. A coin is tossed three times, and the sequence of heads and tails is recorded.(a) Determine the sample space, Ω.(b) List the elements that make up the following events: i.A= exactly two tails, ii.B= at least twotails, iii.C= the last two tosses are heads(c) List the elements of the following events: i.A, ii.A∪B, iii.A∩B, iv.A∩C
Answers
Answer:
See explanation below
Step-by-step explanation:
Here a coin was tossed three times.
Let H = head & T = tail
Find the following:
a) The sample space:
Since a coin is tossed thrice, all possible outcome would be:
S = { HHH, HHT, HTH, HTT, TTT, TTH, THH, THT}
b) i) A = Exactly 2 tails: Here exactly 2 tails were recorded.
A = {HTT, TTH, THT}
ii) B = at least two tails: Here 2 or more tails were recorded.
B = {HTT, TTT, TTH, THT}
iii) C = the last two tosses are heads:
C = { HHH, THH}
c) List the elements of the following events:
i) A. This means all outcomes in A
= {HTT, TTH, THT}
ii) A∪B. A union B, means all possible outcomes present in A or B or in both
= {HTT, TTH, THT, TTT}
iii) A∩B. This means all possible outcomes of A that are present in B.
= {HTT, TTH, THT}
iv) A∩C. All outcomes A that are present in B
= {∅}
The sample space of tossing a coin three times consists of eight possible outcomes: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT. Events A, B, and C can be determined by listing the appropriate outcomes. The intersection and union of events A and B can also be determined.
(a) The sample space, Ω, of tossing a coin three times can be determined by listing all the possible outcomes: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT.
(b) i. A = {HHT, HTH, THH}
ii. B = {TTT, TTH, THT, HTT, HHT, HTH, THH}
iii. C = {HTH, TTH}
(c) i. A = {HHT, HTH, THH}
ii. A∪B = {HHT, HTH, THH, TTT, TTH, THT, HTT, HHT}
iii. A∩B = {HHT, HTH, THH}
iv. A∩C = {HHT, HTH}
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In a sample of 49 adolescents who served as the subjects in an immunologic study, one variable of interest was the diameter of a skin test reaction to an allergen. The sample mean and standard deviation were 21 and 11 mm erythema, respectively. a. Use a z- or t-distribution? Why? b. One-sided or two-sided test? Why? c. Can it be concluded from these data that the population mean is less than 24 mm erythema? d. What is the range on the p-value?
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Answer:
Critical value:
The 90% confidence interval for the population mean bromide concentration is (0.376, 0.39).
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
. This value of z is the critical value
Now, find M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the mean subtracted by M. So it is 0.383 - 0.0066 = 0.376 cc/cubic meter
The upper end of the interval is the mean added to M. So it is 0.383 + 0.0066 = 0.39 cc/cubic meter
The 90% confidence interval for the population mean bromide concentration is (0.376, 0.39).
of angle x?
Answers
Answer:
A.) 48°
Step-by-step explanation:
There is a right angle and an angle of 42°
Therefore
x=180-90-42. (sum of int angles of triangle)
x=48°
Answer:
(A) 48
Step-by-step explanation:
Triangles have 180°, so all you have to do is subtract the numbers you already know from 180.
180-42 = 138
The square on the left corner means that degree is a right angle. Right angles are always 90°.
138-90 = 48degrees
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Pentagon
Hexagon
Rectangle
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19 ÷ 5 = 3 with a remainder of 4
Since there are 5 terms in the pattern, the 19th term is equivalent to the 4th term in the pattern. Therefore, the 19th term is a square.
Answers
Denote the sum by S. So
S = 5 + 11 + 17 + 23 + ... + 83
There's a constant difference of 6 between consecutive terms in S, so the 3 terms before 83 are 77, 71, and 65. So
S = 5 + 11 + 17 + 23 + ... + 65 + 71 + 77 + 83
Gauss's approach involves inverting the sum:
S = 83 + 77 + 71 + 65 + ... + 23 + 17 + 11 + 5
If we add terms in the same position in the sums, we get
2S = (5 + 83) + (11 + 77) + ... + (77 + 11) + (83 + 5)
and we notice that each grouped term on the right gives a total of 88. So the right side consists of several copies n of 88, which means
2S = 88n
and dividing both sides by 2 gives
S = 44n
Now it's a matter of determining how many copies get added. The terms in the sum form an arithmetic progression that follows the pattern
11 = 5 + 6
17 = 5 + 2*6
23 = 5 + 3*6
and so on, up to
83 = 5 + 13*6
so n = 13, which means the sum is S = 44*13 = 572.
Final answer:
To find the sum of the given arithmetic series, we can use Gauss's approach by finding the number of terms and then calculating the sum using the formula for the sum of an arithmetic series.
Explanation:
To find the sum of the given series, we can use Gauss's approach. The series is an arithmetic progression with a common difference of 6. We can find the number of terms in the series using the formula for the nth term of an arithmetic sequence and then use the formula for the sum of an arithmetic series to find the sum.
- Find the number of terms (n):
- The first term (a) is 5, and the common difference (d) is 6.
- Find the last term (l) using the formula: l = a + (n - 1)d
- Substitute the values and solve for n: 83 = 5 + (n - 1)6
- Simplify and solve for n: n = 15
- Find the sum (S):
- The formula for the sum of an arithmetic series is: S = (n/2)(a + l)
- Substitute the values and solve for S: S = (15/2)(5 + 83)
- Calculate the sum: S = 15(44)
- Simplify the sum: S = 660
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Final answer:
After subtracting the setup fee from the total cost, the remaining amount ($142.50) is divided by the number of t-shirts (15) to find the cost of each shirt, which is $9.5.
Explanation:
The total cost for the T-shirt order is $162.50 and this includes a $20 setup fee. If you subtract this setup fee from the total cost, you will be left with the total cost of the actual T-shirts.
This gives us: $162.50 - $20 = $142.50.
The total cost of the T-shirts is $142.50, and this is for the 15 members of the club. To find out a cost of each shirt, you would divide this amount by the number of shirts, which is 15:
$142.50 / 15 = $9.5.
So, the company charges $9.5 for each shirt.
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Answer:
x=9.5
Step-by-step explanation:
Let be the cost of each shirt. From the information provided in the problem, we can setup the following equation:
Solving for will give us the answer:
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