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3 years ago

13

Ruby conducted a survey and found that 5/6 of her classmates have a pet and 2/3 of those pets are dogs. what fraction of her cla

ssmate has dogs?

1 answer:

bekas [8.4K]3 years ago

3 0

It would be 1/6th of them has dogs.

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James is making a paper chain from different colored paper strips. He joins the links in the following pattern: red, blue, red,

Whitepunk [10]

Answer:

red

Step-by-step explanation:

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2 years ago

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

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3 years ago

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3 years ago

How can you find the value of x? in 3x= 2 1/4

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Answer:Tap for more steps... By the Sum Rule, the derivative of x 4 + 3 x 2 x 4 + 3 x 2 with respect to x x is d d x [ x 4] + d d x [ 3 x 2] d d x [ x 4] + d d x [ 3 x 2]. Differentiate using the Power Rule which states that d d x [ x n] d d x [ x n] is n x n − 1 n x n - 1 where n = 4 n = 4.

Step-by-step explanation:

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3 years ago

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3 years ago

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