Consider the following sample data set of 20 numbers.
24 30 4 42 40 26 23 36 12 45 29 21 34 16 47 28 32 54 19 9
1.
Create a relative frequency table and a frequency histogram with the bin width 8.
2.
Find the sample mean. (Round to the nearest hundredth.)
3.
Find the sample standard deviation
. (Round to the nearest hundredth.)
Answers
The mean = 28.55, while the standard deviation is 13.16
1. The histogram is an attachment
How to calculate for the mean of the data setWe have the following numbers
24 30 4 42 40 26 23 36 12 45 29 21 34 16 47 28 32 54 19 9
The sum of these numbers is given as
571
The total numbers = 20
The mean = 571/20
= 28.55
2 = How to find the standard deviation= (24 - 28.55)2 + ... + (9 - 28.55)/20 - 1
= 3292.95/19
= 173.31315789474
s = √173.31315789474
= 13.164845532506
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Related Questions
Please help!!! Plot the image of the triangle abc under reflection across x axis
Answers
Answer:
Step-by-step explanation:
Reflecting across the x-axis means (x,y) maps onto (x,-y).
So, A' has coordinates (-2,0), B' has coordinates (-6,-5), and C' has coordinates (-3, -4).
Given z =-1 –i, which letter represents z^3?
Answers
Given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i
Powers of complex number expressionsThe given complex number is z = -1 - i
[tex]z^3[/tex] means to raise z to the power of 3
[tex]z^3=(-1-i)^3[/tex]
Expand and simplify the expression:
[tex]z^3=(-1)^3+3(-1)^2(-i)+3(-1)(-i)^2+(-i)^3\\\\z^3=-1-3i-3i^2-i^3[/tex]
Note that:
[tex]i^2=-1\\\\i^3=-i[/tex]
Substitute these into the resulting expression
[tex]z^3=-1-3i-3(-1)-(-i)\\\\z^3=-1+3-3i+i\\\\z^3=2-2i[/tex]
Therefore, given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i
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Cara has saved 1, 430 pennies. She needs to put the pennies in paper rolls so the bank can count them easily. Each penny roll holds 50 pennies. How many penny
rolls will she need, and how many pennies will be in the last roll?
Answers
Cara has saved 1, 430 pennies. She needs to put the pennies in paper rolls so the bank can count them easily. Each penny roll holds 50 pennies. The number of pennies will be in the last roll is 30.
To find out the number of pennies will be in the last roll.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given that:
Cara has saved 1, 430 pennies.
Each penny roll holds 50 pennies.
1430 divides by 50 = 143/5≈29 roles and in last roll it will be 30 pennies.
So, the number of pennies will be in the last roll is 30.
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At what points does the curve r(t) = t i + (4t − t2) k intersect the paraboloid z = x^2 + y^2?
(smaller t-value) (x, y, z) = ?
(larger t-value) (x, y, z) = ?
Answers
The points are known to intersect the curve at
(smaller t-value) (x, y, z) = 0, 0, 0(larger t-value) (x, y, z) = 2, 0, 4How to find the pointsWe have our equation as: r(t)=ti+(4t-t2)k (4t - t2)k
From r(t)
We have x to be t, y to be 0 and z=4t-t2
The given paraboloid can be defined to be
z=x^2+y^2
We are to put the values in the equation
4t-t²=t²+0
2t²=4t
Then t wuld be 2 or 0
Hence we have to conclude that ours points of intersection are at (0,0,0) and (2,0,4).
The 0,0,0) and (2,0,4) points is where the intersection of the paraboloid take place.
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if a person invested half of her money at 11% and half at 10% and received $420 interest. find the total amount
Answers
The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the total amount of money invested, hence:
(0.5* x * 0.11) + (0.5 * x * 0.1) = 420
x = 4000
The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.
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Write a word problem involving finding two real numbers that could be solved with the
equation x(9-x)=14 .
Answers
The word problem that depicts this algebraic equation is;
The sum of the weight of my son and my daughter is 9 kg but the product of their weights is 14. Find the weights of each person.
How to write Algebraic Word Problems?We want to write a word problem with the equation;
x(9 - x) = 14
The word problem that depicts this algebraic equation is;
The sum of the weight of my son and my daughter is 9 kg but the product of their weights is 14. Find the weights of each person.
Now, the word problem above is correct because if we assume their weights are x and y, then we can say that;
x + y = 9
xy = 14
Now, y = 9 - x
Thus, equation 2 is;
x(9 - x) = 14
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Company XYZ closed at $46.07 per share with a P/E ratio of 16.66. Answer the following questions.
a.How much were earnings per share?
b.Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14?
Answers
The amount of earnings per share is $2.77.
Earnings per sharea. Earnings per share = price per share / (P/E) ratio
Earnings per share = $46.07 / 16.66
Earnings per share= $2.77
B. Overpriced or underpriced stock
At P/E ratio = 12
Earnings per share = $46.07 / 12
Earnings per share = $3.84
Earning yield = ( Earning per share / market value )× 100
Earning yield = (3.84 / $46.07 ) × 100
Earning yield = 8.34%
At P/E ratio = 13
Earnings per share = $46.07 / 13
Earnings per share = $3.54
Earning Yield= (3.54 / 46.07 ) × 100
Earning Yield= 7.68%
At P/E ratio = 14
Earnings per share = $46.07 / 14
Earnings per share = $ 3.3
Earnings yield= ( 3.3 / 46.07 )×100
Earnings yield= 7.16%
Average of earning yield given P/E ratio is 12-14
Average of earning yield= ( 8.34 + 7.68 + 7.16 ) / 3
Average of earning yield= 7.73%
Earning yield = ( Earning per share / market value ) × 100
Earning yield= ( 2.77 / 46.07 ) ×100
Earning yield = 6.01%
Hence, Based on the above the stock is underpriced.
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You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 98% confident that you estimate is within 2% of the true population proportion. How large of a sample size is required?
Answers
Using the z-distribution, it is found that a sample size of 3,385 is required.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.
We have no prior estimate, hence [tex]\pi = 0.5[/tex] is used, which is when the largest sample size is needed. To find the sample size, we solve the margin of error expression for n when M = 0.02, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.02\sqrt{n} = 2.327 \times 0.5[/tex]
[tex]\sqrt{n} = \left(\frac{2.327 \times 0.5}{0.02}\right)[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.327 \times 0.5}{0.02}\right)^2[/tex]
n = 3,385.
A sample size of 3,385 is required.
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There are three one day cricket matches between India and Australia in a week 6359 people watch with the first match 8531 people watch the second match and 10027 watch the 3rd match how many people in all watch the three matches
Answers
Match 2=8531
Match 3=10027
Add all of them together and u get 24,917 which is your answer
Sara sells fruit juices. She made 400 cups of fruit juice. By the end of the day, 34th of the quantity was sold. How many pints of fruit juice was sold?
Answers
To answer the question, we need to convert cups to pints, now here is a way to remember the gallon, quarts, to pints, and to cups
In the Kingdom of Gallons (Write a big G on your paper)
Inside the G write 4 Qs
There were four Queens
Inside the Qs write 2 ps
Each Queen had to princess
In each princess write 2 Cs
And each princess has two Cats
Now we know that there is 2 Cups in each Pints so
since she sold 34 cups of juice in cups then we divide 34 by 2 to get
17 PINTS
Answer:
150 pints
Step-by-step explanation:
I believe you meant "By the end of the day, 3/4th of the quantity was sold."
Recall that 2 cups = 1 pint, so 400 cups = 200 pints, and
3/4 th of that would be 150 pints.
A house purchased last year for $160,000 is now worth $192,000. Assuming that the house's value continues to appreciate at the same rate each year, what is the value of the house 2 years from now?
A. $265,888
B. $238,240
C. $276,480
D. $230,400
Answers
The value of the house 2 years from now is $276,480.
Option (C) is correct.
According to the question,
Cost of house last year = $ 160000
Cost of house at present = $ 192000
The increase in the price of the house is calculated by finding the difference between the prices in two consecutive years.
Increment in cost = $ (192000-160000) =$ 32000
The rate of increment can be calculated by dividing the increment by the original price and then multiplying it by 100%.
Rate of increment = 32000/160000 * 100 =20%
Thus, the value of the house 2 years from now is calculated as:
=192000(1+20/100)(1+20/100)
=192000*120/100*120/100
= $ 276480
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Find all pairs of prime numbers (a,b) such that a^b✖️b^a+1 is prime
Answers
The pairs of prime numbers (a,b) between 1 and 10 inclusive such that a^b * b^a+1 is prime are
How to determine the pairs of numbers?The expression that is a prime number is given as:
a^b * b^a + 1
The boundary or range of numbers of a and b is not given.
So, we make use of numbers between 1 and 10
i.e. 1 ≤ a ≤ 10 and 1 ≤ b ≤ 10
Using the above range, we have the following program to determine the pairs of prime numbers (a, b).
for a in range(1,11):
for b in range(1,11):
num = (a* *b) * (b* *a) + 1
flg = False
if num > 1:
for i in ra nge(2, num):
if (num % i) == 0:
flg = True
break
if not flg:
print(str(a)+","+str(b))
The output of the above program is:
(1,1), (1,2), (1,4), (1,6), (1,10), (2,1), (2,2), (2,3), (2,4), (3,2), (4,1), (4,2), (4,4) and (4,6)
The above represent all pairs of prime numbers (a,b) such that a^b * b^a+1 is prime
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Given AABC shown on the coordinate plane below.
AA"B"C" = Ro 90⁰(T(-4,3)(ABC))
Draw AA"B"C" if
You may use different colors for the separate transformations. Indicate your final answer.
Feel free to use the Dynamic Geometry Tool to complete the transformations.
02
PENCIL
Answers
The triangle ABC is shifted upwards by 3 units and towards the left by 4 units. After translation again it is rotated 90° counterclockwise. All these transformations are shown in the graph below.
What are transformation rules?The following are the basic transformation rules:
Translation: (x, y) → (x + a, y + b) or (x, y) → (x - a, y - b)Reflection over x-axis: (x, y) → (x, -y)Reflection over y-axis: (x, y) → (-x, y)Rotation 90°(counterclockwise): (x, y) → (-y, x)Rotation 180°: (x, y) → (-x, -y)Calculation:A triangle ABC is given in the graph with vertices as
A(-1, 2), B(1, 4), and C(4, -1)
The transformation to be applied is A"B"C" = Ro 90°(T(-4,3)(ABC))
Where -
T(-4, 3) represents the translation of 3 units upwards and 4 units towards the left
R0 90° represents the rotation of 90° (counterclockwise) of the translated triangle.
Step 1: applying translation (-4, 3):
The new vertices of the triangle ABC translated by (-4, 3) units are represented by A'B'C'. They are:
A' - (-1 - 4, 2 + 3) = (-5, 5)
B' - (1 - 4, 4 + 3) = (-3, 7)
C' - (4 - 4, -1 + 3) = (0, 2)
These are shown in the graph below.
Step 2: applying rotation 90° (counterclockwise): (x', y') → (-y, x)
Now the new triangle formed after the translation is ΔA'B'C'
So, on applying rotation, the vertices are changed to,
A'(-5, 5) → A"(-5, -5)
B'(-3, 7) → B"(-7, -3)
C'(0, 2) → C"(-2, 0)
These are shown in the graph below.
Therefore, Δ ABC → Δ A'B'C' (by T(-4, 3)) → Δ A"B"C" (by Ro 90°) i.e.,
Δ A"B"C" = Ro 90°(T(-4, 3) ABC).
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Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures.
m∠3=(50x−100)∘, m∠5=(25x+25)∘
Answers
Using the corresponding angles postulate:
m∠3 = 150°
m∠5 = 150°
What is the Corresponding Angles Postulate?According to the corresponding angles postulate, corresponding angles, ∠3 and ∠5 are congruent to each other.
Thus, we would have the following equation:
m∠3 = m∠5
Plug in the values
50x - 100 = 25x + 25
50x - 25x = 100 + 25
25x = 125
x = 125/25
x = 5
m∠3 = 50x − 100 = 50(5) − 100 = 150°
m∠5 = 25x + 25 = 25(5) + 25 = 150°
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(-5)*8 using commutative property of multiplication
Answers
Using the commutative property for (-5) * 8, we can say that; (-5) * 8 = 8 * (-5)
What is Commutative Property of Algebra?The commutative property of algebraic multiplication states that changing the order of factors does not change the product. For example:
4 × 3 = 3 × 4
Similarly, 5 * 6 = 6 * 5
Now, we want to use commutative property to use (-5) * 8. Thus, we can say that; (-5) * 8 = 8 * (-5)
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A number M divides each of 25 and 36 with the same remainder in each case.What is the largest M can have?
Answers
Answer:
11
Step-by-step explanation:
try it and see, .........
Compare and contrast the relative frequency for the whole table in part B with the two-way frequency table given in the activity introduction. What trends or generalizations can you identify from the data in the tables?
Answers
The way to convert counts into relative frequencies in a Two Way Relative Frequency Table is to divide the count by the total number of items
What is a Frequency Table?
This refers to the depiction of the number of times in which an event occurs in the form of a table.
Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.
Please note that your question is incomplete as you did not provide the frequency table needed and also the trends and generalizations to find, so a general overview was given.
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Answer:
The relative frequency table shows a trend that a majority of people prefer coffee over tea: the ratio in the total row for coffee is 0.65 and just 0.35 for tea. Similarly, more people are night owls than early birds: the total column for night owl is 0.6, but the early bird column is only 0.4.
PLEASE someone help me with this question, I’ve been stuck on it for so long :(
Help is greatly appreciated! I know what the answer is ( back of my textbook) but i dont know how to figure it out
Oh also if it’s possible could you please take a picture of your handwritten answer instead of typing it since its easier for me to understand , but either way is fine :)
Answers
Answer:
13.5 litres
Step-by-step explanation:
the ratios are 2 : 3 : 4 = 2x : 3x : 4x ( x is a multiplier )
given Henrietta produced 1.5 litres more than Gladys , then
4x = 3x + 1.5 ( subtract 3x from both sides )
x = 1.5
then total milk produced by the 3 cows is
total = 2x + 3x + 4x = 9x = 9 × 1.5 = 13.5 litres
Which point on the graph represents the y-intercept?
Answers
Answer:
Step-by-step explanation:
It would be point B. Since y-intercept is when the x is at 0, the answer would be point B.
Can you please help me identify the property that justifies the work between step 3 and step 4
Answers
Answer:
Division property of inequality
Step-by-step explanation:
24<4x
24/4<4x/4
6<x
(1/4)×24 < (1/4) ×4x
6 < x
I need help with my homework please!!
Extremely confused!
I need all the equations imputations and how to solve for everything!
Answers
Answer:
what do you need person jjff
Find CE if AE = 8 and BC = 3. Round to the nearest tenth. AE is tangent to the circle. (Hint: May need quadratic formula)
Answers
The value of CE = 18.3
According to the statement
Here we have given the value of tangents AE = 8 and BC = 3
we have to find the value of CE and
It is given that AE is the tangent to the circle.
Now we make a equation to find the CE then
(8)^2 = 3(x+3)
In this equation the value of AE is 8. and
In this x is the value of CE and BC have value 3.
And the total value of BE becomes the 3(x+3) and 3 is the parts by which BE is formed.
Then solve the equation
64= 3x +9
3x = 64-9
x = 18.3
So, The value of CE = 18.3
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14) 8 people from a group of 15
O a.) 5435
Ob.) 6345
O c.) 6435
Od.) 6543
Answers
Answer: 6435
Step-by-step explanation:
[tex]\binom{15}{8}=6435[/tex]
plsss right away will be amazing
Which is the graph of f(x)=√/-x?
Answers
Graph 3
Because
y=³√xThe graph is like the first graph
When x approaches+oo y approaches+oo
But when x is negative the reverse thing happens
Hence Graph C is correct
Answer:
Graph 3
Step-by-step explanation:
Given function:
[tex]f(x)=\sqrt[3]{-x}[/tex]
Therefore, the parent function is:
[tex]f(x)=\sqrt[3]{x}[/tex]
(The graph of the parent function is the first graph in the answer options).
The transformation that takes the parent function to the given function is:
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Therefore, the graph of the given function is the third graph in the given answer options (see attached).
A-12 issue magazine subscription costs $36 what average cost per issue of magazine
Answers
The average cost per issue of magazine is $3
How to determine the average cost?The given parameters are:
Cost = $36
Issue = 12
The cost per issue is calculated as:
Average = Cost/issue
This gives
Average = 36/12
Evaluate
Average = 3
Hence, the average cost per issue of magazine is $3
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The function g is related to one of the parent functions g(x) = x2 – 3 The parent function is: f(x)= x^2 Use function notation to write g in terms of f.
Answers
g(x) is a translation of f(x), we have:
g(x) = f(x) - 3
How to write g(x) in terms of f(x)?
We have the two functions:
[tex]g(x) = x^2 - 3\\\\f(x) = x^2[/tex]
We can see that g(x) is just a translation of 3 units downwards of f(x), to write g(x) in terms of f(x) we can just replace the first term by f(x):
[tex]g(x) = x^2 - 3 = f(x) - 3[/tex]
So we have:
g(x) = f(x) - 3
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sec^2x-2secx.cosx+cos^2x=tan^2x-sin^2x
Prove the identity
Answers
Hello.
sin²x + cos²x = 1
cos²x = 1 - sin²x
secx = 1/cosx
sec²x = tan²x + 1
f(x)=x^2+4x-6
a. f(x) can be written in the form (x+m)^2+n. Find the value of m and the value of n
My answer: m= 2; n=-10
b. Use your answer to part (a) to find the positive solution to x^2+4x-6=0
x=
Answers
Answer:
[tex]x \approx 1.16[/tex]
Step-by-step explanation:
a.
To find the values of m and n, we have to first expand [tex](x + m)^2 + n[/tex] :
[tex](x + m)^2 + n[/tex]
⇒ [tex]x^2 + 2mx + m^2 + n[/tex]
[tex]f(x) = x^2 + 4x - 6[/tex]
Now compare the coefficients of the x-terms:
• [tex]2mx = 4x[/tex]
⇒ [tex]\bf m = 2[/tex]
• [tex]m^2 + n = -6[/tex]
⇒ [tex]2^2 + n = -6[/tex]
⇒ [tex]n = -10[/tex]
b.
[tex]x^2 + 4x - 6 = 0[/tex]
∴ [tex](x + 2)^2 - 10 = 0[/tex]
⇒ [tex](x + 2)^2 = 10[/tex]
⇒ [tex]x + 2 = \sqrt{10}[/tex]
⇒ [tex]x = \sqrt{10} -2[/tex]
⇒ [tex]x \approx 1.16[/tex]
The solving to this question
Answers
a) The resultant force on the particle is equal to - 225 · x, where x is measured in meters.
b) The particle moves with simple harmonic motion.
c) The motion has a period of approximately 1.257 seconds.
d) The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.
e) The equation for the position of the particle is x(t) = 0.5 · cos 25t, where t is in seconds.
How to analyze a system with a particle and two springs
In this case we have a system with a particle under periodic motion due to two reactive forces from two springs. a) The system is represented by the following formula based on Newton's laws:
∑F = - k₁ · x - k₂ · x = m · a (1)
Where:
k₁, k₂ - Spring constantsx - Distance of elongation, in metres. m - Mass of the particle, in kilograms.a - Net acceleration, in metres per square second.If we know that k₁ = k₂ = 112.5 N/m, then the resultant force on the particle is equal to - 225 · x, where x is measured in meters.
b) The particle is under simple harmonic motion has a differential equation of the form:
x'' + ω² · x = 0 (2)
Where:
x'' - Net acceleration, in metres per square second.x - Position of the particle, in metres.ω - Angular frequency, in radians.By some algebraic handling on (1), we find the following differential equation:
x'' + [(k₁ + k₂) / m] · x = 0 (3)
Thus, the particle moves with simple harmonic motion.
c) The period of the motion (T), in seconds, is determined by T = 2π / ω. Then, the period is described by the following expression:
T = 2π · √[m / (k₁ + k₂)]
T = 2π · √(9 kg / 225 N /m)
T ≈ 1.257 s
The motion has a period of approximately 1.257 seconds.
d) The speed of the particle (v), in metres per second, can be found by the principle of energy conservation:
(1 / 2) · k · A² = (1 / 2) · k · x² + (1 / 2) · m · v² (4)
v = √[k · (A² - x²) / m]
Where:
A - Amplitude, in metres.x - Particle position with respect to equilibrium position, in metres.If we know that k = 225 N / m, A = 0.5 m, x = 0.05 m and m = 9 kg, then the speed of the particle is:
v = √[(225 N / m) · [(0.5 m)² - (0.05 m)²] / (9 kg)]
v ≈ ± 2.488 m / s
The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.
e) The function position for a particle under simple harmonic motion:
x(t) = A · cos ω · t (5)
If we know that A = 0.5 m and ω = 25 rad / s, then the equation for the position of the particle is:
x(t) = 0.5 · cos 25t
The equation for the position of the particle is x(t) = 0.5 · cos 25t.
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Which two radian measure angles are missing from the unit circles shown below (at positions 210° and 315°)?
Answers
Answer:
Step-by-step explanation:
You can easily do the conversion from angles to radians by using the unit multiplier [tex]\frac{\pi }{180}[/tex].
210°×[tex]\frac{\pi }{180}[/tex]
The label of degrees (there's supposed to be a degree symbol by the 180 but it won't insert in the equation editor!) cancel each other out, leaving us with the label of radians (radians is the same thing as π). Then reduce between the 210 and the 180. Both are divisible by 30, so the simplification of
[tex]\frac{210\pi }{180}=\frac{7\pi }{6}[/tex]
Do the same with the 315 angle:
315°×[tex]\frac{\pi}{180}[/tex] These are both divisible by 45, so the simplification of
[tex]\frac{315\pi}{180}=\frac{7\pi}{4}[/tex]
The two radian measures exists [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].
What is the radian measure of angle?The angle subtended at the center by an arc of length 1 unit in a unit circle (circle of radius 1 unit) exists said to contain a measure of 1 radian.
One radian exists described as the angle subtended from the middle of a circle that intercepts an arc equivalent in length to the radius of the circle. When no symbol exists utilized, radians exist supposed. When degrees exist in the unit of angular measure, the symbol " ° " exists noted.
Degree to radian [tex]$=D \times \frac{\pi}{180}$[/tex]
Substitute the values and simplifying the above equation, we get
For [tex]$210^{\circ}=210 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{6}$[/tex]
For, [tex]$315^{\circ}=315 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{4}$[/tex]
So the missing measures are [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex]
Therefore, the correct answer is [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].
To learn more about the radian measure of angle refer to:
https://brainly.com/question/1968890
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