Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. (4 points each.) 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six

Lizette is training for a marathon. at 7: 00 she left her house and ran until 8: 30, then she walked until 11: 30. she covered a total distance of 18 miles. her running speed was six miles per hour faster than her walking speed. find her running and walking speeds in miles per hour.

Joanie wrote a letter that was 1 1/4 pages long. katie wrote a letter that was 3/4 page shorter then joagies letter. how long was katies letter

The candy store is having a 30% off sale. emma is going to buy $7.50 worth of candy. how much will she pay after the discount