Simplify a - b - [C- (d - e) - f] - g).
O a-b+C - d+e+f-g
O a - b + C-d + e-f+g
O a + b + C-d + e-f+g
O a+b+c+d+e-f+g

Answer:

a. cosθ = ¹/₂[e^jθ + e^(-jθ)] b. sinθ = ¹/₂[e^jθ - e^(-jθ)]

Step-by-step explanation:

a.We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Adding both equations, we have

e^jθ = cosθ + jsinθ

+

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ + cosθ + jsinθ - jsinθ

Simplifying, we have

e^jθ + e^(-jθ) = 2cosθ

dividing through by 2 we have

cosθ = ¹/₂[e^jθ + e^(-jθ)]

b. We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Subtracting both equations, we have

e^jθ = cosθ + jsinθ

-

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ - cosθ + jsinθ - (-jsinθ)

Simplifying, we have

e^jθ - e^(-jθ) = 2jsinθ

dividing through by 2 we have

sinθ = ¹/₂[e^jθ - e^(-jθ)]

Answer:

∠EFH = 21°

∠HFG = 62°

∠EFG = 83°

Step-by-step explanation:

The diagram showing the angles has been attached to this response.

From the diagram, it can be deduced that;

Angle EFG = angle EFH + angle HFG

=> ∠EFG = ∠EFH + ∠HFG                -------------------(i)

From the question:

∠EFH = (5x + 1)°                    -------------(ii)

∠HFG = 62°                          -------------(iii)

∠EFG = (18x + 11)°                 -------------(iv)

Substitute these values into equation (i) as follows;

(18x + 11) = (5x + 1) + 62

=> 18x + 11 = 5x + 1 + 62

Collect like terms and solve for x

18x - 5x = 1 + 62 - 11

13x = 52

x = 4

Now, to get each measurement, substitute x = 4 into each of equations (ii) - (iv)

∠EFH = (5x + 1)°

∠EFH = (5(4) + 1)°

∠EFH = (20 + 1)°

∠EFH = 21°

∠HFG = 62°              [Does not depend on x]

∠EFG = (18x + 11)°

∠EFG = (18(4) + 11)°

∠EFG = (72 + 11)°

∠EFG = 83°

Conclusion:

∠EFH = 21°

∠HFG = 62°

∠EFG = 83°

Answer: Statistic.

Step-by-step explanation: Statistic are used to refer to numerical measurement pertaining to a sample. A sample refers to a subset of members chosen from a population, which means a smaller representation of the larger group. Hence, in the scenario above, the population is the entire seniors which makes up the group. While the sample is the subset of seniors drawn from the whole. Hence, statistical measures calculated or derived from the sample is called statistic. Hence, the 25% obtained is a statistic.

Answer:

60 ; 20

B.) 1 hour working on problems, 3 hours reading

Step-by-step explanation:

Given the information :

Time - - - Total problems Answered

8am: - - - - 0

9am: - - - - 80

10am: - - - - 140

11am: - - - - -180

noon: - - - - 200

The marginal, or additional, gain from Ana’s second hour of work, from 9:00 AM to 10:00 AM, is ?

(Total problem answered at 10 a.m - Total problems Answered at 9a.m)

(140 - 80) = 60

The marginal gain from Ana’s fourth hour of work, from 11:00 AM to noon, is ?

(Total problem answered at Noon - Total problems Answered at 11a.m)

(200 - 180) = 20

In other to get the best possible exam score,

Since it is assumed that

Solving 70 problems is equivalent to 1 hour of reading in terms of score improvement

Also, it is assumed that the same number of pages is covered for every hour spent whine reading.

Hence it is only during the first hour, that is (8:00 - 9:00) that she was able to solve above 70 questions (80 - 0). Number of questions solved during subsequent hours were not up to 70, hence it would have been more rewarding if they had been used for reading.

Hence, she should have spent 1 hour working on problems and 3 hours reading

Answer:

115°

Step-by-step explanation:

Supplementary angles equal 180.

180-65=115°

Answer:

[tex]\boxed{115}[/tex]

Step-by-step explanation:

Hey there!

Supplementary angles add up to 180º, so we can set up the following.

x = 180 - 65

x = 115º

Hope this helps :)

Answer:

42

Step-by-step explanation:

12880000/140900=94.41

Therefore there is 1 teacher in every 94.41 people so

3860/94.41=42.2

So we would find around 42 teachers in Marshall, IL

Answer: 22

Step-by-step explanation: The range is the difference between the greatest number in the data set and the least numbe rin the data set.

In this case, thats 30 - 8 or 22.

Answer:

22

Step-by-step explanation:

30 - 8 = 22

highest number - lowest number

Answer:

please mark my answer brainliest

Step-by-step explanation:

A.....will be the answer....

Answer:6858

Step-by-step explanation:

4mn. You are multiplying them all together.

Answer:

4mn

Step-by-step explanation:

you would multiply the 2s then the m and n cant multiply so they would stay beside eachother so it would be 4mn

Complete question:

Please find the attached file for task table

Answer:

The minimum cycle time is 50 s

The maximum  cycle time is 50.4 s

Step-by-step explanation:

Given;

production time, t = 7 hours

desired output = demand, D =  500 units

The minimum cycle Time is given by;

Minimum cycle time = maximum task time, from the table the maximum task time is 50 seconds.

Thus, Minimum cycle time = 50 s

The maximum cycle Time is given by;

[tex]CT = \frac{Production \ time}{D} \\\\CT = \frac{7*3600 s}{500 \ units} \\\\CT = 50.4 \ s[/tex]

Thus, Maximum cycle time = 50.4 s

Answer:

x = 5

Step-by-step explanation:

4|0.5x - 2.5| = 0

|0.5x - 2.5|  = 0 / 4

0.5x - 2.5 = 0

0.5x = 2.5

x = 2.5 / 0.5

x = 5

Answer:

[tex] a_n = 16(\frac{1}{4})^{n - 1} [/tex]

Step-by-step explanation:

Given:

Fifth term of a geometric sequence = [tex] \frac{1}{16} [/tex]

Common ratio (r) = ¼

Required:

Formula for the nth term of the geometric sequence

Solution:

Step 1: find the first term of the sequence

Formula for nth term of a geometric sequence = [tex] ar^{n - 1} [/tex], where:

a = first term

r = common ratio = ¼

Thus, we are given the 5th term to be ¹/16, so n here = 5.

Input all these values into the formula to find a, the first term.

[tex] \frac{1}{16} = a*\frac{1}{4}^{5 - 1} [/tex]

[tex] \frac{1}{16} = a*\frac{1}{4}^{4} [/tex]

[tex] \frac{1}{16} = a*\frac{1}{256} [/tex]

[tex] \frac{1}{16} = \frac{a}{256} [/tex]

Cross multiply

[tex] 1*256 = a*16 [/tex]

Divide both sides by 16

[tex] \frac{256}{16} = \frac{16a}{16} [/tex]

[tex] 16 = a [/tex]

[tex] a = 16 [/tex]

Step 2: input the value of a and r to find the nth term formula of the sequence

nth term = [tex] ar^{n - 1} [/tex]

nth term = [tex] 16*\frac{1}{4}^{n - 1} [/tex]

[tex] a_n = 16(\frac{1}{4})^{n - 1} [/tex]

Answer: $787.65

explanation:

(17.70)(40) = $708

17.70 x 1.5 = 26.55

(3)(26.55) = $79.65

$708 + $79.65 = 787.65

Answer:  A) sin 59° = cos 31°

Step-by-step explanation:

Based on the angle and the sides provided, we can establish that

tan 31° = 17/x

Since no hypotenuse is provided and we cannot solve for it, we can rule out options B, C, and D.

We know that the sum of the angles of a triangle is 180°. In a right triangle, we know that one of the angles is 90°, so the other two angles are complimentary  -->   sin Ф = cos (90 - Ф).

Therefore, option A is true.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Normal distribution :

Mean (m) = 1049

Standard deviation (sd) = 189

Number of samples (n) = 16

A) What is the probability that one randomly selected student scores above 1100 on the GRE?

Obtain the z score

Zscore = (x - m) / sd

Zscore = (1100 - 1049) / 189

Zscore = 51 / 189 = 0.2698412 = 0.27

Using the z-table

P(X > 100) = 1 - P(X < 100) = 1 - 0.6064 = 0.3936

B) The sample mean = population mean

Hence sample mean = 1049

The sample standard deviation = standard error

Standard Error (SE) = sd / sqrt(n)

SE = 189/4 = 47.25

Hence shape = normal, standard deviation = 47.25, mean = 1049

C.) P(X < 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 47.25

Zscore = 51 / 47.25 = 1.0793650 = 1.08

Using the z-table :

P(X < 1100) = 0.8599

D.) P(X > 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 47.25

Zscore = 51 / 47.25 = 1.0793650 = 1.08

Using the z-table :

P(X > 1100) = 1 - P(X < 1100) = (1 - 0.8599) = 0.1401

E) if n = 64

SE = 189 / sqrt(64) = 189 / 8 = 23.625

P(X > 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 23.625

Zscore = 51 / 47.25 = 2.1587301 = 2.16

Using the z-table :

P(X > 1100) = 1 - P(X < 1100) = (1 - 0.9846) = 0.0154

The probability decreases as the same distribution hinges towards a Boal distribution with increasing sample size.

(4×10)+(7×1\100) = 40+7/100 =4007/100

4007/100= 40,07

40,07 = 40,070

just add 0 to right side

(40,0700 also = 40,070)

Hope this helps ^-^

Answer:

Step-by-step explanation:

Hello,

We will prove it by induction.

Step 1 - for n=2

2!=2*1=2

2^2=4

and 2 < 4 so this is true for n=2

Step2 - We assume that this is true for k and we have to prove it for k+1.

Induction hypothesis is [tex]k!<k^k[/tex]

[tex](k+1)!=(k+1)k![/tex]

We use the induction hypothesis and we we can write that

[tex](k+1)!=(k+1)k!<(k+1)k^k<=(k+1)(k+1)^k=(k+1)^{k+1}\\\\\text{As }k <= k+1[/tex]

so, we prove it for k+1

Step 3- conclusion

for n >= 2 we just proved that [tex]n!<n^n[/tex]

Answer:

t = -1

Step-by-step explanation:

8 + 9t - 3 + 4    

Combine like terms

(8 - 3 + 4) + 9t

9 + 9t

9t + 9

Get t by itself

9t + 9 = 0

     -9    -9

9t = -9

Divide both sides by 9 to find t

t = -1

Answer:

Answer:

A first of all because the sample involves only rock cods that voluntarily get hooked to the fishing rod, this is a major source of bias as the sample does not represent the whole general population.

Rather adopt stratified sampling stratified basing on Geographical location can be suggested for this study.

II. Because convenient sampling is adopted here data is only gotten from students that eat in the hall in a given period of time so this is a source of bias

Also one study center that is the Hall of only one school is used this is also biased and may affect the result of the study

To avoid this bias a simple random sampling where each student have an equal chance of being selected in the study should be adopted

Iii. this study is using convenient samples. and the effect of head ache medicine may be affected by other medicines too so the headache medicine cannot be the only reason for painrelief so it is better to sample rando amongst patients with headache

Answer is

1. 8(4+2)

8 × 6 = 48

Answer:

Step-by-step explanation:

Other trigonometry identities that we have includes cosθ, sinθ, tanθ, secθ, cosecθ

cosecθ = 1/sinθ

Given cotθ=-1/3 and  sinθ<0, this means that θ falls in the 4th quadrant.

cotθ= 1/tanθ = -1/3

tanθ = -3/1

Since tanθ = opposite/adjacent = -3/1

opposite = -3

adjacent = 1

Using pythagoras theorem to get the hypotenuse, hyp² = opp²+adj²

hyp² = (-3)²+1²

hyp = √9+1

hyp = √10

cosθ = adjacent/hypotenuse = 1/√10

sinθ  = opp/hyp = -3/√10

cosecθ = 1/sinθ = 1/(-3/√10)

cosecθ = -√10/3

secθ = 1/cosθ

secθ = 1/(1/√10)

secθ = 1*√10/1

secθ = √10

Step-by-step explanation:

4x + 5y = 9

-11x - 9y = -20

solution

5y = 4x - 9

divide both side by 5

5y = 4x - 9

5 5

5 cancel at the L.H.S

y = 4x-9

5

insert the value of y in equation ii above

-11x -9(4x-9) = -20

5

-11x - 36x-81 = -20

5

cross multiply at the RHS

-11x- 36x-81 = -100

-47x-81 = -100

-47x = -100+81

-47x = -19

divide both side by -47

-47x = -19

-47 -47

x =

Answer:

.4 is in the 10th place in a number so .4 is one tenth of 1

The given decimal is equivalent to the one tenth of 4.

A decimal number is the representation of a number in whole and a part. The whole is represented by an integer while the part is equivalent to a number divided by the order of 10.

The given number in decimal form is 0.4.

In order to convert it in fraction, it can be written in the form of p/q as follows,

0.4 = 0.4/1

Multiply the numerator and denominator by 10 to obtain,

(0.4 × 10)/(1 × 10) = 4/10      

Hence, the given number is one tenth of 4.

To know more about decimal number click on,

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The yearly expense of the in-state college is $16000.

We are given that;

An out-of-state college where the tuition = $7000 per year.

Now,

The yearly expense of the in-state college is:

=5500+12⋅1000

=5500+12000

=17500

By solving;

The yearly expense of the out-of-state college is:

=7000+12⋅750

=7000+9000

=16000

So, on an annual basis, the less expensive choice is the out-of-state​ college.

Therefore, by algebra the answer will be 16000.

More about the Algebra link is given below.

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Answer:

3^5

Step-by-step explanation:

five factors of 3"

This means we have 3 multiplied 5  times

3 *3*3*3*3

3^5

Answer:

x = 5

Step-by-step explanation:

To find the value of x make sure to get it on one side

First subtract 3x from each side. This makes the equation now

3x + 2 = -8 + 25

Now see what 25 subtract by 8 is (17)

3x + 2 = 17

Next subtract 2 from both sides

3x = 15

Lastly, divide 15 by 3, making x equal 5

x = 5