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Amanda [17]
3 years ago
15

There is a set of 100 obserations with a mean of 46 and a standard deviation of 0. What is the value of smallest obserstion in a

set?
Mathematics
1 answer:
VashaNatasha [74]3 years ago
6 0

Answer:

Solution = 46

Step-by-step explanation:

I believe you meant standard deviation. Standard deviation is defined as the variation of the data set, or the differences between the values in this set. In order for the standard deviation to be 0, all values should be the same.

Now if the mean is 46, the smallest possible number of each value in the data set should be 46 as well.  This is considering the mean is the average of the values, and hence any number of values in the data set being 46 will always have a mean of 46. Let me give you a demonstration -

Ex. [ 46, 46, 46 ], and, [46, 46, 46, 46, 46]\\Average = 46 + 46 + 46 / 3 = 46,\\Average = 46 + 46 + 46 + 46 + 46 / 5 = 46

As you can see, the average is 46 in each case. This proves that a data set consisting of n number of values in it, each value being 46, or any constant value for that matter, always has a mean similar to the value inside the set, in this case 46.<u><em> And, that the value of the smallest standard deviation is 46. </em></u>

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If tan x = .76 and cos x = .22, what is sin x?
andrezito [222]
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3 0
3 years ago
Convert from rectangular to polar coordinates:Note: Choose r and θ such that r is non-negative and 0 ≤ θ &lt; 2πa. (6,0)b. (9,9/
Anuta_ua [19.1K]

Answer:

The polar coordinates are as follow:

a. (6,2π)

b. (18, π/3)

c. (2√2 , 3π/4)

d. (2, 5π /6)

Step-by-step explanation:

To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .

To calculate r, we use Pythagorean theorem:

r = \sqrt{ x^{2} +y^{2} } ---- (1)

To calculate the θ, first we will find out the θ '  using the inverse of cosine as it is easy to calculate.

So,    θ '  = cos ⁻¹  (x/r)

If  y  ≥  0  then  θ  =  ∅

If  y  <  0  then  θ  =  2 π  −  ∅

For a. (6,0)

Sol:

Using the formula in equation (1). we get the value of r as:

r = \sqrt{6^{2} + 0^{2}  }

r = 6

And ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (6/6)

∅  =cos ⁻¹   (1) = 2π

As If  y  ≥  0  then  θ  =  ∅

So ∅ = 2π

The polar coordinates are (6,2π)

For a. (9,9/\sqrt{3})

Sol:

r = 9 + 3(3) = 18

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (9/18)

∅ = cos ⁻¹   (1/2) = π/3

As  If  y  ≥  0  then  θ  =  ∅

then θ  = π/3

The polar coordinates are (18, π/3)

For (-2,2)

Sol:

r =√( (-2)²+(2)² )

r = 2 √2

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (-2/ 2 √2)

∅ = 3π/4

As  If  y  ≥  0  then  θ  =  ∅

then   θ  = 3π/4

The polar coordinates are (2√2 , 3π/4)

For (-√3, 1)

Sol:

r = √ ((-√3)² + 1²)

r = 2

and ∅  = cos ⁻¹  (x/r)

∅  = cos ⁻¹ ( -√3/2)

∅  = 5π /6

As  If  y  ≥  0  then  θ  =  ∅

So  θ  = 5π /6

The polar coordinates are (2, 5π /6)

6 0
3 years ago
Please help with my next question in math.
Vesnalui [34]
The answer is D. 2n + 1
8 0
3 years ago
The volume of a sphere can be determined by the formula V = 4/3 πr^3, where r is the radius. What is the volume of a sphere with
allochka39001 [22]

Answer:

V = \frac{99}{7} x^{9}y^{-6}

Step-by-step explanation:

Given

V = \frac{4}{3}\pi r^3

Required

Find V when

r = \frac{3}{2}x^3y^{-2

Substitute \frac{3}{2}x^3y^{-2 for r in V = \frac{4}{3}\pi r^3

V = \frac{4}{3}\pi * (\frac{3}{2}x^3y^{-2})^3

Open bracket

V = \frac{4}{3}\pi * \frac{3}{2}^3 * x^{3*3}y^{-2*3}

V = \frac{4}{3}\pi * \frac{27}{8} * x^{9}y^{-6}

Simplify the fractions

V = \pi * \frac{9}{2} * x^{9}y^{-6}

Let

\pi = \frac{22}{7}

So:

V = \frac{22}{7}  * \frac{9}{2} * x^{9}y^{-6}

V = \frac{11}{7} * \frac{9}{1} * x^{9}y^{-6}

V = \frac{99}{7}   * x^{9}y^{-6}

V = \frac{99}{7} x^{9}y^{-6}

6 0
3 years ago
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GrogVix [38]

Answer:

c the answer is c


Step-by-step explanation:


5 0
3 years ago
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