Answer:
Solution given:
sin y = -4/5
p/h=4/5
p=4
h=5
b=√{5²-4²)=3
cos y = b/h=-3/5
again
cos x=12/13
b/h=12/13
b=12
h=13
p=√(13²-12²)=5
sin x=p/h=5/13
now
sin[x-y]=sinxcosy-cosxsiny
=5/13×-3/5-(12/13×-4/5)=33/65 is your answer.
Answer:
75/256 in³ < 64/125 in³
Step-by-step explanation:
First, find the volumes of the two 3-D figures:
For Figure 1:
Using the volume formula:
V = l × w × h
= 6/8 × 5/8 × 5/8
= (6/8 × 5/8) × 5/8
= 30/64 × 5/8
V = 150/512
Simplify:
V = 75/256
So Figure 1's volume is 75/256 in³.
For Figure 2:
V = l × w × h
= 4/5 × 4/5 × 4/5
= (4/5 × 4/5) × 4/5
= 16/25 × 4/5
= 64/125
So Figure 2's volume is 64/125 in³.
Now, comparing the two volumes:
You can cross multiply the fractions to figure out which fraction is greater:
Figure 1 Figure 2
<u> 75 </u> = <u> 64 </u>
256 125
75 (125) = 256 (64)
9375 = 16384
So Figure 2 has the greater volume.
Your final result should be:
75/256 in³ < 64/125 in³
The student drinks 182.5 gallons a year. Work: 64 x 365 = 23360/128 = 182.50 gallons
<span>ME = 1.10.
Explanation:
The margin of error, ME, is given by the formula z*(</span>σ<span>/</span>√<span>n).
Since we want a 90% confidence interval, z=1.645.
</span>σ<span>=6, and n=80, giving us ME=1.645*(6/</span>√<span>80). This comes out to 1.10.</span>
