Answer:
10 small boxes and 12 large boxes
Step-by-step explanation:
Let x = number of large boxes
Let y = number of small boxes
We are told that;
volume of each small box = 6 cubic feet
volume of each large box = 22 cubic feet.
Total volume = 324 ft³
Thus;
6x + 22y = 324 - - - (eq 1)
We are told that 22 boxes of paper were shipped.
Thus; x + y = 22 - - - (eq 2)
Making x the subject in eq 2 gives;
x = 22 - y
Put 22 - y for x in eq 1;
6(22 - y) + 22y = 324
132 - 6y + 22y = 324
16y = 324 - 132
16y = 192
y = 192/16
y = 12
So, x = 22 - 12 = 10
Answer:
• c = √89 ≈ 9.434
• A = arcsin(8/√89) ≈ 57.995°
• B = arcsin(5/√89) ≈ 32.005°
Step-by-step explanation:
By the law of cosines, ...
c² = a² + b² -2ab·cos(C)
Since c=90°, cos(C) = 0 and this reduces to the Pythagorean theorem for this right triangle.
c = √(8² +5²) = √89 ≈ 9.434
Then by the law of sines (or the definition of the sine of an angle), ...
sin(A) = a/c·sin(C) = a/c = 8/√89
A = arcsin(8/√89) ≈ 57.995°
sin(B) = b/c·sin(C) = b/c = 5/√89
B = arcsin(5/√89) ≈ 32.005°
Answer:
-8100
Step-by-step explanation:
(2/5)^-2(-3)^4
Given data
and second term
The first term= (2/5)^-2 and
Second term=(-3)^4
Simplify the first term
(2/5)^-2= 2^-2/ 5^-2= 1/2^2 * 1/5^2
=1/4/ 1/25
=1/4*25/1
=100
Simplify the second term
=(-3)^4
= -81
Hence, 100*81
=-8100
Answer:
1,080 Pennies
Step-by-step explanation:
This question is fairly simple, you just have to simplify it. You are starting at already half-full, so you can keep that 1/2 in mind. Then, she adds 360 pennies to get 5/6. If you convert 1/2 into 3/6, you can see that 360 pennies fills 2/6 of the piggy bank. So now you can solve two different ways. The first, you can take 360 and multiply it by 3 to get the amount that can fit in the piggy bank, because 2 * 3 = 6 and that would make it 6/6, or 1. The other way would be to divide 360 by 2 to get 1/6 of the piggy bank, or 180. Then you can multiply 180 by 6 to get the entire amount.
Hope this helped ^-^
