Sarah made a certain number of bracelets for a craft show. Maria made 7 more than Sarah. Julie made 3 times as many as Maria.
2 answers:
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ARITHMETIC CHECK: A sequence is said to be arithmetic if any two consecutive terms differ by the same constant.
So, the test to check if a series is arithmetic is to compute consecutive differences, and see if they all return the same number.
If we subtract the first two terms, we have . If we subtract the third and second terms, we have
.
These two differences returned two different values, so the series is not arithmetic.
GEOMETRIC CHECK: A sequence is said to be geometric if any two consecutive terms are in the same ratio.
So, the test to check if a series is geometric is to compute consecutive ratios, and see if they all return the same number.
If we divide the first two terms, we have
If we divide the third and second terms, we have
Finally, if we divide the last two terms we have
So, all ratios return the same number. This means that the series is geometric, and the common ratio is 1/2
Answer: c. z = 1.35; Reject the null hypothesis
Step-by-step explanation:
Let be the average life expectancy of its batteries.
As per given , we have
Null hypothesis :
Alternative hypothesis :
Since is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.
Test statistic :
where, n= sample size
= sample mean
= Population mean
=population standard deviation
For , we have
Critical one-tailed test value for 0.10 significance level :
Decision : Since critical z value (1.28) < test statistic (1.35), so we reject the null hypothesis .
[When critical value is less than the test statistic value , we reject the null hypothesis .]