Please help ILL MARK BRAINLIEST(17 points too)
1 answer:
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Complete Question:
Which statement about the following equation is true?
A) The discriminant is less than 0, so there are two real roots
B) The discriminant is less than 0, so there are two complex roots
C) The discriminant is greater than 0, so there are two real roots
D) The discriminant is greater than 0, so there are two complex roots
Answer:
C) The discriminant is greater than 0, so there are two real roots
Step-by-step explanation:
The given equation is which by simplification becomes
For a quadratic equation of the form , the discriminant is given by the equation,
If the discriminant D is greater than 0, the roots are real and different
If the discriminant D is equal to 0, the roots are real and equal
If the discriminant D is less than 0, the roots are imaginary
For the quadratic equation under consideration, a = 2, b = -9, c = 3
Let us calculate the discriminant D
D = (-9)² - 4(2)(3)
D = 81 - 24
D = 57
Since the Discriminant D is greater than 0, the roots are real and different.
Answer:
50.34% probability that the sample mean would differ from the true mean by less than 1.1 months
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 random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If a sample of 74 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.1 months
This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So
X = 120.1
By the Central Limit Theorem
has a pvalue of 0.7517
X = 117.9
has a pvalue of 0.2483
0.7517 - 0.2483 = 0.5034
50.34% probability that the sample mean would differ from the true mean by less than 1.1 months