Two coins are tossed. Assume that each event is equally likely to occur. a) Use the counting principle to determine the number of sample points in the sample space. b) Construct a tree diagram and list the sample space. c) Determine the probability that no tails are tossed. d) Determine the probability that exactly one tail is tossed. e) Determine the probability that two tails are tossed. f) Determine the probability that at least one tail is tossed.
Answers
Answer:
(a) 4 sample points
(b) See attachment for tree diagram
(c) The probability that no tail is appeared is 1/4
(d) The probability that exactly 1 tail is appeared is 1/2
(e) The probability that 2 tails are appeared is 1/4
(f) The probability that at least 1 tail appeared is 3/4
Step-by-step explanation:
Given
[tex]Coins = 2[/tex]
Solving (a): Counting principle to determine the number of sample points
We have:
[tex]Coin\ 1 = \{H,T\}[/tex]
[tex]Coin\ 2 = \{H,T\}[/tex]
To determine the sample space using counting principle, we simply pick one outcome in each coin. So, the sample space (S) is:
[tex]S = \{HH,HT,TH,TT\}[/tex]
The number of sample points is:
[tex]n(S) = 4[/tex]
Solving (b): The tree diagram
See attachment for tree diagram
From the tree diagram, the sample space is:
[tex]S = \{HH,HT,TH,TT\}[/tex]
Solving (c): Probability that no tail is appeared
This implies that:
[tex]P(T = 0)[/tex]
From the sample points, we have:
[tex]n(T = 0) = 1[/tex] --- i.e. 1 occurrence where no tail is appeared
So, the probability is:
[tex]P(T = 0) = \frac{n(T = 0)}{n(S)}[/tex]
This gives:
[tex]P(T = 0) = \frac{1}{4}[/tex]
Solving (d): Probability that exactly 1 tail is appeared
This implies that:
[tex]P(T = 1)[/tex]
From the sample points, we have:
[tex]n(T = 1) = 2[/tex] --- i.e. 2 occurrences where exactly 1 tail appeared
So, the probability is:
[tex]P(T = 1) = \frac{n(T = 1)}{n(S)}[/tex]
This gives:
[tex]P(T = 1) = \frac{2}{4}[/tex]
[tex]P(T = 1) = \frac{1}{2}[/tex]
Solving (e): Probability that 2 tails appeared
This implies that:
[tex]P(T = 2)[/tex]
From the sample points, we have:
[tex]n(T = 2) = 1[/tex] --- i.e. 1 occurrences where 2 tails appeared
So, the probability is:
[tex]P(T = 2) = \frac{n(T = 2)}{n(S)}[/tex]
This gives:
[tex]P(T = 2) = \frac{1}{4}[/tex]
Solving (f): Probability that at least 1 tail appeared
This implies that:
[tex]P(T \ge 1)[/tex]
In (c), we have:
[tex]P(T = 0) = \frac{1}{4}[/tex]
Using the complement rule, we have:
[tex]P(T \ge 1) + P(T = 0) = 1[/tex]
Rewrite as:
[tex]P(T \ge 1) = 1-P(T = 0)[/tex]
Substitute known value
[tex]P(T \ge 1) = 1-\frac{1}{4}[/tex]
Take LCM
[tex]P(T \ge 1) = \frac{4-1}{4}[/tex]
[tex]P(T \ge 1) = \frac{3}{4}[/tex]
Related Questions
The five number summary of a dataset is given as
0, 4, 12, 14, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
The five number summary of a dataset is given as
2, 8, 14, 18, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
.
.
Answers
Given:
The five number summary of two data sets are given as:
a) 0, 4, 12, 14, 20
b) 2, 8, 14, 18, 20
To find:
The range for the outliers.
Solution:
We know that,
An observation is considered an outlier if it is below [tex]Q_1-1.5(IQR)[/tex]
An observation is considered an outlier if it is above [tex]Q_3+1.5(IQR)[/tex]
Where, IQR is the interquartile range and [tex]IQR=Q_3-Q_1[/tex].
The five number summary of two data sets are given as:
0, 4, 12, 14, 20
Here, [tex]Q_1=4[/tex] and [tex]Q_3=14[/tex].
Now,
[tex]IQR=14-4[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29][/tex]
An observation is considered an outlier if it is below -11.
An observation is considered an outlier if it is above 29.
The five number summary of two data sets are given as:
2, 8, 14, 18, 20
Here, [tex]Q_1=8[/tex] and [tex]Q_3=18[/tex].
Now,
[tex]IQR=18-8[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33][/tex]
An observation is considered an outlier if it is below -7.
An observation is considered an outlier if it is above 33.
Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 17, reflected across the x-axis, and shifted by 19 units left.
A. g(x) = −17ln (x + 19)
B. g(x) = 17ln (x − 19)
C. g(x) = 17ln (x + 19)
D. g(x) = −17ln (x − 19)
Answers
Answer:
b
Step-by-step explanation:
ANSWER. EXPLANATION. The given logarithmic function is. The transformation,. stretches the graph of y=f(x) vertically by a factor of c units ...
4 votes
ANSWER[tex]y = - 3 ln(x - 7) [/tex]EXPLANATIONThe given logarithmic function is [tex]f(x) = ln(x) [/tex]The transformation, [tex]y = - cf(x - k)[/tex]stretches
What is the mapping for a reflection in the line y=-1
Answers
Answer:
0
Step-by-step explanation:
the key mapping for a reflection in the line y=-1 is 0
The distance between point (3,0) and (7, 2p) is √80. Find the value of p.
Answers
Distance = √[ ( 7 - 3 )^2 + ( 2p - 0 )^2 ]
Distance = √(4)^2 + ( 2p)^2
Distance = √16 + 4p^2
As the question said : Distance = √80
√80 = √16 + 4p^2
Thus :
16 + 4p^2 = 80
Subtract both sides 16
16 - 16 + 4p^2 = 80 - 16
4p^2 = 64
Divide both sides by 4
4p^2 ÷ 4 = 64 ÷ 4
p^2 = 16
Thus :
p = 4 or p = - 4
To what extent do syntax textbooks, which analyze the structure of sentences, illustrate gender bias? A study of this question sampled sentences from 10 texts.23 One part of the study examined the use of the words "girl," "boy," "man," and "woman." We will call the first two words juvenile and the last two adult. Is the proportion of female references that are juvenile (girl) equal to the proportion of male references that are juvenile (boy)? Here are data from one of the texts:
Answers
Answer: Hello your question is incomplete attached below is the complete question
answer:
i) 0.8 , standard error = 0.0516
ii) 0.39, standard error = 0.0425
Step-by-step explanation:
i) proportion of Juveniles reference for females ( f )
= x₁ / n₁ = 48 / 60 = 0.8
standard error = [tex]\sqrt{\frac{0.8(1-0.8)}{60} }[/tex] = 0.0516
ii) Proportion of Juveniles reference for males ( m )
= x₂ / n₂ = 52 / 132 = 0.39
standard error = [tex]\sqrt{\frac{0.39(1-0.39)}{132} }[/tex] = 0.0425
What is the answer to 6,1=? 8,2=20, 12,3=20, 10,5=52, 6,1=?
Answers
can u plz check if the question is right
a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to find x.)
Answers
Set the proportion as shown:
2660/4.75 = x/1
Cross multiply:
4.75x = 2660
Divide both sides by 4.75
x = 560
Answer: 560 miles per hour
Pam’s eye-level height is 324 ft above sea level, and Adam’s eye-level height is 400 ft above sea level. How much farther can Adam see to the horizon? Use the formula d = StartRoot StartFraction 3 h Over 2 EndFraction EndRoot, with d being the distance they can see in miles and h being their eye-level height in feet.
1 mi
StartRoot 6 EndRoot mi
19 mi
19 StartRoot 6 EndRoot mi
Answers
9514 1404 393
Answer:
(b) √6 mi
Step-by-step explanation:
Putting the given heights into the formula, we find the difference in distances to be ...
Adam' horizon distance = √((3/2)(400)) = 10√6 . . . miles
Pam's horizon distance = √((3/2)(324)) = 9√6 . . . . miles
Then the difference Adam can see is farther than the distance Pam can see by ...
10√6 -9√6 = √6 . . . miles
Evaluate the expression 2x - (4y - 3) + 5xz, when x = -3, y = 2, and z = -1.
Answers
Answer:
4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
2x - (4y - 3) + 5xz
x = -3
y = 2
z = -1
Step 2: Evaluate
Substitute in variables: 2(-3) - (4(2) - 3) + 5(-3)(-1)(Parenthesis) Multiply: 2(-3) - (8 - 3) + 5(-3)(-1)(Parenthesis) Subtract: 2(-3) - 5 + 5(-3)(-1)Multiply: -6 - 5 + 15Subtract: -11 + 15Add: 4A farmer weighs a dozen chicken eggs. The heaviest egg is 56 g.
Answers
Step-by-step explanation:
hi
what is your question?
Step-by-step explanation:
please tell full questions
which point lies on the line defined by 7x - 7y = -43
Answers
Answer:
(-6,0) and (0,-6) are the points on the graph
Find the area of a circle with a radius of 6 ft. Round off your answer to one decimal point. (The formula for the area of a circle is A = ar?)
Answers
Answer:
Using 3.14 for pi A = 113.0 ft^2
Using the pi button A = 113.1 ft^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi ( 6)^2
A = 36 pi
Using 3.14 for an approximation for pi
A = 36(3.14) = 113.04
To 1 decimal
113.0
Using the pi button
A = 113.0973355
A = 113.1
Which of the following is the graph of…
Answers
Answer:
A
Step-by-step explanation:
Try graphing the function on desmos
Buses on a particular route stop in front of De Anza College every 20 minutes between 3:00 p.m. and 1:00 a.m. The waiting times are equally likely. We asked the 33 people waiting at 6:45 p.m. how long they had been waiting, and then calculated the average wait time for those people.
The probability that the average wait time is no more than 15 minutes is:____.
a. 1.
b. 0. 7500.
c. 0. 7769.
d. 0.
The distribution of the average wait times is:
a. N(10 , 1. 0050).
b. U(0 , 20).
c. N(10 , 5.7735).
d. Exp (1 20).
Answers
Answer:
1. a. 1
2. a. N(10 , 1. 0050)
Step-by-step explanation:
The average time for the people waiting for the bus will be no longer than 15 minutes. There are 33 people who were observed and their waiting time did not exceed 15 minutes. The probability is therefore 1 for the wait time.
help again please i need to pass this
Answers
√50x³y
= √5²×2×x²×x×y
= 5x√2xy
d is the correct answer
Answer:
here
Step-by-step explanation:
g Kristina Karganova invites 17 relatives to a party: her mother, aunts, uncles, brothers, 1 male cousin, and female cousins. If the chances of any one guest arriving first are equally likely, find the probabilities that the first guest to arrive is as follows. (a) A brother or an uncle (b) A brother or a cousin (c) A brother or her mother (a) The total number of outcomes is nothing and the number of outcomes in the event is nothing.
Answers
Answer:
7 / 17 ;
10 / 17 ;
5 / 17
Step-by-step explanation:
Guests :
Mother = 1
Aunts = 3
Uncles = 3
Brothers = 4
Male cousin = 1
Female cousin = 5
_________________
Total guests = 17
Since each of the guests have an equal probability of arrival :
Probability that first guest to arrive :
Brother or uncle :
Number of brothers =4
Number of uncles = 3
P(brother or uncle) = required outcome / Total possible outcomes
Required outcome (number of brothers + uncles) = (4 + 3) = 7
Total possible outcomes = total guests = 17
P(brother or uncle) = 7 / 17
2.)
P(brother or cousin) :
Required outcome = (number of brothers + cousins) = (4 + 1 + 5) = 10
Total possible outcomes = total guests = 17
P(brother or cousin) = 10/17
3.)
P(brother or mother) ;
Required outcome = (number of brothers + mother) = (4+1) = 5
Total possible outcomes = total guests = 17
P(brother or mother) = required outcome / Total possible outcomes = 5 / 17
Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?
Answers
Answer:
682
Step-by-step explanation:
191,919 + 262,626
454545 ÷ 666 = 682.5
Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.
Question 27 of 58
Select the equation that represents the problem. Let x represent the unknown
number.
Mr. Jefferson bought 336 markers for his class. The
markers came in packs of 12. How many packs did he
buy?
A. 336 - x= 12
B. 12x= 336
O C. 336x= 12
O D. x + 12 = 336
SUBMIT
Answers
Answer:
B.
Step-by-step explanation:
The answer is B.
If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation?
a. 300x1 + 125x2 > = 4,000
b. 300x1 + 125x2 < = 4,000
c. 425(x1 + x2) < = 4,000
d. 300x1 + 125x2 = 4,000
Answers
Answer:
b. 300x1 + 125x2 < = 4,000
Step-by-step explanation:
Maximum of 4,000 hours
This means that the the total amount of labor has to be of at most 4,000, that is:
[tex]T \leq 4000[/tex]
300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor
The total amount of labor is:
[tex]T = 300x1 + 125x2[/tex]
Uniting the two equations:
[tex]T \leq 4000[/tex]
[tex]300x1 + 125x2 \leq 4000[/tex]
And thus the correct answer is given by option b.
please help me with this
Answers
9514 1404 393
Answer:
92°
Step-by-step explanation:
The "givens" tell you the E and F are midpoints of their respective segments. That means EF ║ AB and angles DBF and EFC are "corresponding" angles with respect to transversal BC and those parallel lines. Corresponding angles are congruent, so ...
m∠DBF = m∠EFC = 92°
Enter the solutions from least to greatest.
f(x) = (x – 3)(2x – 8)
Answers
Answer:
The zeroes of the function are: 3 and 4
Step-by-step explanation:
Find f(2) given f(x) = -3x^2 + 2x+11
Answers
Answer:
Answer:f(2)=-3(2)^2+2*2+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3
hence, f(2)=3
(x + y, 2) = (13, 2x - y)
Answers
Answer: (x, y) = (5,8)
Step-by-step explanation:
x + y = 13 2x - y = 2
y = -x + 13
2x - (-x + 13) = 2 3x =15
x=5
x=5 y = -x + 13
y = -(5) + 13 = 8
find x on this special right triangle, 45 is not an option!!!!
Answers
let the line between 2 tria be y
sin 60/8√2 = sin 90/y
y=13.06
sin 45/13.06 = sin 90/x
x=18.46
Answer:
First, find the hypotenuse of the right triangle with the 60° & 30°.
Hypotenuse = hsin(x) = opposite side/hypotenuse[tex]sin(60) = \frac{8\sqrt{2}}{h} \\\\sin(60)h=8\sqrt{2}\\\\\frac{\sqrt{3}}{2} h=8\sqrt{2}\\\\h=\frac{8\sqrt{2}}{\frac{\sqrt{3}}{2}}=8\sqrt{2}*\frac{2}{\sqrt{3}} =\frac{16\sqrt{2} }{\sqrt{3}} =\frac{16\sqrt{2}(\sqrt{3}) }{\sqrt{3}(\sqrt{3})} =\frac{16\sqrt{6} }{3}[/tex]
Use that side length to find x.
sin(x) = opposite side/hypotenuse[tex]sin(45)=\frac{\frac{16\sqrt{6}}{3}}{x}\\\\sin(45)x=\frac{16\sqrt{6}}{3} \\\\\frac{\sqrt{2}}{2}x=\frac{16\sqrt{6}}{3} \\\\x=\frac{\frac{16\sqrt{6}}{3}}{\frac{\sqrt{2}}{2}}=\frac{16\sqrt{6}}{3}*\frac{2}{\sqrt{2}}=\frac{16\sqrt{2}\sqrt{3}(2)}{3\sqrt{2} }=\frac{32\sqrt{3} }{3}[/tex]
lim(x-0) (sinx-1/x-1)
Answers
lim ( sinx-1)/(x-1)
x=>0
apply x=0
(sin(0)-1)/(0-1)
(0-1)/(-1)
=1
An Experiment to investigate the relation between two physical quantities was performed where 10 data pairs were collected. You are to perform regression analysis to describe the relation between the two quantities using a polynomial. What are the possible values for the order of that polynomial?
a) from 0 to 10
b) from 1 to 9
c) from 1 to 10
d) Any integer
Answers
Answer:
d). Any Integer.
Step-by-step explanation:
Regression analysis is characterized as the statistical method that is employed to determine the association between a dependent, as well as, the independent variable(one or more). It
As per the question, the probable values for the arrangement of a polynomial would be 'any integer' in order to determine the relationship among the different variables(the two physical quantities). Since a regression analysis helps in knowing the factors that influence the other and the factors that do not affect much in order to reach a reliable conclusion. Thus, any of the values can be examined to examine the association among them. Hence, option d is the correct answer.
A hotel has 210 units. All rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant. Each occupied room costs $24 per day to service and maintain. What should the hotel charge per day in order to maximize daily profit
Answers
Answer: [tex]\$162[/tex]
Step-by-step explanation:
Given
There are 210 units of hotel
Each room charge $90 when fully occupied
occupied room charges is $24 per day
Suppose x rooms are vacant, so, there 210-x occupied
Daily expense on maintenance[tex]=(210-x)\times 24[/tex]
Earning from 210-x rooms[tex]=(210-x)(90+x)[/tex]
Profit(P)=Earning - Expense
[tex]\Rightarrow P=(210-x)(90+x)-(210-x)24\\\Rightarrow P=21,600+210x-90x-x^2-5040+24x\\\Rightarrow P=-x^2+144x+16,560\\[/tex]
To get the maximum profit, determine the derivative of P w.r.t. x and equate it to zero
[tex]\Rightarrow \dfrac{dP}{dx}=-2x+144\\\\\Rightarrow -2x+144=0\\\\\Rightarrow x=72[/tex]
Charges for maximum profit is [tex]90+72=\$162[/tex]
Number of occupied rooms are [tex]210-72=138[/tex]
The hotel charge per day will be $162 in order to maximize daily profit.
Given that, Hotel has 210 units
Let us consider that x rooms are vacant.
Total occupied rooms = [tex](210-x)[/tex]
Since, Each occupied room costs $24 per day to service and maintain
So, Total expense = [tex]24*(210-x)=5040-24x[/tex]
Since, For all rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant.
So, Total earing = [tex](210-x)*(90+x)=-x^{2} +120x+21600[/tex]
Profit = Total earning - Total expense
[tex]P=-x^{2} +120x+21600-5040+24x\\\\P=-x^{2} +144x+16560[/tex]
In order to maximize profit, Differentiate profit expression with respect to x.
[tex]\frac{dP}{dx}=\frac{d}{dx}(-x^{2} +144x+16560) \\\\\frac{dP}{dx}=-2x+144=0\\\\\\x=\frac{144}{2}=72[/tex]
Thus, Hotel charges per day for maximum profit = [tex]90+x=90+72=162[/tex]
Learn more:
https://brainly.com/question/19578119
please give me correct answer
Answers
Answer:
36 = 17+19 ---> They are twin primes and their sum is 3684 = 41+43 ---> They are twin Primes and sum is 84120 = 59+61 ---> They also are twin primes and their sum is 120144 = 71+73 ---> They are also twin primes and the sum is 144What is the equation of exponential regression equation? Round all numbers you your answer to three decimal places
Answers
Given:
Consider the below figure attached with this question.
The value in the given figure are:
[tex]a=0.2094539899[/tex]
[tex]b=2.507467975[/tex]
[tex]r^2=0.9435996398[/tex]
[tex]r=0.9713905701[/tex]
To find:
The exponential regression equation for the given values (Rounded to three decimal places).
Solution:
The general form of exponential regression equation is:
[tex]y=a\cdot b^x[/tex] ...(i)
Where, a is the initial value and b is the growth/decay factor.
The given values are:
[tex]a=0.2094539899[/tex]
[tex]b=2.507467975[/tex]
Round these numbers to three decimal places.
[tex]a\approx 0.209[/tex]
[tex]b\approx 2.507[/tex]
Putting [tex]a=0.209, b=2.507[/tex] in (i) to find the exponential regression equation.
[tex]\hat{y}=0.209\cdot 2.507^x[/tex]
Hence, the correct option is C.
Find two consecutive even numbers whose sum is 758.
Answers
Answer:
378 and 380
Step-by-step explanation:
The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.
Answer:
Step-by-step explanation:
Let the first number = x
Let the second number = x + 2
x + x + 2 = 758 Collect like terms
2x + 2 = 758 Subtract 2
2x = 758 - 2 Combine
2x = 756 Divide by 2
2x/2 = 756/2
x = 378
The first number is 378
The second number 380
If your teacher is really fussy, you can do it this way.
Let the first number = 2x
Let the second number = 2x + 2
The reason for this is to guarantee that both numbers were even to start with.
2x + 2x+2 = 758 Combine like terms
4x + 2 = 758 Subtract 2
4x = 756 Divide by 4
x = 756/4
x = 189
Therefore 2x = 378
2x + 2 = 380 Just as before.
