Use a case $1$-case $2$ ratio box to solve this problem. Don's heart beats $225$ times in $3$ minutes. At that rate, how many times will his heart beat in $5$ minutes?

In 20 minutes, how many more times does a gerbil's heart beat than a rabbit's?

The A string of a violin is a little too tightly stretched. Beats at 4.00 per second are heard when the string is sounded together with a tuning fork that is oscillating accurately at concert A (440 Hz). What is the period of the violin string oscillation?

A police siren contains at least two frequencies, producing the wavering sound (beats). Explain how the siren sound changes as a police car approaches, passes, and moves away from a pedestrian.

If h(t) is a person's heart rate in beats per minute t minutes into an exercise session, what does

$$\int_{0}^{30} h(t) d t$$

represent?

A heart pacemaker is designed to operate at 72 beats/min using a 7.5-$\mu$F capacitor in a simple RC circuit. What value of resistance should be used if the pacemaker is to fire when the voltage reaches $63$ percent of maximum?

A dragonfly can beat its wings 30 times per second. Write an equation in slope-intercept form that shows the relationship between flying time in seconds and the number of times the dragonfly beats its wings. _

Assuming the heart beats once every second, how many times does the heart beat in 1 year? How many times does it beat in 40 years? 70 years?

Two strings are vibrating at the same frequency of 150 Hz. After the tension in one of the strings is decreased, an observer hears four beats each second when the strings vibrate together. Find the new frequency in the adjusted string.

What are the possible frequencies of the second string if one guitar string is tuned to a frequency of $352 \mathrm{~Hz}$ and another string on another guitar produces 7 beats per second when played together with the first string?

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. A simple random sample of 153 men results in a standard deviation of 11 .3 beats per minute . The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute; see the accompanying StatCrunch data below for this test. What do the results indicate about the effectiveness of using the range rule of thumb with the "normal range" from 60 to 100 beats per minute for estimating CJ in this case?

$$\begin{matrix} \text{One sample variance hypothesis test:}\\ \text{$\sigma^2$: Variance of variable}\\ \text{$H_0 : \sigma^2$ = 100}\\ \text{$H_A : \sigma^2\ne$100}\\\\ \text{Hypothesis test results:}\\ \text{Variable} & \text{Sample Var.} & \text{DF} & \text{Chi-Square Stat} & \text{P-value}\\ \text{PULSE} & \text{128.40282} & \text{152} & \text{195.17229} & \text{0.0208}\\ \end{matrix}$$

Find mean, median, mode, and range. Which measure of central tendency best describes each group of data? Explain. resting heart rate in beats per minute: 79 72 80 81 40 72

Flight Characteristics "

$$\begin{matrix} \text{Type of Insect} & \text{Wing Beats (per second)} & \text{Flight Speed (kilometers per hour)}\\ \text{Hummingbird moth} & \text{85} & \text{17.8}\\ \text{Bumblebee} & \text{250} & \text{10.3}\\ \text{Housefly} & \text{190} & \text{7.1}\\ \end{matrix}$$

" -Based on the data, is there a relationship between the rate at which an insect beats its wings and the speed at which it flies? Explain. What factors besides wing-beat rate might affect flight speed?

One loudspeaker is producing a tone of frequency 236.30 Hz and a second loudspeaker a tone of frequency 236.50 Hz. What is the shortest time interval that you have to listen to the sound from the two loudspeakers to hear three beats?