Mandy went rock climbing at the climbing gym for 2 1/2 hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for 1 1/2 times as long. How much time did she spend rock climbing in all?

6 1/4 hours

Step-by-step explanation:

For Mandy,

On Thursday at the climbing gym ,she spent = 2 1/2 hours rock climbing

= 5/2 hours rock climbing

On Saturday, she went to Castle Rock State Park and climbed for 1 1/2 times as long

= 3/2 times as long as she did at the climbing gym

= 3/2 × (5/2 hours)

= 15/4 hours

The time she spent rock climbing in all is calculated as:

= 5/2 hours + 15/4 hours

Find L.C.M = 4

= (2×5) + (15 × 1)/ 4

= 10 + 15/4

= 25/4 hours

= 6 1/4 hours.

Therefore, she spent 6 1/4 hours rock climbing.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47