<u>Answer:</u>
Total Volume of composite figure = 635.2 cm³
<u>Steps:</u>
CV = h×3.14×(d/2)²
CV = 5×3.14(8/2)²
CV = 5×3.14(4)²
CV = 5×3.14×16
CV = 5×50.24
CV = 251.2 cm³
RV = h×w×l
RV = 4×8×12
RV = 4×96
RV = 384 cm³
TV = CV + RV
TV = 251.2 + 384
TV = 635.2 cm³
The required number of litres of pure and 85% maple syrup required to produce 150 litres of 96% maple syrup is 40 litres and 110 litres respectively.
Let :
Amount of pure (100%) maple syrup = a
Amount of 85% map’e syrup = b
Creating a system of equation :
- a + b = 150 - - - (1)
- 100%a + 85%b = 96% × 150
- a + 0.85b = 144 - - - - (2)
From (1)
Substitute a = 150 - b into (2)
- 150 - b + 0.85b = 144
- -0.15b = 144 - 150
- -0.15b = - 6
- b = 40
From (1)
- a = 150 - b
- a = 150 - 40
- a = 110
Therefore, 40 litres of pure maple syrup and 110 litres of 85% maple syrup will be used.
Learn more : brainly.com/question/24601782
Answer:
The regular price of the ticket was $12.
Step-by-step explanation:
Let us call 
the regular price of the tickets, and if she had bought tickets at this price, the total cost would have been
.
But Holly got $4 off the regular ticket price, that means one ticket cost her
and if she bought 23 tickets it cost her
and we are told this equals $184; therefore we have
now we solve this equation the following way:
Thus, the regular price was $12.
The car was going 103 miles per hour.. please mark me brainliest
Take the dot product, if the dot product is zero, they are orthogonal
<span>the dot product here is 15(-5) + 45(12) so the vectors are not orthogonal </span>
<span>to see if they are parallel, take the dot product again, using the definition </span>
<span>u dot v = mag u x mag v cos (theta) where mag is the magnitude of the vector and theta is the angle between them </span>
<span>we know from above that u dot v = 465 </span>
<span>mag u = sqrt[15^2+45^2]=47.43 </span>
<span>mag v = sqrt[5^2+12^2]=13 </span>
<span>so we know: </span>
<span>cos(theta) = 465/(47.43x13) = 0.75 </span>
<span>
so theta = 41 deg</span>
