Answer: B
Step-by-step explanation:????
Troll
- Make an equation representing the number of vehicles needed.
We have six drivers so
x + y ≤ 6
That's not really an equation; it's an inequality. We want to use all our drivers so we can use the small vans, so
x + y = 6
- Make an equation representing the total number of seats in vehicles for the orchestra members.
s = 25x + 12y
That's how many seats total; it has to be at least 111 so again an inequality,
25x + 12y ≥ 111
We solve it like a system of equations.
x + y = 6
y = 6 - x
111 = 25x + 12y = 25x + 12(6-x)
111 = 25x + 72 - 12x
111 - 72 = 13 x
39 = 13 x
x = 3
Look at that, it worked out exactly. It didn't have to.
y = 6 - x = 3
Answer: 3 buses, 3 vans
Answer:
perimeter = (18 +9π) cm
area = (81 -20.25π) cm^2
Step-by-step explanation:
The perimeter of the shaded area is the circumference of the circle added to two sides of the square. The circumference of the circle is π times the diameter, so the perimeter is ...
p = 2(9 cm) + π(9 cm) = (18 +9π) cm
___
The area of the shaded portion is the difference between the area of the square and the area of the circle. The area of the square is the square of the diameter. The area of the circle is π/4 times that value.
A = (9 cm^2) + (π/4)(9 cm^2) = (81 +20.25π) cm^2
_____
Comment on circle area
The formula you often see is ...
A = πr^2 . . . . r is the radius
since r = d/2, where d is the diameter, this can also be written as ...
A = π(d/2)^2 = (π/4)d^2
Here, the diameter of the circle is the same as the side length of its enclosing square, so the area of the circle is π/4 times the area of the enclosing square.
After clarification we see the respective diameters are
We're asked about the ratio
Now we can go through the choices.
A. If a = 4 and b = 6, then cell a is 100 times greater than cell b.
It would be more proper to say the diameter of cell A is 100 times the diameter of cell B, but yes, this is TRUE.
B. If a = 4 and b = 6, then cell b is 100 times greater than cell a.
FALSE. 10 to the minus 4 is 100 times bigger than 10 to the minus 6, so a is bigger.
C. If a = 4 and b = 6, then cell a is 2 times greater than cell b.
FALSE. We already calculated its 100 times bigger.
D. If a = 4 and b = 6, then cell b is 2 times greater than cell a.
FALSE.
Answer:
The absolute brightness of the Cepheid star after a period of 45 days is -5.95
Step-by-step explanation:
Since the absolute magnitude or brightness of a Cepheid star is related to its period or length of its pulse by
M = –2.78(log P) – 1.35 where M = absolute magnitude and P = period or length of pulse.
From our question, it is given that P = 45 days.
So, M = –2.78(log P) – 1.35
M = –2.78(log 45) – 1.35
M = –2.78(1.6532) – 1.35
M = -4.60 - 1.35
M = -5.95
So, the absolute magnitude or brightness M of a Cepheid star after a period P of 45 days is -5.95
