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Thepotemich [5.8K]
2 years ago
13

The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent t

he number of new releases, and let y represent the number of classics. If the librarian had a budget of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of new-release and classic movies bought?
Mathematics
1 answer:
Galina-37 [17]2 years ago
8 0

Answer:

x = 1, y = 60

Step-by-step explanation:

Value of new-releases (x) = $20 each

Value of classic (y) = $8 each

Total budget = $500

Equation : 20x + 8y = 500

The librarian wants to purchase maximum DVDs. She can get more DVDs of classic movies for $8 as they are less costly.

Lets assume the librarian buys at least one new-release DVD.

x=1

20x + 8y = 500

8y + 20(1) = 500

y = 60

<em>Therefore, in a budget of $500, the librarian can purchase 60 classic movies and 1 new-release.</em>

!!

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The factors of these outcomes are:
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2 = 1 x 2
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1 is not a prime number. So the numbers which have 2 prime factors are 4 and 6.

Thus, number of favorable outcomes = 2

The probability of rolling a number with exactly 2 prime factors = 2/6 = 1/3
3 0
2 years ago
24. ABCDE and PQRST are regular pentagons.
SIZIF [17.4K]

Answer:

126°

Step-by-step explanation:

In quadrilateral DSRC, SR || DC (given)

AP = BQ = CR = DS = ET (given)

\therefore CR bisects \angle DCB

\therefore m\angle DCR=\frac{108\degree}{2}

(108\degree is the measure of an angle of pentagon)

\therefore m\angle DCR=54\degree

\because m\angle DCR + m\angle SRC=180\degree

(Measure of interior angles on the same side of transversal)

\therefore 54\degree + m\angle SRC=180\degree

\therefore  m\angle SRC=180\degree- 54\degree

\therefore  m\angle SRC=126\degree

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2 years ago
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You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week
aliya0001 [1]

Answer:

q = -6p + 104

Step-by-step explanation:

Linear function:

A linear function has the following format:

q = mp + b

In which m is the slope and b is the q-intercept.

One week you charged $4 per guest and averaged 80 guests per night. The next week you charged $10 per guest and averaged 44 guests per night.

This means that we have these following points: (4,80), (10,44).

Finding the slope:

With a pair of points, the slope is given by the change in q divided by the change in p.

Change in q: 44 - 80 = -36

Change in p: 10 - 4 = 6

Slope: m = \frac{-36}{6} = -6

So

q = -6p + b

Finding b:

We replace one of the points. Replacing (4,80).

q = -6p + b

80 = -6*4 + b

b = 104

So

q = -6p + 104

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Share 747 pounds in the ratio 2:7 between tom and ben
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2x+7x=747
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