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2 years ago

A jury pool consists of 50 potential jurors and how many ways can a jury of 12 be selected

Mathematics

1 answer:

bija089 [108]2 years ago

5 0

Solution:

we are given that

A jury pool consists of 50 potential jurors.

Wee have been asked to find the number of ways can a jury of 12 be selected.

As we know from the concept of combination that r person can be selected out of n in ncr ways. where

$n_C_r=\frac{n!}{r!(n-r)!}$

Now substitute the values we get

${50}_C_{12}=\frac{50!}{12!(50-12)!}\\
\\
{50}_C_{12}=\frac{50!}{12!38!}\\
\\
{50}_C_{12}=121399651100\\$

Hence the required number of ways is 121399651100

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Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

y = -x + 1 ==> x + y = 1

y = -x + 4 ==> x + y = 4

y = 2x + 2 ==> -2x + y = 2

y = 2x + 5 ==> -2x + y = 5

This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

2 years ago

Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x 2 Find F[G(x)] - F(x). 4x + 4 4x + 2 4x

Allushta [10]

Answer:

4x + 4

Step-by-step explanation:

F(x) = 2x - 1

G(x) = 3x + 2

H(x) = x²

We have to calculate the expression F(G(x)) - F(x)

F(G(x)) means the composition of functions F(x) and G(x). In order to find F(G(x)) we have to replace ever occurrence of x in F(x) with the value of G(x). So,

F(G(x)) = 2(3x+2) - 1 = 6x + 4 - 1 = 6x + 3

Thus,

F(G(x)) - F(x) = 6x + 3 - (2x - 1)

= 6x + 3 -2x + 1

= 4x + 4

Therefore, the expression F(G(x)) - F(x) equals 4x + 4

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2 years ago

The point (p,q) is on the graph of values from a ratio table. What is another point on the graph?

Anestetic [448]

In the previous activities, we constructed a number of tables. Once we knew the first numbers in the table, we were often able to predict what the next numbers would be. Whenever we can predict numbers in one row of a table by multiplying numbers in another row of a table by a given number, we call the relationship between the numbers a ratio. There are ratios in which both items have the same units (they are often called proper ratios). For example, when we compared the diameter of a circle to its circumference, both measured in centimeters, we were using a same-units ratio. Miles per gallon is a good example of a different-units ratio. If we did not specifically state that we were comparing miles to gallons, there would be no way to know what was being compared!

When both quantities in a ratio have the same units, it is not necessary to state the unit. For instance, let's compare the quantity of chocolate chips used when Mary and Quinn bake cookies. If Mary used 6 ounces and Quinn used 9 ounces, the ratio of Mary's usage to Quinn's would be 2 to 3 (note that the order of the numbers must correspond to the verbal order of the items they represent). How do we get this? One way would be to build a table where the second row was always one and a half times as much as the first row. This is the method we used in the first two lessons. Another way is to express the items being compared as a fraction complete with units:

6 ounces
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2 years ago

Read 2 more answers

A company produces a cardboard box in the shape of a rectangular prism. The surface area of the box is represented by S=10x2, wh

OLEGan [10]

S = 10x^2

S/10 = x^2

+or-sqrt(S/10) = x

+or- sqrt(S10)/10 = x

_inverse = +or-sqrt(10x)/10

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2 years ago