An animal shelter spends $3.00 per day to care for each bird and $8.50 per day to care for each cat. Kayla noticed that the shel
2 answers:
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You have the following expression:
To verify the identity, you have that the left side of the equation becomes:
(1 + cosx)(1 - cosx) = (1 - cos^2 x)
because of the product of an expression by its conjugate result in a difference of squares. Or simplfy by expanding the factors and simplying.
Next, you have:
1 - cos^2 x = sin^2 x
because the Pythagorean identity.
Then, the identity is verified.
Answer:
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
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 z-score 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 p-value, 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.
The average midterm score of students in a certain course is 70 points.
This means that
29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.
This means that
Find the probability that the average midterm score of these students is at most 75 points.
This is the pvalue of Z when X = 75. So
By the Central Limit Theorem
has a pvalue of 0.98.
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
Answer:
Step-by-step explanation:
1. Add 19 to both sides.
2. Divide both sides by 2.