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OLEGan [10]
1 year ago
8

Find f(g(x)) simplify completely f(x)= x^2+5x+2 g(x)=3x

Mathematics
2 answers:
Sindrei [870]1 year ago
8 0

Answer:

<u>f(g(x)) = 9x² + 15x + 2</u>

Step-by-step explanation:

  • f(x) = x² + 5x + 2
  • g(x) = 3x

<u>Solving f(g(x))</u>

  • f(g(x))
  • f(3x)
  • f(3x) = (3x)² + 5(3x) + 2
  • f(3x) = 9x² + 15x + 2
  • <u>f(g(x)) = 9x² + 15x + 2</u>
elena-s [515]1 year ago
8 0

Answer:

f(g(x)) = 9x^2 + 15x + 2

Step-by-step explanation:

<u>Step 1:  State the equations</u>

f(x) = x^2 + 5x + 2

g(x) = 3x

<u>Step 2:  Insert the equation and solve</u>

f(g(x)) = (g(x))^2 + 5(g(x)) + 2

f(3x) = (3x)^2 + 5(3x) + 2

f(3x) = 9x^2 + 15x + 2

f(g(x)) = 9x^2 + 15x + 2

Answer:  f(g(x)) = 9x^2 + 15x + 2

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Papa john is 50 years old. His age is 2 years more than 3 times the age of Jimmy John. How old is Jimmy?
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Answer:

<h2>Jimmy is 16 old.</h2>

Step-by-step explanation:

J - the age of Jimmy John

50 - the age of Papa John

3J + 2 - the age of Papa John

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3J + 2 = 50             <em>subtract 2 from both sides</em>

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3 years ago
The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26
hjlf

Answer:

Probability that next week's show will have between 30 and 37 million viewers is 0.2248.

Step-by-step explanation:

We are given that the distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million.

<em>Let X = number of viewers for the American Idol television show</em>

So, X ~ N(\mu=26,\sigma^{2}=8^{2})

Now, the z score probability distribution is given by;

          Z = \frac{X-\mu}{\sigma} ~ N(0,1)

where, \mu = population mean = 26 million

            \sigma = standard deviation = 8 million

So, probability that next week's show will have between 30 and 37 million viewers is given by = P(30 < X < 37) = P(X < 37) - P(X \leq 30)

    P(X < 37) = P( \frac{X-\mu}{\sigma} < \frac{37-26}{8} ) = P(Z < 1.38) = 0.91621

    P(X \leq 30) = P( \frac{X-\mu}{\sigma} \leq \frac{30-26}{8} ) = P(Z \leq 0.50) = 0.69146

<em>Therefore, P(30 < X < 37) = 0.91621 - 0.69146 = 0.2248</em>

Hence, probability that next week's show will have between 30 and 37 million viewers is 0.2248.

4 0
3 years ago
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