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sladkih [1.3K]
3 years ago
12

The event coordinator asks you to determine how many students participated in the track-and-field day. The total number of stude

nts in seventh and eighth grade combined is 584; 5/8 of them are seventh graders and 3/8 of them are eighth graders. If 4/5 of the seventh graders participated in track-and-field day and 7/8 of the eighth graders participated, about how many total students participated? Describe the process you used to find your answer.
Mathematics
1 answer:
kakasveta [241]3 years ago
8 0
584 is the total number of students in the school.

5/8 are in seventh grade and 3/8 are in eighth grade.

4/5 of the seventh graders participated in the track meet, so there were (4/5 · 5/8) · 584 students in the seventh grade participating in the track meet.

7/8 of the eighth graders participated, so there were (7/8 · 3/8) · 584 students in the eighth grade participating in the track meet.

So, all together, there were

(4/5 · 5/8) · 584 + (7/8 · 3/8) · 584 students from the school in the track meet.

Let's simplify as you asked:

(4/5 · 5/8) · 584 + (7/8 · 3/8) · 584 = [(4/5 · 5/8) + (7/8 · 3/8)] · 584 (distributive property - factoring)

= [20/40 + 21/64] · 584 (multiply fractions)

= (1/2 + 21/64) 584 (reduce the first fraction to lowest terms)

= (32/64 + 21/64) 584 (getting a common denominator)

= (53/64) 584 (combine/add the two fractions)

= 483.625 (multiply together)

All together, there were: 483.625 students in the meet.
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Answer:

26 rows

Step-by-step explanation:

this is like a rectangle length×width situation.

seats per row = s

number of rows = r

s × r = 884

s = r + 8

so, we can use e.g. the second equation in the first :

(r + 8) × r = 884

r² + 8r = 884

r² + 8r - 884 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = r

a = 1

b = 8

c = -884

r = (-8 ± sqrt(8² - 4×1×-884))/(2×1) =

= (-8 ± sqrt(64 + 3536))/2 = (-8 ± sqrt(3600))/2 =

= (-8 ± 60)/2 = -4 ± 30

r1 = -4 + 30 = 26

r2 = -4 - 30 = -34

a negative number did not make any sense for the number of rows, so r = 26 is our answer.

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2 years ago
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3 years ago
Find the exact value of csc(-1860).
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well, let's check that,   \bf \cfrac{1860}{360}\implies \cfrac{31}{6}\implies 5\frac{1}{6}\implies 5+\frac{1}{6}

now, this is a negative angle, so it's going clockwise, like a clock moves, so it goes around the circle clockwise 5 times fully, and then it goes 1/6 extra.

well, we know 360° is in a circle, how many degrees in 1/6 of 360°?  well, is just 360/6 or their product, and that's just 60°.

so -1860, is an angle that goes clockwise, negative, 5 times fully, then goes an extra 60° passed.

5 times fully will land you back at the 0 location, if you move further down 60° clockwise, that'll land you on the IV quadrant, with an angle of -60°.

therefore, the csc(-1860°) is the same as the angle of csc(-60°), which is the same as the csc(360° - 60°) or csc(300°).

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