Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d=−6.
1 answer:
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Answer:
3.2 km/h
Step-by-step explanation:
1. Approach
The average speed is the rate at which one travels. It can be found by diving the total distance traveled over the total time it took to cover that distance. In essence, the following formula can be used to find the average speed:
In this situation, one is asked to find the difference between two people's average speed. One is given the following information:
Lena: 24 miles 1.5 hours
Ras: 36km 1 hour 15 minutes
First, convert all of the numbers into the correct units (km) and (hours). Then find the average speed for each person. Finally, subtract the smaller speed from the larger speed to find the difference in the average speeds.
1. Find Lena's average speed
The problem asks one to find the average speed in the units (km/h). However, the distance Lena covered is given in (miles). Therefore, one has to multiply it by the conversion factor (1.6) in order to convert it from (miles) to (km).
24miles * 1.6 = 38.4
Now find the average speed by using the formula:
Substitute,
2. Find Ras's average speed
Use a similar approach to work out Ras's average speed, as was used to find Lena's average speed. Since Ras's time spent is given in both hours and minutes, one must convert it to just minutes. There are (60) minutes in an hour, thus, one can rewrite the number as the following:
Now find the average speed:
Substitute,
3. Find the difference between the speeds
Since Ras's speed is greater, subtract Lena's speed from Ras's speed.
Ras - Lena
= 28.8 - 25.6
= 3.2
Answer:
a) Null hypothesis:
Alternative hypothesis:
b) t =-7.44
c)
d) Reject Null hypothesis. The is enough evidence to conclude that the mean prediction error is not equal to 0.
We reject the null hypothesis because the . So we can conclude that the difference is significantly different from 0 at 5% of significance.
Step-by-step explanation:
Assuming this output:
t(observed value) =-7.44
t(Critical value )= 1.984
DF = 98
p value (two tailed) < 0.0001
a) What are the null and alternative hypothesis
Null hypothesis:
Alternative hypothesis:
The reason is because the output says a bilateral test so for this case w eselect this option.
b) Identify the statistic
The correct formula for the statistic is given by:
Based on the output the calculated value its t =-7.44
c) Identify the p value
We have the degrees of freedom given 98
Based on the alternative hypothesis the p value is given by:
d) State the final conclusion that addresses the original claim
Reject Null hypothesis. The is enough evidence to conclude that the mean prediction error is not equal to 0.
We reject the null hypothesis because the . So we can conclude that the difference is significantly different from 0 at 5% of significance.