Star A is 4 light years away from Earth. Star B is 10 light years away from Earth. When you observe both stars from Earth they appear to have the same brightness. How do the stars’ apparent magnitudes compare? Are they the same or different?

Aresearcher plans to conduct a test of hypotheses at the 1% significance level. she designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. the probability that the researcher will commit a type ii error for the particular alternative value of the parameter at which she computed the power is: a. 0.90. b. 0.01. c. 0.10. d. equal to 1

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

Using a pedometer, you walk 3000 steps in 20 minutes, so your speed is 150 steps/min. each of your steps is 0.7 m long. what is your speed? 150 steps/min=/s=/h