In a random sampling from a survey concerning music listening habits, 140 out of 180 at-home mothers preferred salsa to heavy metal. Taking all the data from the survey, 392 at-home mothers expressed a preference for salsa over heavy metal. How many at-home mothers would you estimate took part in the survey?
To estimate the total number of at-home mothers who took part in the survey, we can use the concept of proportion.
Let's assume "x" represents the total number of at-home mothers who took part in the survey.
According to the sample, 140 out of 180 at-home mothers preferred salsa to heavy metal. This can be written as a proportion: 140/x = 180/x.
We are also given that a total of 392 at-home mothers expressed a preference for salsa over heavy metal. This proportion can be written as: 392/x.
Since both proportions represent the same concept (preference for salsa over heavy metal), we can set them equal to each other:
140/x = 392/x
We can solve this equation for x:
140x = 392x
140 = 392
Dividing both sides by 140 gives:
x = 392/140
x = 2.8
Since we cannot have a fraction of a person, we round up to the nearest whole number:
x ≈ 3
Therefore, we can estimate that approximately 3 at-home mothers took part in the survey.
The answer is either of these choices, which is it?
A)
494 mothers
B)
504 mothers
C)
513 mothers
D)
499 mothers
The answer is:
D) 499 mothers
Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
If 4 times a number is added to -8, the result is equal to 12 times the number. Find the number.
Let's represent the number as x.
The given condition states that "4 times a number is added to -8, the result is equal to 12 times the number."
This can be written as the equation:
4x - 8 = 12x
Now, let's solve for x.
Subtract 4x from both sides of the equation to isolate the x term:
-8 = 8x
Divide both sides by 8 to solve for x:
-8/8 = x
Simplifying:
-1 = x
Therefore, the number is -1.
3y/10 - 7 = y/5 - 6 Answer must have no fractions
To eliminate the fractions, we can start by multiplying every term in the equation by the least common multiple (LCM) of the denominators, which is 10 in this case.
10 * (3y/10) - 10 * 7 = 10 * (y/5) - 10 * 6
This simplifies to:
3y - 70 = 2y - 60
Next, let's isolate the y term on one side of the equation by subtracting 2y from both sides:
3y - 2y - 70 = 2y - 2y - 60
This simplifies to:
y - 70 = -60
Finally, let's isolate the y term on one side of the equation by adding 70 to both sides:
y - 70 + 70 = -60 + 70
This simplifies to:
y = 10
Therefore, the solution to the equation is y = 10.
The formula p = 15 + 5d/11 describes the pressure of sea water, p, in pounds per square foot, at a depth of dfeet below the surface. If a diver was subjected to a pressure of 15 pounds per square foot, to what depth did she descend? At what depth is the pressure 127 pounds per square foot?
Answer is one of these:
A)
276.4 ft; 276.4 ft
B)
2 ft; 248.4 ft
C)
244.4ft; 244.4 ft
D)
0 ft; 246.4 ft
To find the depth at which the pressure is 15 pounds per square foot, we can set the equation equal to 15 and solve for d:
15 + 5d/11 = 15
Multiplying both sides of the equation by 11 to eliminate the fraction:
165 + 5d = 165
Subtracting 165 from both sides of the equation:
5d = 0
Dividing both sides of the equation by 5:
d = 0
Therefore, the diver did not descend at all (0 feet).
To find the depth at which the pressure is 127 pounds per square foot, we can set the equation equal to 127 and solve for d:
15 + 5d/11 = 127
Multiplying both sides of the equation by 11 to eliminate the fraction:
165 + 5d = 1397
Subtracting 165 from both sides of the equation:
5d = 1232
Dividing both sides of the equation by 5:
d = 1232/5
Simplifying:
d = 246.4
Therefore, the depth at which the pressure is 127 pounds per square foot is approximately 246.4 feet.
The answer is:
D)
0 ft; 246.4 ft.
Solve for slope of the line (-5, 17) and (-13, 8)
Answer has to be any of these choices:
-9/8
-25/18
8/9
9/8