True or false the equation of a rational function does not have to contain a rational expression

A movie-theater employee notes an inverse relationship between the theater's popcorn sales and its nacho sales. On a given night

zubka84 [21]

the employee earned $1813 from Nachos

Explanation:

The theater's popcorn sales is inversely proportional to nacho sales

Let theater's popcorn = P

nacho sales = N

$P\text{ }\alpha\text{ }\frac{1}{N}$

Equating the relationship:

$\begin{gathered} P\text{ = k(}\frac{1}{N}) \\ P\text{ = }\frac{k}{N} \\ \text{where k = constant of proportionality} \end{gathered}$

when theater sales = $2,254

Nacho sales = $1,628

$\begin{gathered} 2254\text{ =}\frac{k}{1628} \\ k\text{ = 2254(1628)} \\ k\text{ = 3}669512 \end{gathered}$

The relationship becomes:

$P\text{ = }\frac{3669512}{N}$

When cost of the theater popcorn = $2,024

The cost from nachos = ?

We would use the relationship to get the above:

$\begin{gathered} 2024\text{ = }\frac{3669512}{N} \\ 2024N\text{ = 3669512}18 \\ N\text{ = }\frac{\text{3669512}}{2024} \\ N\text{ = }1813 \end{gathered}$

Hence, the employee earned $1813 from Nachos

6 0

1 year ago

HELP FAST PLEASE!!!!

liq [111]

You are asked to solve the equation $8 cos^{2} x-3cosx=0$ . I have chosen to use x instead of theta but the work is the same.

Notice that you have a quadratic equation set equal to 0. The expression at left can be factored. We do this as follows:
$cosx(8cosx-3)=0$

You have a product (at left) that equals to zero so one or both of the terms equals zero. That is,
cosx=0 and/or $8cosx-3=0$

To solve the first we are looking for an angle measure between 0 and 180 degrees door which the cos of that angle is 0. You can use your calculator and input $cos ^{-1}0=$ and will find the answer to be 90 degrees. You might also know this from the graph of the cosine function.

The second equation can be solved as follows:
$8cosx-3=0$
$cosx=3/8$
You are looking for an angle whose cosine is 3/8 and can use the cosine inverse function on your calculator. Input $Cos^{-1}(3/8)=$ . The answer will be extremely close to 68 degrees and is 68 degrees when rounded.

Thus the two solutions we are looking for are 90 degrees and 68 degrees.

Please note that for this to work your calculator needs to be in degrees (not radians) and that you can control this in the “mode”.

7 0

4 years ago

The lunch lady had 5 pound of lasagna. If she makes 1/4-pound servings using this amount of lasagna, how many servings can she m

jekas [21]

She could make 20 servings of lasagna.

There are 4 servings per pound of lasagna, and there are 5 pounds total.
4 x 5 = 20

6 0

3 years ago

What is the probability of spinning red on the image shown?

Mashcka [7]

Answer:

37.5%

Step-by-step explanation:

Red is 3/8 so you convert that into a percentage.

8 0

3 years ago

250 grams of sugar cost 150 dollars at Shop X. 100 grams of sugar cost 95 dollars at Shop Y. What is the difference in cost per

nata0808 [166]

<h2>Answer:</h2>

350 dollars

<h2>Step-by-step explanation:</h2>

<em>(step 1) Find the cost per kilogramme of sugar in shop X</em>

In shop X:

250 grams of sugar costs 150 dollars.

<em>Remember that;</em>

1000 grams = 1 kilogramme.

=> 250 grams will be equal to 0.25 kilogramme

Therefore (replacing 250 grams with 0.25 kilogramme) in shop X;

0.25 kilogramme of sugar costs 150 dollars

Now, if

0.25 kilogramme = 150 dollars,

=> 1 kilogramme = 150 dollars x 1 kilogramme / 0.25 kilogramme

=> 1 kilogramme = 600 dollars

Therefore, the cost per kilogramme of sugar in shop X is 600 dollars

<em>(step 2) Find the cost per kilogramme of sugar in shop Y</em>

In shop Y:

100 grams of sugar costs 95 dollars.

<em>Remember that;</em>

1000 grams = 1 kilogramme.

=> 100 grams will be equal to 0.1 kilogramme

Therefore (replacing 100 grams with 0.1 kilogramme) in shop Y;

0.1 kilogramme of sugar costs 95 dollars

Now, if

0.1 kilogramme = 95 dollars,

=> 1 kilogramme = 95 dollars x 1 kilogramme / 0.1 kilogramme

=> 1 kilogramme = 950 dollars

Therefore, the cost per kilogramme of sugar in shop Y is 950 dollars

<em>(step 3) Find the difference in cost per kilogramme of sugar between the two shops</em>

The difference is calculated by subtracting the cost per kilogramme of sugar in shop X from the cost per kilogramme of sugar in shop Y. i.e

=> cost per kilogramme of sugar in shop Y - cost per kilogramme of sugar in shop X

=> 950 dollars - 600 dollars

=> 350 dollars.

Therefore, the difference in cost per kilogramme is 350 dollars

3 0

3 years ago