Step-by-step explanation:
(2m + 4) / 8 = w
2m + 4 = 8w
2m = 8w - 4
m = 4w - 2
John's hourly rate is 1/8 of the room per hour.
Rick's hourly rate is 1/2 of the room per hour.
Molli's hourly rate would be 3/8 of the room per hour.
It takes Molli 2 2/3 hours to paint the room alone.
Explanation
Since John paints the entire room (100%=1) in 8 hours, he would paint 1/8 of the room in 1 hour.
Since Rick paints the entire room (100%=1) in 2 hours, he would paint 1/2 of it in 2 hour.
We do not yet know Molli's rate, so we will call it x.
We know that 1/8+1/2+x = 1 hour.
We will use 8 as a common denominator:
1/8+4/8+8x/8 = 1
Adding the numerators,
(1+4+8x)/8 = 1
Multiply both sides by 8:
1+4+8x = 8
Add like terms:
5+8x = 8
Subtract 5 from both sides:
5+8x-5=8-5
8x=3
Divide both sides by 8:
8x/8 = 3/8
x = 3/8
Molli's rate is 3/8.
Since she can paint 3/8 of the room in 1 hour, we can set up the equation
3/8x = 1
Divide both sides by 3/8:
3/8x ÷ 3/8 = 1 ÷ 3/8
x = 1/1 ÷ 3/8 = 1/1 × 8/3 = 8/3
x = 2 2/3
This is the amount of time it takes Molli to paint the entire room.
PLOT:
-2, 0.022
-1, 0.067
0, 0.2
1, 0.6
2, 1.8
Answer:
15hrs
Step-by-step explanation:
We can start by expressing the speed of the second trip as x. This means that the first trip must be x-1, and second (x-1)-1=x-2. Next we can form an equation with the information that the third day hike takes 30 min longer than second day hike. Since we now the distance of both days, we can express them in time. So...
... We can solve by finding a LCM of all three expressions. Doing so we get 2x(x-2). Now multiplying out with the new denominators, we get 36(x-2)+x(x-2)=28x. Solving as a quadratic equation, the solution comes out to be x=6, x=-12. But as speed can't be negative, only solution is x=6. Now we get the speed of each day's hike. First day=x-1=5, second day=6, third day =x-2=4. Finding the time is simple, just do distance/speed. First day=12.5/5=2.5hrs. Second day=18/6=3hrs. Third day=14/4=3.5hrs. Adding total hrs up... 2.5+3+3.5=9. Finally step is accounting for the 2hr digging time per day. 2hrs*3= 6hrs. 6hrs+9hrs=15hrs. Hope this helps!
Answer:
The value of the standardized z-test statistic is -6.4.
Step-by-step explanation:
The test statistic is:

In which X is the sample mean,
is the value tested at the null hypothesis, and s is the standard error.
0.28 is tested at the null hypothesis:
This means that 
p ^ 0.216 with SE 0.01
This means that 
Then



The value of the standardized z-test statistic is -6.4.