ \\ c = \dfrac{2800}{\dfrac{24010000}{8c^4}} \\ \\ \\ c = \dfrac{2800*8c^4}{24010000} \\ \\ c = 0.000933c^4 \\ \\ \dfrac{c}{c^4}= 0.000933 \\ \\ \dfrac{1}{c^3} = 0.000933 \\ \\ \dfrac{1}{0.000933} = c^3 \\ \\ 1071.81 = c^3\\ \\ c= \sqrt[3]{1071.81} \\ \\ c = 10.234[/tex]

From (5)

[tex]a =\dfrac{4900}{8c^2}[/tex]   -----(5)

[tex]a =\dfrac{4900}{8* 10.234^2}[/tex]

a = 5.8481

Recall that :

b = [tex]\dfrac{350}{ac}[/tex]

b = [tex]\dfrac{350}{5.8481*10.234}[/tex]

b =5.848

Therefore ; the dimensions that will minimize the cost of constructing the box is:

a = 5.8481  in ;   b = 5.848 in  ; c = 10.234 in

The dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches and this can be determined by using the given data.

Given :

According to the given data the total cost is given by:

C = 8ac + 14ab + 8cb   --- (1)

The volume of the rectangular box is (V = abc = 350 inch cube). So, the value of b is given by:

[tex]\rm b = \dfrac{350}{ac}[/tex]

Now, substitute the value of 'b' in the equation (1).

[tex]\rm C = 8ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]

First differentiating the above equation with respect to c.

[tex]\rm C_c = 8a-\dfrac{4900}{c^2}[/tex]   --- (2)

Now, differentiating the above equation with respect to a.

[tex]\rm C_a = 8c-\dfrac{2800}{a^2}[/tex]    --- (3)

Now, equate equation (2) and equation (3) to zero.

From equation (2):  

[tex]\rm a=\dfrac{4900}{8c^2}[/tex]    ----- (4)

From equation (3):

[tex]\rm c=\dfrac{2800}{8a^2}[/tex]   ----- (5)

Now, from equations (4) and (5).

[tex]\rm c = \dfrac{2800}{8\left(\dfrac{4900}{8c^2}\right)^2}[/tex]

Now, simplifying the above expression in order to get the value of c.

c = 10.234

Now, put the value of 'c' in equation (5) in order to get the value of 'a'.

a = 5.8481

The value of 'b' is given by:

[tex]\rm b = \dfrac{350}{5.8481\times 10.234}[/tex]

b = 5.848

So, the dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches.

For more information, refer to the link given below:

https://brainly.com/question/19770987

Answer:

Option C.

Step-by-step explanation:

We have to see the common things we have in both graphs and express them:

1. There is a value x=a≠0, where g(a)=f(a)=0

2. The slope of g(x) is of opposite sign of the slope of f(x). Then f(x)=m*g(cx) with m<0.

3. The slope of f(x) seems to be higher than the slope of g(x)

A. As the slopes are different, this is not adequate.

B. As the slopes are different, this is not adequate.

C. This can be adequate, as it applies to all the observations we have made.

D. This is not adequate because f(0)≠g(-2*0).

The only adequate option then is C.

Answer:

The fraction that this is true for = 7/13

Step-by-step explanation:

From the above question

Let the numerator be represented by a

Let the denominator be represented by b

If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3

This means:

a + 5/b + 5 = 2/3

Cross Multiply

3(a + 5) = 2(b + 5)

3a + 15 = 2b + 10

Collect like terms

3a - 2b = 10 - 15

3a - 2b = -5..........Equation 1

If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4

This means:

a - 5/b - 5 = 1/4

Cross Multiply

4(a - 5) = 1(b - 5)

4a - 20 = b - 5

Collect like terms

4a - b = 20 - 5

4a - b = 15..........Equation 2

b = 4a - 15

3a - 2b = -5..........Equation 1

4a - b = 15..........Equation 2

Substitute 4a - 15 for b in equation 1

3a - 2b = -5..........Equation 1

3a - 2(4a - 15) = -5

3a - 8a + 30 = -5

Collect like terms

3a - 8a = -5 - 30

-5a = -35

a = -35/-5

a = 7

Therefore, the numerator of the fraction = 7

Substitute 7 for a in Equation 2

4a - b = 15..........Equation 2

4 × 7 - b = 15

28 - b =15

28 - 15 = b

b = 13

The denominator = b is 13.

Therefore,the fraction which this is true for = 7/13

To confirm

a) If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3

This means:

a + 5/b + 5 = 2/3

7 + 5/ 13 + 5 = 2/3

12/18 = 2/3

Divide numerator and denominator by of the left hand side by 6

12÷ 6/ 18 ÷ 6 = 2/3

2/3 =2/3

If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4

This means:

a - 5/b - 5 = 1/4

7 - 5/13 - 5 = 1/4

2/8 = 1/4

Divide the numerator and denominator of the left hand side by 2

2÷2/8 ÷ 2 = 1/4

1/4 = 1/4

From the above confirmation, the fraction that this is true for is 7/13

Answer:

0.078

Step-by-step explanation:

The probability P(A) of an event A happening is given by;

P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]

From the question;

There are two events;

(i) Drawing a first card which is a king: Let the event be X. The probability is given by;

P(X) = [tex]\frac{number-of-possible-outcomes-of-event-X}{total-number-of-sample-space}[/tex]

Since there are 4 king cards in the pack, the number of possible outcomes of event X = 4.

Also, the total number of sample space = 52, since there are 52 cards in total.

P(X) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

(ii) Drawing a second card which is a queen: Let the event be Y. The probability is given by;

P(Y) = [tex]\frac{number-of-possible-outcomes-of-event-Y}{total-number-of-sample-space}[/tex]

Since there are 4 queen cards in the pack, the number of possible outcomes of event Y = 4

But then, the total number of sample = 51, since there 52 cards in total and a king card has been removed without replacement.

P(Y) = [tex]\frac{4}{51}[/tex]

Therefore, the probability of selecting a first card as king and a second card as queen is;

P(X and Y) = P(X) x P(Y)

= [tex]\frac{1}{13} * \frac{4}{51}[/tex] = 0.078

Therefore the probability is 0.078

Answer:

72mile/hr

Step-by-step explanation:

Let d be distance in mile

Let r be average rate in mile/hr

Let t be time in hr

d = r × t

t = d/r

360/r = t ........1

Also

The question stated that the average speed was 6 less to travel a distance of 330mile at the same time.

Since the average speed is r, hence 6 less that r = r-6 at the same time

Therefore

330/r-6 = same time ( t ) .......2

Equate 1 and 2

360/r = 330/r-6

Cross multiply

360(r-6) = 330(r)

360r - 360×6 = 330r

360r - 2160 = 330r

Collecting like terms

- 2160 = 330r - 360r

- 2160 = - 30r

Divide both sides by - 30

- 2160/ - 30 = - 30r/ - 30

r = 72mile/hr

Hence the average speed is 72mile/hr

Answer:

The graphs for the lines of the costs are in the attachment. For this answer you have to first determine the equations for each cost. Since Hammy's Froyo charges $2.40 for the container and $.40 for each ounce, the equation would be y=.40x+2.40. For Yogurt Palace, which charges $0.80 for each ounce, the equation would be y=.80x.

Answer:

B

Step-by-step explanation:

Answer:

The answer for this Question is Elementary

It is B.

Looks like the given function is

[tex]f(x)=\dfrac1{9-x}[/tex]

Recall that for |x| < 1, we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :

[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]

Then

[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]

which converges for |(x - 4)/5| < 1, or -1 < x < 9.

Answer:

-2.05

Step-by-step explanation:

From the given information,

Let consider [tex]\mu[/tex] to represent the population mean

Therefore,

The null and alternative hypothesis can be stated as :

[tex]H_o :\mu=9[/tex]

[tex]H_1 :\mu<9[/tex]

From the hypothesis , the alternative hypothesis is one tailed (left)

when the level of significance = 0.020, the Z- critical value can be determined from the standard normal distribution table

Hence, the Z-critical value at ∝ = 0.020 is -2.05

Recall the Pythagorean identity,

[tex]1-\cos^2t=\sin^2t[/tex]

To get this expression in the fraction, multiply the numerator and denominator by [tex]1+\cos t[/tex]:

[tex]\dfrac{t\sin t}{1-\cos t}\cdot\dfrac{1+\cos t}{1+\cos t}=\dfrac{t\sin t(1+\cos t)}{\sin^2t}=\dfrac{t(1+\cos t)}{\sin t}[/tex]

Now,

[tex]\displaystyle\lim_{t\to0}\frac{t\sin t}{1-\cos t}=\lim_{t\to0}\frac t{\sin t}\cdot\lim_{t\to0}(1+\cos t)[/tex]

The first limit is well-known and equal to 1, leaving us with

[tex]\displaystyle\lim_{t\to0}(1+\cos t)=1+\cos0=\boxed{2}[/tex]

Answer:

The  margin of error is [tex]MOE = 9.68[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is [tex]n= 16[/tex]

     The  standard deviation is [tex]\sigma = 15[/tex]

     The  confidence level is  [tex]C = 99[/tex]%

Generally the level of significance is mathematically evaluated as

     [tex]\alpha = 100 - C[/tex]

     [tex]\alpha = 100 - 99[/tex]

     [tex]\alpha = 1%[/tex]%

   [tex]\alpha = 0.01[/tex]

The  critical value of  [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is  

     [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

The  reason obtaining the critical value of  [tex]\frac{\alpha }{2}[/tex] instead of  [tex]\alpha[/tex] is because we are  considering the two tails of the area normal distribution curve which is not inside the 99% confidence interval

   Now the margin of error is evaluated as

              [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

            [tex]MOE = 2.58 * \frac{15}{\sqrt{16} }[/tex]

           [tex]MOE = 9.68[/tex]

Answer:

2 < x < ∞

Step-by-step explanation:

We want where the value of y is less than zero

The value of the graph is  less than zero is from x=2 and continues until x = infinity

2 < x < ∞

Answer:

[tex]\boxed{2 < x < \infty}[/tex]

Step-by-step explanation:

The value of y should be less than 0 for the graph of the function to be negative.

In the graph, when it startes from x is 2 the value becomes less than 0 and it keeps continuing until x is equal to infinity.

[tex]2 < x < \infty[/tex]

Answer:

x = 1

Step-by-step explanation:

Set up the rational expression with the same denominator over the entire equation.

Since the expression on each side of the equation has the same denominator, the numerators must be equal

5x =4x+1

Move all terms containing x to the left side of the equation.

Hope this can help you

You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:

[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]

We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].

We also need to have

[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]

Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means

[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]

Then

[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]

So we end up with

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

Answer:

Step-by-step explanation:

In the form ...

  y(t) = Asin(ωt +φ)

you have ...

The translation from ...

  y(t) = 2sin(4πt) +5cos(4πt)

is ...

  A = √(2² +5²) = √29 . . . . the amplitude

  ω = 4π . . . . the angular frequency in radians per second

  φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift

Then, ...

  y(t) = √29·sin(4πt +1.1903)

_____

Comment on the conversion

You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)

If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.