Researchers at the University of Wisconsin at Madison conducted an experiment to study the effect of meditation on the immune system. The researchers randomly assigned volunteers to one of two treatments. One group completed an 8-week course in meditation and actively practiced meditation during this period. The other group received no meditation training and did not meditate during the 8-week period. At the end of the experiment researchers gave the subjects a flu shot. A healthy immune system will produce antibodies in response to a vaccine. At 4-weeks and 8-weeks after the flu shot, researchers did a blood test to measure the levels of antibodies produced against the vaccine. Both groups had an increased level of antibodies, but the meditators had a significantly greater increase in antibodies than the non-meditators. Psychosomatic Medicinepublished the results in 2003 in an article titled "Alterations in Brain and Immune Function Produced by Mindfulness Meditation." Stress can harm the immune system. So stress could be a confounding factor in this experiment. Which of the following features of the experiment design is the best way to control the effects of stress on the results of the experiment?

a. use volunteers (bople who have time to volunteer for a study are probably not stressed out by a busy life)
b. use random assignment to treatment groups
c. use a control group for comparison

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.