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There are 600 students in the third grade, of which there are twice as many girls as boys. How many boys and girls are there in the third grade?


Teacher Li bought a total of 50 apples and oranges. If you buy 10 more oranges, the number of oranges will be twice that of apples. How many grass fruits and oranges did Teacher Li buy?


In a finite group ,show that the number of elements of order d is a.multiple of phi(d)



Fill in the following blanks to complete the statement using the word: Perspective, isometric, or exploded:


  1. The blank view is best used for determining the dimensions of the object.
  2. The blank view is best used for showing how the object will look once it has been built
  3. The blank view is best used for assembling the object.

If an electronics company wants to shrink the dimensions of a Tablet measuring 20cm wide by 25cm high by a scale factor of 2/5, what is the new width of the Tablet?

( recall that the scale factor is given by either model/original Or model:original.



Solve the following measurements:


  1. On a certain map, the straight-line distance between Pas ans Winnipeg is 4.1cm. If the scale of the map is 1cm=120cm, how far apart are the Pas and Winnipeg, to the nearest kilometer?
  2. On a scale drawing of a house, the scale is 1cm:4cm. If the actual house is 30cm, what is the length of the line in the drawing that represents the width of the house?




State whether the following scale factors represent an Enlargement, Reduction or No change.


  1. A scale factor of 4/3 applied to an object that describes?
  2. A scale factor of 0.95 applied to an object describes?
  3. A scale factor of 6:6 applied to an object describes?
  4. A scale factor of ⅕ applied to an object describes?
  5. A scale factor of 130% applied to an object describes?
  6. A scale factor of 75% applied to an object describes?
  7. A scale factor of 3.5 applied to an object describes?

Determine if the following statements are true or false. Show work please.


  1. 4/15=2/7                                   2. 4/6=10/15

A survey of 36 students was conducted to find out how many students enjoy playing volleyball, and 17 said they did. If 68 students were surveyed, how many would you say enjoy playing volleyball?


(2+√y)^2-(2-√y)^2=8√y but in your solution it is equal to 4√y what's the reason.