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3 years ago

he has 14 coins and 2 one-dollar bills. witch describes the relationship between the coin and the dollar bills?

Mathematics

2 answers:

polet [3.4K]3 years ago

5 0

Answer:

14:2

Step-by-step explanation:

1 coin is one part, one bill is one part

14:2

Oduvanchick [21]3 years ago

3 0

Multiply 2 by 7 and get 14

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Answer:

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2 years ago

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jok3333 [9.3K]

Your answer would be - 3/10

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3 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

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

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3 years ago

Make a line plot for each set of data.

Gala2k [10]

Answer:

Look at Step by Step

Step-by-step explaination

All you need to do is find the frequency of the test scores.

70 = 2 dots

75 = 0

80 = 3 dots because there are 3 students that got a 80 %

85 = 3 dots because there are 3 students that got a 80 %

90 = 4 dots because there are 4 students that got a 90 %

95 = 3 dots

100+ = 0 dots

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3 years ago

Which two ratios are equivalent to 10 : 12? 11:13 and 20:24 B. 10:12 and 11:13 C. 5:6 and 20:24

Readme [11.4K]

Answer: 5;6

Step-by-step explanation:

10 divided by 2 is 5

12 divided by 2 is 6 and plus I got this answer correct

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3 years ago