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Dahasolnce [82]
3 years ago
6

The restaurant sells their arnold palmer for 4 cups for 5$. What is the price of 1 cup?

Mathematics
1 answer:
prohojiy [21]3 years ago
7 0

Answer:

$1.25

Step-by-step explanation:

Set up a proportion, use inverse operations, and solve;

cups : price

4 : 5

/4  /4

1 : 5/4

1 : 1.25

1 cup to $1.25

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3 years ago
Let f(x)=5e^3x and g(x)=2/3ln(5x); find (f(g))(2)
Sedbober [7]

Answer:

<h2>a) 500</h2>

Step-by-step explanation:

(f\circ g)(x)=f\bigg(g(x)\bigg)\\\\(f\circ g)(2)=f\bigg(g(2)\bigg)\\\\f(x)=5e^{3x},\ g(x)=\dfrac{2}{3}\ln(5x)\\\\(f\circ g)(x)\to\text{in}\ f(x)\ \text{replace}\ x\ \text{with the expression}\ \dfrac{2}{3}\ln(5x):\\\\(f\circ g)(x)=5e^{3\cdot\frac{2}{3}\ln(5x)}=5e^{2\ln(5x)}\qquad\text{use}\ \ln a^n=n\ln a\\\\(f\circ g)(x)=5e^{\ln(5x)^2}\qquad\text{use}\ a^{\log_ab}=b\\\\(f\circ g)(x)=5(5x)^2=5(5^2x^2)=5(25x^2)=125x^2\\\\(f\circ g)(2)\to\text{put}\ x=2\\\\(f\circ g)(2)=125(2^2)=125(4)=500

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