pH = f(x) = -log₁₀x
1. Graphs
I used Excel to calculate the pH values and draw the graphs (see the Figure).
f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.
The points at which pH = 0 and pH = 1 are indicated by the large red dots.
2. x = 0.5
When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.
3. Transformations
(a) ƒ(x) = -log(x) + 1
This function has no y-intercept, because log(0) is undefined.
(b) ƒ(x +1) = -log(x + 1)
f(0) = -log(0 + 1) = -log(1) = 0
This function has a y-intercept at (0,0).
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Answer:
25%
Step-by-step explanation:
This question is about conditional probability. Let's say that the probability of raining on Saturday is X=true and the probability of raining on Sunday is Y=true. There is a 15% it will rain on both Saturday and Sunday, to put into the equation it will be:
P(X= true ∩ Y = true) = P(X = true) * P(Y = true)= 0.15
There is a 60% chance of rain on Saturday, mean the equation is
P(X = true) = 0.6
The question is asking for the chance of rain on Sunday or P(Y = true). If we substitute the second equation to first, it will be:
P(X = true) * P(Y = true)= 0.15
0.6* P(Y = true)= 0.15
P(Y = true)= 0.15/0.6
P(Y = true)= 0.25 = 25%
Answer:
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Step-by-step explanation:
Also HII <3
Answer:
11 m and 7 m
Step-by-step explanation:
Width = x
Length = x+4
P=2L+2W
P=2(x+4) + 2x=4x +8
36 = 4x + 8
4x = 28
x=7 Width
x+4=7+4=11 Length
Answer:
(a) z=-0.59
(b) Joe will invest in Mean Corporation. The probability of getting an annual return grater than 11% is 72.3%.
Step-by-step explanation:
We have a normal distribution for the annual return of the stock.
This distribution has mean of 13.9% and s.d. of 4.9%.
If X=11%, we can calculate its corresponding z-value as:
The z-value is z=-0.5918.
The probabilty of P(X>11%)=P(y>-0.5918) is, by the standarized normal distribution table, equal to 0.723.
As its P(y>-0.5918)=P(X>11%)=0.723 bigger than the 70% threshold, Joe will invest in Mean Corporation.
