Find the smallest positive integer k such that 360k is a cube number.
2 answers:
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If Ann can build the model in 3 hours, then in 1 hour she gets 1/3 of it done. Likewise, if Sam can build the model in 6 hours, then in 1 hour he gets 1/6 of it done. We are looking to find how long it takes when they combine their efforts, so we will add the two together and set it equal to 1/x, x being the number of hours it takes for both of them to get the whole job done. The equation then looks like this: . You will have to find the common denominator to add those fractions, and once you do, cross multiply to solve for x.
Answer:
Step-by-step explanation:
Hello!
The objective of the study is to determine whether the magnets are effective in treating pain. For these two independent groups of individuals with equal affections were randomly sampled, one was treated with magnets and the other group of individuals, call it control group, was treated with a placebo treatment.
The information for both samples is:
X₁: pain measurement using a visual analog scale after the individual received magnet treatments.
X₁~N(μ₁;σ₁²)
n₁= 20
X[bar]₁= 0.46
S₁= 0.93
X₂: pain measurement using a visual analog scale of an individual of the control groups.
X₂~N(μ₂;σ₂²)
n₂= 20
X[bar]₂= 0.41
S₂= 1.26
The claim is that the pain reductions of the control group have more variation than the pain reductions of the target group. If it's so then we could suspect that the population variance of the control group, σ₂², will be greater than the population variance of the magnet group, σ₁².
To test the relationship between these two population variances you have to conduct a variance ratio test using the Snedecors F statistic.
The hypotheses are:
H₀: σ₂² ≤ σ₁²
H₁: σ₂² > σ₁²
α: 0.05
This hypothesis test is one-tailed to the right, there is only one critical value:
The decision rule for the test is:
If ≥ 2.17, then the decision is to reject the null hypothesis.
If < 2.17, then the decision is to not reject the null hypothesis.
Since the calculated value of F is less than the critical value, the decision is to reject the null hypothesis. So using a 5% significance level the decision is to not reject the null hypothesis, you can conclude that the population variance of the pain reduction of the control group is less or equal than the population variance of the pain reduction on individuals treated with magnets.
I hope it helps!