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3 years ago

2 numbers have to be a fraction and to numbers have to be an equivalent decimal the 4 numbers are 6,5,2,1

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

4 0

Answer:

Fraction = 6/5 and decimal = 1.2.

Step-by-step explanation:

We have 6/5 :

Divide 6 by 5 gives us 1 1/5 = 1.2.

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6 fl oz= how many cups

natima [27]

1 oz = 0.125 cups so 6 oz = 0.75 cups

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3 years ago

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The USA won 15 Wimbledon championships. Sweden and Switzerland both won 7. Australia won 6, German won 4, and Spain won 2. Write

mihalych1998 [28]

Well you add the total of championships. 15+7+7+6+4+2=41
The ratio is 6:41
This means that Australia won 6 of the 41 championships.

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3 years ago

Subtract using the number line. <br><img src="https://tex.z-dn.net/?f=%20-%201%20%5Cfrac%7B1%7D%7B3%7D%20%20-%20%20%5Cfrac%7B1%7

Allisa [31]

Answer:

- 1 2/6 - 1/6

- 1 3/6

-1 1/2

Step-by-step explanation:

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3 years ago

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Trigonometric question, 30 points, will give brainliest.

Elis [28]

$\bf \textit{ roots of complex numbers, DeMoivre's theorem} \\\\ \sqrt[n]{z}=\sqrt[n]{r}\left[ cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\ sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left[ 32\left[ cos\left( \frac{\pi }{3} \right) +i~sin\left( \frac{\pi }{3} \right) \right] \right]^{\frac{1}{5}}$

$\bf 32^{\frac{1}{5}}\left[ cos\left( \frac{\pi +2\pi (0)}{15} \right)+i~sin\left( \frac{\pi +2\pi (0)}{15} \right) \right]\implies \stackrel{\textit{first root, k = 0}}{2\left[ cos\left( \frac{\pi }{15} \right)+isin\left( \frac{\pi }{15} \right) \right]}$

$\bf 32^{\frac{1}{5}}\left[ cos\left( \frac{\pi +2\pi (1)}{15} \right)+i~sin\left( \frac{\pi +2\pi (1)}{15} \right) \right]\implies \stackrel{\textit{second root, k = 1}}{2\left[ cos\left( \frac{7\pi }{15} \right)+isin\left( \frac{7\pi }{15} \right) \right]} \\\\\\ \stackrel{\textit{third root, k = 2}}{2\left[ cos\left( \frac{13\pi }{15} \right)+isin\left( \frac{13\pi }{15} \right) \right]}\qquad \bigotimes$

$\bf \stackrel{\textit{fourth root, k = 3}}{2\left[ cos\left( \frac{19\pi }{15} \right)+isin\left( \frac{19\pi }{15} \right) \right]}\qquad \bigotimes \\\\\\ \stackrel{\textit{fifth root, k =4}}{2\left[ cos\left( \frac{5\pi }{3} \right)+isin\left( \frac{5\pi }{3} \right) \right]}\qquad \bigotimes$

6 0

3 years ago

"We might think that a ball that is dropped from a height of 15 feet and rebounds to a height 7/8 of its previous height at each

tatyana61 [14]

Answer:

Total Time = 4.51 s

Step-by-step explanation:

Solution:

- It firstly asks you to prove that that statement is true. To prove it, we will need a little bit of kinematics:

y = v_o*t + 0.5*a*t^2

Where, v_o : Initial velocity = 0 ... dropped

a: Acceleration due to gravity = 32 ft / s^2

y = h ( Initial height )

h = 0 + 0.5*32*t^2

t^2 = 2*h / 32

t = 0.25*√h ...... Proven

- We know that ball rebounds back to 7/8 of its previous height h. So we will calculate times for each bounce:

$1st : 0.25*\sqrt{15}\\\\2nd: 0.25*\sqrt{15} + 0.25*\sqrt{15*\frac{7}{8} } + 0.25*\sqrt{15*\frac{7}{8} } = 0.25*\sqrt{15} + 0.5*\sqrt{15*\frac{7}{8} }\\\\3rd: 0.25*\sqrt{15} + 0.5*\sqrt{15*\frac{7}{8} } + 2*0.25*\sqrt{15*(\frac{7}{8} })^2\\\\= 0.25*\sqrt{15} + 0.5*\sqrt{15*\frac{7}{8} } + 0.5*\sqrt{15*(\frac{7}{8} })^2\\\\4th: 0.25*\sqrt{15} + 0.5*\sqrt{15*\frac{7}{8} } + 0.5*\sqrt{15*(\frac{7}{8} })^2 + 2*0.25*\sqrt{15*(\frac{7}{8} })^3 \\\\$

$= 0.25*\sqrt{15} + 0.5*\sqrt{15*\frac{7}{8} } + 0.5*\sqrt{15*(\frac{7}{8} })^2 + 0.5*\sqrt{15*(\frac{7}{8} })^3$

- How long it has been bouncing at nth bounce, we will look at the pattern between 1st, 2nd and 3rd and 4th bounce times calculated above. We see it follows a geometric series with formula:

Total Time ( nth bounce ) = Sum to nth ( $\frac{1}{2}*\sqrt{15*(\frac{7}{8})^(^i^-^1^) } - \frac{1}{4}*\sqrt{15}$ )

- The formula for sum to infinity for geometric progression is:

S∞ = a / 1 - r

Where, a = 15 , r = ( 7 / 8 )

S∞ = 15 / 1 - (7/8) = 15 / (1/8)

S∞ = 120

- Then we have:

Total Time = 0.5*√S∞ - 0.25*√15

Total Time = 0.5*√120 - 0.25*√15

Total Time = 4.51 s

5 0

3 years ago