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2 years ago

Please help me with this !!!

Mathematics

2 answers:

allsm [11]2 years ago

5 0

Answer:

Step-by-step explanation:

I assume that QP = 18 cm and m∠Q = 72°

liraira [26]2 years ago

3 0

Answer:

$\fbox {P = 6.76 cm}$

Step-by-step explanation:

Finding the missing angle :

22° + ∠R + 72° = 180°
∠R = 180° - 94°
∠R = 86°

Applying the Law of Sines :

$\boxed {\frac{sin P}{P} = \frac{sin R}{PQ}}$

Substituting the known values :

sin 22° / P = sin 86° / 18
P = sin 22° × 18 / sin 86°
P = 0.374606593 × 18 / 0.99756405
P = 6.76 cm

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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.

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

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: