Answer:
Part A
The bearing of the point 'R' from 'S' is 225°
Part B
The bearing from R to Q is approximately 293.2°
Step-by-step explanation:
The location of the point 'Q' = 35 km due East of P
The location of the point 'S' = 15 km due West of P
The location of the 'R' = 15 km due south of 'P'
Part A
To work out the distance from 'R' to 'S', we note that the points 'R', 'S', and 'P' form a right triangle, therefore, given that the legs RP and SP are at right angles (point 'S' is due west and point 'R' is due south), we have that the side RS is the hypotenuse side and ∠RPS = 90° and given that 
= 
, the right triangle ΔRPS is an isosceles right triangle
∴ ∠PRS = ∠PSR = 45°
The bearing of the point 'R' from 'S' measured from the north of 'R' = 180° + 45° = 225°
Part B
∠PRQ = arctan(35/15) ≈ 66.8°
Therefore the bearing from R to Q = 270 + 90 - 66.8 ≈ 293.2°
If there are 15 nickels which is $0.75 and 12 dimes which is $1.20, then that would equal $1.95 and be 27 coins.
Answer:
A 100 lb person will weight 40 lb on Mars
Step-by-step explanation:
Given:
Weight on Mars directly varies as its weight on earth.
Let weight on Mars be = 
Let weight on Earth be = 
Its known that:
∝
Thus
where 
is constant of proportionality.
when 
, then 
thus, we have
dividing both sides by 95.
∴ 
Thus when 
, would be calculated as
∴ 
(Answer)
∴ A 100 lb person will weight 40 lb on Mars.
Answer:
Length = 30
Width = 5
Step-by-step explanation:
So the formula for perimeter is
P = 2L+2W
And we know that:
L = 6W
So then we put in all the information that we do know
70 = 2(6W)+2W
And pop that into a calculator and you get W=5
So now we put that information into L = 6W to get:
L = 6×5
L = 30
If starting out, there are 100 marbles and Zoe pulls out a 5 and doesn't replace it, then there are 99 marbles left to choose from. So, there are 9 digits 1-10 (not including #5) making the proportion you have left 9/99 which simplifies to 1/11
