How to do this question plz answer me step by step plzz plz plz plz plz I really struggling

 48

There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.

1 min = 60 sec

30 min = 1800 sec (multiply both sides by 30)

1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")

The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.

There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.

Extra info:

If you're curious about finding the more accurate value, then you could follow these steps

1 prize = 2014 seconds

x prizes = 86400 seconds (number of seconds in a full day)

1/x = 2014/86400

1*86400 = x*2014

86400 = 2014x

2014x = 86400

x = 86400/2014

x = 42.8997020854021

Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.

D. sin m∠C = 2 square root of 5 all over 5

Step-by-step explanation:

The triangle ABC is a right angled triangle. The angle ∠C is where we are asked to find.  The side AB measures 6 , AC measures 3 and the side BC measures 3√5.

The longest side of a right angle triangle is the hypotenuse, that means the side with length  3√5 is the hypotenuse.

Therefore side BC is the hypotenuse side and we are asked to find the angle C. AB is the opposite side while AC is the adjacent side.

Using

sin C = opposite/hypotenuse = 6/3√5 = 2/√5 = 2√5/5

cos C = adjacent/hypotenuse = 3/3√5 = 1/√5