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liberstina [14]
3 years ago
15

A small college has 1200 students and 80 professors. The college is planning to increase enrollment to 1450 students next year.

How many new professors should be hired to keep the ratio of students to professors the same
Mathematics
1 answer:
aleksley [76]3 years ago
4 0
The ratio of the students to the professors is 1200:80 = 30:2 = 15.
- After enrollment the number of students will be 1450.
- So the number of professors after enrollment will become the unknown number, x.

➡️ 1200/80 = 1450/x

➡️ 1200x = 1450 * 80

➡️ 1200x = 116,000

➡️ x = 116,000/1200

➡️ x= 96.67

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What is the quotient
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3 0
4 years ago
For the functions f(x) = x^2+ 8x + 2 and g(x) = -5+9, find (f•g)(x)and (f.g)(-1).
Ne4ueva [31]

Answer:  (f·g)(x) = -5x³ - 31x² + 62x + 18

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(fog)(-1) = 310

<u>Step-by-step explanation:</u>

f(x) = x² + 8x + 2          g(x) = -5x + 9

(f·g)(x) = (x² + 8x + 2)(-5x + 9)

          = -5x³ + 9x²

                    - 40x² + 72x

            <u>                    - 10x + 18</u>

          = -5x³ - 31x² + 62x + 18

(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18

         =  -5(-1)  - 31(1)    - 62      + 18

         =    5     -   31      - 62      + 18

         =  -70

****************************************************************************************

(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2

           = 25x² - 90x + 81

                       - 40x + 72

              <u>                   +   2</u>

           = 25x² - 130x + 155

(fog)(-1) = 25(-1)² - 130(-1) + 155

            =   25    +  130    + 155

            = 310

<em>It wasn't clear if you wanted multiplication or composition so I solved both.</em>

6 0
3 years ago
Jennifer wants to take a trip around the world. She plans to deposit $125 at the beginning of each month into an investment with
andre [41]
The formula of the future value of annuity due is
A=p [(1+r/k)^(kn)-1)/(r/k)]×(1+r/k)
A future value of annuity due
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R interest rate 0.0375
K compounded monthly 12
N time 8 years
Solve for A
A=125×(((1+0.0375÷12)^(12
×8)−1)÷(0.0375÷12))×(1
+0.0375÷12)
=14,012.75
4 0
3 years ago
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