In circle A, ZBAE ZDAE. What is the value of x?
1 answer:
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The correct choice of this question with the given polynomial is <em>"The zeros are </em>-2<em> and </em>8<em>, because the factors of g are (x + </em>2<em>) and (x - </em>8<em>)"</em>. (Correct choice: H)
<h3>How to analyze a second orden polynomial with constant coefficients</h3>
In this case we have a second order polynomial of the form <em>x² - (r₁ + r₂) · x + r₁ · r₂</em>, whose solution is <em>(x - r₁) · (x - r₂)</em> and where <em>r₁</em> and <em>r₂</em> are the roots of the polynomial, which can be real or complex numbers but never both according the fundamental theorem of algebra.
If we know that <em>g(x) =</em> <em>x² -</em> 6 <em>· x -</em> 16, then the <em>factored</em> form of the expression is <em>g(x) = (x - </em>8<em>) · (x + </em>2<em>)</em>. Hence, the correct choice of this question with the given polynomial is <em>"The zeros are </em>-2<em> and </em>8<em>, because the factors of g are (x + </em>2<em>) and (x - </em>8<em>)"</em>.
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Answer:
B. Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal.
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.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
35 gas ovens
A consumer group has determined that the distribution of life spans for gas ovens has a mean of 15.0 years and a standard deviation of 4.2 years. This means that:
40 electric ovens.
The distribution of life spans for electric ovens has a mean of 13.4 years and a standard deviation of 3.7 years.
Which of the following best describes the sampling distribution of barXG - bar XE, the difference in mean life span of gas and electric ovens?
By the Central Limit Theorem, the shape is approximately normal.
Mean:
Standard deviation:
So the correct answer is given by option b.