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3 years ago

Josh mixed 2 cartons of orange juice, 3 bottles of soda waterland 6 cans of

Mathematics

1 answer:

gulaghasi [49]3 years ago

4 0

Answer:

9.5 gallons

Step-by-step explanation:

Josh mixed 2 cartons of orange juice, 3 bottles of soda water and 6 cans of

cocktail fruits to make a fruit punch.

Each carton of juice is 1 gallon and 3 quarts.

Therefore, 2 cartons will be:

2 * (1 gallon + 3 quarts) = 2 gallons and 6 quarts

1 quart = 0.25 gallon

6 quarts = 6 * 0.25 = 1.5 gallons

Therefore, Josh poured 3.5 gallons of orange juice.

Each soda water bottle contains 6 quarts. There are 3 bottles of soda water.

Therefore, the number of gallons that the soda water bottle contains is:

3 * 6 * 0.25 = 4.5 gallons

The cans of cocktail fruit are 2 pints each. There are 6 cans of cocktail fruit.

1 pint = 0.125 gallon

2 pints = 0.25 gallons

=> 6 cans of cocktail fruit is:

6 * 0.25 = 1.5 gallons

The amount of fruit punch that Josh made is the sum of all components:

3.5 + 4.5 + 1.5 = 9.5 gallons

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

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

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

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
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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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The null hypothesis claims that the proportion of community college students who work full-time is 0. 45. The alternative hypoth

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The stronger the evidence is against the null hypothesis, the higher the divergence from it.

What do you mean by null hypothesis ?

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is $H_{0}$ . To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts employ the null hypothesis,

The null hypothesis states that the percentage of the population who works full time is 0.45.

As a result, 450 persons who are randomly selected from a population of 1000 work full-time.

A different hypothesis states that the ratio is higher than 0.45.

In the options provided, the proportion for the first option is 300/1000, or 0.3.

In the second choice, 500/1000 equals 0.5

Third alternative: 700/1000 = 0.7

Therefore, the stronger the evidence is against the null hypothesis, the higher the divergence from it.

To learn more about the null hypothesis from the given link.

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