Jocelyn makes more than $195 but not over $645. The amount she has to pay is 15% of the excess of 196. Find this first via subtraction.
421 - 195 = $226 over
Take 15% of this
226 x .15 = $33.9
The tax also includes a $14.4 addition to this 15%.
33.9 + 14.4 = $48.3 total income tax
If the original container can hold 64 halogen lamps and the new container can hold 8 lamps, then
64/8 = 8
There will 8 smaller containers needed to pack all of the 64 lamps from the original large cubed-shaped container.
I use the sin rule to find the area
A=(1/2)a*b*sin(∡ab)
1) A=(1/2)*(AB)*(BC)*sin(∡B)
sin(∡B)=[2*A]/[(AB)*(BC)]
we know that
A=5√3
BC=4
AB=5
then
sin(∡B)=[2*5√3]/[(5)*(4)]=10√3/20=√3/2
(∡B)=arc sin (√3/2)= 60°
now i use the the Law of Cosines
c2 = a2 + b2 − 2ab cos(C)
AC²=AB²+BC²-2AB*BC*cos (∡B)
AC²=5²+4²-2*(5)*(4)*cos (60)----------- > 25+16-40*(1/2)=21
AC=√21= 4.58 cms
the answer part 1) is 4.58 cms
2) we know that
a/sinA=b/sin B=c/sinC
and
∡K=α
∡M=β
ME=b
then
b/sin(α)=KE/sin(β)=KM/sin(180-(α+β))
KE=b*sin(β)/sin(α)
A=(1/2)*(ME)*(KE)*sin(180-(α+β))
sin(180-(α+β))=sin(α+β)
A=(1/2)*(b)*(b*sin(β)/sin(α))*sin(α+β)=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)
A=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)
KE/sin(β)=KM/sin(180-(α+β))
KM=(KE/sin(β))*sin(180-(α+β))--------- > KM=(KE/sin(β))*sin(α+β)
the answers part 2) areside KE=b*sin(β)/sin(α)side KM=(KE/sin(β))*sin(α+β)Area A=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)
cannot be changed to a mixed number. 10 could divide both numerator and denominator. And you get 2.
Answer:
C. 272
Step-by-step explanation:
Since we know 85% of the students participated last year we can assume the same amount will participate this year so to find the answer you simply do the total number of students (320) multiplied by 85% or .85 to get the best guess of how many students will participate this year.
