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1 month ago

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The function c(x) = 0.5x+70 represents the cost c (in dollars) of renting a truck from a moving company, where x is the number o

f miles you drive the truck.
a. Graph the function and identify its domain and range. Write your answers as inequalities.

Thankss!!!!

2 answers:

babunello [11.8K]1 month ago

6 0

Answer:

b) h(x) = –2x + 200

Step-by-step explanation:

The moving rates from one company can be characterized by the function f(x) = 3x + 400, where x indicates the miles moved.

Another moving company's rates can be defined as g(x) = 5x + 200.

To find the function that represents the difference in costs between the two moving companies, we express it as h(x) = f(x) – g(x).

Thus, we get:

h(x) = 2x + 200

h(x) = –2x + 200

h(x) = 5x – 200

h(x) = 5x + 600

PIT_PIT [12.4K]1 month ago

3 0

Function given: c(x) = 0.5x + 70.

Here, c represents the cost in dollars while x indicates the miles driven in the truck.

By comparing this with the slope-intercept format y=mx+b, we find:

Slope m = 0.5, which can be expressed as 1/2.

The y-intercept b = 70.

To graph this, we start by plotting the y-intercept at 70 and then add more points based on the rise/run ratio, which is 1/2.

The plotted line shown in red illustrates the function.

It can be observed that the initial cost is $70, corresponding to zero miles driven.

The x values denote the domain while C(x) portrays the range.

We can use x values that are 0 or above, and C values that are 70 or more.

Thus, Domain: x≥0 and Range: C(x)≥70.

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a. 0.0124 = 1.24% ang posibilidad na itigil ang paggawa kapag ang sample mean ay 16 inches.

b. 0.0241 = 2.41% ang posibilidad na itigil ang paggawa kung ang mean ay lumipat sa 16.05 inches.

c. 0.5 = 50% ang posibilidad na hindi makagambala sa produksyon kung ang mean ay lumipat sa 16.25 inches.

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Upang masagot ang tanong na ito, kinakailangan nating maunawaan ang normal probability distribution at ang central limit theorem.

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Kapag ang distribusyon ay normal, ginagamit natin ang z-score formula.

Sa isang set na may mean $\mu$ at standard deviation $\sigma$ , ang z-score ng sukat X ay ibinibigay ng:

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Ang Z-score ay sumusukat kung gaano karaming standard deviations ang sukat ay mula sa mean. Pagkatapos makuha ang Z-score, titingnan natin ang z-score table at hahanapin ang p-value na kaugnay ng z-score na ito. Ang p-value na ito ay ang posibilidad na ang halaga ng sukat ay mas maliit kaysa sa X, na ibig sabihin ay ang percentile ng X. Sa pamamagitan ng pagbawas ng 1 sa p-value, makakakuha tayo ng posibilidad na ang halaga ng sukat ay mas mataas sa X.

Central Limit Theorem

Itinataguyod ng Central Limit Theorem na, para sa isang normal na ipinamamahaging random variable X, na may mean $\mu$ at standard deviation $\sigma$ , ang sampling distribution ng sample means na may sukat n ay maaaring i-approximate sa isang normal na distribusyon na may mean $\mu$ at standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

Ipagpalagay na ang standard deviation ng diameter ng mga rims ay 0.3 inches. Ang samples ay 9.

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a. Kalkulahin ang posibilidad na itigil ang paggawa kapag ang sample mean ay 16 inches.

$\mu = 16$ Narito ang

Mas mataas sa 16.25:

Ito ay 1 na ibinawas mula sa p-value ng Z kapag X = 16.25. Kaya

$Z = \frac{X - \mu}{\sigma}$

Sa pamamagitan ng Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{16.25 - 16}{0.1}$

$Z = 2.5$

$Z = 2.5$ may p-value na 0.9938

1 - 0.9938 = 0.0062

Mas mababa sa 15.75:

Ito ay p-value ng Z kapag X = 15.75. Kaya

$Z = \frac{X - \mu}{s}$

$Z = \frac{15.75 - 16}{0.1}$

$Z = -2.5$

$Z = -2.5$ may p-value na 0.0062

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2*0.0062 = 0.0124

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Narito ang

Mas mataas sa 16.25:

$Z = \frac{X - \mu}{s}$

$Z = \frac{16.25 - 16.05}{0.1}$

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Mas mababa sa 15.75:

Ito ang p-value ng Z kapag X = 15.75. Kumbaga

$Z = \frac{X - \mu}{s}$ may p-value na 0.0013

$Z = \frac{15.75 - 16.05}{0.1}$

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Sa pagitan ng 16.25 at 15.75 na may $\mu = 16.25$ . Ito ang p-value ng Z kapag X = 16.25 na ibinawas mula sa p-value ng Z kapag X = 15.75.

X = 16.25

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$Z = \frac{15.75 - 16.25}{0.1}$

$Z = -5$

$Z = -5$ may p-value na 0

0.5 - 0 = 0.5

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