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3 years ago

Find the mode, median, mean, and range for each data set. Round the mean to two decimals places, where necessary.

Mathematics

2 answers:

gayaneshka [121]3 years ago

8 0

Answer:

The median, mean, and mode of the data set are 2, 1.9, and 1.

Step-by-step explanation:

To find the median of a data set, line up all values from greatest to least and find the number in the center. For example, in the set 1, 2, 3, 2 would be the median. In this case, the order would be 1, 1, 1, 1, 2, 2, 2, 3, 3, 3. The two numbers in the middle are 2 and 2, their average is 2, so that would be the median. The mean of a data set is the average of all data values in a set. In this case, there are 10 data values, and their total sum is 19, so the mean of this data set is 1.9. The mode of a data set is the value that occurs the most in a set. In this case, 1 occurs four times, 2 occurs three times, and 3 occurs three times, so the mode of this data set is 1.

Vitek1552 [10]3 years ago

6 0

Answer:

Mode: 1

Mean: 1.9

Range: 2

Step-by-step explanation:

Mode: the number that occurs more often

Mean: To find the mean, add all the numbers together then divide by the number of numbers.

Range: is the difference between the largest and the smallest value.

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Mode: 1,1,1,1,2,2,2,3,3,3. 1 is mostly being occurred so 1 is the mode.

Mean: 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 = 19 divided by 10 equals 1.9.

Range: the largest number is 3. The smallest number is 1. 3 - 1 = 2

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3 years ago

Which equation represents a circle with the same center as the circle shown but with a radius of 2 units?

Daniel [21]

Answer:

Option 2: (x-4)^2 + (x-5)^2 = 4

Step-by-step explanation:

The given circle's center is: (4,5)

And the radius is 4 units.

We are told in the question that the center will remain same only the radius will be changed.

The center is denoted by (h,k) = (4,5) and radius is 2

Standard equation of circle is:

(x-h)^2 + (y-k)^2 = r^2

So the equation of another circle with same center and radius of 2 units will be:

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4 years ago

The rod is made of A-36 steel and has a diameter of 0.22 in . If the rod is 4 ft long when the springs are compressed 0.7 in . a

ziro4ka [17]

The force in the rod when the temperature is 150 °F is 718.72 pounds-force.

<h3>How to determine the resulting the resulting force due to mechanical and thermal deformation</h3>

Let suppose that rod experiments a quasi-static deformation and that both springs have a linear behavior, that is, force ( $F$ ), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to temperature increase creates a spring deformation additional to that associated with mechanical contact.

Given simmetry considerations, we derive an expression for the spring force ( $F$ ), in pounds-force, as a sum of mechanical and thermal effects by principle of superposition:

$F = k\cdot (\Delta x + 0.5\cdot \Delta l)$ (1)

Where:

$k$ - Spring constant, in pounds-force per inch.
$\Delta x$ - Spring deformation, in inches.
$\Delta l$ - Rod elongation, in inches.

The rod elongation is described by the following thermal dilatation formula:

$\Delta l = \alpha \cdot L_{o}\cdot (T_{f}-T_{o})$ (2)

Where:

$\alpha$ - Coefficient of linear expansion, in $\frac{1}{^{\circ}F}$ .
$L_{o}$ - Initial length of the rod, in inches.
$T_{o}$ - Initial temperature, in degrees Fahrenheit.
$T_{f}$ - Final temperature, in degrees Fahrenheit.

If we know $k = 1000\,\frac{lb}{in}$ , $\Delta x = 0.7\,in$ , $\alpha = 6.5\times 10^{-6}\,\frac{1}{^{\circ}F}$ , $L_{o} = 48\,in$ , $T_{o} = 30\,^{\circ}F$ and $T_{f} = 150\,^{\circ}F$ , then the force in the rod at final temperature is:

$F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right]$