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rodikova [14]
3 years ago
11

Question 2(Multiple Choice Worth 5 points) (04.01)The Boardman family walked two over five of a mile in two over seven of an hou

r. What is their unit rate in miles per hour?
Mathematics
1 answer:
Zolol [24]3 years ago
4 0

Answer:

The unit rate in miles per hour = <em>1.4 miles/hr</em>

Step-by-step explanation:

Given that:

Distance walked by Boardman family = Two over five of a mile = \frac{2}{5}\ miles

Time taken by Boardman family = Two over seven of an hour = \frac{2}{7}\ hour

To find:

The unit rate in the miles per hour = ?

Solution:

Formula for the rate or the speed can be given as:

Speed = \dfrac{Distance}{Time}

Putting the values:

\Rightarrow \dfrac{\frac{2}5}{\frac{2}7}\\\Rightarrow \dfrac{7}{5}\\\Rightarrow \bold{1.4\ miles/hr}

So, the unit rate in miles per hour = <em>1.4 miles/hr</em>

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According to data from a medical​ association, the rate of change in the number of hospital outpatient​ visits, in​ millions, in
GaryK [48]

Answer:

a) f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient​ visits, in​ millions, is given by:

f'(t)=0.001155t(t-1980)^{0.5}

a) To find the function f(t) you integrate f(t):

\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt

To solve the integral you use:

\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}

Next, you replace in the integral:

\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C

Then, the function f(t) is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient​ visits.

Hence C' = 264,034,000

The function is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000

b) For t = 2015 you have:

f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7

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3 years ago
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alukav5142 [94]

Answer:

A.

Step-by-step explanation:

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