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juin [17]
2 years ago
13

The percentage of people given an antirheumatoid who suffer severe, moderate, or minor side effects are 11, 20 and 69%, respecti

vely. Assume that people react independently and that 20 people are given the medicine. Determine the following. Round your answers to four decimal places (e.g. 98.7654). (a) The probability 2, 4, and 14 people will suffer severe, moderate, or minor side effects, respectively.
Mathematics
1 answer:
Snowcat [4.5K]2 years ago
6 0

Answer:2.9235

Step-by-step explanation:

Since 20 people are administered the medicine and;

11% of the 20 people suffer severe i.e 11% of 20 = 2.2 people

20% of them suffer moderate i.e

20% of 20 = 4 people and;

69% of the 20 people suffer minor side i.e

69% of 20 = 13.8 people

Therefore the probability 2, 4, and 14 people will suffer severe, moderate, or minor side effects, respectively will be;

2/2.2 + 4/4 + 14/13.8 (i.e possible outcome/total outcome)

This will give us 2.9235

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In a certain classroom ,12.5% of the students own at least one pet. If there are 32 students in the classroom,how many students
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Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ
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y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}

The arc length of the curve is

\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx

which has a value of about 5.99086.

Let f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}. Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

\ell_i=\dfrac{i-1}2

r_i=\dfrac i2

with 1\le i\le10.

These subintervals have midpoints given by

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4

Over each subinterval, we approximate f(x) with the quadratic polynomial

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

so that the integral we want to find can be estimated as

\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It turns out that

\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6

so that the arc length is approximately

\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086

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1 year ago
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