The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50
+ 10 log x. Suppose each of the x objects increases its sound power by 10 decibels, so that the new total sound power, in decibels, is given by the function g(x) = f(x) +10
which shows the graphs of f(x) and g(x)?
which shows the graphs of f(x) and g(x)?
1 answer:
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the complete question in the attached figure
1) Find the probability that all nine victims would select the same person. You should enter your answer as a decimal, not as a percent. Do not round, as your answer should be a terminating decimal.
P=(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)=0.000000512
2) what is the probability that the first victim picks SOMEONE? ANYONE?
P=(1/5)=0.20 ---------------- > 20%
3) Now let’s look at victim #2. What is the probability that they pick the same person as victim #1?
P=(1/5)*(1/5)=0.04 --------------> 4%
4) Now let’s look at victim #3. What is the probability that they pick the same person as victim #1?
P=(1/5)*(1/5)*(1/5)=0.008 --------------> 0.8%
5) Now let's look at victim #9. What is the probability that they pick the same person as victim #1?
P=(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)=0.000000512
6) Once you find all those probabilities, what rule would apply?
the probability is given by (1/5)^n
n=number of victims that pick the same person---------> in this problem = 9
P=(1/5)^9= 0.000000512
Answer:
Shift 2 unit left
Flip the graph about y-axis
Stretch horizontally by factor 2
Shift vertically up by 2 units
Step-by-step explanation:
Given:
Parent function:
Transformation function:
Take -2 common from transform function f(x)
Now we see the step-by-step translation
Shift 2 unit left ( x → x+2 )
Flip the graph about y-axis ( (x+2) → - (x+2) )
Stretch horizontally by factor 2 [ -x(x+2) → -2(x+2) ]
Shift vertically up by 2 units [ f(x) → f(x) + 2 ]
Simplify the function:
Hence, Using four step of transformation to get new function
Answer:
The 90th percentile for the distribution of the total contributions is $6,342,525.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sums of size n, the mean is and the standard deviation is
In this question:
The 90th percentile for the distribution of the total contributions
This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then
By the Central Limit Theorem
The 90th percentile for the distribution of the total contributions is $6,342,525.