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3 years ago

Can anyone help out?

Mathematics

1 answer:

yuradex [85]3 years ago

5 0

#20)

18 cups together but ratio of purple to orange = 4:5

4 + 5 = 9

so 18/ 9 = 2

2 x 4(cups of purple) = 8

2 x 5(cups of orange) = 10

Answer:

10 cups of orange

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Find the inverse laplace transform of: (2 s + 4) / (s - 3)^3

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Answer:

$e^{3t}(2t+5t^{2})$

Step-by-step explanation:

$L^{-1}[\frac{2s+4}{(s-3)^{3}} ]=$

Using the Translation theorem to transform the s-3 to s, that means multiplying by and change s to s+3

Translation theorem: $L^{1} [F(s-a)=L^{-1}[F(s)|_{s \to s-a}\\ L^{1} [F(s-a)=e^{at} f(t)$

$L^{-1}[\frac{2s+4}{(s-3)^{3}} ]=e^{3t} L^{-1}[\frac{2(s+3)+4}{s^{3}} ]$

Separate the fraction in a sum:

$e^{3t} L^{-1}[\frac{2s+10}{s^{3}} ]=e^{3t} L^{-1}[\frac{2s}{s^{3}}+\frac{10}{s^{3}} ]=e^{3t} (L^{-1}[\frac{2}{s^{2}}]+ L^{-1}[\frac{10}{s^{3}}])$

The formula for this is:

$L^{-1}[\frac{n!}{s^{n+1}} ]=t^{n}$

Modify the expression to match the formula.

$e^{3t} (2L^{-1}[\frac{1}{s^{1+1}}]+ \frac{10}{2} L^{-1}[\frac{2}{s^{2+1}}])=e^{3t} (2L^{-1}[\frac{1}{s^{1+1}}]+ 5 L^{-1}[\frac{2}{s^{2+1}}])$

Solve

$e^{3t} (2L^{-1}[\frac{1}{s^{1+1}}]+ 5 L^{-1}[\frac{2}{s^{2+1}}])=e^{3t}(2t+5t^{2} )$

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3 years ago

The quotient of four and a number increased by 23.

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Answer:

Step-by-step explanation:

4/(x+23)

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3 years ago

Of the 800 participants in a marathon, 120 are running to raise money for a cause. How many participants out of 100 are running

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Answer:

15 % are running for a cause.

Step-by-step explanation:

120 out of 800 are running for a cause.

So out of 100, 120 / 8

= 15 are running for a cause.

15 out of a 100 = 15%.

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3 years ago

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A hockey goalie loses 2 3/5 rating points each time his team loses. If his team loses 8 games in a row, what number represents t

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Answer:

$20\frac{4}{5}$

Step-by-step explanation:

We have been given that a hockey goalie loses 2 3/5 rating points each time his team loses. His team loses 8 games in a row.

To find the number that will represent the change in goalie's ratings after losing 8 games we will multiply 8 by $2\frac{3}{5}$ .

$8*(2\frac{3}{5})$

Let us convert our mixed fraction into improper fraction.

$8*\frac{13}{5}$

$\frac{8*13}{5}$

$\frac{104}{5}$

$20\frac{4}{5}$

Therefore, $20\frac{4}{5}$ will represent the change in the goalie's rating points.

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3 years ago

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Answer:

The interval is : (7.206 , 7.794)

Step-by-step explanation:

The mean is = 7.5

Standard deviation = 3

n = 400

At 95% confidence interval, the z score is 1.96

$7.5+1.96(\frac{3}{\sqrt{400} } )$

And $7.5-1.96(\frac{3}{\sqrt{400} } )$

$7.5+0.294$ and $7.5-0.294$

So, the interval is : (7.206 , 7.794)

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4 years ago