Select the correct answer.

What is the mean of the data set? {50 54 62 48 49 52}

Fynjy0 [20]

To find the mean of a data set, you have to add all of the numbers and divide by the number of data.
So
50 + 54 + 62 + 48 + 49 + 52
To get 315.
315 divided by 6 is 52.5
So the mean of he data set is 52.5
Hope this helps :)

5 0

3 years ago

Read 2 more answers

Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Anestetic [448]

Answer:

Step-by-step explanation:

Let the rectangle have (x,y,z) as vertex in positive octant. The rectangular box has to be necessarily symmetrical about all the three axes.

Then the sides of the box would be

$2x,2y,2z$

Volume = $8xyz$

Maximize volume subject to

$x^2+y^2+z^2 =1$

i.e. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Use Lagrangian multipliers , we have

$∇f(x,y,z)=λ∇g(x,y,z)$ at the maximum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dividing we get

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Similarly $y^2=z^2$

Thus we get $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Hence dimensions are

(2x,2y,2z)

So dimensions are

$\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } )$

3 0

3 years ago

A cyclist rides in a circle with speed 5 m/s. What is his centripetal

Anna71 [15]

Option A

The centripetal acceleration is 1.32 $ms^{-2}$

Solution:

From given question,

A cyclist rides in a circle with speed 5 m/s

The circle has a radius of 19 m

To find: Centripetal acceleration

The formula for Centripetal acceleration is given as:

$a_c = \frac{v^2}{r}$

Where,

$a_c$ = centripetal acceleration

r is the radius and v is the velocity

From given statement,

radius = r = 19 m

velocity = v = 5 m/s

Substituting the values in above formula, we get

$a_c = \frac{5^2}{19}\\\\a_c = \frac{25}{19}\\\\a_c = 1.315 \approx 1.32$

Thus centripetal acceleration is 1.32 $ms^{-2}$

6 0

3 years ago

2. (-5+ 6n to the 3rd power) + (1- 2n to the 2nd power)

Alja [10]

I think it would -4 + 6n to the power of 3 - 2n to the power of 2. I could be wrong. If so, you can report it as an error or something.

4 0

4 years ago

What is the average rate of change from x = −3 to x = −4?

Vika [28.1K]

Answer:

-2

Step-by-step explanation:

Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue. We have the work form of a positive upwards-opening parabola as

$y=a(x-h)^2+k$

where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex. We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1). Now we will fill in the work form equation and solve for a:

$-1=a(-2-(-3))^2-3$

which simplifies a bit to

$-1=a(1)^2-3$

and

-1 = a(1) - 3. Therefore, a = 2 and our parabola is

$y=2(x+3)^2-3$

Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4. Do this by subbing in the values of x one at a time to find y. When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3). When x = -4, y = -1 so the coordinate of that point is (-4, -1). The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:

$m=\frac{-1-(-3)}{-4-(-3)} =\frac{2}{-1}=-2$

And there you have it! I'm very surprised that this question sat unanswered for so very long! I'm sorry I didn't see it earlier!

5 0

3 years ago