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3 years ago

The table shows the favorite subjects of students in a recent survey

1 answer:

3 0

More students picked math because if you simplify the fraction to art that is 0.16 so if you compare the 2.0.16 is less than 0.28

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A foreman for an injection-molding firm admits that on 55% of his shifts, he forgets to shut off the injection machine on his li

motikmotik

Answer:

0.8594

Step-by-step explanation:

Let a denote the event of forgetting to shut off machine and b be the event of being defective.

-A foreman forgets to shut off machine 55% of the time.

-If he forgets, 15% of molds are defective.

-If he does not, 3% of molds are defective.

#The probability that he forgot to shut off the machine is calculated as:

$P(a \ and \ b)=0.55\times 0.15\\\\=0.0825\\\\$

P(a and ~b)=0.55(1-0.15)=0.4675

P(~a and b) = (1-0.55)*0.03=0.0135

P(~a and ~b) = (1-0.55)*(1-0.03)=0.4365

#Conditional probability is defined as:

$P(a|b)=\frac{P(a \ and\ b)}{P(a)}\\\\=\frac{P(a \ and \ b)}{[(P(a \ and \ b)+P(\~a \ and \ b)}\\\\\\=\frac{0.0825}{0.0825+0.0135}\\\\\\=0.8594$

Hence, the probability that the foreman forgot to shut off the machine the previous night is 0.8594

5 0

3 years ago

Determine which of the indicated column vectors are eigenvectors of the given matrix

gladu [14]

]Eigenvectors are found by the equation $(A-\lambda I) \vec{v} = 0$$ implying that $\det(A-\lambda I) = 0$ . We then can write:

$A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ]$

And:

$\det(A-\lambda I) = (4-\lambda)(1-\lambda) - 10 = 0$

Gives us the characteristic polynomial:

$\lambda^2 - 5 \lambda -6 = 0 \implies \lambda_1 = -1, \lambda_2 = 6$

So, solving for each eigenvector subspace:

$\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]$

Gives us the system of equations:

$4x + 2y = -x \newline 5x + y = - y$

Producing the subspace along the line $y = -\frac{5}{2} x$

We can see then that 3 is the answer.

7 0

3 years ago

Use the number line given to choose the best answer for the question.

Taya2010 [7]

Answer:

can you put the number line

Step-by-step explanation:

7 0

3 years ago

Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (4, −5, 2) and parallel

Nataliya [291]

Answer:

Step-by-step explanation:

From the given information, the symmetric equations for the line pass through(4, -5, 2) i.e ( $x_o, y_o, z_o$ ) and are parallel to $\dfrac{x+5}{1} = \dfrac{y}{2}= \dfrac{z-3}{1}$

The parallel vector to the line i + zj+k = ai + bj + ck

Hence, the equation for the line is :

$x = x_o + at \\ \\ x = y_o + bt \\ \\ x = z_o + ct$

x = 4 + t

y = -5 + 2t

z = 2 + t

Thus, x, y, z = ( 4+t, -5+2t, 2+t )

The symmetric equation can now be as follows:

$\begin {vmatrix} x = 4+ t \\ \\ \dfrac{x-4}{1} = t \begin {vmatirx} \end {vmatrix}$ $\begin {vmatrix} y = - 5+2t \\ \\ \dfrac{y+5}{2} =t \end {vmatrix}$ $\begin {vmatrix} z =2+t \\ \\ \dfrac{z-2}{1} =t \end {vmatrix}$