1. Which verbal expression does NOT represent 32u?

8. The Wilson family was one of the first to come to the U.S. They had 6 children. Assuming that the probability of a child bein

melamori03 [73]

Total children = 6
1) Probability of 4 girls =4/6=0.66
Probability of at least 4 girls >_ 0.66

That is greater or equal to 0.66

2) probability of 5 girls = 5/ total children
=5/6=0.83
Probability of at most 5 girls <_ 0.83
That is less than equal to 0.83

7 0

2 years ago

The cost per hour of running an assembly line in a

nlexa [21]

Answer:

the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

Step-by-step explanation:

if there is no mistake in the problem description, I read the following function :

C(x) = y = 0.3x² - 1.2x + 2

I don't know if you learned this already, but to find the extreme values of a function you need to build the first derivative of the function y' and find its solutions for y'=0.

the first derivative of C(x) is

0.6x - 1.2 = y'

0.6x - 1.2 = 0

0.6x = 1.2

x = 2

C(2) = 0.3×2² - 1.2×2 + 2 = 0.3×4 - 2.4 + 2 = 1.2-2.4+2 = 0.8

so, the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

5 0

2 years ago

How many times does the earth spin in a year

grigory [225]

365........................

8 0

3 years ago

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Which classification best describes the following system of equations?

wolverine [178]

The given system of equations is consistent and independent so, $\fbox{\begin\\\ \bf option (3)\\\end{minispace}}$ is correct.

Further explanation:

A system of equations is said to be a consistent system if the solution exists and if the solution does not exist then it is an inconsistent system.

If a consistent system has a unique solution then it is an independent system of equations but if the number of solutions is infinite then it is a dependent system of equations.

Label the given equations as shown below:

$\boxed{x-2y+4z=3}$ …… (1)

$\boxed{12x+5y-3z=36}$ …… (2)

$\boxed{9x-10y+5z=27}$ …… (3)

The augmented matrix for the above equations is, as follows:

$\left[\begin{array}{ccc}1&-2&4\\12&5&-3\\9&-10&5\end{array}\Biggm\vert\begin{array}{c}3\\26\\27\end{array}\right]$

Apply row transformation $R_{2}\rightarrow R_{2}-12R_{1}$ and $R_{3}\rightarrow R_{3}-9R_{1}$ as,

$\left[\begin{array}{ccc}1&-2&4\\0&29&-51\\0&8&-31\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right]$

Now, apply row transformation $R_{2}\rightarrow R_{2}-4R_{3}$ and $R_{3}\rightarrow R_{3}-3R_{2}$ as,

$\left[\begin{array}{ccc}1&-2&4\\0&-3&73\\0&-1&188\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right]$

Now, apply row transformations $R_{2}\rightarrow -R_{2}+2R_{3}$ and $R_{3}\rightarrow R_{3}+R_{2}$ as,

$\left[\begin{array}{ccc}1&-2&4\\0&1&303\\0&0&491\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right]$

The equations obtained from the above augmented matrix are,

$\begin{aligned}x-2y+4z&=3\\y+303z&=0\\491z&=0\end{aligned}$

The first equation is simplified to obtain the value of z as,

$\begin{aligned}491z&=0\\z&=0\end{aligned}$

Substitute $0$ for $z$ in the equation $y+303z=0$ to obtain the value of $y$ as,

$\begin{aligned}y+(303\cdot0)&=0\\y&=0\end{aligned}$

Now, substitute $0$ for $z$ and $0$ for $y$ in the equation $x-2y+4z=3$ to obtain the value of $x$ as,

$\begin{aligned}x-(2\cdot0)+(4\cdot0)&=3\\x&=3\end{aligned}$

Therefore, the value of $x$ is $3$ , the value of $y$ is $0$ and the value of $z$ is $0$ and the system has a unique solution.

Thus, the given system of equations is consistent and independent.

Option (1)

Here, the first option is inconsistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (1) is incorrect.

Option (2)

Here, the second option is consistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (2) is incorrect.

Option (3)

Here, the third option is consistent and independent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (3) is correct.

Option (4)

Here, the fourth option is inconsistent and independent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (4) is incorrect.

Learn more:

1. A problem on circle brainly.com/question/9510228.

2. A problem on general equation of a circle brainly.com/question/1506955.

Answer details

Grade: High school

Subject: Mathematics

Chapter: System of linear equations

Keywords: Equations, unique solution, independent, dependent, consistent, inconsistent, infinite solutions, homogeneous equation, non- homogeneous equation, determinant.

5 0

2 years ago

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What would be the answer for 3 times negative 2 plus 1

Rudiy27

Answer:-5

Step-by-step explanation:

3 x-2 = -6 + 1= -5

5 0

2 years ago

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