Answer:
The 95% confidence interval is "87.94, 91.86".
Step-by-step explanation:
The given values are:
Sample batches,
n = 25
Sample mean concentration,
= 89.9 mg
Amount of chemical,
σ = 5
α = 0.05
The critical value from Z table will be:
= 
= 
= 
Now,
The confidence interval will be:
= 
On substituting the values, we get
= 
= 
= 
Lower limit will be:
= 
= 
Upper limit will be:
= 
= 
Answer:
a) 1/14
b) 1/56
c) 1/28
d) 5/28
Step-by-step explanation:
a) Since tickets are being selected without replacement, this means that the pool of outcomes diminishes with each selection. For the first pick, there are a total of 8 tickets to choose from, and 4 of those are purple. Therefore, the probability that the first ticket is purple is 4/8=1/2. For the second ticket, the total number of remaining tickets is 7, and the number of purple tickets is 3, meaning that the probability is 3/7. For the final ticket, 6 remaining tickets and 2 of them being purple yields a probability of 2/6=1/3. Multiplying all of these together, you get 1/2*3/7*1/3=1/14.
b) Similarly to the previous problem, the first probability is 3/8, followed by 2/7, and then by 1/6. Multiplying these together, you get a probability of 1/56.
c) The probability that the first two tickets are purple are 1/2 and 3/7, as we have already calculated. For the final ticket, there are 6 possible remaining with 1 of them being gold. This means a probability of 1/6, which yields a total of 1/28.
d) Since there are 5 tickets originally that aren't blue, the probability for the first pick is 5/8, followed by 4/7 and 3/6=1/2. Multiplying these together, you get a final answer of 5/8*4/7*1/2=5/28.
Hope this helps!
Answer:
Answer D) B, C, and D
Step-by-step explanation:
Point D is 2 and point B is -2, meaning they are opposites of each other. Point C is 0, which is it's own opposite
Answer:
To find the equation of a line given two points, we need to start by finding the slope. You can do that given the slope formula below:
m(slope) = (y2 - y1)/(x2 - x1)
In this equation, you would use the first point of (x1, y1) and the second point of (x2, y2). Then you plug in and find the slope.
After that, you can use the slope and the first point to plug into slope intercept form for the end result.
y - y1 = m(x - x1)
In which m is the slope you just found and (x1, y1) is the point.
