Solve for x.
StartFraction x over 3 EndFraction minus StartFraction 5 over 6 EndFraction equals StartFraction 3 left-parenthesis x minus 3 right-parenthesis over 12 EndFraction
Answer options with 5 options
A.
x equals negative StartFraction 19 over 7 EndFraction
B.
x equals 1
C.
x equals StartFraction 29 over 7 EndFraction
D.
x equals 7
E.
x equals 19
To solve for x, we want to isolate the variable on one side of the equation.
Start by simplifying both fractions on the left side of the equation. The LCM of 3 and 6 is 6, so multiply the first fraction by 2/2 and the second fraction by 1/2:
(x/3) - (5/6) = (3(x-3))/12
(2x/6) - (5/6) = (3x-9)/12
Next, multiply through by 6 to eliminate the denominators:
2x - 5 = (3x-9)/2
Next, multiply through by 2 to eliminate the fraction:
4x - 10 = 3x - 9
Subtract 3x from both sides:
x - 10 = -9
Add 10 to both sides:
x = 1
Therefore, the solution is x = 1.
The correct answer is (B) x equals 1.
Determine whether each question is an example of a statistical question. Drag each question to the correct classification in the table.
Response area with 2 blank spaces
Statistical Question
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,begin underline,Not,end underline, a Statistical Question
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Answer options with 5 options.
Unfortunately, there are no answer options provided, so I am unable to determine which question belongs in the "Statistical Question" or "Not a Statistical Question" category. Please provide the questions so that I can assist you further.
A rectangular prism is shown.
A rectangular prism is 12 inches long, 4 inches wide, and 5 inches high.
Question
What is the surface area of the rectangular prism?
Answer options with 5 options
A.
21 inches squared
B.
84 inches squared
C.
128 inches squared
D.
240 inches squared
E.
256 inches squared
To find the surface area of a rectangular prism, we need to calculate the area of each face and then add them together.
The rectangular prism has 6 faces: 2 rectangular faces on the top and bottom, and 4 rectangular faces on the sides.
The top and bottom faces each have dimensions of 12 inches by 4 inches, so their combined area is 12 inches * 4 inches * 2 = 96 square inches.
The side faces each have dimensions of 12 inches by 5 inches, so their combined area is 12 inches * 5 inches * 2 = 120 square inches.
Adding those two areas together, we get a total surface area of 96 square inches + 120 square inches = 216 square inches.
Therefore, the correct answer is (E) 216 inches squared.
An oil company uses cylindrical storage tanks. Each tank has a radius of 14 feet and is 27 feet tall.
What is the volume of a tank?
Answer options with 4 options
A.
378 pi feet cubed
B.
756 pi feet cubed
C.
5,292 pi feet cubed
D.
21,168 pi feet cubed
To find the volume of a cylinder, we use the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height.
In this case, the radius of the tank is given as 14 feet and the height is 27 feet.
Plugging these values into the formula, we get:
V = π(14^2)(27)
= π(196)(27)
= 5,292π feet cubed
Therefore, the volume of the tank is 5,292π feet cubed.
The correct answer is (C) 5,292π feet cubed.
What is the slope of the line perpendicular to 2 x minus 3 y equals 8?
Answer options with 4 options
A.
negative 3-halves
B.
negative 2-thirds
C.
2-thirds
D.
3-halves
To find the slope of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.
To determine the slope of the given line, we need to rewrite the equation in the slope-intercept form (y = mx + b), where m represents the slope.
Starting with the given equation: 2x - 3y = 8
Rearranging the equation to isolate y:
-3y = -2x + 8
y = (2/3)x - 8/3
Now we can see that the slope of the given line is 2/3.
To find the slope of the line perpendicular to this line, we take the negative reciprocal of 2/3:
-(3/2) = -3/2
Therefore, the slope of the line perpendicular to 2x - 3y = 8 is -3/2.
The correct answer is (A) negative 3-halves.
The radius of circle P is five times the radius of circle Q.
How do the areas of the two circles compare?
Answer options with 5 options
A.
The area of circle P is StartFraction 1 over 25 EndFraction times the area of circle Q.
B.
The area of circle P is StartFraction 1 over 5 EndFraction times the area of circle Q.
C.
The area of circle P is 5 times the area of circle Q.
D.
The area of circle P is 10 times the area of circle Q.
E.
The area of circle P is 25 times the area of circle Q.