Response:
Detailed explanation:
Hello!
Stratified sampling involves the categorization of the population into subgroups based on pre-established criteria for the study. These subgroups consist of homogeneous units concerning the relevant characteristics. In this instance, individuals in the groups will represent only one of the two potential opinions (support or not support) and not both.
The researcher determines the sample size desired, considering several factors such as finances, material availability, and accessibility to experimental subjects (for instance, if they are endangered species, larger sample sizes may not be feasible).
One might conduct proportionate stratified sampling by selecting a proportion of respondents who answered "yes" along with those who answered "no."
In this sampling method, taking a specific proportion from each subgroup allows for a more straightforward extrapolation of results to the overall populations. For example, if you needed a sample size of n = 20, each stratum would ideally contain half, meaning 10 from the “yes” group and 10 from the “no” group.
I hope this is helpful!
Let x represent the amount invested at 6% and y the amount at 9%.
The equation x+y=8,500 leads to x=8500-y.
For the interest rates, we know 6%=0.06 and 9%=0.09.
The equation becomes 0.06x + 0.09y=667.5 (substituting for x to use only y).
Expanding yields: 0.06(8500-y)+0.09y=667.5.
Solving this gives us 510-0.06y+0.09y=667.5 (-510).
This simplifies to 0.03y=117.5 (/0.03), yielding y=$3916.67 for the 9% investment.
Thus, X=8500-Y results in x=$4583.33 for the 6% investment.
Because SI units are structured around powers of 10, you can shift the decimal point to convert; imperial units lack that base-10 organization, so the decimal-shifting method doesn't apply.
An equivalent decimal represents the same quantity as another decimal; here, the 0 does not contribute any value.
The likelihood of all sprinklers functioning properly in a fire stands at 0.0282. This was determined via the Binomial probability distribution since the activation of sprinklers occurs independently. There are two potential outcomes: they either function correctly or they do not. The binomial distribution is used to calculate the probabilities over multiple trials. The resulting equation b(x; n, P) = P(X=x) considers the number of successes, probability of success in a singular attempt, and the number of trials involved. The computations conclude with the probability being reflected as 0.0282.
