Ten identical cards are numbered 1 to 10. the cards are shuffled. one card is selected at random. what is the probability that the number written on it is: 10? 5? not 10? an odd number? a number less than 4? a number greater than 7?

To solve these, basically find out how many numbers satisfy your requirment, then divide that number by 10. Simplify your fraction and you have your probability.

probability of getting a 10: 1/10
probability of getting a 5: 1/10
probability of not getting 10: 9/10
probability of getting an odd number: 5/10
probability of getting a number less than 4: 3/10
probability of getting a number greater than 7: 3/10

Hope this helps, and muchas luck on your math!

Let x be the initial width, then the initial length is x+20.
If Elise decreases this length by 8 feet, she will get the new length  x+20-8=x+12.

 If Elise increases the width by 10 feet, she will get the new width x+10.

The new perimeter will be x+12+x+12+x+10+x+10=4x+44=172, 4x=172-44, 4x=128,  x=128÷4, x=32.

The initial width is 32 ft and the initial length is 32+20=52 ft.

The new width will be 32+10=42 ft, the new length will be 32+12=44 ft.