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3 years ago

7

Biologists have noticed that the chirping of crickets of a certain species is related to temperature, and the relationship appea

rs to be very nearly linear. A cricket produces 113 chirps per minute at 73 degrees Fahrenheit and 172 chirps per minute at 87 degrees Fahrenheit.Find a linear equation that models the temperature T as a function of the number of chirps per minute N.T(N)= ?

1 answer:

lilavasa [31]3 years ago

5 0

Answer:

$T(N) = \dfrac{14N}{59} + \dfrac{2725}{59}$

Step-by-step explanation:

We are given the following in the question:

The relation between chirping of crickets and temperature is a linear function.

$T(N) = aN + b$

where and b are constants. T(N) is the the temperature in Fahrenheit and N is the number of chirps per minute.

"A cricket produces 113 chirps per minute at 73 degrees Fahrenheit"

$73 = 113a+b$

"A cricket produces 172 chirps per minute at 87 degrees Fahrenheit"

$87 = 172a+b$

Solving the two equations, we get,

$87-73 = 172a - 113a\\14 = 59a\\\\a =\dfrac{14}{59}\\\\73 = 113(\dfrac{14}{59}) + b\\\\b = 73 - 113(\dfrac{14}{59})\\\\b = \dfrac{2725}{59}$

Thus, the required linear function is:

$T(N) = \dfrac{14N}{59} + \dfrac{2725}{59}$

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Every time you have your cholesterol measured, the measurement may be slightly different due to random fluctuations and measurem

zmey [24]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a i

$P(X < 185 ) = 0.3085$

a ii

$P(X > 195 ) = 0.3085$

a iii

$P(185 < X < 195 ) = 0.3829$

b

$x = 208.8$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 190$

The standard deviation is $\sigma = 10$

Generally the probability is less than 185 is mathematically represented as

$P(X < 185 ) = P(\frac{X - \mu }{\sigma } < \frac{185 - 190 }{10 } )$

Generally $\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ \ of \ X)$

=> $P(X < 185 ) = P(Z< -0.5)$

From the z-table the p value of (Z< -0.5) is

$P(Z< -0.5) = 0.3085$

So

$P(X < 185 ) = 0.3085$

Generally the probability is less than 185 is mathematically represented as

$P(X > 195 ) = P(\frac{X - \mu }{\sigma } > \frac{195 - 190 }{10 } )$

=> $P(X > 195 ) = P(Z > 0.5)$

From the z-table the p value of (Z > 0.5) is

$P(Z > 0.5) = 0.3085$

So

$P(X > 195 ) = 0.3085$

Generally the probability is less than 185 is mathematically represented as

$P(185 < X < 195 ) = P( \frac{185 - 190 }{10 } < \frac{X - \mu }{\sigma } < \frac{195 - 190 }{10 } )$

=> $P(185 < X < 195 ) = P(-0.5 < Z > 0.5)$

=> $P(185 < X < 195 ) = P(Z < 0.5 ) - P(Z < -0.5)$

From the z-table the p value (Z < 0.5) and (Z < -0.5) is

$P(Z < 0.5) = 0.6915$

and

$P(Z < - 0.5) = 0.3085$

So

=> $P(185 < X < 195 ) = 0.6915 - 0.3085$

=> $P(185 < X < 195 ) = 0.3829$

Generally the level of cholesterol the 97th percentile represents is mathematically evaluated as

$P(X < x ) = 0.97$

=> $P(X < x ) = P(\frac{X - \mu}{\sigma } < \frac{x - 190}{10 } ) = 0.97$

=> $P(X < x ) = P(Z < \frac{x - 190}{10 } ) = 0.97$

From the z-table the z-score for 0.97 is

$z-score = 1.88$

=>

$\frac{x - 190}{10 } = 1.88$

=> $x = 208.8$

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3 years ago

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mart [117]

Answer:

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Step-by-step explanation:

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2 years ago

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guapka [62]

Answer:370mm^3

Step-by-step explanation:

You would first find the area of the whole rectangle without the hole, so (15)(30)=450

Next find the area of the hole, (8)(10)=80

To find the area you must subtract the area of the hole from the rectangle.

450-80=370

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2 years ago

Gulf gully and jump rope road are a pretty far distance.If the scale for the map is 0.5 inches=2.3 miles,what is the actual dist

Nezavi [6.7K]

Answer:

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Step-by-step explanation:

To find the distance, set up a proportion. A proportion is two equal ratios set equal to each other. We form the ratios by using corresponding values. We write a ratio of $\frac{map}{real world}$ and simplify.

We know $\frac{map}{real world}=\frac{0.5in}{2.3 miles}$ . We know the distance on the map is 12 cm and 6 cm whish converts to 4.7 inches and 2.4 inches. We can write $\frac{4.7in}{xmiles}$ and $\frac{2.4in}{xmiles}$

We set them equal.

$\frac{0.5}{2.3}=\frac{4.7}{x}$

and

$\frac{0.5}{2.3}=\frac{2.4}{x}$

To solve each proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

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3 years ago

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Andrei [34K]

K is the right answer for the problem!

6 0

3 years ago