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3 years ago

6

WRITE AN EQUATION 331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students we

re in each bus?

1 answer:

Molodets [167]3 years ago

3 0

Answer:

probably 331-7=6x

Step-by-step explanation:

cause you take away 7 and have 324, then divide by 6 and end up with 54 soooo

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120% of what number is 48

postnew [5]

Answer:

40

120 percent (calculated percentage %) of what number equals 48? Answer: 40.

8 0

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

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

3 0

3 years ago

Answers for the 2 boxes please

pochemuha

(-3,-6) this is the answer you can also double check by plugging it into a calculator

6 0

3 years ago

During the month of February, Fabulous Feet Shoe Mart sold 30 pairs of red loafers. After an ad campaign to boost sales, they so

blagie [28]

20%

20% of 30 =6
30+6 = 36

6 0

3 years ago

Read 2 more answers

The parents' club will need 100 of the same item for international night. They have a budget of $250. The choices are 100 baseba

Nuetrik [128]

Answer:

The parents' club can afford to buy 100 Baseball hats or 100 sports bottles.

Step-by-step explanation:

Given:

Item to be bought = 100

Total Budget = $250

Cost of each Baseball Hat = $2.45

Cost of each sports bottles = $2.50

Cost of each flag = $2.75

We need to find which items can they afford to buy.

Solution:

each Baseball Hat = $2.45

100 Baseball Hat = Cost of 100 Baseball Hat

Using Unitary method we get;

Cost of 100 Baseball Hat = $2.45\times 100 =\$245$

each sports bottles = $2.50

100 sports bottles = Cost of 100 sports bottles

Using Unitary method we get;

Cost of 100 sports bottles = $2.5\times 100 =\$250$

each flag = $2.75

100 flags = Cost of 100 flags

Using Unitary method we get;

Cost of 100 flags = $2.75\times 100 =\$275$

Hence from above we can see that;

Cost of 100 Base ball hat and 100 sports bottles are within the budget while Cost of 100 flags exceed the budget.

So we can say that;

The parents' club can afford to buy 100 Baseball hats or 100 sports bottles.

6 0

3 years ago