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shepuryov [24]
2 years ago
5

Graph the line that represents a proportional relationship between ddd and ttt with the property that an increase of 0.20.20, po

int, 2 units in ttt corresponds to an increase of 1.81.81, point, 8 units in ddd. What is the unit rate of change of ddd with respect to ttt? (That is, a change of 111 unit in ttt will correspond to a change of how many units in d?d?d, question mark)

Mathematics
1 answer:
mafiozo [28]2 years ago
3 0

Answer:

Part a) The unit rate of change of d with respect to t is equal to 9

Part b) The graph of the line in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, t, and d, represent a proportional variation if it can be expressed in the form d/t=k or d=kt

step 1

Find the value of k

we have

t=0.2, d=1.8

k=d/t

substitute

k=\frac{1.8}{0.2}=9

so

the linear equation is equal to

d=9t

step 2

using a graphing tool

graph the line d=9t

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Answer: 76.19\%

Step-by-step explanation:

<h3> The complete exercise is: " A theatre has the capacity to seat people across two levels, the Circle, and the stalls. The ratio of the number of seats in the circle to a number of seats in the stalls is 2:5. Last Friday, the audience occupied all the 528 seats in the circle and \frac{2}{3} of the seats in the stalls. What is the percentage of occupancy of the theatre last Friday?"</h3>

Let be "s" the total number of seats in the Stalls.

The problem says that the ratio of the number of seats in the Circle to the number of seats in the Stalls is 2:5.

Since the number of seats that were occupied last Friday was 528 seats, we can set up the following proportion:

\frac{2}{5}=\frac{528}{s}

Solving for "s", we get:

s*\frac{2}{5}=528\\\\s=528*\frac{5}{2}\\\\s=1,320

So the sum of the number of seats in the Circle and the number of seats in the Stalls, is:

Total=1,320\ seats+528\ seats=1,848\ seats

 We know that \frac{2}{3} of the seats in the Stalls were occupied. Then, the number of seat in the Stalls that were occupied is:

(1,320)(\frac{2}{3})=880

Therefore, the total number of seats that were occupied las Friday is:

Total\ occupied=880\ seats+528\ seats=1,408\ seats

Knowing this, we can set up the following proportion, where "p" is the the percentage of occupancy of the theatre last Friday:

\frac{100}{1,848}=\frac{p}{1,408}

Solving for "p", we get:

(1,408)(\frac{100}{1,848})=p\\\\p=76.19\%

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