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3 years ago

Brooke bought 6 bags of powdered sugar. She got a total of 4 2/3 cups of sugar. How many cups of sugar were in each bag

Mathematics

1 answer:

Marina86 [1]3 years ago

7 0

Answer:

6.5 bags of sugar in each bag

Step-by-step explanation:

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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:

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

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

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

$S_{n}=910.22\ ft$

8 0

3 years ago

What is the missing number in 12,24,72,288

Ronch [10]

12*2=24
24*3=72
72*4=288
n*(x+1)
288*(4+1)
288*5=1440

5 0

4 years ago

What is the measure of DOA

mixas84 [53]

Hi there!

The answer would be 120 so D.

Add all the measurements: 20 + 60 + 40 and you get 120.

Hope this helps ;)

7 0

4 years ago

What is the percent of change from 5,000 to 900 ?

nadezda [96]

Answer: 82% decrease

Step-by-step explanation:

Initial number =5000

Final number = 900

Change in numbers = 5000 - 900 = 4100

Since 5000 > 900 ( the change is a decrease)

Thus, the percent change =

(4100/5000) x 100%

= 82%

Thus, the percent of change from 5,000 to 900 is 82% decrease

7 0

4 years ago

Read 2 more answers

The area of a rectangular city park is 25/54 square miles. The length of the park is 5/9 mile. What is th width, in miles, of th

wolverine [178]

Answer:

0.833 miles

Step-by-step explanation:

Because you know the area, you can use the formula for area of a rectangle. Just plug in what you know and solve.

$\frac{25}{54} = \frac{30}{54}w$

30/54 is the same as 5/9.

$(\frac{25}{54})54 = (\frac{30}{54}w)54$

Multiply by its denominator.

$25=30w$

Simplify

$25/30=30w/30$

Divide by 30

$w=\frac{5}{6}$

5/6 is roughly 0.833

7 0

3 years ago