6x − 2y = 3 (equation 1) 5x + 3y = 4 (equation 2)

Answers

Answer 1

Answer:

Answer:

there is the answer to do

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Although still a sophomore at college, John O'Hagan's son Billy-Sean has already created several commercial video games and is currently working on his most ambitious project to date: a game called K that purports to be a "simulation of the world." John O'Hagan has decided to set aside some office space for Billy-Sean against the northern wall in the headquarters penthouse. The construction of the partition will cost $8 per foot for the south wall and $12 per foot for the east and west walls.What are the dimensions of the office space with the largest area that can be provided for Billy-Sean with a budget of $432?south wall length ft -east and west wall length -What is its area?

Answers

Answer:

27 feet for the south wall and 18 feet for the east/west walls

Maximum area= $486\ ft^2$

Step-by-step explanation:

Optimization

This is a simple case where an objective function must be minimized or maximized, given some restrictions coming in the form of equations.

The first derivative method will be used to find the values of the parameters that control the objective function and the maximum value of that function.

The office space for Billy-Sean will have the form of a rectangle of dimensions x and y, being x the number of feet for the south wall and y the number of feet for the west wall. The total cost of the space is

C=8x+12y

The budget to build the office space is $432, thus

$8x+12y=432$

Solving for y

$\displaystyle y=(432-8x)/(12)$

The area of the office space is

$A=xy$

Replacing the value found above

$\displaystyle A=x\cdot (432-8x)/(12)$

Operating

$\displaystyle A= (432x-8x^2)/(12)$

This is the objective function and must be maximized. Taking its first derivative and equating to 0:

$\displaystyle A'= (432-16x)/(12)=0$

Operating

$432-16x=0$

Solving

$x=432/16=27$

$x=27\ feet$

Calculating y

$\displaystyle y=(432-8\cdot 27)/(12)$

$y=18\ feet$

Compute the second derivative to ensure it's a maximum

$\displaystyle A'= (-16x)/(12)$

Since it's negative for x positive, the values found are a maximum for the area of the office space, which area is

$A=xy=27\ ft\cdot 18\ ft\n\n\boxed{A=486\ ft^2}$

Rita's graduation picnic will cost $3 for every attendee. At most how many attendees can there be if Rita only budgets a total of $87 dollars for her graduation picnic?

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To figure out how many attendees Rita can have at her picnic, we must divide the total amount that she has in her budget for her graduation picnic ($87) by the cost for every attendee ($3).

$87/$3 = 29

Therefore, Rita can have at most 29 attendees if Rita has the above cost parameters.

Hope this helps!

Manuel ate 1 and 3 of a crackers on a plate. his brother ate 1 and 4 of the crackers.there where 5 crackers left on the plate.how many crackers were on the plate to begin with?

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Answer:

1/3 + 1/4 = 4/12 + 3/12 = 7/12

7/12 = both brothers ate 7 crackers out of 12 crackers

there were 5 crackers left on the plate means 5/12 crackers left on the plate

answer: 12 crackers at the beginning

Step-by-step explanation:

If the true mean is 50 and we reject the hypothesis that μ = 50, what is the probability of Type II error? Hint: This is a trick question.

Answers

Answer:

Zero

Step-by-step explanation:

Given that:

the true mean is 50 and we reject the hypothesis that μ = 50

The probability of the Type II error will be zero, given that we reject the null hypothesis. This has nothing to do with if it is true or false.

Type II error is occurs when you accept a false null hypothesis. The probability of this error is denoted by beta which relies on sample size and population variance.

The probability of rejecting is equal to one minu beta. i.e it is the researchers goal to reject a false null hypothesis.

Let a1equals[Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 2 3rd Row 1st Column negative 1 EndMatrix ], a2equals[Start 3 By 1 Matrix 1st Row 1st Column negative 7 2nd Row 1st Column negative 7 3rd Row 1st Column 2 EndMatrix ], and bequals[Start 3 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column negative 22 3rd Row 1st Column h EndMatrix ]. For what value(s) of h is b in the plane spanned by a1 and a2?

Answers

Answer:

For h= 25, b in the plane spanned by a1 and a2

Step-by-step explanation:

$a1= \left[\begin{array}{c}1\n2\n-1\end{array}\right] \na2 = \left[\begin{array}{c}-7\n-7\n2\end{array}\right] \n\nb = \left[\begin{array}{c}3\n-22\nh\end{array}\right]$

we have to find value of h for which b in the plane spanned by a1 and a2.

For this the linear systems given by the following augmented matrix must be consistent.

$\left[\begin{array}{cc|c}1&-7&3\n2&-7&-22\n-1&2&h\end{array}\right]$

Reduce the augmented matrix into row echelon form:

$R_(2) - 2R_(1) , R_(3) + R_(1)\n\n\left[\begin{array}{cc|c}1&-7&3\n0&7&-28\n-0&-5&h+3\end{array}\right]\n\n7R_(3)+5R_(2)\n\n\left[\begin{array}{cc|c}1&-7&3\n0&7&-28\n-0&0&7h-175\end{array}\right]$