The "k" value should have units and should be negative.
k = -.07 / seconds
Half-Life = ln (.5) / k
Half-Life = ln (.5) / -.07
Half-Life = -.693147 / -.07
Half-Life = 9.9 seconds
(actually, wkpedia says half-life of Krypton 91 is 8.57 seconds)
elapsed time = half-life * log (bgng amt / end amt) / log (2)
elapsed time = 9.9 * log (100 / 10) / 0.30102999566
elapsed time = 9.9 * 1 / 0.30102999566
<span><span>elapsed time = 9.9 * 3.3219280949
</span>
</span><span><span><span>elapsed time = 32.8870881395
</span>
</span>
</span>
<span>elapsed time = 32.89 seconds (rounded)
Source:
http://www.1728.org/halflife.htm
</span>
The correct answers are:
- The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
- The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
Further explanation:
Given equations are:
2x-y = -5
x+3y = 22
We have to check whether the given statements are true or not. In order to find that we have to put the points in the equations
Putting the point in 2x-y = -5
![2x - y = -5\\2(7) -19 = -5\\14-19 = -5\\-5 = -5](https://tex.z-dn.net/?f=2x%20-%20y%20%3D%20-5%5C%5C2%287%29%20-19%20%3D%20-5%5C%5C14-19%20%3D%20-5%5C%5C-5%20%3D%20-5)
Putting the point in x+3y=22
![7 + 3 (19) = 22\\7 + 57 = 22\\64 \neq 22](https://tex.z-dn.net/?f=7%20%2B%203%20%2819%29%20%3D%2022%5C%5C7%20%2B%2057%20%3D%2022%5C%5C64%20%5Cneq%2022)
The point satisfies the first equation but doesn't satisfy the second. So,
1. The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
This statement is true as the point satisfies the first equation
2. The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true.
This Statement is false.
3. The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
This statement is true.
4. The ordered pair (7, 19) is a solution to the system because it makes both equations true.
This statement is false as the ordered pair doesn't satisfy both equations.
Keywords: Solution of system of equations, linear equations
Learn more about solution of linear equations at:
#LearnwithBrainly
Answer:
10
Step-by-step explanation:
Answer:
There is no significant difference between the two averages at 5% level
Step-by-step explanation:
Given that a a college student is interested in testing whether business majors or liberal arts majors are better at trivia.
The student gives a trivia quiz to a random sample of 30 business school majors and finds the sample’s average test score is 86. He gives the same quiz to 30 randomly selected liberal arts majors and finds the sample’s average quiz score is 89
Thus he has done a hypothesis testing for comparison of two means of different subjects. n =30
![H_0: Mean of business majors = Mean of liberal arts majos\\H_a:Mean of business majors \neq Mean of liberal arts majos](https://tex.z-dn.net/?f=H_0%3A%20Mean%20of%20business%20majors%20%3D%20Mean%20of%20liberal%20arts%20majos%5C%5CH_a%3AMean%20of%20business%20majors%20%5Cneq%20%20Mean%20of%20liberal%20arts%20majos)
Since which is better is not claimed we use two tailed test here
We find that p value
our alpha
Since p >alpha, we find that there is no significant difference between the averages of these two groups and null hypothesis is accepted
X = games won
y = games lost
x + y = 72
x = 2y + 15
2y + 15 + y = 72
3y + 15 = 72
3y = 72 - 15
3y = 57
y = 57/3
y = 19 <=== lost games
x = 2y + 15
x = 2(19) + 15
x = 53 <=== won games