civonamzuk

Excellent work, heureka!!! Can you find the length of a?

In a school of 520 students, 40% are girls. 1/2 of the girls and 1/3 of the boys travel to school by bus. How many students travel to schools by bus?

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Girls          520 * 0.4 = 208

Boys          520 - 208 = 312

Girls who travel by bus    1/2(208) = 104

Boys who travel by bus    1/3(312) = 104

Students who travel to schools by bus = 208  or 40% of all students. 

 https://web2.0calc.com/questions/urgent-help-needed_6   (Solved by textot, Feb 7, 2021)

A very clever method is used to solve this problem. 

Medians AX and BY of triangle ABC are perpendicular at point O. AX = 12 and BC = 10.

a. Find AO and BY

b. Find the length of median CZ

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The Median Theorem states that the medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from the vertices to the midpoint of the opposite sides.

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If AX = 12, then AO = 2/3(AX), and OX = 1/3(AX)     AO = 8       OX = 4

If OX = 4, and BX = 5, then BO = 3        (I'll let you find BY) 

CZ you can calculate using CX, OX, and ∠CXO.          (∠CXO ≈ 143.13º)

CPhill, where did 1/4 come from?!

It's 1/6 NOT 1/4

(¹/₆) / 4 = ¹/₂₄

Sam needs to read ¹/₂₄ of the book each day. 

Britt can buy 12 complete sets and have $1.40 change in his pocket. 

Homer is giving some cookies to each of his three brothers. To the oldest, he gives half of the cookies and half a cookie. He then gives half of what is now left and half a cookie to his second brother. Finally, he gives half of what is now left and half a cookie to his third brother. At no time is a cookie broken or cut. How many cookies did Homer have to begin with? 

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IF Homer had 100 cookies, he would give 50.5 cookies to his oldest brother, 25.25 to his second brother, and 12.625 to his third brother.

The ratio of given cookies is as follows:   50.5 : 25.25 : 12.625     or     4 : 2 : 1

So, Homer had 7 cookies, and he gave them all to his brothers:

Oldest          3.5 + .5 = 4

Second        1.5 + .5 = 2

Third              .5 + .5 = 1

No cookie needed to be broken! 

If x, y, and z are real numbers for which

x + y - z = -8

x - y + z = 18

-x + y + z = 30

Then what is xyz?

2x =10

2y = 22

2z = 48

xyz = 1320

Triangle ABC has circumcenter O. If AB = 10 and [OAB] = 50 find the circumradius of triangle ABC.

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AB = 10           [OAB] = 50

Let M be a midpoint of AB

Altitude   OM = (2 * 50) / 10 = 10

OA = OB => R   (Circumradius)

R = sqrt(AM² + OM²) = √125