1.Which statement is true when two objects are 20 miles apart but one is much bigger?
2 answers:
1. C. Gravitational attraction exists between the two objects.
Explanation:
Gravitational attraction is always exerted between two objects which have mass, and its magnitude is given by:
where G is the gravitational constant, m1 and m2 the masses of the two objects, and r the separation between them. Since the two objects have for sure non-zero masses m1 and m2, even if they are 20 miles apart, the value of the gravitational attraction F is non-zero, so the correct answer is C.
2. D. Two atoms come together to form a molecule.
Explanation:
this outcome is actually caused by the electrostatic forces between the two atoms, not by gravitational force. In fact, gravitational force becomes relevant only when the masses of the two objects involved are large enough: this is the case for planets, stars, galaxies, and objects in the universe. However, two atoms have very small masses, so the gravitational force between them is really negligible. On this smaller scales, the electrostatic force is much stronger than the gravitational force, so the electrostatic force is the real responsible for the formation of bonds between atoms.
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Answer:
a. μ 3 ± 1.8 = [1.2,4.8]
b. The correct answer is option D. No, because the sample size is large enough.
Explanation:
a. The population mean can be determined using a confidence interval which is made up of a point estimate from a given sample and the calculation error margin. Thus:
μ±(t*s)/sqrt(n)
where:
μ = is the 95% confidence interval estimate
x_ = mean of the sample = 3
s = standard deviation of the sample = 5.8
n = size of the sample = 41
t = the t statistic for 95% confidence and 40 (n-1) degrees of freedom = 2.021
substituting all the variable, we have:
μ 3 ± (2.021*5.8)/sqrt(41) = 3 ± 1.8 = [1.2,4.8]
b. The correct answer is option D. No, because the sample size is large enough.
Using the the Central Limit Theorem which states that regardless of the distribution shape of the underlying population, a sampling distribution of size which is ≥ 30 is normally distributed.