Answer:
Cooper needs 39.8 mL milk for his recipe
Step-by-step explanation:
Let B be the quantity of butter
and
m be the quantity of milk
<u>So according to given statement the whole mixture measures 70.4 mL while butter measures 30.6mL</u>
so,
B+m = 70.4
30.6 + m = 70.4
m = 70.4 - 30.6
m = 39.8 mL
Cooper needs 39.8 mL milk for his recipe ..
Step 1
<u>Find the measure of angle x</u>
we know that
If ray NP bisects <MNQ
then
m<MNQ=m<PNM+m<PNQ ------> equation A
and
m<PNM=m<PNQ -------> equation B
we have that
m<MNQ=(8x+12)°
m<PNQ=78°
so
substitute in equation A
(8x+12)=78+78-------> 8x+12=156------> 8x=156-12
8x=144------> x=18°
Step 2
<u>Find the measure of angle y</u>
we have
m<PNM=(3y-9)°
m<PNM=78°
so
3y-9=78------> 3y=87------> y=29°
therefore
<u>the answer is</u>
the measure of x is 18° and the measure of y is 29°
Answer:
The total cost of the bond is none of the given choices.
Step-by-step explanation:
The selling price of a $1000 bond = $99.875
The brokerage fee = 5.5 %
Now, 5.5% of $99.875 = 
So, the brokerage fee = $5.493
Now, to find out the total cost of the bond:
Total Cost = The selling Price + Brokerage Price
= $99.875 + $5.493
= $105.368
or, the total price of the $1000 bond is $ 105.368.
Hence, the total cost of the bond is none of the given choices.
Original position: P1=(0,0)
<span>You drive 30 miles due east in a half hour: x=+30 miles, t1=1/2 hour=0.5 hours
</span><span>Then, you turn left and drive 30 miles north in 1 hour: y=+30 miles, t2=1 hour
Rectangular coordinates of final position: P2=(x,y)→P2=(30,30)
Total time: t=t1+t2=0.5 hours+1 hour→t=1.5 hours
Average speed: S ave=d/t
Total distance: d=x+y=30 miles+30 miles→d=60 miles
S ave = 60 miles / (1.5 hours)
S ave = 40 miles/hour
Velocity is a vector, the magnitude of this vector is the magnitude of the vector of change of position dividing by the total time t
The vector of change of position: s=P1-P2=(30,30)-(0,0)=(30-0,30-0)→
s=(30,30)
Magnitude of vector s=sqrt[30^2+30^2]=sqrt[30^2*2]=sqrt[30^2]*sqrt(2)
Magnitude of vector s=30*sqrt(2) miles
Magnitude of velocity vector = Magnitud of vector s / t
Magnitude of velocity vector = [30*sqrt(2) miles] / (1.5 hours)
Magnitude of velocity vector = 20*sqrt(2) miles / hour
Magnitude of velocity vector=20*1.4142 miles / hour
Magnitude of velocity vector=28.284 miles/hour
Polar coordinates of your position=(r, theta)
r=Magnitude of vector s=30*sqrt(2) miles
theta=tan^(-1) (y/x) = tan^(-1) [(30 miles) / (30 miles)]
theta=tan^(-1) (1)→theta=45°=Pi/4 (Pi=3.1416)
Polar coordinates of your position: ( 30*sqrt(2) miles, 45°)
Polar coordinate of your position: ( 30*sqrt(2) miles, Pi/4 )
Answers:
Average speed: 40 miles / hour
Velocity: 20*sqrt(2) miles / hour = 28.284 miles / hour
Rectangular coordinates of your position = (30,30)
Polar coordinates of your position=(30*sqrt(2) miles,45°)
Polar coordinates of your position=(30*sqrt(2) miles,Pi/4)</span>
