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dsp73
1 year ago
13

Each school year, the seventh graders who study Life Science participate in a special field trip to the city zoo. In 2010, the s

chool paid $1,260 for 84 students to enter the zoo. In 2011, the school paid $1,050 for 70 students to enter the zoo. In 2012, the school paid $1,395 for 93 students to enter the zoo.
a. Is the price the school pays each year in entrance fees proportional to the number of students entering the zoo?
b. Explain why or why not.
c. Identify the constant of proportionality, and explain what it means in the context of this situation.
d. What would the school pay if 120 students entered the zoo?
e. How many students would enter the zoo if the school paid $1,425?
Mathematics
1 answer:
Mrac [35]1 year ago
3 0

Answer:

A. No it is not proportional.

B. The price goes up then down, and all years equal the same amount per student.

C. Constant proportionality starts at (0,0) and is constantly increasing.

D. $1,800 15×120=1,800

E. 95 students because 1,425÷15=95

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On her first day in a hospital, Kiri receives u1 milligrams (mg) of a therapeutic drug. The amount of the drug Kiri receives inc
Valentin [98]

Answer:

a. 21 = u1 + 6·d

b. 29 = u1 + 10·d

c. d = 2, u1 = 9

Step-by-step explanation:

a. The given parameters are;

The amount of therapeutic drug Kiri receives on her first at the hospital = u1 milligrams

The amount of drug increase received by Kiri each day = d

The amount of drug Kiri received on the seventh day = 21 mg

The amount of drug she received on the eleventh day = 29 mg

Therefore, we have an arithmetic progression with the formula for the nth term given as follows;

aₙ = a₁ + (n - 1)·d

Where;

a₁ = u1

n = The number of terms

Therefore, for the 7th day, the amount of drugs she receives, which is 21 milligrams, is given as follows;

a₇ = u1 + (7 - 1)·d = u1 + 6·d = 21

The equation for the amount of drugs she receives in terms of u1 and d on the seventh day is given as follows;

21 = u1 + 6·d

b. For the eleventh day, the amount of drugs she receives, which is 29 milligrams, is given as follows;

a₁₁ = u1 + (11 - 1)·d = u1 + 10·d = 29

Therefore, the equation for the amount of drugs she receives in terms of u1 and d on the  eleventh day is given as follows;

29 = u1 + 10·d

c. Therefore, we have two equations which are given as follows;

21 = u1 + 6·d................(1)

29 = u1 + 10·d..............(2)

Subtracting equation (1) from equation (2) gives;

29 - 21 = (u1 + 10·d) - (u1 + 6·d)

8 = 4·d

d = 8/4 = 2

d = 2

From equation (1), we have;

21 = u1 + 6·d = u1 + 6×2 = u1 + 12

21 = u1 + 12

21 - 12 = u1

∴ u1 = 9

d = 2, u1 = 9.

4 0
1 year ago
The width of a rectangle is the length minus 3 units. The area of the rectangle is 54 units. What is the width, in units, of a r
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Width of the rectangle is 9 units

Step-by-step explanation:

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54 = x (x - 3)

54 = x² - 3x

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x = -6, 9 (negative value is neglected)

x = 9 units

4 0
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