The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)
4x+3y=12
3y=-4x+12
y=-4x/3+12/3
So a line perpendicular to the bank will be:
y=3x/4+b, and we need it to pass through (7,5) so
5=3(7)/4+b
5=21/4+b
20/4-21/4=b
-1/4=b so the perpendicular line is:
y=3x/4-1/4
So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:
(3x-1)/4=(-4x+12)/3 cross multiply
3(3x-1)=4(-4x+12)
9x-3=-16x+48
25x=51
x=51/25
x=2.04
y=(3x-1)/4
y=(3*2.04-1)/4
y=1.28
So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(7-2.04)^2+(5-1.28)^2
d^2=38.44
d=√38.44
d=6.2 units
Since he can run at 10 uph...
t=d/v
t=6.2/10
t=0.62 hours (37 min 12 sec)
So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.
Answer:
And rounded up we have that n=421
Step-by-step explanation:
We know that the sample proportion have the following distribution:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by
and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that
and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We assume that a prior estimation for p would be
since we don't have any other info provided. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=421
Answer:
9
Solution:
Write it in an algebraic form (x is your number)
2x-11=7
Now solve
2x=7+11=18
X=18/2=9
Answer:
Jackhammer =$25
Discount= 18%
Final Price= $25*0.82*1.06 = $ 21.73
Answer:
y=1/4x-1
Step-by-step explanation:
i knew the general equation of the line and i knew the slope would be a fraction because the line is rlly flat
-1 would be the b and i plugged in simple fraction values for m
i checked in desmos and they look similar
hope this helps and is correct <3