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2 years ago

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When a researcher asked 35 people if they liked a new brand of toilet paper; 22 said 'yes', 8 said 'no' and 5 were 'undecided'.

if a person is ramdomly selected from this group of people, what is the probability that you select a person who said 'undesided'?

1 answer:

ella [17]2 years ago

5 0

It is a 5 to 30 chance that you select someone who said undecided

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anyanavicka [17]

Answer: 4/5

Step-by-step explanation:

3 0

2 years ago

Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

3 0

2 years ago

A square in the board below and a letter in the word ATTENTION is chosen at

kolezko [41]

Answer:

4 /15

Step-by-step explanation:

From the number cube :

Count of Numbers greater than 4 = 16

Sample space of number cube = 20

P(number greater than 4) = 16 / 20 = 4/5

Word : ATTENTION

Count of letters in attention = 9

Count of T's in attention = 3

P(choosing T) = 3 / 9 = 1/3

P(greater than 4, then T) = 4/5 * 1/3 = 4 /15

5 0

2 years ago

A math class conducted an experiment where each student flipped a coin 10 times. The class flipped heads 158 heads and 172 tails

kari74 [83]

Answer:

It will not always be 50%it sometimes be less or more

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

one rectangle has a length 10 cm and width 5 cm the second rectangle has length 12 cm and width 4 cm are the two rectangles simi

tatuchka [14]

Answer:

No, they aren't similar.

Step-by-step explanation:

<u><em>Let's take the proportionality of their sides to check whether they are similar or not:</em></u>

$\frac{10}{5} = \frac{12}{4}$

=> 2 ≠ 3

So, they are not similar.

8 0

3 years ago