Mathematics, 06.02.2023 14:00, jjimenez0276

Use Cramer's rule to solve the system or to determine that the system is inconsistent or contains dependent equations.

Answers: 1

Show answers

Answers

answered: dondre54

In order to solve the system using Cramer's rule, first let's put the system in matrix form:

$\begin{gathered} \begin{bmatrix}{1} & {1} \\ {1} & {-1}\end{bmatrix}\begin{bmatrix} & {x} \\ & {y}\end{bmatrix}=\begin{bmatrix} & {7} \\ & {1}\end{bmatrix}\\ \\ D\cdot X=B \end{gathered}$

The matrix D is the matrix with the coefficients of x and y from each equation.

The determinant of a 2x2 matrix is given by the product of the terms in the main diagonal minus the product of terms in the secondary diagonal:

$|D|=1\cdot(-1)-1\cdot1=-1-1=-2$

The matrix Dx is given by the matrix D after switching the first column with the coefficient matrix B:

$\begin{gathered} Dx=\begin{bmatrix}{7} & {1} \\ {1} & {-1}\end{bmatrix}\\ \\ |Dx|=7\cdot(-1)-1\cdot1=-7-1=-8 \end{gathered}$

And the matrix Dy is given by the matrix D after switching the second column with the coefficient matrix B:

$\begin{gathered} Dy=\begin{bmatrix}{1} & {7} \\ {1} & {1}\end{bmatrix}\\ \\ |Dy|=1\cdot1-7\operatorname{\cdot}1=1-7=-6 \end{gathered}$

Now, solving the system, we have:

$\begin{gathered} x=\frac{|Dx|}{|D|}=\frac{-8}{-2}=4\\ \\ y=\frac{|Dy|}{|D|}=\frac{-6}{-2}=3 \end{gathered}$

answered: Guest

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !

answered: Guest

step-by-step explanation:

i found the life tables for the year 2012.

life table of males at age 30. probability of dying between ages x and x+1

total population:

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old.

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497