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3 years ago

What is the probability that a stamp chosen at random is a commemorative or a special delivery stamp?

Mathematics

1 answer:

Ksivusya [100]3 years ago

3 0

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

$P(\text{ getting a commemorative stamp})=0.16$

and

$P(\text{getting a special delivery stamp})=0.18$

So, we need to find,

$P(\text{getting either a commemorative or a special delivery stamp})\\=P(\text{getting a commemorative stamp})+P({\text{ getting a special delivery stamp})$

(∵they are independent events .)

$P(\text{getting either a commemorative or a special delivery stamp})\\=0.16+0.18\\=0.34$

So, option 'D' is correct.

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Help please? I don’t know much about consecutive integers...

Ugo [173]

Consecutive intergers are numbers that follow each other in order.

The correct answer is 26 and 27 because it equals to 53 which is the closest to 52.

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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

Find the ratio and unit rate.<br> 216 cherry pieces in 6 bags of candy

Charra [1.4K]

Answer:

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36 rate

Step-by-step explanation:

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3 years ago

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xenn [34]

The answer should be 7/8

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3 years ago

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Lilly takes a train each day to work that averages 35 miles per hour. On her way home, her train ride follows the same path and

Klio2033 [76]

Answer: $2.5=\frac{n}{35}+\frac{n}{45}$

Step-by-step explanation:

1. To find the equation asked, you must add the times:

$t_{total}=t_1+t_2$

Where $t_1$ is the time takes Lilly in her path to work and $t_2$ is the time takes Lilly in her path to home.

2. You must use the following formula of speed and solve for the time

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Where n is the distance, V is the speed and t is the time.

3. You know that Lilly takes a train each day to work that averages 35 miles per hour, then, you can write the following expression:

$35=\frac{n}{t_1}\\t_1=\frac{n}{35}$

4. And her train ride follows the same path at 45 miles per hour:

$45=\frac{n}{t_2}\\t_2=\frac{n}{45}$

5. Then, you obtain the following equation:

$2.5=\frac{n}{35}+\frac{n}{45}$

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3 years ago

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