Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
May August
95 100
72 80
78 95
50 65
89 85
92 98
75 70
90 96
65 87
The appropriate test is a paired t test :
d = difference between May and August
d = (-5, -8, -17, -15, 4, -6, 5, -6, -22)
The hypothesis :
H0 : μd = 0
H1 : μd ≠ 0
The test statistic :
T = dbar / (Sdbar/√n)
Where, dbar and Sdbar are the mean and standard deviation of 'd' respectively.
Using calculator :
dbar = - 7.777 ; Sdbar = 9.052
Test statistic = - 7.777 / (9.052 /√9)
Test statistic = - 2.577
The Pvalue, df = n - 1 = 9 - 1 = 8
Pvalue(-2.577, 8) = 0.0327
At α = 0.05
Pvalue < α ; WE reject the H0 ; and conclude that there has been a change in score
1.8>4.7+w
Does anyone know what this may be ? Thank you very much .
Answer:
-2.9 > w
Step-by-step explanation:
1.8>4.7+w
Subtract 4.7 from each side
1.8-4.7>4.7-4.7+w
-2.9 > w
Answer:
w = -2.9
Step-by-step explanation:
Measure and record the lengths of the sides of ABC and FGH.
Answer:
can you please send the picture of the diagram.
Step-by-step explanation:
Answer:
ABC:
AB-5 units
BC-12.65 units
AC-15 units
FGH:
FG-5 units
GH-12.65 units
FH-15 units
Step-by-step explanation:
PLATO SAMPLE ANSWER
a fair coin is flipped. if the flip results in a head, then a fruit is selected from a basket containing 8 apples, 2 bananas, and 6 cantaloups. if the flip results in a tail, then a fruit is selected from a basket containing 6 apples and 4 bananas. what is the probability that the flip resulted in tails, given that the fruit selexted is a banana g
Solution :
We have given two baskets :
[tex]$H_1$[/tex] : 8 apples + 2 bananas + 6 cantaloupes = 16 fruits
[tex]$H_2$[/tex] : 6 apples + 4 bananas = 10 fruits
A fair coin is made to flipped. If the [tex]\text{flip}[/tex] results is head, then the fruit is selected from a basket [tex]$H_1$[/tex].
If the flip results in tail, then the fruit is selected from the basket [tex]$H_2$[/tex].
Probability of head P(H) = [tex]1/2[/tex]
Probability of tail P(T) = [tex]1/2[/tex]
if given event is :
B = selected fruit is BANANA
We have to calculate : P(T|B)
Probability of banana if the flip results is head P(B|H) = [tex]$\frac{2}{16}$[/tex]
Probability of banana if the flip results is tail P(B|T) = [tex]$\frac{4}{10}$[/tex]
From the Bayes' theorem :
Probability of flip results is tail when selected fruit is BANANA.
[tex]$P(T|B) = \frac{P(B|T)\ P(T)}{P(B|T) \ P(T) + P(B|H)\ P(H)}$[/tex]
[tex]$=\frac{\frac{4}{10} \times \frac{1}{2}} {\frac{4}{10} \times \frac{1}{2} + \frac{2}{16} \times \frac{1}{2}}$[/tex]
[tex]$=\frac{\frac{1}{5}}{\frac{1}{5}+\frac{1}{16}}$[/tex]
[tex]$=\frac{\frac{1}{5}}{\frac{21}{80}}$[/tex]
[tex]$=\frac{16}{21}$[/tex]
∴ [tex]$P(\ T|B\ )=\frac{16}{21}$[/tex]
Convert 2546 in base 10 to base 5
Answer:
40141
Step-by-step explanation:
what is the perfect square of 96
Step-by-step explanation:
We determined above that the greatest perfect square from the list of all factors of 96 is 16.
6+7=10
13+8=18
32+21=32
11+34=0
31+03=?
process please
Answer:
6+7=13
13+8=21
32+21=52
11+34=46
31+03=34
Step-by-step explanation:
im not sure in the 31+03
a playing card is chosen at random from a standard deck of cards. what is the probability of choosing 5 of diamonds or one jack
Answer:
1/52
Step-by-step explanation:
Can you please me me
Step-by-step explanation:
1 since a tank holds 121/2 gallons of gas 121/2 multiplied by two it gives 25 -30 it gives 5 450 divided by two it gives 225-25 i guess.
find the missing side length in the image below
Answer:
The missing side length is of 5.
Step-by-step explanation:
The sides are proportional, which means that the missing side can be found using a rule of three.
x - 10
3 - 6
Applying cross multiplication:
[tex]6x = 30[/tex]
[tex]x = \frac{30}{6} = 5[/tex]
The missing side length is of 5.
urgent please help! will give brainliest
Answer:
The answer is A
Step-by-step explanation:
(-2,-3) (3,-4) (0,-1) (-7,3)
inverse means the opposite signs
(2,3) (-3,4) (0,1) (7,-3)
Betadine solution is a 10% povidone-iodine solution. Express this strength both as a fraction and as a ratio.
Step-by-step explanation:
Fraction =
[tex] \frac{10}{100} = \frac{1}{10} [/tex]
Ratio is 1 : 10
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y2 = 2x, x = 2y;
about the y-axis
b) Sketch the region
c) Sketch the solid, and a typical disk or washer.
Answer:
V = 34,13*π cubic units
Step-by-step explanation: See Annex
We find the common points of the two curves, solving the system of equations:
y² = 2*x x = 2*y ⇒ y = x/2
(x/2)² = 2*x
x²/4 = 2*x
x = 2*4 x = 8 and y = 8/2 y = 4
Then point P ( 8 ; 4 )
The other point Q is Q ( 0; 0)
From these two points, we get the integration limits for dy ( 0 , 4 )are the integration limits.
Now with the help of geogebra we have: In the annex segment ABCD is dy then
V = π *∫₀⁴ (R² - r² ) *dy = π *∫₀⁴ (2*y)² - (y²/2)² dy = π * ∫₀⁴ [(4y²) - y⁴/4 ] dy
V = π * [(4/3)y³ - (1/20)y⁵] |₀⁴
V = π * [ (4/3)*4³ - 0 - 1/20)*1024 + 0 )
V = π * [256/3 - 51,20]
V = 34,13*π cubic units
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. ASA Postulate
Answer:
ACB = JCB
Step-by-step explanation:
ASA means angle - (included) side - angle.
we have one angle confirmed.
we have the connected side BC confirmed (the diagram shows that the side is shared, so it is not only congruent, it is actually identical).
now we need confirmation for the angle at the other end point of that side.
Can someone do these please? ❤️
Answer:
-49
8
Step-by-step explanation:
-196/4 =
-49
(3+u)^2
-------------
8
Let u=5
(3+5)^2
-------------
8
(8)^2
-------------
8
64
-----
8
8
Michael wants to buy an efficient Smart car that according to the latest EPA standards gets 33 mpg in the city and 40 mpg on the highway. The car that Michael picked out costs $18,560. His dad agreed to purchase the car if Michael would pay it off in equal monthly payments for the next 64 months. The equation y= - 290x +18,560 represents the amount, y
(in dollars), that Michael owes his father after x months.
(a) How much does Michael owe his dad after 3 months?
(b) Determine the slope of the line and interpret its meaning in the context of this problem.
(c) Interpret the meaning of the slope in the context of this problem.
The amount Michael owes his father increases or decreases by ___ per month.
Answer:
17690
Step-by-step explanation:
The amount Michael owes is given by :
y = - 290x +18,560
x = number of months ; y = amount owed
Amount owed after 3 months :
Put x = 3 in the equation :
y= - 290(3) +18,560
y = - 870 + 18560
y = 17690
According to the general form of a linear equation :
y = mx + c
Where, m = slope ; c = intercept
The slope = - 290 ; Intercept = 18560
Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month
The intercept shows that the original amount borrowed is 18560
Amount Michael owes his father decreases by 290 per month.
A deli sandwich shop is offering either a ham or turkey sandwich, either tomato or vegetable soup, and either coffee or milk for their lunch special. Which tree diagram below shows all of the combinations for a sandwich, soup, and beverage?
Answer:
A.
Step-by-step explanation:
A. is the answer because they list all of the sandwiches, soups, and beverages with every possible combination.
Of the travelers arriving at a small airport, 60% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 50% are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.
What is the probability that the person
a. is traveling on business?
b. is traveling for business on a privately owned plane?
c. arrived on a privately owned plane, given that the person is traveling for business reasons?
d. is traveling on business, given that the person is flying on a commercially owned plane?
Answer:
a) 0.55 = 55% probability that the person is traveling on business
b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.
c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
50% of 60%(major airlines)
70% of 20%(privately owned airplanes)
80% of 100 - (60+20) = 20%(comercially owned airplanes). So
[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]
0.55 = 55% probability that the person is traveling on business.
Question b:
70% of 20%, so:
[tex]p = 0.7*0.2 = 0.14[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
Question c:
Event A: Traveling for business reasons.
Event B: Privately owned plane.
0.55 = 55% probability that the person is traveling on business.
This means that [tex]P(A) = 0.55[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
This means that [tex]P(A \cap B) = 0.14[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]
0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
Question d:
Event A: Commercially owned plane.
Event B: Business
80% of those arriving on other commercially owned planes are traveling for business reasons.
This means that:
[tex]P(B|A) = 0.2[/tex]
0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
a. 15
b. 16
c. 9
d. 14
Answer:
15
Step-by-step explanation:
1-0 =1
3-1 =2
6-3=3
10-6=4
We are adding 1 more each time
10+5 = 15
which polygon will NOT tessellate a plane?
Step-by-step explanation:
the answer is regular octagon
i think
Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 30% of the passengers are on business while on ordinary jets 25% of the passengers are on business. Of Global's air fleet, 60% of its capacity is provided on jumbo jets. (Hint: The 25% and 30% values are conditional probabilities stated as percentages.)
a) What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
b) What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?
Answer:
a) 0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.
b) 0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
Event A: Jumbo
Event B: Business
60% of its capacity is provided on jumbo jets.
This means that [tex]P(A) = 0.6[/tex]
On jumbo jets, 30% of the passengers are on business
This means that [tex]P(B|A) = 0.3[/tex]
Desired probability:
We want to find [tex]P(A \cap B)[/tex], so:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A) = 0.6*0.3 = 0.18[/tex]
0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.
b) What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?
Event A: Ordinary
Event B: Non-business
60% of its capacity is provided on jumbo jets.
So 100 - 60 = 40% are ordinary, which means that [tex]P(A) = 0.4[/tex]
On ordinary jets 25% of the passengers are on business.
So 100 - 25 = 75% are non-business, that is [tex]P(B|A) = 0.75[/tex]
Desired probability:
We want to find [tex]P(A \cap B)[/tex], so:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A) = 0.75*0.4 = 0.3[/tex]
0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.
How many ways are there to choose three distinct integers between 1 and 20 inclusive such that the numbers form an arithmetic sequence?
*please try to answer by tomorrow/
Answer:
probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)
=194/285 or 0.6807.
Step-by-step explanation:
The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.
The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.
Hence
|E'| = C(14,3)
= 14×13×12/3!.
Therefore probability P(E')
= |E'|/|S|
= (14×13×12)/(20×19×18)
= (14×13×2)/(20×19×3)
=(7×13)/(5×19×3)
= 91/285.
Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.
Graph: y – 3 = 1/2 (x + 2)
Answer:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Step-by-step explanation:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Answer: See below
Concept:
There are different forms of linear equations:
Slope-intercept form: y = mx + bPoint-slope form: y - y₁ = m (x - x₁)Standard form: Ax + By = CIntercept form: x / x₁ + y / y₁ = 1Solve:
Given: y - 3 = 1/2 (x + 2)
Here, we can see the linear equation is in the form of point-slope form.
x₁ = -2
y₁ = 3
m = 1/2
Point included in the graph = (-2, 3)
Slope of the graph = 1/2
Hope this helps!! :)
Please let me know if you have any questions
Please help me with this!
9514 1404 393
Answer:
7x -5 = 9x = 2Step-by-step explanation:
A) If we let x represent "a number", then "seven times a number" is 7x. When 5 is subtracted from that, we have ...
7x -5 . . . . . 5 subtracted from 7 times a number
This is said to be 9, so ...
7x -5 = 9 . . . . . . . 5 from 7 times a number is 9. Your equation.
__
B) To solve this, we can add 5 to both sides. This eliminates the constant term we don't want on the left.
7x = 14
Now, we can divide by 7, the coefficient of x that we don't want.
x = 14/7
x = 2
1->dương vô cùng 1/x*(9+lnx^2)dx
It looks like you are trying to compute the improper integral,
[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]
or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then
[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]
A worker in the automobile industry works an average of 43.7 hours per week. Assume the distribution is normal with a standard deviation of 1.6 hours.
(i) What is the probability that a randomly selected automobile worker works less than 40 hours per week?
(ii) If 15 automobile workers are randomly selected, what is the probability that the sample mean of working time is more than 45 hours per week?
Answer:
The solution is:
(1) 0.0104
(2) 0.0008
Step-by-step explanation:
Given:
Mean,
[tex]\mu = 43.7[/tex]
Standard deviation,
[tex]\sigma = 1.6[/tex]
(1)
⇒ [tex]P(X<40) = P(\frac{x-\mu}{\sigma}<\frac{40-43.7}{1.6} )[/tex]
[tex]=P(z< - 2.3125)[/tex]
[tex]=P(z<-2.31)[/tex]
[tex]=0.0104[/tex]
(2)
As we know,
n = 15
⇒ [tex]P(\bar X > 45)= P(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } } >\frac{45-43.7}{\frac{1.6}{\sqrt{15} } } )[/tex]
[tex]=P(z> 3.15)[/tex]
[tex]=1-P(z<3.15)[/tex]
[tex]=1-0.9992[/tex]
[tex]=0.0008[/tex]
Which of the following is a monomial?
A. 8x^2 +7x+3
B. √x-1
C. 9/x
D. 7x
Answer:
7x is monomial according to question.
What is the domain of f(x)=square root of 9-14x
Answer: 6.9
Step-by-step explanation:
An ice cream store determines the cost of its sundaes by using the formula C = 0.50s + 0.35n + 0.25t, where C is the total cost in dollars, s is the number of scoops of ice cream, n is the number of scoops of nuts, and t is the number of liquid toppings. A Nutty Sundae costs $3.55. It has 3 scoops of nuts and 2 different liquid toppings. How many scoops of ice cream are in this sundae?
Answer:
4 scoops of ice cream
Step-by-step explanation:
Plug in the total cost, number of scoops of nuts, and number of liquid toppings into the formula. Then, solve for s:
C = 0.50s + 0.35n + 0.25t
3.55 = 0.50s + 0.35(3) + 0.25(2)
3.55 = 0.50s + 1.05 + 0.5
3.55 = 0.50s + 1.55
2 = 0.50s
4 = s
So, the sundae had 4 scoops of ice cream.
A construction crane lifts a bucket of sand originally weighing 145 lbs at a constant rate. Sand is lost from the bucket at a constant rate of .5lbs/ft. How much work is done in lifting the sand 80ft?
Answer: [tex]10,000\ lb.ft[/tex]
Step-by-step explanation:
Given
Initial weight of the bucket is [tex]145\ lb[/tex]
It is lifted at constant rate and rate of sand escaping is [tex]0.5\ lb/ft[/tex]
At any height weight of the sand is [tex]w(h)=145-0.5h[/tex]
Work done is given by the product of applied force and displacement or the area under weight-displacement graph
from the figure area is given by
[tex]\Rightarrow W=\int_{0}^{80}\left ( 145-0.5h \right )dh\\\\\Rightarrow W=\left | 145h-\dfrac{0.5h^2}{2} \right |_0^{80}\\\\\Rightarrow W=\left [ 145\times 80-\dfrac{0.5(80))^2}{2} \right ]-0\\\\\Rightarrow W=11,600-1600\\\\\Rightarrow W=10,000\ lb.ft[/tex]
help me solve this trig
Hello there!
Previously, we learnt that to solve the equation, we have to isolate the sin, cos, tan, etc first.
First Question
The first question has sin both sides. Notice that if we move sin(theta) to left. We get:-
[tex] \displaystyle \large{2 {sin}^{2} \theta - sin \theta = 0}[/tex]
We can common factor out the expression.
[tex] \displaystyle \large{sin \theta(2sin \theta - 1) = 0}[/tex]
It is a trigonometric equation in quadraric pattern.
We consider both equations:-
First Equation
[tex] \displaystyle \large{sin \theta = 0}[/tex]
Remind that sin = y. When sin theta = 0. It means that it lies on the positive x-axis.
We know that 0 satisfies the equation, because sin(0) is 0.
Same goes for π as well, but 2π does not count because the interval is from 0 ≤ theta < 2π.
Hence:-
[tex] \displaystyle \large { \theta = 0,\pi}[/tex]
Second Equation
[tex] \displaystyle \large{2sin \theta - 1 = 0}[/tex]
First, as we learnt. We isolate sin.
[tex] \displaystyle \large{sin \theta = \frac{1}{2} }[/tex]
We know that, sin is positive in Quadrant 1 and 2.
As we learnt from previous question, we use π - (ref. angle) to find Q2 angle.
We know that sin(π/6) is 1/2. Hence π/6 is our reference angle. Since π/6 is in Q1, we only have to find Q2.
Find Quadrant 2
[tex] \displaystyle \large{\pi - \frac{\pi}{6} = \frac{6\pi}{6} - \frac{\pi}{6} } \\ \displaystyle \large{ \frac{5\pi}{6} }[/tex]
Hence:-
[tex] \displaystyle \large{ \theta = \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]
Since both first and second equations are apart of same equation. Therefore, mix both theta from first and second.
Therefore, the solutions to the first question:-
[tex] \displaystyle \large \boxed{ \theta = 0,\pi, \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]
Second Question
This one is a reciprocal of tan, also known as cot.
[tex] \displaystyle \large{cot3 \theta = 1}[/tex]
For this, I will turn cot to 1/tan.
[tex] \displaystyle \large{ \frac{1}{tan3 \theta} = 1}[/tex]
Multiply whole equation by tan3 theta, to get rid of the denominator.
[tex] \displaystyle \large{ \frac{1}{tan3 \theta} \times tan3 \theta = 1 \times tan3 \theta } \\ \displaystyle \large{ 1= tan3 \theta }[/tex]
We also learnt about how to deal with number beside theta.
We increase the interval, by multiplying with the number.
Since our interval is:-
[tex] \displaystyle \large{0 \leqslant \theta < 2\pi}[/tex]
Multiply the whole interval by 3.
[tex] \displaystyle \large{0 \times 3 \leqslant \theta \times 3 < 2\pi \times 3} \\ \displaystyle \large{0 \leqslant 3 \theta < 6\pi }[/tex]
We also know that tan is positive in Quadrant 1 and Quadrant 3.
and tan(π/4) is 1. Therefore, π/4 is our reference angle and our first theta value.
When we want to find Quadrant 3, we use π + (ref. angle).
Find Q3
[tex] \displaystyle \large{\pi + \frac{\pi}{4} } = \frac{5\pi}{4} [/tex]
Hence, our theta values are π/4 and 5π/4. But that is for [0,2π) interval. We want to find theta values over [0,6π) interval.
As we learnt previously, that we use theta + 2πk to find values that are in interval greater than 2π.
As for tangent, we use:-
[tex] \displaystyle \large{ \theta + \pi k = \theta}[/tex]
Because tan is basically a slope or line proportional graph. So it gives the same value every π period.
Now imagine a unit circle, and make sure to have some basic geometry knowledge. Know that when values addition by 180° or π would give a straight angle.
We aren't using k = 1 for this because we've already found Q3 angle.
Since we know Q1 and Q3 angle in [0,2π).
We can also use theta + 2πk if you want.
First Value or π/4
[tex] \displaystyle \large{ \frac{\pi}{4} + 2\pi = \frac{9\pi}{4} } \\ \displaystyle \large{ \frac{\pi}{4} + 4\pi = \frac{17\pi}{4} }[/tex]
Second Value or 5π/4
[tex] \displaystyle \large{ \frac{5\pi}{4} + 2\pi = \frac{13\pi}{4} } \\ \displaystyle \large{ \frac{5\pi}{4} + 4\pi = \frac{21\pi}{4} }[/tex]
Yes, I use theta + 2πk for finding other values.
Therefore:-
[tex] \displaystyle \large{3 \theta = \frac{\pi}{4} , \frac{5\pi}{4} , \frac{9\pi}{4}, \frac{17\pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} }[/tex]
Then we divide every values by 3.
[tex] \displaystyle \large \boxed{\theta = \frac{\pi}{12} , \frac{5\pi}{12} , \frac{9\pi}{12}, \frac{17\pi}{12} , \frac{13\pi}{12} , \frac{21\pi}{12} }[/tex]
Let me know if you have any questions!
