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AleksandrR [38]
3 years ago
5

The school nurse made a presentation about smoking to the 7th grade class. She said that smoking hurts your health. She said it

also hurts your pocket! She said that a pack of cigarettes costs about $5.28 plus 5% sales tax. How much would a person spend on cigarettes in a year if he smoked one package of cigarettes on each of the 365 days of the year?
Mathematics
1 answer:
andrew-mc [135]3 years ago
4 0

Answer:

$2,022.10

Step-by-step explanation:

First find the price with tax so multiply 5% by 5.28 then add that to the total before tax. 0.05x5.28=0.264

0.26+5.28=5.54

So knowing how much she spends per day, we multiply it by the total of das in a year to know how much is spent in a year.

5.54x365=2022.10

So the total spent on cigarettes a year is $2,022.10

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Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets.
Ray Of Light [21]

Answer:

she should charge $7.395 per ticket in order to make the most money.

Step-by-step explanation:

From the given information:

If Rosalie charges $5   then 1175 people will attend the circus performance

If Rosalie charges $7   then 935 people will attend the circus performance

Let x be the cost and y to be the number of people that will attend the performance . Then, we will have two points which are;

(5, 1175) and (7, 935)

The slope(m) of this points = \dfrac{\Delta y}{\Delta x}

= \dfrac{y_2-y_1}{x_2-x_1}

=\dfrac{935-1175}{7-5}

Slope (m) = \dfrac{-240}{2}

Slope (m) = -120

However; we can now have the linear equation:

y-y_1 = m(x-x_1)

y-1175= -120(x-5)

y-1175= -120x+600

y= -120x+600+1175

y= -120x+1775

The linear function is : y = -120x + 1775

Now; the total amount of money she can now earn is:

f(x) = xy

f(x) = x(-120x + 1775)

f(x) = -120x² + 1775x

The above expression is a quadratic equation; Using the quadratic formula; we have:

=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}

where; a = -120 ; b = +1775 and c = 0

=\dfrac{-(1775) \pm \sqrt{(1775)^2-4(-120)(0)}}{2(-120)}

=\dfrac{-(1775) +  \sqrt{(1775)^2-4(-120)(0)}}{2(-120)}  \ \ \ \ \ OR  \ \ \ \  \dfrac{-(1775) -\sqrt{(1775)^2-4(-120)(0)}}{2(-120)}

=\dfrac{-(1775) +  \sqrt{(1775)^2}}{(-240)}  \ \ \ \ \ OR  \ \ \ \  \dfrac{-(1775) -\sqrt{(1775)^2}}{(-240)}

=\dfrac{-(1775) +  (1775)}{(-240)}  \ \ \ \ \ OR  \ \ \ \  \dfrac{-(1775) - (1775)}{(-240)}

=\dfrac{0}{(-240)}  \ \ \ \ \ OR  \ \ \ \  \dfrac{-3550}{(-240)}

=     0        OR         14.79

Since; we are considering the value greater than zero

x = 14.79

maximum value of x = 14.79/2 = 7.395

Thus ; she should charge $7.395 per ticket in order to make the most money.

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Two negative integers have a sum of -13 and a product of 42. What are the integers?
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