Answers
Answer: 6
Step-by-step explanation:
Related Questions
Please show work, thank you
Answers
Answer:
[tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{1}{12}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Special Limit Rule [L’Hopital’s Rule]: [tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]
Indeterminate FormsDifferentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36}[/tex]
Step 2: Find Limit Pt. 1
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{\sqrt{36} - 6}{36 - 36}[/tex]Simplify: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{0}{0}[/tex]We see that we get 0 divided by 0, an indeterminate form.
Step 3: Find Limit Pt. 2
Use L'Hopital's Rule.
[Limit] Differentiate: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \lim_{x \to 36} \frac{(\sqrt{x} - 6)'}{(x - 36)'}[/tex][Limit] Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \lim_{x \to 36} \frac{(\sqrt{x})' - (6)'}{(x)' - (36)'}[/tex][Limit] Differentiate [Derivative Rule - Basic Power Rule]: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \lim_{x \to 36} \frac{\frac{1}{2\sqrt{x}}}{1}[/tex][Limit] Simplify: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \lim_{x \to 36} \frac{1}{2\sqrt{x}}[/tex][Limit] Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{1}{2\sqrt{36}}[/tex]Evaluate: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{1}{12}[/tex]∴ the limit as x approaches 36 of the given function is equal to one-twelfths.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
We are given with a limit and we need to find it's value , but first recall the identity which is the main key to this question :
[tex]{\boxed{\bf{a^{2}-b^{2}=(a+b)(a-b)}}}[/tex]Now , consider the limit we have ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}}[/tex]
Let's try direct substitution first ;
[tex]{:\implies \quad \displaystyle \sf \dfrac{\sqrt{36}-6}{36-36}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{6-6}{0}=\dfrac00}[/tex]
Here , we get an indeterminate form , so direct substitution didn't worked. So , consider again :
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}}[/tex]
Can be further written as ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{(\sqrt{x})^{2}-6^{2}}}[/tex]
Using the above identity we have ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{(\sqrt{x}-6)}{(\sqrt{x}-6)(\sqrt{x}+6)}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\cancel{(\sqrt{x}-6)}}{\cancel{(\sqrt{x}-6)}(\sqrt{x}+6)}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{1}{\sqrt{x}+6}}[/tex]
Now , put the limit
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{\sqrt{36}+6}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{6+6}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{12}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\displaystyle \bf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}=\dfrac{1}{12}}}}[/tex]
the zoo has 400 employess 72 percent of them are part time employess how many employess work full-time
Answers
Answer:
112
Step-by-step explanation:
There are 400 employees. If 72 of them work part-time, then 72% of 400 = 400*72%. This equals 288. Then you subtract that from 400 because the rest of them should be full-time workers. 400-288=112.
Answer:
112
Step-by-step explanation:
400 x 0.72 = 288, so that's the number of part-time employees.
400 - 288 = 112
.
Question 3 of 5
Ms. Bowen has 36 students in her class. This is 8 more
students than Ms. Arnold has.
How many students does Ms. Arnold have? Choose the correct equation and
answer
O A. x+8 = 36
x = 28 students
O B. x+8 = 36
x = 44 students
O C. X+44 = 36
x = 70 students
D. x+ 36 = 8
x = 44 students
SUBMIT
I will mark brainiest on
Answers
Answer:
A
Step-by-step explanation:
28 + 8 is 26
Identify the linear inequality from the graph
Answers
Answer:
B) y < 3/4x -2
Step-by-step explanation:
First, to eliminate 2 options let's see what sign we should use. The ≤ is a solid line where < is a dotted line. Next, you need to know which way to flip the sign. If it is under the line it is the < symbol.
Pls help! Answer quick
Answers
Answer:
Thursday
Step-by-step explanation:
Positive sign denotes that it has gained
Construction on Greenville High School’s football stadium costs $2,580 plus an additional $230 per day for labor. Construction on the school’s new baseball stadium costs $1,290 plus an additional $552.50 per day for labor.
What is the cost when both construction projects cost the same amount?
Answers
Answer: 4,856
Step-by-step explanation:
YEEE
The difference of a certain number and 4 is 36. What is the number
Answers
Answer:
40
Step-by-step explanation:
since you can just add 4 to 36 to get 40.
Answer:
40
Step-by-step explanation:
Let n represent the number then...
n-4=36
Add 4 to both sides
n-4+4=36+4
n=40
The number is 40
Someone pls help asap I really need the answer real quick
Answers
Answer:
380.16
Step-by-step explanation:
To find the capacity of a tank: multiply the length by the width to get the area. Then multiply the area by height to get volume. Finally, multiply the volume by 7.48 gallons per cubic foot to get capacity.
The value of expression x
2 + 3x
2 − 5n − 2 when x = 2 is
Answers
2 + 3x
= 5
X = 5Have a Nice day
Giving brainlyist to the person with the correct answer
Answers
Answer:
10 x 20
Step-by-step explanation:
it's 10 on the side of the shaded area, and 20 on the opposing side, so in this case, it must be 10 x 20 = 200.
hope it helps
Answer:
Your answer would be B!
Hope this helps.
In Cincinnati, fireworks are launched from a large barge on the Ohio River for a Labor Day celebration.
Their flight can be modeled by the function h(t) = -4.9(t - 4)2 + 80, where h is the height in meters and t is the time in seconds.
Suppose that buildings obstruct the fireworks. So, the barge is relocated 30 meters to the east.
Write a function to model the path of the fireworks in the new location.
Answers
The function to model the path of the fireworks in the new location is -4.9(t - 4)^2 + 50
Equations and expressionGiven the height reached by the flight expressed as:
h(t) = -4.9(t - 4)^2 + 80
If the barge is relocated 30 meters to the east, the new function will be derived by subtracting 30 from the initial function
New function = -4.9(t - 4)^2 + 80 - 30
New function = -4.9(t - 4)^2 + 50
Hence the function to model the path of the fireworks in the new location is -4.9(t - 4)^2 + 50
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How much money will be in Account A at the end of 3 years? $ How much money will be in Account B at the end of 3 years? $.
Answers
Account A is having $1,093 after 3 years. and Account B is having $1,120 after 3 years.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
Elisa put $1,000 in each bank.
Account A: gives her at a rate of 3% per annum compounded annually.
Account B: $40 bonus is added to the account each year.
After 3 years, account A will have
[tex]\rm Account \ A = 1000(1.03)^3\\\\Account \ A = 1093[/tex]
Account A is having $1,093 after 3 years.
After 3 years, account B will have
[tex]\rm Account \ B= 1000 + 3(40)\\\\Account \ B= 1,120[/tex]
Account B is having $1,120 after 3 years.
More about the compound interest link is given below.
https://brainly.com/question/25857212
Answer:
A ; 1092.73
B ; 1120
Step-by-step explanation:
The ages of two girls are in the ratio of 2:3 . 6 years hence the ratio of the girls will be 11 : 13 find their present age .
Answers
I NEED HELP BAD PLEASE HELP ME!!!!!!
Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Mila's account went into overdraft. To get back to a positive balance, she deposited money at a steady rate of $39.92 per week. After 3 weeks, she had $93.29 in the account. What was the balance when the account went into overdraft?
Answers
Answer:
The balance when the account went into overdraft was -38.02
Explanation:
Let x be the balance when the account went into overdraftTo get back to a positive balance he deposited money at a steady rate of $20.06 per week. Amount deposited per week = $20.06Amount deposited 8 weeks = Now amount in account after 8 weeks =x+160.48We are given that After 8 weeks, he had $122.46 in the account.So,x+160.48=122.46x=122.46-160.48x=-38.02
evaluate the function when x=4
Answers
The graph of the function is defined in the attached file please find it.
Graph function:[tex]\to \bold{x=4}[/tex]
In the given question, the x-axis holds a value that is "4".The holding value is "4" which is a positive number, and in the graph, it represents the positive value, which is defined in the attached file please find the attached file.Find out more information about the function here:
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Ya'll FR get 50 points if you answer this.
Why is the graph shown a line of best fit?
A) The graph shows a line of best fit because the association is zero.
B) The graph shows a line of best fit because the points fit around the line.
C) The graph shows a line of best fit because there is a straight line.
D) The graph shows a line of best fit because the points are plotted evenly above and below the line.
Answers
Answer:
I would say B
Step-by-step explanation:
A. would make no sense and the graph will always have a straight line unless its compairing something and it does not have anything to do with 0 because it shows where it starts
Problème:
Une épreuve de patinage de vitesse se déroule sur une piste dont les dimensions sont les suivantes:
Deux lignes droites de 82,19 m chacune et deux virages semi-circulaires de 75 m de diamètre.
1)Quelle est la longueur de la piste?
2)Les filles disputent une course sur 3000 m et les hommes sur 5000 m. Combien les concurrents doivent-ils parcourir de tours?
Merci d'avance.
Answers
Answer:
1) 314.38 m
2) Je ne sais pas.
can anyone help me to get the answers please its important 5. An item marked at ₹ 340 is sold for ₹ 324. What is the discount? 6. ___________ is the amount which we pay when we buy items
Answers
Unit 8: right triangles & trigonometry date: ________________________ per: _______ homework 2: special right triangles.
Answers
The sides and angles of a triangle can be determined using trigonometry ratios
The values of x, y and z are [tex]x = 14\sqrt 2[/tex], [tex]y =14[/tex] and [tex]z = 14\sqrt 3[/tex]
How to determine the missing values of the triangleThe upper triangle is a right triangle with an angle measure of 45 degrees.
So, the value of x is:
[tex]x = 14\sqrt 2[/tex]
Next, we calculate the hypotenuse (h) of the lower triangle using:
[tex]h^2 = (14\sqrt 2)^2 + (14\sqrt 2)^2[/tex]
So, we have:
[tex]h^2 = 784[/tex]
Take the square roots of both sides
[tex]h = 28[/tex]
The value of y is then calculated using the following sine ratio
[tex]\sin(30) = \frac y{28}[/tex]
Make y the subject
[tex]y =28 * \sin(30)[/tex]
Evaluate
[tex]y =14[/tex]
The value of z is then calculated using the following cosine ratio
[tex]\cos(30) = \frac z{28}[/tex]
Make z the subject
[tex]z =28 * \cos(30)[/tex]
Evaluate
[tex]z =28 * \frac{\sqrt 3}{2}[/tex]
[tex]z = 14\sqrt 3[/tex]
Hence, the values of x, y and z are [tex]x = 14\sqrt 2[/tex], [tex]y =14[/tex] and [tex]z = 14\sqrt 3[/tex]
Read more about right triangles at:
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help me. I need help
Answers
Answer:
3 ------------- √9
6 ------------- ³√216
7 ------------- ³√343
8 ------------- √64
9 ------------ ³√729
10 ----------- √100
Step-by-step explanation:
Hope this helps .
Answer:
[tex]1. \sqrt{9} =3[/tex]
[tex]2. \sqrt[3]{729}=9[/tex]
[tex]3. \sqrt{100} =10[/tex]
[tex]4. \sqrt[3]{216} =6[/tex]
[tex]5. \sqrt{64} =8[/tex]
[tex]6. \sqrt[3]{343} = 7[/tex]
Step-by-step explanation:
[tex]1. \sqrt{9} =3[/tex] [tex]3*3=9[/tex]
[tex]2. \sqrt[3]{729}=9[/tex]
[tex]\sqrt[3]{9^3}=9[/tex]
[tex]3. \sqrt{100} =10[/tex] [tex]10*10=100[/tex]
[tex]4. \sqrt[3]{216} =6[/tex]
[tex]\sqrt[3]{6^3}=6[/tex]
[tex]5. \sqrt{64} =8[/tex] [tex]8*8=64[/tex]
[tex]6. \sqrt[3]{343} = 7[/tex]
[tex]\sqrt[3]{7^3}=7[/tex]
Hope this helps!
Tommy’s team has won 15 games and lost 10 games. What percent of its games has the team won?
Answers
Answer:
60%
Step-by-step explanation:
10 + 15
25
15/35 = 60%
We need to first find the total number of games so 15 plus 10 gets us 25. Then we take and divide the number of games won by the total number played, getting us 60%.
Have an amazing day!!
PLEASE RATE!!
Edward drove 275 miles in 212 hours and 357.5 miles in 314 hours. If he drove at a constant rate, how much distance did he travel every hour? Enter your answer in the box below.
Answers
The average distance that he travelled every hour is; 2.4357 miles per hour
What is the average distance?He drove 275 miles in 212 hours.
Now, to find the rate of distance per hour;
Distance per hour = 275/212 = 1.2972 miles per hour
He drove 357.5 miles in 314 hours.
Distance per hour = 357.5/314
Distance per hour = 1.1385 miles per hour
Thus, his average distance per hour = 1.2972 + 1.1385 = 2.4357 miles per hour
Read more about average distance at; https://brainly.com/question/308777
Circle O has a circumference of 88 cm.
What is the length of the radius of the circle?
cmין
Answers
Answer:
r = 14 cm
Step-by-step explanation:
Circumference = 2πr = 88
=> r = 88 / 2 x 22/7
=> r = 88 x 7 / 44
=> r = 2 x 7
=> r = 14 cm
Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet. What is the quadratic equation that would model this scenario? x2 = (2x)(x – 16) x2 = (x)(x – 16) x2 = (x)(x 16) x2 = (2x)(x 16).
Answers
The quadratic equation that would model this scenario is
[tex]x^{2} = 2x(x-16)[/tex]
Let us take the side of the square = x
Area of the square = x²
Length of the rectangular garden = 2x
Width of the rectangular garden = x-16
So, the area of the new vegetable garden = length*width
Area of the new or rectangular vegetable garden = 2x(x-16)
What is a quadratic equation?The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by [tex]ax^2+bx+c[/tex]coefficient [tex]x^{2}[/tex]non-zero.
Since it is given that
Area of square garden = area of the rectangular garden
[tex]x^{2} = 2x(x-16)[/tex]
Thus, the quadratic equation that would model this scenario is
[tex]x^{2} = 2x(x-16)[/tex]
To get more about quadratic equations refer to:
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Answer:
its a
Step-by-step explanation:
Solve this problem. What is x?
Don’t forget to use the equation a^2 + b^2 = c^2
SHOW YOUR WORK.
Answers
Step-by-step explanation:
a²+b²=c²
THIS is the Pythagorean theorem which is:
Hypotenuse² + Base² = perpendicular ²
Thus inputting values:
(√117)² + (6)² = (x)²
117 + 36 = x²
x² = 153
x= √153 (ans)
help me pleaseeeeeeeee
Answers
Answer:
Angles on a straight line add up to 180 degrees so for the 129 degrees you will take 180 - 129 = 51. In the triangle you will add 51 and 55 = 106 but remember in a triangle all angles should be equal to 180. So 180 - 106 = 74. X=74degrees
Since the exterior angle is 129 degrees, the other angle supplementary to it would equal 51.
After you know that, add 51 + 55 = 106
180 - 106 = 74, so the measure of x is 74 degrees.
hehehehehehhelphelphelpgelpggepkepewnwe
Answers
(6,5)
If you start at the origin (which is (0,0)) and go 6 right, that's six for x. If you then go 5 up, that means y is 5.
(6,5)
Answer:
(6,5)
Step-by-step explanation:
6 is on the x-axis, and 5 is on the y-axis
Is this right. Can you explain? Algebra
Answers
Answer:no the correct answer should be (4,1)
Step-by-step explanation:
I reduced the equations to linear form then I used substitution to find the cordinents.
Two trains, train A and train B,weigh a total of 161 tons. Train A is heavier than train B. The difference of their weights is 125 tons. What is the weight of each train?
Answers
Answer:
Train A : 143 tons ; Train B : 18 tons
Step-by-step explanation:
Call train A as A, train B as B
A + B = 161t
A - B = 125t
A = (161+125) : 2 = 143t
B = 143t - 125t = 18t
Brown Law Firm collected data on the transportation choices of its employees for their morning commute. The table shows the percentages of the type of transportation of the male and female employees. A 5-column table has 3 rows. The first column has entries Male, female, total. The second column is labeled public with entries 12, 8, 20. The third column is labeled Own with entries 20, 10, 30. The fourth column is labeled other with entries 4, 6, 10. The fifth column is labeled total with entries 36, 24, 60. Consider the following events: A: The employee is male. B: The employee is female. C: The employee takes public transportation. D: The employee takes his/her own transportation. E: The employee takes some other method of transportation. Which two events are independent? A and C A and D B and D B and E.
Answers
The two events out of the listed events which are independent events are given by: Option A: A and C
What is chain rule in probability?For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(A|B)[/tex]
What is law of total probability?Suppose that the sample space is divided in n mutual exclusive and exhaustive events tagged as
[tex]B_i \: ; i \in \{1,2,3.., n\}[/tex]
Then, suppose there is event A in sample space.
Then probability of A's occurrence can be given as
[tex]P(A) = \sum_{i=1}^n P(A \cap B_i)[/tex]
Using the chain rule, we get
[tex]P(A) = \sum_{i=1}^n P(A \cap B_i) = \sum_{i=1}^n P(A)P(B_i|A) = \sum_{i=1}^nP(B_i)P(A|B_i)[/tex]
How to form two-way table?Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] values of Y are there as [tex]Y_1, Y_2, ..., Y_k[/tex]rows and left to the columns. There will be [tex]n \times k[/tex]values will be formed(excluding titles and totals), such that:
Value([tex]i^{th}[/tex] row, [tex]j^{th}[/tex] column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex]values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
Suppose that two events are denoted by A and B.
They are said to be independent event if and only if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
The given frequency table is:
[tex]\begin{array}{ccccc} &\text{Public}&\text{Own}&\text{Others}&\text{Total}\\\text{Male}&12&20&4&36\\\text{Female}&8&10&6&24\\\text{Total}&20&30&10&60\end{array}[/tex]
The probability table for the same labels would be:
[tex]\begin{array}{ccccc} &\text{Public}&\text{Own}&\text{Others}&\text{Total}\\\text{Male}&12/60&20/60&4/60&36/60\\\text{Female}&8/60&10/60&6/60&24/60\\\text{Total}&20/60&30/60&10/60&1\end{array}[/tex]
The events A, B,C,D and E are given as:
A: The employee is male. B: The employee is female. C: The employee takes public transportation. D: The employee takes his/her own transportation.E: The employee takes some other method of transportation.Checking all the listed options one by one, for them being independent:
Case 1: A and CP(A) = P(The employee is male. ) = 36/60
P(C) = P(The employee takes public transportation.) = 20/60[tex]P(A \cap C) = 12/60 \\\\ P(A)P(C) = \dfrac{36 \times 20}{60^2} = 12/60[/tex]
[tex]P(A \cap C) = P(A)P(C)[/tex]
Thus, A and C are independent events.
Case 2: A and DP(A) = P(The employee is male. ) = 36/60
P(D) = P(The employee takes his/her own transportation.) = 30/60
[tex]P(A\cap D) = 20/60\\\\P(A)P(D) = \dfrac{30 \times 36}{60^2} = 12/60 \neq P(A \cap D)[/tex]
Thus, A and D are not independent events.
Case 3: B and DP(B) = P(The employee is female. ) = 24/60
P(D) = P(The employee takes his/her own transportation.) = 30/60
[tex]P(B \cap D) = 10/60 \neq P(B)P(D)=\dfrac{24 \times 30}{60^2} = 12/60[/tex]
Thus, B and D are not independent events.
Case 4: B and EP(B) = P(The employee is female. ) = 24/60
P(E) = P(The employee takes some other method of transportation.) = 10/60
[tex]P(B \cap E) = 6/60 \neq P(B)P(E)= \dfrac{24 \times 10}{60^2} = 4/60[/tex]
Thus, B and E are not independent events.
Thus, the two events out of the listed events which are independent events are given by: Option A: A and C
Learn more about independent events here:
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Answer:
First option!!
"A and C"
Step-by-step explanation:
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