An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Use the notation "4H", for example, to denote the outcome that the die comes up "4" and the coin comes up "heads", and "3HT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin.
a. Construct a tree diagram to show the 18 elements of the Sample Space S.
b. List the elements corresponding to the event A that a number less than 3 occurs on the die.
c. List the elements corresponding to the event B that two tails occur.
d. List the elements corresponding to the event C that a head and tail occur.
e. List the elements corresponding to the event A'.
f. List the elements corresponding to the event A' ∩B.
g. List the elements corresponding to the event A ∪ B.
h. Draw a Venn diagram to illustrate events A, B, and C.
i. Are A and B mutually exclusive? Are A and C mutually exclusive? Are B and C mutually exclusive?
Answers
Answer:
Kindly check attached picture and explanation
Step-by-step explanation:
A.) The tree diagram is attached in the picture below.
B.) Number less than 3 :
Event A:
A = {1HH, 1HT, 1TT, 1TH, 2H, 2T}
C.)
Event B:
B = {1TT, 3TT, 5TT}
D.)
Event C:
C = {1HT, 1TH, 3HT,3TH,5HT, 5TH}
E.)
A' = Elements not in A = number ≥ 3
A' = {3HH,3HT, 3TT, 3TH, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}
Question f and G are not well formatted ;
h. Check attached picture
I) i. Are A and B mutually exclusive? Are A and C mutually exclusive? Are B and C mutually exclusive?
A and B are mutually exclusive if AnB = ∅
Check :
AnB = {1TT}
Hence, A and B are not mutually exclusive
A and C
AnC = {1HT, 1TH}
A and C are not mutually exclusive.
B and C
BnC = ∅
B and C are mutually exclusive
Related Questions
A freight train travels 50 miles per hour. Write a linear function that describes the distance the train travels over time. Then make a graph to show the distance the train travels in 5 hours.
Answers
Answer:
d = 50h
d = distance traveled
h = hours
Step-by-step explanation:
(4/5)-2 solution
simplify the equation
Answers
Step-by-step explanation:
first we will take comman then
[tex] \frac{4}{5} - \frac{2 \times 5}{5} [/tex]
then 4 - 10
it will be
[tex] \frac{6}{5} [/tex]
or
[tex]1 \frac{1}{5} [/tex]
i hope it will help
Answer:
Solution is [tex]\frac{-6}{5}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5} - 2[/tex]
Set common denominators
[tex]\frac{4}{5} - \frac{10}{5}[/tex]
Subtract
[tex]\frac{4}{5} - \frac{10}{5} = \frac{-6}{5}[/tex]
Put the expressions in order from least to greatest value
Answers
Answer:
Least: [tex]\sqrt[6]{64}[/tex]
2nd least: ([tex]\sqrt{64}[/tex])²
2nd greatest: [tex]\sqrt{81}[/tex] · [tex]\sqrt{81}[/tex]
Greatest: 1/64^-2
Step-by-step explanation:
[tex]\sqrt[6]{64}[/tex] = 2
([tex]\sqrt{64}[/tex])² = 64
[tex]\sqrt{81}[/tex] · [tex]\sqrt{81}[/tex] = 9 · 9 = 81
1/64^-2 = 4,096
Find this value for brainiest
1+9^14
Answers
Answer: 2.2876792e+13
Step-by-step explanation: calculator
What’s the value of X on the parallelogram below?
Answers
Answer:
I think x is 34.75.
Step-by-step explanation:
Same side interior angles are supplementary to each other. Angle C and angle E are congruent to each other.
(4x-20)+61=180
4x+41=180
subtract 41 from both sides
4x=139
x=34.75
PLEASE HELP I ATTACHED THE PICTURE
Answers
Answer:
option 3 is correct
Step-by-step explanation:
because ....
It has to be Option 3/C
Exlaination: I have done this problem before and got it right.
PLS ANSWERRRRRRRRRRR
Answers
Bc I’ve done this before
Abel saved 43 more nickels than dimes. After he spent 17 dimes he had twice as many nickels than dimes. How many coins did he have left?
Answers
Answer:
180 coins
Explanation:
N = number of nickels (no nickels spent)
D = number of dimes initially saved
D' = number of dimes left after spending
1) N = D + 43
2) D' = D - 17
3) N = 2*D' = 2*(D - 17)
Set equations 1) and 3) equal to each other and solve for D:
D + 43 = 2*(D - 17)
D + 43 = 2*D - 34
D = 43 + 34 = 77
N = D + 43 = 77 + 43 = 120 nickels left
D' = D - 17 = 77 - 17 = 60 dimes left
Total coins left = 120 + 60 = 180 coins (I hope this is not too confusing for you)
Number of nickels 120, number of dimes 60 and total number of coins 180.
Given that, Abel saved 43 more nickels than dimes. After he spent 17 dimes he had twice as many nickels than dimes.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let
N = number of nickels (no nickels spent)
D = number of dimes initially saved
D' = number of dimes left after spending
N = D + 43 ..........(1)
D' = D - 17 ..........(2)
N = 2×D' = 2×(D - 17) ..........(3)
Set equations (1) and (3) equal to each other and solve for D:
D + 43 = 2×(D - 17)
D + 43 = 2D - 34
D = 43 + 34 = 77
N = D + 43 = 77 + 43 = 120 nickels left
D' = D - 17 = 77 - 17 = 60 dimes left
Total coins left = 120 + 60 = 180 coins
Therefore, number of nickels 120, number of dimes 60 and total number of coins 180.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
please help I'll give brainliest to the correct answer.
A triangle has side lengths 5, 7, and 11. Classify the triangle by it's angles. show your work.
Answers
Answer:
it is probably a right triangle
Step-by-step explanation:
right angle because 11 is 7 beside and 5 under
Answer:
i think its a right angle, not sure tho
Step-by-step explanation:
Which expression is equivalent to , if y > 0?
A.
B.
C.
D.
Answers
Answer:
D. 126y²Step-by-step explanation:
Given expression:
3[tex]\sqrt{2y^3}[/tex]· 7[tex]\sqrt{18y}[/tex]Simplify:
21 [tex]\sqrt{2*18*y^{3+1}}[/tex] = 21[tex]\sqrt{36y^4}[/tex] = 21(6y²) = 126y²Correct choice is D
Answer:
D. 126y²
Step-by-step explanation:
an = n2- 5
A) {1, -4, 4, 11, 116...}
B) {1, 2, 3, 4, 5, 6, ...}
C) { -4, 11, 116, 13451,...}
D) { -4, -1, 4, 11, 20,...}
Answers
Answer:
D
Step-by-step explanation:
if to substitute values of n=1;2;3;4;5 into
[tex]a_n=n^2-5[/tex]
then a₁=-4; a₂=-1; a₃=4; a₄=11; a₅=20.
It means the answer {-4, -1, 4, 11, 20,...} is correct.
I need help on this ?
Answers
Answer:
The Void
Step-by-step explanation:
no one can help you now
How do u do this one ???
Answers
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices- a, b, c, d, e- and only one correct answer. What is the probability that he answered both of the problems correctly? Write your answer as a fraction in simplest form.
Answers
1 correct answer out of 5 = 1/5
1/5 x 1/5 = 1/25
What is the 3rd number in the sequence 2n +2?
Answers
Answer:
it would be 2 right by the question mark
Step-by-step explanation:
so 2 is a number the n is going to be a number and then that leaves the last 2 left
MARKING BRAINLIEST
Which sentence is an example of an objective summary from Cynthia Crossen's "A Culinary Wasteland"?
A. Furthermore, Mr. Schlosser's appraisal is not comprehensive but a hodgepodge of impressions, statistics, anecdotes and prejudices.
B. As a stickler about statistics, I was disturbed by Mr. Schlosser's cavalier manipulation of data, which produced some startling — and, frankly, unbelievable — "facts."
C. Americans are addicted to cheap, bad food, he argues, and like all addictions, this one exacts broad and often unseen costs from the community.
D. Taking individual responsibility for one's impact on the global economy is far more complicated than just saying no to fast food, as Mr. Schlosser advises.
Answers
(6x2 - 10x +9)+(-5x2 + 9x-5)=
Answers
Answer:
x² - x + 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
(6x² - 10x + 9) + (-5x² + 9x - 5)
Step 2: Simplify
Combine like terms (x²): x² - 10x + 9 + 9x - 5Combine like terms (x): x² - x + 9 - 5Combine like terms (Z): x² - x + 4At the not much fun amusement park, Otaka Shawa paid $25.75 for three game of mini-marbles-golf and two rides on the slow-go-karts,while Soren Derkeister paid $35.75 for four games of mini-marbles-golf and three rides on the slow-go-karts. How much did each activity cost?
Answers
3m + 2g = 25.75
4m + 3g = 35.75
We’ll take the top equation and solve for g in terms of m.
2g = -3m + 25.75
g = (-3m + 25.75)/2
Then substitute that mess, um, expression, I to the second equation to solve for m.
4m + 3[(-3m + 25.75)/2] = 35.75
4m + (-9m + 77.25)/2 = 35.75
4m -4.5m + 38.625 = 35.75
-0.5m = -2.875
0.5m = 2.875
m = 5.75
Now we pick an equation, plug in the numerical value of m, and solve for a numerical value of g
3m + 2g = 25.75
3(5.75) + 2g = 25.75
17.25 + 2g = 25.75
2g = 8.50
g = 4.25
Checking the math:
4m + 3g = 35.75
4(5.75) + 3(4.25) = 23 + 12.75 = 35.75
Mini marbles golf cost $4.25, slow go karts cost $5.75.
Convert the fraction to a decimal 5/15
Answers
Explanation:
5/15 simplified is equal to 1/3
1/3 as a fraction is 0.3333 repeating
Draw a pair of adjacent complementary angle
Answers
Answer:
one angle can be 50 degrees and the other angle will be 40 degrees
Step-by-step explanation:
complementary is when 2 angles add up to 90 degrees
please help me . i'm trying to get my grades up and i'm struggling
Answers
Answer:
D
Step-by-step explanation:
just took that test
write the following sets in explicit form and determine the cardinality of
each set.
a) μ = {x: x is a positive counting number less 25}
Answers
Answer:
As the givens set μ has 24 elements.
Therefore,
Cardinality = 24Step-by-step explanation:
Given
μ = {x: x is a positive counting number less 25}
The set of natural numbers is often termed as the Counting number set.
As the counting numbers are less than 25.
Thus, the set μ is:
μ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}
We know that cardinality of the set is the number of elements in a given set.
As the givens set μ has 24 elements.
Therefore,
Cardinality = 24Can someone help me with 13-16 I’ll mark brainliest please guys I’m begging
Answers
How to solve your problem:
2a+13−0+65b
Simplify:
1. Add the numbers -
2a+13+0+65b = 2a+13+65b
2. Rearrange terms
2a+13+65b = 2a+65b+13
Solution: 2a+65b+13
The answer is B.
3 1/2 + 8 3/4 + 7 5/12 + 1 1/5 =
Answers
Answer:
25 3/5
Step-by-step explanation:
i think
Answer:
7/2+35/4+89/12+6/5=210+525+445+72/60=1252/60=313/15
Step-by-step explanation:
A force of 90 Newtons is applied to a 20 cm2 surface.
The force applied is then increased by 5 Newton’s and the surface area is increased by 5 cm^2
Answers
The given question is incomplete. The complete question is:
A force of 90 Newton's is applied to a [tex]20cm^2[/tex] surface. The force applied is then increased by 5 Newton's and the surface is increased by [tex]5cm^2[/tex]. What percentage does the outcome decrease by
Answer: The outcome decreases by 15.5 %
Step-by-step explanation:
Pressure is defined as the ratio of force per unit area.
[tex]Pressure=\frac{Force}{Area}[/tex]
Case 1: [tex]P_1=\frac{90N}{20cm^2}=4.5Ncm^{-2}[/tex]
Case 2: [tex]P_2=\frac{95N}{25cm^2}=3.8Ncm^{-2}[/tex]
Decrease in pressure = [tex]P_1-P_2[/tex] = [tex](4.5-3.8) Ncm^{-2}=0.7Ncm^{-2}[/tex]
Percentage decrease = [tex]\frac{0.7}{4.5}\times 100\%=15.5\%[/tex]
Thus the outcome decreases by 15.5 %
Evaluate: xy+2x^2, if x=0.1 and y=9.8
Answers
Answer: 1
Step-by-step explanation:
[tex](0.1)(9.8)+2(0.1)^2\\0.98+0.02=1[/tex]
1/3y-13=8? What is the answer
Answers
Answer:
y=63
Step-by-step explanation:
Start off by adding 13 to both sides:
1/3y-13=8
+13 +13
Now you have this:
1/3y=21
Now multiply each side by 3/1 (3) to get your answer:
(3) 1/3y=21 (3)
Y=63
Check your answer:
63/3=21 21-13=8
I hope this helps, and have a great day! <3 :)
Square root of. 100
Answers
Answer:
10
Step-by-step explanation:
10 squared is 100
This is because 10•10 equals 100.
Hope this helps!! :)
Demi has 221 songs on her phone. The songs take up 884 megabytes of storage . Each song takes up same amount of space . How many megabytes do 135 of these songs take up?
Answers
Answer:
540 megabytes
Step-by-step explanation:
We will first need to find out how much space a singular song will take up. We will do this by the storage taken up (884) by the number of songs she has:
884 / 221 = 4 mb taken up per song
Then we want to find out how many megabytes 135 of these songs take up, so we will multiply the mb taken up per song (4) by the number of songs we want to find (135):
4 x 135 = 540 megabytes
Edit: made a mistake in my original answer, apologies!
A rectangular garden has a width of 10 feet and a length of 14 feet. A cement walkway is added around the outside of the garden. The area of the garden and the walkway together are 320 square feet. What is the width of the walkway
Answers
Answer:
The width of the walkway is of 12.86 feet.
Step-by-step explanation:
Area of a rectangle:
The area of a rectangle of length l and width w is given by:
A = lw
A rectangular garden has a width of 10 feet and a length of 14 feet.
So the area of the rectangular garden is of 10*14 = 140 square feet.
The area of the garden and the walkway together are 320 square feet.
So the area of the walkaway is of 320 - 140 = 180 square feet.
What is the width of the walkway
It has the same length of the garden, of 14. So
[tex]14w = 180[/tex]
[tex]w = \frac{180}{14}[/tex]
[tex]w = 12.86[/tex]
The width of the walkway is of 12.86 feet.