Answer:
The amount of ounces, Y, of the 12% substance is 3.33 ounces
Step-by-step explanation:
The word problem has the task of discovering the required amount of the substance containing the 12% cottonseed required to create a snore suppressing substance with 8% cottonseed
Let the amount of the substance with 6% cottonseed in the 10 ounce substance be X and the amount of the substance with 12% cottonseed be Y
We have;
X×6% + Y×12% = 10 ounce × 8%
Which gives;
0.06×X + 0.12×Y = 0.08×10..........(1)
X + Y = 10.....................................(2)
Putting X = 10 - Y, we have;
0.06×(10 - Y) + 0.12×Y = 0.08×10
0.6 - 0.06·Y + 0.12·Y = 0.8
0.06·Y = 0.8 - 0.6 = 0.2
Y = 0.2/0.06 = 10/3 = 3.33 ounces
X = 10 - Y = 10 - 3.33 = 6.67 ounces
Therefore, the amount of ounces, Y, of the 12% substance = 3.33 ounces.
Answer:
m^2 × n^-2
m^2×n^-2
Because a^2/b^2 = a^2b^-2
Answer:
10 boards
Step-by-step explanation:
In this case we can reverse the calculation or whatever you call it
<em>X</em>(how many boards)x3,75 (length per board)= 36 (total length for the table)
now we reverse it by writing 36/3,75 and we get 9,6.
but we need a whole board/number. which means instead of having 9 and 0.6 boards, we add an entire board instead. 9+1=10
Answer:
aₙ= 47 -3n
Step-by-step explanation:
44, 41, 38, 35, 32
This is AP with 1st term of 44 and common difference of -3
nth term of this AP:
- aₙ= a₁+(n-1)d= 44+(n-1)*(-3)= 44 - 3n+3= 47-3n
Answer:
Statement of triangle proportionality:
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then that line divides these two sides proportionally.
From the statement: If then,
Show that:
Consider and
Reflexive property states that the value is equal to itself.
[Angle] {Reflexive property of equality}
Corresponding angles theorem states that if the two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent(i., e equal).
[Angle]
[Angle]
AA Similarity states that the two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.
then, by AA similarity theorem:
By segment addition postulates:
AB = FA +FB and AC = AG + GC
Corresponding sides in similar triangles are proportional
.....[1]
Substitute AB = FA +FB and AC = AG + GC in [1]
we have;
Separate the fraction:
Simplify:
Subtract 1 from both sides we get;
hence proved