In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between f = 1/4 * c + 40 , chirps and outdoor temperature is where c is the number of chirps per minute and ƒ is the temperature in degrees Fahrenheit. a. Suppose 110 chirps are heard in a minute. According to this model, what is the outdoor temperature? b. If it is 75 deg * F outside, about how many chirps can we expect to hear in one minute? c. The equation is only a good model of the relationship when the outdoor temperature is at least 55 deg * F (Below that temperature, crickets aren't around or inclined to chirp.) How many chirps can we expect to hear in a minute at that temperature?
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The graph of a linear equation, y = mx + b, will have a slope value of m, and an initial value or y-intercept of b, which is the point on the y-axis that the line intercepts.

Given the equation, f = ¼c + 40, where:

f = temperature in degrees Fahrenheit

c = number of chirps

1/4 represents the temperature in °F per chirp

40 represents the initial temperature

a. Substitute c = 110 into the equation, f = ¼c + 40:

f = ¼(110) + 40

f = 67.5

The outdoor temperature is predicted to be 67.5 °F.

b. Substitute f = 75 into the equation, f = ¼c + 40:

75 = ¼c + 40

75 - 40 = ¼c

35 = 1/4c

4(35) = c

c = 140

140 chirps would be heard in a minute.

c. Substitute f = 55 into the equation, f = ¼c + 40:

55 = ¼c + 40

55 - 40 = ¼c

15 = c/4

4(15) = c

c = 60

Expect to hear 60 chirps at that temperature.

d. The graph for f = ¼c + 40 is in the attachment.

e. 1/4 is the unit rate or slope, which is the temperature in °F per chirp.

f. 40 tells us about the equation of the relationship that the initial temperature where we can start expecting the crickets to chirp starts from 40 °F.

Learn more about the linear graph on:

https://brainly.com/question/19040584

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