Does the graph represent a function ? Why or Why not ?
1 answer:
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A function assigns the values. The average rate of change for the given function g(x) is 1.
<h3>What is a Function?</h3>A function assigns the value of each element of one set to the other specific element of another set.
The average rate of change of a function is given by the formula,
Average rate of change, = [f(b)-f(a)]/(b-a), [a,b]
Where a is the lower limit and b is the upper limit.
Given the upper limit for the function is 0, therefore, the value of a is 0, similarly, the value of b is -9. Thus,
a = 0
g(a) = 0²+10(0)+20 = 20
b = -9
g(b) = (-9)²+10(-9)+20 = 11
The average rate of change for the function g(x), can be written as,
Hence, the average rate of change for the given function g(x) is 1.
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Answer:
As the number is a prime number. Therefore, option 'c' is true.
Step-by-step explanation:
Let us take the number 7 and divide it by 4
We know that
as
so the remainder is 3. ∵
As 7 is a prime number, and when we divide the prime number 7 by 4, we get the remainder 3.
Thus, the number is a prime number. Therefore, option 'c' is true.
Answer:
P(939.6 < X < 972.5) = 0.6469
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 normal distributions can be 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.
CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.
This means that
Sample of 57:
This means that
Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.
This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So
X = 972.5
By the Central Limit Theorem
has a pvalue of 0.6915
X = 939.6
has a pvalue of 0.0446
0.6915 - 0.0446 = 0.6469
So
P(939.6 < X < 972.5) = 0.6469