Graph of Parallel lines shows a system of equations with no solutions
Step-by-step explanation:
Consider a set of equations
If we solve this both equations using any one of the solving method, (Substitution method) then we will get
substituting the following x in 2nd equation (21x + 6y = 24) We get
Put y= -2 in x equation
Comparing these (x,y) values we can understand that they never meet at a point
Answer: a) P = 0.5, b) P = 0.07
Step-by-step explanation:
Hi!
Lets call X₁ the time at which you arrive, and X₂ the time at which Bob arrives. Both are random variables with uniform density in the interval [0, 60] (in minutes). Their joint distribuition is uniform over the square in the image, with value P = 1/(60*60) = 1/3600.
a) For you to get more cake than Bob, you should arrive earlier. This event is A = { X₁ < X₂ }, the shaded triangle in the figure.The area of this event (set) is half the total area of the square, so P(A) = 0.5.
It makes sense, beacuse its equally probable for you or Bob to arrive earlier, as both have uniform density over the time interval.
b) In this case you arrive later than Bob, but less than 5 minutes later. So the event is B = { X₂ < X₁ < (X₂ + 5) } . This is the gray shaded area in b) part of the image. Its area is the difference two triangles (half square - blue triangle), then the probability is:
Answer:
The 99% confidence interval estimate of the mean body temperature of all healthy humans is (97.955F, 98.245F).
98.6F is above the upper end of the interval, which means that the sample suggests that the mean body temperature could be lower than 98.6F.
Step-by-step explanation:
The first step is finding the confidence interval
The sample size is 103.
The first step to solve this problem is finding how many degrees of freedom there are, that is, the sample size subtracted by 1. So
Then, we need to subtract one by the confidence level and divide by 2. So:
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 102 and 0.005 in the t-distribution table, we have .
Now, we need to find the standard deviation of the sample. That is:
Now, we multiply T and s
For the lower end of the interval, we subtract the mean by M. So 98.1 - 0.145 = 97.955F.
For the upper end of the interval, we add the mean to M. So 98.1 + 0.145 = 98.245F.
The 99% confidence interval estimate of the mean body temperature of all healthy humans is (97.955F, 98.245F).
98.6F is above the upper end of the interval, which means that the sample suggests that the mean body temperature could be lower than 98.6F.