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Lera25 [3.4K]
3 years ago
13

Answer these 2 questions and you get 15 points

Mathematics
1 answer:
Lyrx [107]3 years ago
4 0

Question 1: Option B: \frac{10}{14}=\frac{5}{7}

Question 2: Option C: \frac{12}{18}=\frac{4}{6}

Solution:

Question 1:

Given ratio is \frac{10}{14}.

To find the equivalent ratio of \frac{10}{14}.

10 and 14 have the common factor 2.

So divide both numerator and denominator by the common factor 2.

$\frac{10}{14}=\frac{10\div2}{14\div 2}

    $=\frac{5}{7}

$\frac{10}{14}=\frac{5}{7}

Hence option B is the correct answer.

Question 2:

Given ratio is \frac{10}{14}.

To find the equivalent ratio of \frac{12}{18}.

12 and 18 have the common factor 3.

So divide both numerator and denominator by the common factor 3.

$\frac{12}{18}=\frac{12\div3}{18\div 3}

    $=\frac{4}{6}

$\frac{12}{18}=\frac{4}{6}

Hence option C is the correct answer.

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Step 1

Revenue (sometimes referred to as sales revenue) is the amount of gross income produced through sales of products or services. This, in the context of the question, means that the revenue generated from the sales of tickets is given by the function below. We are now required to find the price that tickets will be sold at in a day based on the function that will make the revenue to be equal to $0.

The revenue is given by the function;

\begin{gathered} f(p)=150p-5p^2 \\ f(p)\text{ is the revenue and should be equal to 0 according to the question.} \\ p=\text{ The price of tickets for the day for the revenue to be 0} \end{gathered}

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\begin{gathered} 0=150p-5p^2 \\ p(150-5p)=0----(\text{factorize)} \\ p=0 \\ 0r \\ 150-5p=0 \\ 150=5p \\ \frac{5p}{5}=\frac{150}{5} \\ p=30 \\ p=0\text{ or 30} \end{gathered}

Therefore the revenue to be zero, the price of the ticket will be $0 or $30 but the question asked us how high the ticket price will be to get a revenue of 0. Both 0 and 30 gave us revenue of 0 but $30 is higher therefore, the answer will be $30.

Check;

\begin{gathered} 150p-p^2=0 \\ \text{If the price of tickets=0} \\ 150(0)-5(0^2)=0 \\ \text{If p=30} \\ 150(30)-5(30^2)=4500-4500=0 \end{gathered}

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Step 3

The equation you can write for revenue of $700 is;

\begin{gathered} 700=150p-5p^2 \\ 5p^2-150p+700=0_{} \end{gathered}

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