Answer:
1) The probability that ten students in a class have different birthdays is 0.883.
2) The probability that among ten students in a class, at least two of them share a birthday is 0.002.
Step-by-step explanation:
Given : Assume there are 365 days in a year.
To find : 1) What is the probability that ten students in a class have different birthdays?
2) What is the probability that among ten students in a class, at least two of them share a birthday?
Solution :
Total outcome = 365
1) Probability that ten students in a class have different birthdays is
The first student can have the birthday on any of the 365 days, the second one only 364/365 and so on...
The probability that ten students in a class have different birthdays is 0.883.
2) The probability that among ten students in a class, at least two of them share a birthday
P(2 born on same day) = 1- P( 2 not born on same day)
![\text{P(2 born on same day) }=1-[\frac{365}{365}\times \frac{364}{365}]](https://tex.z-dn.net/?f=%5Ctext%7BP%282%20born%20on%20same%20day%29%20%7D%3D1-%5B%5Cfrac%7B365%7D%7B365%7D%5Ctimes%20%5Cfrac%7B364%7D%7B365%7D%5D)
![\text{P(2 born on same day) }=1-[\frac{364}{365}]](https://tex.z-dn.net/?f=%5Ctext%7BP%282%20born%20on%20same%20day%29%20%7D%3D1-%5B%5Cfrac%7B364%7D%7B365%7D%5D)
The probability that among ten students in a class, at least two of them share a birthday is 0.002.
Answer:
The answer is D. 12x - 3.
Step-by-step explanation:
To add these functions, we just add the terms.
f(x) + g(x) = (7x - 4) + (5x + 1)
7x - 4 + 5x + 1 | Simplify
7x + 5x - 3
12x - 3.
Taking the 3 solutions as 3 different terms, we can create an equation as follows:
Solution 1 : 10mL with 20% acid
Solution 2 : 30mL with x% acid
Solution 3 : 40mL with 32% acid
Since solution 1 + solution 2 = solution 3, let us substitute the given values we have:
10(0.2) + 30(x) = 40(0.32)
2 + 30x = 12.8
To solve for the unknown concentration x, we subtract 2 from both sides:
2 + 30x - 2 = 12.8 - 2
30x = 10.8
Dividing both sides by 30:
30x/30 = 10.8/30
x = 0.36
Therefore the unknown solution is 36% acid.
Answer:
a) percentage of respondents that favored neither Obama nor Romney in terms of likeability = 7%
b) For a given survey of 500, the number of respondents that favored Obama than Romney is 145.
Step-by-step explanation:
Given that none of those surveyed can favour the two candidates at the same time,
n(Universal set) = n(U) = 100%
n(Obama) = n(O) = 61%
n(Romney) = n(R) = 32%
n(That favour Obama and Romney) = n(O n R) = 0%
To calculate for the number that favour neither of the candidates
n(O' n R')
n(U) = n(O) + n(R) + n(O n R) + n(O' n R')
100 = 61 + 32 + 0 + n(O' n R')
n(O' n R') = 100 - 93 = 7%
b) For a given survey of 500, how many more respondents favored Obama than Romney?
Number of those surveyed that favour Obama = 61% of 500 = 305
Number of those surveyed that favour Romney = 32% of 500 = 160
Difference = 305 - 160 = 145
Answer:
11.58%
Step-by-step explanation:
The initial volume if blood flowing through the artery is given by
To achieve a new volume of 155% (55% increase) of the initial volume, the new radius must be:
![V'= 1.55V\\1.55V=k(r')^4\\1.55kr^4 = k(r')^4\\(\sqrt[4]{1.55}*r)^4=(r')^4 \\(1.1158*r)^4=(r')^4 \\r'=1.1158*r](https://tex.z-dn.net/?f=V%27%3D%201.55V%5C%5C1.55V%3Dk%28r%27%29%5E4%5C%5C1.55kr%5E4%20%3D%20k%28r%27%29%5E4%5C%5C%28%5Csqrt%5B4%5D%7B1.55%7D%2Ar%29%5E4%3D%28r%27%29%5E4%20%5C%5C%281.1158%2Ar%29%5E4%3D%28r%27%29%5E4%20%5C%5Cr%27%3D1.1158%2Ar)
Since the new radius is 1.1158 times larger than the initial radius, the percentage increased is:
