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
To find the slope of the line passing through the points (-5, 17) and (-13, 8), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Let's label the coordinates as follows:
(x1, y1) = (-5, 17)
(x2, y2) = (-13, 8)
Substituting these values into the formula:
slope = (8 - 17) / (-13 - (-5))
= (8 - 17) / (-13 + 5)
= (-9) / (-8)
= 9 / 8
Therefore, the slope of the line passing through the given points is 9/8.
The answer is:
9/8
A convention manager finds that she has $1170, made up of twenties and fifties. She has a total of 36 bills. How many fifty-dollar bills does the manager have?
Let's assume the manager has x fifty-dollar bills and y twenty-dollar bills.
According to the given information,
1. The manager has a total of 36 bills: x + y = 36.
2. The total amount of money she has is $1170: 50x + 20y = 1170.
To find the number of fifty-dollar bills, we can solve the system of equations.
First, we'll solve the first equation for y:
y = 36 - x.
Next, we'll substitute this value of y into the second equation:
50x + 20(36 - x) = 1170.
Expanding and simplifying:
50x + 720 - 20x = 1170,
30x + 720 = 1170,
30x = 1170 - 720,
30x = 450.
Dividing both sides by 30:
x = 450 / 30,
x = 15.
Therefore, the manager has 15 fifty-dollar bills.
Answer: The manager has 15 fifty-dollar bills.
Gloria collected 34 fantail and comet goldfish. There were 6 fewer fantails than comets. How many comets did Gloria have?
Let's assume the number of comet goldfish Gloria has is x.
According to the given information, the number of fantail goldfish is 6 fewer than the number of comet goldfish. So, the number of fantail goldfish is x - 6.
The problem states that Gloria collected a total of 34 goldfish, which can be represented by the equation:
(x - 6) + x = 34.
Combining like terms:
2x - 6 = 34.
Adding 6 to both sides of the equation:
2x = 40.
Dividing both sides of the equation by 2:
x = 20.
Therefore, Gloria has 20 comet goldfish.
Answer: Gloria has 20 comet goldfish.
reduce 12/29 to one of these answers
30/11
-10
-2
2
To reduce the fraction 12/29, we need to find the greatest common divisor (GCD) of the numerator (12) and the denominator (29) and divide both numerator and denominator by the GCD.
The GCD of 12 and 29 is 1 because there are no common factors other than 1.
Dividing both numerator and denominator by 1, we obtain:
12/29 = 12/29
Therefore, the fraction 12/29 cannot be reduced further.
Answer: None of the given answers are equivalent to 12/29.
Then \frac{-2x\cdot 9}{2}+3=-\frac{7x}{4} cannot be 12/29
To solve the equation: \(\frac{-2x \cdot 9}{2} + 3 = -\frac{7x}{4}\)
First, let's simplify both sides of the equation:
\(\frac{-18x}{2} + 3 = -\frac{7x}{4}\)
Simplifying further:
\(-9x + 3 = -\frac{7x}{4}\)
Now, let's multiply both sides of the equation by 4 to eliminate the fraction:
\(4(-9x + 3) = 4(-\frac{7x}{4})\)
\(-36x + 12 = -7x\)
Next, let's add 36x to both sides:
\(-36x + 36x + 12 = -7x + 36x\)
\(12 = 29x\)
To isolate x, divide both sides by 29:
\(\frac{12}{29} = x\)
Therefore, the solution to the equation is \(x = \frac{12}{29}\).
Answer: \(x = \frac{12}{29}\).
The answer has to be one of those four
30/11
-10
-2
2
Which of these is the answer?
Apologies for the confusion. Let's solve the equation with the given options.
\(\frac{-2x \cdot 9}{2} + 3 = -\frac{7x}{4}\)
Simplifying both sides:
\(-9x + 3 = -\frac{7x}{4}\)
Now, let's multiply both sides by 4 to eliminate the fraction:
\(4(-9x + 3) = 4 \left(-\frac{7x}{4}\right)\)
\(-36x + 12 = -7x\)
Next, let's add 36x to both sides:
\(-36x + 36x + 12 = -7x + 36x\)
\(12 = 29x\)
To isolate x, divide both sides by 29:
\(\frac{12}{29} = x\)
Therefore, the solution to the equation is \(x = \frac{12}{29}\).
None of the given options: 30/11, -10, -2, or 2, match the solution x = 12/29.
Apologies for any confusion caused.
Find the perimeter (or circumference) and area of the figure. For the circle, give the exact value and then use π, or 3.14 for an approximation.
2.5 yards
The answers are any of these 4:
A)
circumference = 2.5π ≈ 15.70 yd
area = 6.25π ≈ 19.63 sq yd
B)
circumference = 5π ≈ 15.70 yd
area = 25π ≈ 31.40 sq yd
C)
circumference = 5π ≈ 15.70 yd
area = 6.25π ≈ 19.63 sq yd
D)
circumference = 2.5π ≈ 15.70 yd
area = 25π ≈ 78.50 sq yd
well?
Apologies for the delay. Let's calculate the perimeter (circumference) and area of the figure with a radius of 2.5 yards.
The circumference of a circle can be calculated using the formula: circumference = 2πr, where r is the radius.
Substituting the given radius of 2.5 yards, we have:
circumference = 2π(2.5) = 5π
Using 3.14 as an approximation for π, we have:
circumference ≈ 5(3.14) = 15.70 yards
Therefore, the approximate circumference is 15.70 yards.
The formula for the area of a circle is: area = πr^2
Substituting the given radius of 2.5 yards, we have:
area = π(2.5)^2 = π(6.25)
Using 3.14 as an approximation for π, we have:
area ≈ 3.14(6.25) = 19.63 square yards
Therefore, the approximate area is 19.63 square yards.
The correct answer is:
A)
circumference = 2.5π ≈ 15.70 yards
area = 6.25π ≈ 19.63 square yards
Find the perimeter (or circumference) and area of the figure. For the circle, give the exact value and then use π, or 3.14 for an approximation.
Figure: Rectangle
1 side is 3yd
1 side is 9yd
Answers:
A)
perimeter = 12 yd
area = 54 sq yd
B)
perimeter = 24 yd
area = 27 sq yd
C)
perimeter = 12 yd
area = 27 sq yd
D)
perimeter = 24 yd
area = 54 sq yd
Which is correct?
To find the perimeter and area of the rectangle, we can utilize the formulas for each.
The perimeter of a rectangle is given by the equation: perimeter = 2(length + width).
Given that one side is 3 yards and the other side is 9 yards, we have:
perimeter = 2(3 + 9) = 2(12) = 24 yards.
Therefore, the correct answer for the perimeter is:
B) perimeter = 24 yd.
To calculate the area of a rectangle, we use the formula: area = length × width.
Using the given dimensions of 3 yards for one side and 9 yards for the other side, we have:
area = 3 × 9 = 27 square yards.
Therefore, the correct answer for the area is:
C) area = 27 sq yd.
Hence, the correct answer is:
C) perimeter = 12 yd and area = 27 sq yd.
Find the perimeter (or circumference) and area of the figure. For the circle, give the exact value and then use π, or 3.14 for an approximation.
The shape has 4 sides.
One side is 7in, one is 9in, one is 13in, one is 25in.
Answers are:
A)
perimeter = 54 in.
area = 253 sq in.
B)
perimeter = 76 in.
area = 325 sq in.
C)
perimeter = 54 in.
area = 325 sq in.
D)
perimeter = 76 in.
area = 253 sq in
To find the perimeter of the figure with 4 sides, we need to sum up the lengths of all sides.
Given that the sides are 7in, 9in, 13in, and 25in, we have:
Perimeter = 7in + 9in + 13in + 25in = 54in.
Therefore, the correct answer for the perimeter is:
A) perimeter = 54 in.
Since we are not given any information about the shape being a circle or having right angles, we cannot calculate the area accurately. Therefore, none of the given options regarding the area are correct.
Find the perimeter of a square picture frame with a side length of 5.7 inches.
The perimeter of a square can be found by multiplying the length of one side by 4, since all sides of a square are equal in length.
For a square picture frame with a side length of 5.7 inches, the perimeter would be:
Perimeter = 5.7 inches + 5.7 inches + 5.7 inches + 5.7 inches = 4 * 5.7 inches
Calculating this:
Perimeter = 22.8 inches
Therefore, the perimeter of the square picture frame is 22.8 inches.
A rectangular room measures 17 ft by 18 ft. Find the cost of installing a strip of wallpaper around the room if the wallpaper cost $0.55 per foot.
To find the cost of installing a strip of wallpaper around the room, we need to calculate the perimeter of the room and then multiply it by the cost per foot.
The formula for the perimeter of a rectangle is given by:
perimeter = 2 * (length + width)
Given that the length of the room is 17 ft and the width is 18 ft, we have:
perimeter = 2 * (17 ft + 18 ft)
perimeter = 2 * 35 ft
perimeter = 70 ft
Now, we can calculate the cost of installing the strip of wallpaper:
cost = (perimeter) * (cost per foot)
cost = 70 ft * $0.55 per ft
cost = $38.50
Therefore, the cost of installing a strip of wallpaper around the room would be $38.50.
A hotel is building a fitness center measuring 261 ft × 42 ft.
The flooring to cover the space is made of a special 3-layered cushioned tile and costs per square foot.
How much will it cost for the new flooring?