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Anton [14]
2 years ago
15

A high school drama club is putting on their annual theater production. There is a maximum of 800 tickets for the show. The cost

s of tickets are $6 before the day of the show and $9 on the day of the show. To meet the expenses of the show, the club must sell at least $5,000 worth of tickets.a) write a system of inequalities that represent this situation.b) the club sells 440 tickets before the show. Is it possible to sell enough additional tickets on the day of the show to at least meet the expenses of the show? Justify your answer.
Mathematics
1 answer:
astra-53 [7]2 years ago
3 0
<span>a.) Let x be the number of tickets sold before the event and y the number of tickets sold on the day of the event. Then x + y =< 800 and 6x + 9y >= 5000. (b.) Suppose the club sold 440 tickets before the event, i.e. x = 440, maximum number of tickets remaining to be sold = 800 - 440 = 360. Maximum amount realized from the sales supposing all tickets were sold = 6(440) + 9(360) = 2640 + 3240 = $5880 which is greater than $5000. Therefore, it is possible for the club to sell enough additional tickets on the day of the show to meet the expenses of the show.</span>
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The skittles jar has a radius of 3.5 cm and a height of 11.5 cm. using the two given boxes for reference what would be a good es
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Step-by-step explanation:

We know that the first container held 192 skittles. Knowing the dimension of the container we can calculate the volume of 192 skittles:

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Volume of 1 skittle = 80 / 192 = 0.42 cm³

We also know that the second container held 258 skittles. Knowing the dimension of the container we can calculate the volume of 258 skittles:

Volume of 258 skittles = 12 × 3 × 3 = 108 cm³

Volume of 1 skittle = 108 / 258 = 0.42 cm³

We found that the volume of  1 skittle is equal to 0.42 cm³. Now we calculate the volume of the skittles jar:

volume of cylinder = π × radius² × height

volume of skittles jar = 3.14  × 3.5² × 11.5 = 442 cm³

Now we can calculate the number of skittles in the jar:

number of skittles in the jar = volume of the jar / skittle volume

number of skittles in the jar = 442 / 0.42 = 1052 which is close the C) 1059

Learn more about:

volume of cylinder

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7 0
3 years ago
What is the greatest common factor of the terms of the polynomial −25y3 + 15y2 − 5y
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The sector area of a region of a circle is 23 mi². The central angle, 0 (theta), is 25°. What is the radius?
densk [106]

The radius of the sector is 10.27 miles

<h3>How to find the radius of a sector?</h3>

The area of a sector can be represented as follows;

area of a sector = ∅ / 360 × πr²

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Therefore,

∅= 25 degrees

area of the sector  = 23 miles²

area of a sector = ∅ / 360 × πr²

23 = 25 / 360 × πr²

cross multiply

23 × 360  = 25πr²

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divide both sides by 25

πr² =  8280 / 25

πr² =  331.2

r² =  331.2 / 3.14

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r = √105.477707006

r = 10.2702336877 miles

Therefore, the radius of the sector is 10.27 miles

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