Which number has a 4 with a value ten times less than the 4 in the number 123,469?
1 answer:
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Given:
y is proportional to x.
y=10 and x=8.
To find:
The constant of proportionality and the equation for the proportional relationship.
Solution:
y is proportional to x.
...(i)
Where, k is the constant of proportionality.
Putting y=10 and x=8, we get
Putting in (i), we get
Therefore, the contestant of proportionality is and the equation for the proportional relationship is
.
Answer:
a)
The null hypothesis is
The alternative hypothesis is
b-1) The value of the test statistic is t = 1.86.
b-2) The p-value is of 0.0348.
Step-by-step explanation:
Question a:
Test if the battery life is more than twice of 5 hours:
Twice of 5 hours = 5*2 = 10 hours.
At the null hypothesis, we test if the battery life is of 10 hours or less, than is:
At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:
b-1. Calculate the value of the test statistic.
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
In which X is the sample mean, is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
10 is tested at the null hypothesis:
This means that
In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
This means that
Then
The value of the test statistic is t = 1.86.
b-2. Find the p-value.
Testing if the mean is more than a value, so a right-tailed test.
Sample of 45, so 45 - 1 = 44 degrees of freedom.
Test statistic t = 1.86.
Using a t-distribution calculator, the p-value is of 0.0348.
Because in '1/8', there are 8 whole number but one shaded and in '1/10', there are 10 whole number and one shaded. as you see in the picture, the smaller the denominator is(when it goes up), the more bigger it is than those below. So 1/8 is greater than 1/10. but 1/8 is smaller than 1/3, because remember:
*The more you go down(or the higher the denominator is), the more you are making the fraction into more smaller pieces.
*The more you go down(or the higher the denominator is), the more you are making the fraction into more smaller pieces.