Which equations have a leading coefficient of 3 and a constant term of –2? check all that apply. 0 = 3x2 2x – 2 0 = –2 – 3x2 3 0
1 answer:
The equations which have a leading coefficient of 3 and a constant term of –2 are 0 = 3x² +2x - 2 and 0=3x²-1x-2.
<h3>What is a quadratic equation?</h3>A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
Here,(<em>a,b, c</em>) is the real numbers and (x) is the variable.In this equation, a is the coefficient of the highest term and c is the constant term.
The equations which has the leading coefficient of 3 and a constant term of –2 has to be find out.
The first equation given in the problem is,
In this equation, the coefficient of the term which has the highest power is 3 and the constant term is -2. Thus, this option is correct.
The second equation given in the problem is,
Rearrange the equation as,
In this equation, the coefficient of the term which has the highest power is -3 and the constant term is 1. Thus, this option is not correct.
The third equation given in the problem is,
In this equation, the coefficient of the term which has the highest power is 3 and the constant term is 2. Thus, this option is not correct.
The fourth equation given in the problem is,
Rearrange the equation as,
In this equation, the coefficient of the term which has the highest power is 3 and the continuant term is -2. Thus, this option is correct.
Hence, the equations which have a leading coefficient of 3 and a constant term of –2 are 0 = 3x² +2x - 2 and 0=3x²-1x-2.
Learn more about the quadratic equation here;
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Using the Central Limit Theorem, we have that:
a) Yes, it can be used, as np > 10 and n(1 - p) > 10.
b) There is a 0.0475 = 4.75% probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean
and standard deviation
, as long as
and
.
For the sample, we have that:
- np = 85 > 10.
- n(1 - p) = 15 > 10.
Hence the normal approximation can be used.
As for part B, if we have p = 0.9 and n = 100, the mean and the standard error are given by:
.
The probability of a sample proportion of 85% of less is the <u>p-value of Z when X = 0.85</u>, hence:
By the Central Limit Theorem
Z = -1.67
Z = -1.67 has a p-value of 0.0475.
There is a 0.0475 = 4.75% probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less.
More can be learned about the Central Limit Theorem at brainly.com/question/24663213
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