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2 years ago

Uber charges a $5 pickup fee and $0.25 per mile. define variables and write an equation to model this situation.

Mathematics

1 answer:

Degger [83]2 years ago

8 0

Answer:

See below

Step-by-step explanation:

$5 pickup fee
$0.25 per mile

<u>Equation</u>

y = 0.25x + 5

<u>Cost of 5 miles:</u>

y = 0.25(5) + 5 = $6.25

<h3>KC yellow Cab Co.</h3>

$1.75 pickup fee
$0.75 per mile

<u>Equation</u>

y = 0.75x + 1.75

<u>Cost of 5 miles:</u>

y = 0.75(5) + 1.75 = $5.5

Comparing the cost we see KC yellow Cab Co. is better value for a 5 mile ride.

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For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th

alexira [117]

Answer:

The inner function is $h(x)=4x^2 + 8$ and the outer function is $g(x)=3x^5$ .

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

Step-by-step explanation:

A composite function can be written as $g(h(x))$ , where $h$ and $g$ are basic functions.

For the function $f(x)=3(4x^2+8)^5$ .

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have $4x^2+8$ inside parentheses. So $h(x)=4x^2 + 8$ is the inner function and the outer function is $g(x)=3x^5$ .

The chain rule says:

$\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)$

It tells us how to differentiate composite functions.

The function $f(x)=3(4x^2+8)^5$ is the composition, $g(h(x))$ , of

outside function: $g(x)=3x^5$

inside function: $h(x)=4x^2 + 8$

The derivative of this is computed as

$\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4$

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

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2 years ago

The lengths of one-year-old baby girls can be described using a normal distribution with a mean of 29 inches and a standard devi

crimeas [40]

The '68-95-99.7' rule says

-About 68% of values fall within one standard deviation of the mean.

-About 95% of the values fall within two standard deviations from the mean.

-Almost all of the values — about 99.7% — fall within three standard deviations from the mean.

Here $31.4=29+2*1.2 26.6=29-2*1.2$

Therefore, the probability

$P(26.6$

The required probability

$P(L$

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1 year ago

A statue in the park is 24 feet tall and has a width of 36 inches. Chase was in

NeTakaya

Answer:

<u>22.33 feet tall / 267.96 inches tall</u>

Step-by-step explanation:

The statue is 36 inches wide. If Chase made his model of the statue 16 inches wide, he decreased it by 20 inches. Now change the inches into feet. 36 inches would be 3 feet, 16 inches would be 1.33 feet and 20 inches would be 1.67 feet. <u>24ft - 1.67 = 22.33ft.</u> Now change the answers to inches. 22.33ft will be 267.96 inches tall.

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2 years ago

The minute hand of a clock in a clock tower has a length of 36 inches.

Paul [167]

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