A ball is dropped from a height if 30 feet the ball bounces after each bounce the height attained by the ball is 60% of the previous height write an nth term formula to model the situation what is the maximum height attained by the ball after five bouncesA.0.12ft
B.6.40ft
C.2.33ft
D.1.40ft

Answers

Answer 1

Answer: This information will be modeled using the formula
thus we shall have:
Sn=ar^n
where:
a=first term
r=common ratio
from the information:
a=30 ft
r=60/100=3/5=0.6
therefore the formula will be
Sn=30(0.6)^n
where n is the number of terms:
thus when n=5 th sum will be:
S5=30(0.6)^5
S5=30(0.6)^5
S5=2.33 ft
Answer: 2.33 ft

Answer 2

Answer:

Answer:

2.33

Step-by-step explanation:

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a radio station claims that the amount of advertising per hour of broadcast time has an average of 17 minutes and a standard deviation equal to 2.7 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 11 minutes. Calculate the z-score for this amount of advertising time

Answers

Answer:

z-score for 11 minutes of advertising time is $z=(-6)/(2.7)\approx -2.222$

Step-by-step explanation:

Z-scores measure the distance of any data point from the mean in units of standard deviations and are useful because they allow us to compare the relative positions of data values in different samples.

The z-score for any single data value can be found by the formula:

$z=(data \:value- \:mean)/(standard \:deviation)$

From the information given we know:

Data value = 11 minutes
Mean = 17 minutes
Standard deviation = 2.7 minutes

$z=(11-17)/(2.7) = (-6)/(2.7)\approx -2.222$

The difference between seven and triple the input

Answers

Answer: 3x - 7

x = some input number

3x = triple the input

3x - 7 = difference of triple the input and 7

Quick! Please Help Me ASAP!

Answers

Answer:

Step-by-step explanation:

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound- shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph

Answers

Answer:

15.74% of the player's serves were between 115 mph and 145 mph

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 100, \sigma = 15$

What percentage of the player's serves were between 115 mph and 145 mph

This is the pvalue of Z when X = 145 subtracted by the pvalue of Z when X = 115.

X = 145

$Z = (X - \mu)/(\sigma)$

$Z = (145 - 100)/(15)$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

X = 115

$Z = (X - \mu)/(\sigma)$

$Z = (115 - 100)/(15)$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

0.9987 - 0.8413 = 0.1574

15.74% of the player's serves were between 115 mph and 145 mph

Final answer:

A total of 27% of the player's serves at the U.S. Open Tennis Championship were between 115mph and 145mph. This was found using the Empirical Rule which applies to a normal distribution of serve speeds.

Explanation:

This problem is a classic example of the use of the Empirical Rule in statistics. The Empirical Rule, also known as the 68-95-99.7 rule, applies to a normal distribution, which is a bell-shaped curve (mound-shaped and symmetric) as mentioned in the problem. This rule states that approximately 68% of the data falls within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Given that the mean serve speed is 100 mph and the standard deviation is 15 mph, serves of 115 mph are one standard deviation above the mean and serves of 145 mph are three standard deviations above the mean. Therefore, we are looking for the percentage of serves between these two values. According to the Empirical Rule, this would be 95% (coverage for up to 2 standard deviations) minus 68% (coverage for up to 1 standard deviation), which equals 27%. So, 27% of the player's serves were between 115 mph and 145 mph.

Learn more about Empirical Rule here:

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Hey can you please help me posted picture of question

Answers

Each leaf on the tree diagram represents a possible combination. So we are to find the total number of combinations for the given scenario.

There are 5 ways to select the pant, 7 ways to select a shirt and 3 ways to select the shoes.

Total number of combinations will be the product of all these ways the dress items can be selected.

So, number of combination of outfits = 5 x 7 x 3 = 105

Therefore, option B gives the correct answer

Which are true about the area of a circle