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3 years ago

A student solved the following problem and made an error:

Mathematics

1 answer:

liubo4ka [24]3 years ago

8 0

All the steps were correct except the final statement. The mistake was in Line 6.

Line 6 triangle ABC is congruent to triangle EFD by SAS.

<span>This does not follow. The SAS postulate states that if two sides and the included angle of one triangle is congruent to two sides and the included angle of another triangle. The student only proved that one side of the triangle (AC) is congruent to the side of another triangle (EF) .</span>

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Solve for w. 5w + 9z = 2z + 3w w = w equals negative StartFraction 7 Over 2 EndFraction z.Z w = w equals negative StartFraction

TEA [102]

Answer:

w = -7z/2

Step-by-step explanation:

We need to solve for w in terms of z.

The equation given is:

5w + 9z = 2z + 3w

Collect like terms:

5w - 3w = 2z - 9z

2w = -7z

w = -7z/2

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Answer:

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pav-90 [236]

Using the normal approximation to the binomial, it is found that:

The mean of X is of 52 samples.
The standard deviation of X is of 4.2661 samples.
0.0017 = 0.17% probability that less than half without any traces of pesticide.

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Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, with mean given by:

$E(X) = np$

And standard deviation of:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Z-score formula is used, which, in a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

Each z-score has an associated p-value, which measures the percentile of measure X.

--------------------------------

65% of samples had no pesticide, thus $p = 0.65$
80 samples, thus $n = 80$

The mean of X is of:

$E(X) = np = 0.65(80) = 52$

The standard deviation of X is of:

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{80(0.65)(0.35)} = 4.2661$

Using the approximation and continuity correction, the probability is $P(X < 40 - 0.5) = P(X < 39.5)$ , which is the p-value of Z when X = 39.5. Thus: