In an observational study, only one group is studied, and in an expirement, two groups are studied.
Answer:
see explanation
Step-by-step explanation:
3x and 144 are adjacent angles on a straight line and sum to 180°
3x + 144 = 180 ( subtract 144 from both sides )
3x = 36 ← value of 3x
divide both sides by 3
x = 12
and
2y - 5 and 95 are vertically opposite angles and are congruent, so
2y - 5 = 95 ← value of 2y - 5
add 5 to both sides
2y = 100 ( divide both sides by 2 )
y = 50
Then
x + y = 12 + 50 = 62
They are called the order of operations, or PEMDAS. Hope this helps!
Answer:
30 ml of 45% salt solution and 20 ml of 30% salt solution.
Step-by-step explanation:
Let x be the amount of 45% salt solution and y be the amount of 30% salt solution
the two equation will be:
x+y=60 -- A
0.45x+0.3y=0.4(60) -- B
Solve by substitution
Rewrite Equation A
x+y=60
x=60-y --- C
Substitute C into B
0.45(60-y)+0.3y=24
27-0.45y+0.3y=24
-0.15y=-3
y=20
<u>Substitute</u> the y=20 into equation C
x=60-20
x=30
Therefore, there was 30 ml of 45% salt solution and 20 ml of 30% salt solution.
I'm assuming you want the total surface area.
This is a trapezoidal prism. The bases are the parallel faces running horizontal (parallel to the ground) and they are congruent trapezoids. The lateral sides are rectangles.
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Lateral Faces:
The back face (hidden from view) is a rectangle that is 12 inches by 3 inches, so it has an area of 12*3 = 36 sq inches
The front slant faces on the left and right are each 3*5 = 15 sq inches in area
The front center lateral face has area of 6*3 = 18 sq inches
The total lateral surface area is 15+18+15+36 = 84 sq inches
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The bases are each the same trapezoid. The trapezoid has two parallel sides of 12 and 6 inches. Call this b1 and b2. The height of the trapezoid is h = 4. Imagine the trapezoid is laid flat in a 2D perspective instead of a 3D one.
The area of one trapezoid is...
A = h*(b1+b2)/2
A = 4*(12+6)/2
A = 4*(18)/2
A = 72/2
A = 36
So the area of both base faces combined is 2*36 = 72
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The total surface area is then found by adding the total lateral surface area (84) and the total base area (72) to get 84+72 = 156
Final Answer: 156 square inches
