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poizon [28]
3 years ago
14

As part of the National Health and Nutrition Examination Survey, subjects were asked how long they slept the preceding night, an

d the following times (hours) were reported: 8, 7, 5, 7, 4, 7, 6, 7, 8, 8, 8, 6 How would you describe the mode?
Mathematics
1 answer:
Alex Ar [27]3 years ago
4 0

Answer:

Mode = 7,8

Step-by-step explanation:

We are given the following data set:

8, 7, 5, 7, 4, 7, 6, 7, 8, 8, 8, 6

This is the data for number of hours slept the preceeding night.

We have to find the mode of the data.

It is described as the most frequent observation in the sample.

Sorted Data:

4, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8

Both observation 8 and 7 repeated 4 times each.

Thus, the mode of data is 7 and 8.

Thus, it is a bi-modal data.

7 hours and 8 hours are the most frequent number of hours of sleep preceeding night.

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Step-by-step explanation:

7 0
3 years ago
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Y=-x^2+6x-4<br> Find the Axis of Symmetry and the Vertex, Also solve the whole equation.
Inessa [10]

Answer:

1. <em>Axis of symmetry</em>: x = 3

2. <em>Vertex:</em> (3,5)

3. <em>Solution of the equation</em>:

<u />

  • x-intercepts:

               (3-\sqrt{5},0) \\\\(3+\sqrt{5},0)

  • y-intercept: (0, -4)

Explanation:

<u>1. Equation:</u>

    y=-x^2+6x-4

<u>2. </u><em><u>Axis of symmetry:</u></em>

That is the equation of a parabola, whose standard form is:

                 y=ax^2+bx+c

Where:    

                 a=-1;b=6;c=-4

The axis of symmetry is the vertical line with equation:

               x=-b/2a

Substitute  a=-1,\text{ and }b=6

          x=-6/[(2)(-1)]=-6/(-2)=3

Thus, the axis of symmetry is:

            x=3

<em><u>3. Vertex</u></em>

<em><u /></em>

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

               y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5

Therefore, the vertex is (3, 5)

<u>4. Find the x-intercepts</u>

The x-intercepts are the roots of the equation, which are the points wher y = 0.

        y=-x^2+6x-4=0

Use the quadratic equation:

       x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\x=\frac{-6\pm\sqrt{(-6)^2-4(-1)(-4)} }{2(-1)}\\\\x_1=3-\sqrt{5} \\\\x_2=3+\sqrt{5}

<u>5. Find the y-intercept</u>

<u />

The y-intercet is the value of y when x=0:

         y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4

7 0
3 years ago
What is the side length of the square if A=81 m squared
Nesterboy [21]

Answer:

The side length is 9m

Step-by-step explanation:

A = 81 m^2

Since the figure is a square, we know the area of a square is A = s^2 where s is the side length

81 m^2 = s^2

Take the square root of each side

sqrt(81 m^2 ) = sqrt( s^2)

9 m = s

The side length is 9m

8 0
3 years ago
Identify the vertex of g(x) = (x + 14)? - 8.
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Do you think you can send a picture of the problem I’m not really understanding
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A flower bed in the shape of a rectangular prism is 10 feet long, 1 foot wide, and 0.5 foot deep.
Lemur [1.5K]

Answer:

it is 5 feet squared

Step-by-step explanation:

multiply them all

5 0
3 years ago
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