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saveliy_v [14]
2 years ago
12

Consider the exponential functions below.

Mathematics
1 answer:
klio [65]2 years ago
3 0

The functions in order from least to greatest according to their average rates of change are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]

<h3>How to order the functions?</h3>

The rate of change is calculated using:

m = \frac{y_2 -y_1}{x_2 -x_1}

For function g at the interval [2,3], we have:

m = \frac{g(3) - g(2)}{3- 2}

This gives

m = \frac{20 - 4}{3- 2}

m =16

For function h at the interval [0,2], we have:

m = \frac{h(2) - h(0)}{2- 0}

Where:

h(2) = 3(3)^2 - 9 = 18

h(0) = 3(3)^0 - 9 = -6

This gives

m = \frac{18 + 6}{2 - 0}

m = 12

For function f at the interval [1,2], we have:

m = \frac{f(2) - f(1)}{2- 1}

This gives

m = \frac{12 - 6}{2 - 1}

m = 6

Hence, the functions are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]

Read more about average rates of change at:

brainly.com/question/8728504

#SPJ1

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3 years ago
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimeters,
tiny-mole [99]

Answer:

Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.

Step-by-step explanation:

We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7.

A random sample of 39 steel bolts is selected.

Let \bar X = <u><em>sample mean diameter</em></u>

The z score probability distribution for sample mean is given by;

                            Z  =  \frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} }  } }  ~ N(0,1)

where, \mu = population mean diameter = 141 millimetres

           \sigma = standard deviation = 7 millimetres

           n = sample of steel bolts = 39

Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P(\bar X > 141.4 millimetres)

      P(\bar X > 141.4) = P( \frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} }  } } > \frac{141.4-141}{\frac{7}{\sqrt{39} }  } } ) = P(Z > 0.36) = 1 - P(Z \leq 0.36)

                                                            = 1 - 0.6406 = <u>0.3594</u>

The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.

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