1) He worked 4 hours leaving 6 more hours for him.
rate for A alone 6 baker
rate for A & B together 4
1/a+1/b=1/x
1/6+1/b=1/4
1/b=1/4-1/6
1/b=6/24-4/24
1/b=2/24
1/b=1/12
b=12
rate for wife alone 12 hours for the remaining 6 hours
check
1/6+1/12=1/4
12/72+6/72=1/4
18/72=1/4
ok
codewa
But we want to know how long it would have taken her for the whole job not just part of it
he works twice as fast as she does so the job that takes him 10 hours alone would take her 20 hours alone.
2) jessica and cynthia work in a pet shop.
it takes jessica 6 hours to groom all the pets but cynthia needs 8 hours to groom them.
if jessica starts to groom 1 hour before cynthia joins, how long will it take them to finish?
:
let t = time it takes them to finish (C's working time)
then
t+1 = J's working time
let 1 = completed job (all pets groomed)
:
A shared work equation, each does a fraction of the job, the two fractions add up to 1
%28%28t%2B1%29%29%2F6 + t%2F8 = 1
Multiply by the least common multiple of 6 and 8, 24. cancel the denominators
4(t+1) + 3t = 24
4t + 4 + 3t = 24
4t + 3t = 24 - 4
7t = 20
t = 20/7
t = 26%2F7 hrs, which is: 2 + 6%2F7*60 = 2 hrs 51.43 min to finish the job
3) math club takes 40 minutes
science takes 50 minutes.
rate * time = quantity
quantity = 1 set up of the tables.
rate for math club is 1/40 of all the tables in 1 minute.
rate for science club is 1/50 of all the tables in 1 minute.
math club works for 10 minutes.
rate * time = quantity
1/40 * 10 = 10/40 = 1/4 of the tables are already set up by the math club.
there are 3/4 of the tables that still need to be set up.
rate * time = quantity
the rates of the math club and the science club are additive.
(1/40 + 1/50) * time = 3/4 of the tables that still need to be set up.
common denominator is 200.
(5/200 + 4/200) * time = 3/4.
9/200 * time = 3/4
time = 3/4 * 200/9 = 600 / 36 = 16 and 2/3 minutes.
total time required is 10 + 16 + 2/3 minutes = 26 + 2/3 minutes.
how to check.
10 minutes is used to do 1/4 of the tables.
16 + 2/3 minutes is used to do the remaining 3/4 of the tables.
combined rate of math and science club is 9/200 of the tables in 1 minute.
math club rate of 1/40 * 10 = 10/40 = 1/4 of the tables.
combine rate of 9/200 * (16 + 2/3) = 9/200 * 50/3 = 450/600 = 9/12 = 3/4 of the tables.
1/4 + 3/4 = 1 = all of the tables.
The sum of interior angles of a triangle is 180°, and a linear pair is supplementary (adds to 180°). The appropriate choice is
... G. w = 105°, because ...
_____
In short, an exterior angle is equal to the sum of the opposite interior angles.
... w = 180 - (180 - (45 + 60)) = 180 -180 +45 +60
... w = 45 +60
Answer:
A. 
B. 42.2 million
Step-by-step explanation:
Part A:
Given:
Newspapers circulated in year 2004, 
Newspapers circulated in year 2014, 
Let the time 
start at the year 2004. So, 
For the year 2014, 
Therefore, linear relationship between newspapers circulated and time passed since 2004 is given as:
Therefore, the equation describing the relationship is:
Part B:
For the year 2018, 
Plug in 14 for in the above equation and solve for 
. This gives,
Therefore, in the year 2018, the newspaper circulation will be 42.2 million.
Answer:
a) 5355
b) 6372.45
Step-by-step explanation:
4500 * 1.19 = 5355
5355 * 1.19 = 6372.45
Answer:
5 units
Step-by-step explanation:
Please see attached pictures for the full solution.
(This distance is the perpendicular distance between the 2 parallel lines, which is the shortest distance between them.)
