<span> Honor roll Not on honor roll Total
Received math class requested 315 64 379
Did not get math class requested 41 80 121
Total 356 144 500
Honor roll: request granted: 315/356 = 0.88 x 100% = 88%
Not Honor roll request granted: 64/144 = 0.44 x 100% = 44%
Honor roll students were given preference in granting request than those not in the honor roll.</span>
Suppose
At the same time, we can write
Note that 
(just reverse the sum). Let's pair the first terms of 
and 
, and the second, and the third, and so on:
Now, each grouped term in the sum on the right side adds to 151. There are 52 grouped terms on that same side (because there are 50 numbers in the range of integers 51-100, plus 50 and 101), which menas
But , as we pointed out, so
<h3>
Answer: 130</h3>
Explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
Simple interest,
FV=P(1+ni)
FV=future value=2500
P=present value, invested amount
n=number of years, =3
i=annual interest rate, =0.095
2500=P(1+3(0.095))
Solve for P.
Answer:
Volume_stack = 214 n^3
Step-by-step explanation:
The volume of the stack is the sum of the volume of the two boxes
The rectangular box has a volume of
V_rectbox = long*wide*height
V_rectbox = 6 in * 5in * 5 in = 150 in^3
The volume of the cube is
V_cube = long*wide*height , but since all its sides are equal
V_cube = side^3 = (4 in)^3 = 64 in^3
Volume_stack = V_rectbox + V_cube = 150 in^3 + 64 in^3
Volume_stack = 214 n^3
