Answer:
If two points that are coplanar are also __ collinear
Using Euler's relation, derive the following relationships:a. Cosθ=½(e^jθ+e^−jθ)b. Sinθ=½(e^jθ−e(^−jθ)
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)]
Ana is a hard-working college junior. One Saturday, she decides to work nonstop until she has answered 200 practice problems for her chemistry course. She starts work at 8:00 AM and uses a table to keep track of her progress throughout the day. She notices that as she gets tired, it takes her longer to solve each problem. Time Total Problems Answered 8:00 AM 0 9:00 AM 80 10:00 AM 140 11:00 AM 180 Noon 200 The marginal, or additional, gain from Ana’s second hour of work, from 9:00 AM to 10:00 AM, is ? problems. The marginal gain from Ana’s fourth hour of work, from 11:00 AM to noon, is ? problems. Later, the teaching assistant in Ana’s chemistry course gives her some advice. The teaching assistant says, “Based on past experience, working on 70 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour.” For simplicity, assume students always cover the same number of pages during each hour they spend reading. Given this information, in order to use her 4 hours of study time to get the best exam score possible, how many hours should she have spent working on problems and how many should she have spent reading? A. 0 hours working on problems, 4 hours reading B. 1 hour working on problems, 3 hours reading C. 3 hours working on problems, 1 hour reading D. 4 hours working on problems, 0 hours reading
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
prove that n!<n^n for n≥2
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]
The population of a city has increased by 27% since it was last measured. If the current population is 25400, what was the previous population
Answer:6858
Step-by-step explanation:
6x+2=-8+3x+25 whats the answer to x?
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
for the right triangle shown, which equation is correct?
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.
Rewrite this number in appropriate scientific notation of 4,770,000
Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?
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]
You have a choice between going to an in-state college where you would pay $5500 per year for tuition and an out-of-state college where the tuition is $7000 per year. The cost of Iiving is much higher at the in-state college, where you can expect to pay $1000 per month in rent, compared to $750 per month at the other college Assuming all other factors are equal, which is the less expensive choice on an annual (12-month) basis? The yearly expense of the in-state college is $_____and the yearly expense of the out-of-state college is $______. Thus on an annual basis, the less expensive choice is the (1)_______college. (Simplify your answers.) in-state out-of-state
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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0.4 is one tenth of what number
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.
What is a Decimal number?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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For the third week of July, Susan Gray worked 43 hours. Susan earns $17.70 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. Calculate the following for the third week of July (round your responses to the nearest cent if necessary
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
Determine whether the underlined number is a statistic or a parameter. a sample of seniors selected and it is found that 25% own a computer
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.
What is the image of (-7,-2) after a reflection over the y-axis?
PLEASE HELP!!! Which expression is equivelent to 32 + 16 1. 8(4+2) 2. 8(24+8) 3. 4(2+7) 4. 7(24+8)
Answer is
1. 8(4+2)
8 × 6 = 48
g if cot=-1/3 and sin<0 find each function value only using the appropriate trigonometric identites
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
For each of the following studies, identify the source(s) of sampling bias and describe (i) how it might affect the study conclusions and (ii) how you might alter the sampling method to avoid the bias.
(a) To study the size distribution of rock cod (Epinephelus puscus) off the coast of southeastern Australia, scientists recorded the lengths and weights for all cod captured by a commercial fishing vessel on one day (using standard hook-and-line fishing methods).
(b) A nutritionist is interested in the eating habits of college students and observes what each student who enters a dining hall between 8:00 A.M. and 8:30 A.M. chooses for breakfast on a Monday morning.
(c) To study how fast an experimental painkiller relieves headache pain residents of a nursing home who complain of headaches are given the painkiller and are later asked how quickly their headaches subsided.
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
Determine the minimum and maximum cycle times in seconds for a desired output of 500 units in a seven-hour day.
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
8+9t-3+4 please help me
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
What is the solution to 4|0.5x - 2.5| = 0?
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
The combined (verbal + quantitative reasoning) score on the GRE (Graduate Record Exam) is normally distributed with mean 1049 and standard deviation 189. Suppose n = 16 randomly selected students take the GRE on the same day.
a. What is the probability that one randomly selected student scores above 1100 on the GRE?
b. Describe the sampling distribution of the sample mean for the 16 students (description should include mean, standard deviation and shape).
c. What is the probability that a random sample of 16 students has a mean GRE score that is less than 1100?
d. What is the probability that a random sample of 16 students has a mean score that is more than 1100?
e. If the sample size in (d) above was increased to 64, what affect would it have on the probability (more, less, the same, can't tell) and why?
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.
Which angle is supplementary to 65 degrees
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 :)
What is the range of the following numbers: 12,8,17,12,15,18,30
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
For the following exercises, write the equation of the tangent line in Cartesian coordinates for the given parameter t
x=et ,y=(t-1)2 ,at(1,1)
Answer:
y+2x = 3
Step-by-step explanation:
The formula for finding the equation of a tangent line is expressed using the point slope equation y-y0 = m(x-x0) where:
m is the slope of the line and (x0, y0) is a point on the line.
m = dy/dx = dy/dt ÷ dx/dt
dy/dt = 2(t-1)
dx/dt = e^t
m = 2(t-1)/e^t
If x = e^t, and x = 1
1 = e^t
Taking ln of both sides
ln1 = lne^t
t = ln1
t = 0
Substituting t = 0 into the slope formula:
m = 2(t-1)/e^t
m = 2(0-1)/e^0
m = 2(-1)/1
m = -2/1
m = -2
Substituting the slope m= -2 and the given point (1,1) into the formula for calculating the equation of tangent line we will have;
y-1 = -2(x-1)
y-1 = -2x+2
y+2x = 2+1
y+2x = 3
Hence the equation of the tangent line in Cartesian coordinates for the given parameter t is y+2x = 3
If there are 140,900 teachers and 12,880,000 people in Illinois, how many teachers would we expect to find in Marshall, IL, a city of 3,860 people?
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
ANYONEEEE ? I need to help
Answer:
please mark my answer brainliest
Step-by-step explanation:
A.....will be the answer....
Find two decimals that are equivalent to (4×10)+(7×1\100
(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 ^-^
PLEAS HELP 2m · 2n would be the same as _____.
4 mn
2 m + n
2 mn
2 m - n
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
4x + 3 x - 6 equals 29 what is X
What is the solution to the system of linear equations? Please show steps 4x + 5y = 9
−11x − 9y = −20
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 =
Which of the following expressions means "five factors of 3"?
Options: 3^5
5^3
5 divided by 3
I know it's definitely not the third option. Please explain your answer so I understand, thank you!
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