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adoni [48]
3 years ago
15

Suppose that a compensation professional would like to calculate the median salary. he orders four salaries as follows: $20,000,

$22,000, $24,000, $26,000. what is the median salary for this data set?
Mathematics
1 answer:
Anastasy [175]3 years ago
8 0
The median means the middle number.
First, you put them in order from least to greatest.
Then, you look to see which number is in the middle.

Since there are only four numbers given, you have to go in between two of the numbers.

The median is in between 22,000 and 24,000.

20,000  22,000  _  24,000  26,000

The number that is equally between 22,000 and 24,000 is 23,000.

The median for the set of data is $23,000.

Hope this helps!
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Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, an
Natasha_Volkova [10]

Answer:

The volume of the solid is 243\sqrt{2} \ \pi

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0  ≤ ρ²   ≤   81

0  ≤ ρ   ≤  9

The intersection that takes place in the sphere and the cone is:

x^2 +y^2 ( \sqrt{x^2 +y^2 })^2  = 81

2(x^2 + y^2) =81

x^2 +y^2 = \dfrac{81}{2}

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

z = \sqrt{x^2+y^2}

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; \dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}

Thus, volume: V  = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4}  \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho   ^2 \ sin \phi \ d\rho \   d \theta \  d \phi

V  = \int \limits^{\pi/2}_{\pi/4} \ sin \phi  \ d \phi  \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho   ^2 d\rho

V = \bigg [-cos \phi  \bigg]^{\pi/2}_{\pi/4}  \bigg [\theta  \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3}  \bigg ]^{9}_{0}

V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]

V = 243\sqrt{2} \ \pi

4 0
3 years ago
In the figure below what is the value of x?
vazorg [7]

Answer:

The value of x is 106

Step-by-step explanation:

Let us solve the question

In the given figure

∵ The triangle in the given figure has two sides equal

→ That means the triangle is an isosceles triangle

∴ The triangle is isosceles

∵ In the isosceles triangle, the base angles are equal in measures

∵ The measure of one base angle is 37°

∴ The measure of other base angle is 37°

→ The sum of the measures of the interior angles of a Δ is 180°

∵ 37° + 37° + x = 180°

→ Add the like terms

∴ 74° + x = 180°

→ Subtract 74 from both sides

∵ 74 - 74 + x = 180 - 74

∴ x = 106

∴ The value of x is 106

7 0
3 years ago
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