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3 years ago

Jon has 2/3 of an hour to do some training. It takes him 1/6 of an hour to run one trail. How many times can he run the trail

Mathematics

1 answer:

djverab [1.8K]3 years ago

4 0

Jon will be able to run 2 trails because 1/6 time 2 equals 2/6 you can simplify it to 1/3 and 1/3 + 1/3= 2/3

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Rzqust [24]

Answer:

Group B has the higher median by 0.5 inches. The IQR for Group A is smaller. IQR for Group B is 2 inches.

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3 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

Write first 10 pirme numbers and find median

likoan [24]

Answer:

2 3 5 7 11 13 17 19 23 27

Step-by-step explanation:

12 I think

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3 years ago

Zack, Rachel, and Maddie are unraveling a huge ball of yarn to see how long it is. As they move away from each other, they form

Korolek [52]

We are tasked to solve the three angles given that we have the measurements of the sides such as
a = Zack to Rachel distance
b = Rachel to Maddie distance
c = Maddie to Zack distance

a =3
b =2.5
c =4

Solving the angles we need to use Law of Cosines:
cos A = 2.5² + 4² -3² /2*2.5*4
A = 48.59°

cos B=3² + 4² - 2.5² / 2*3*4
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C=180 - 48.59° - 38.625°
C= 92.79°

The three angles are 48.59°,38.63° and 92.79°.

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4 years ago

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Bogdan [553]

If the population was 40,000 at the beginning of 2009, at the end of 2009 it has increased by 10% and became 44,000.

By the same way, at the end of 2010, it became $44000 + \frac{44000*10}{100} = 48400$

At the end of 2011, the population was $48400 + \frac{48400 * 10}{100} = 53240$

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3 years ago