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3 years ago

There are thirty seven students in the Service Club. They have to vote to send 4 representatives to a board meeting:

Mathematics

1 answer:

Molodets [167]3 years ago

3 0

Picking 4 students out of 37 students would be a permutation.

This is written with the total students first, the letter P then the number of students getting picked:

The answer would be D. 37P4

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They 1107 Kids divided by 56 Teams how many kids are in a team

Montano1993 [528]

Answer:

It has to be less than 20 kids per team.

Step-by-step explanation:

Because 1107/56 is 19.767857142.

7 0

3 years ago

Read 2 more answers

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software,

vichka [17]

Answer:

A(-1,0) is a local maximum point.

B(-1,0) is a saddle point

C(3,0) is a saddle point

D(3,2) is a local minimum point.

Step-by-step explanation:

The given function is

$f(x,y)=x^3+y^3-3x^2-3y^2-9x$

The first partial derivative with respect to x is

$f_x=3x^2-6x-9$

The first partial derivative with respect to y is

$f_y=3y^2-6y$

We now set each equation to zero to obtain the system of equations;

$3x^2-6x-9=0$

$3y^2-6y=0$

Solving the two equations simultaneously, gives;

$x=-1,x=3$ and $y=0,y=2$

The critical points are

A(-1,0), B(-1,2),C(3,0),and D(3,2).

Now, we need to calculate the discriminant,

$D=f_{xx}(x,y)f_{yy}(x,y)-(f_{xy}(x,y))^2$

But, we would have to calculate the second partial derivatives first.

$f_{xx}=6x-6$

$f_{yy}=6y-6$

$f_{xy}=0$

$\Rightarrow D=(6x-6)(6y-6)-0^2$

$\Rightarrow D=(6x-6)(6y-6)$

At A(-1,0),

$D=(6(-1)-6)(6(0)-6)=72\:>\:0$ and $f_{xx}=6(-1)-6=-18\:$

Hence A(-1,0) is a local maximum point.

See graph

At B(-1,2);

$D=(6(-1)-6)(6(2)-6)=-72\:$

Hence, B(-1,0) is neither a local maximum or a local minimum point.

This is a saddle point.

At C(3,0)

$D=(6(3)-6)(6(0)-6)=-72\:$

Hence, C(3,0) is neither a local minimum or maximum point. It is a saddle point.

At D(3,2),

$D=(6(3)-6)(6(2)-6)=72\:>\:0$ and $f_{xx}=6(3)-6=12\:>\:0$

Hence D(3,2) is a local minimum point.

See graph in attachment.

3 0

3 years ago

An angle is created from points C, A, and B with vertex A. An arc is drawn from point A and intersects rays AC and AB. The inter

Minchanka [31]

Answer:

Bisecting an angle ⇒ answer a

Step-by-step explanation:

* Lets revise the steps of bisecting an angle

- How to construct a bisector of angle XYZ

1. Open the compass to any width, and place its pin at the angle’s

vertex Y and draw an arc cuts the two rays of the angle YX and YZ

at two points M and N respectively

2. Open the compass to another width and place its pin at M and draw

an arc between the two rays YX and YZ

3. Without changing the width of the compass place its pin at N and

draw another arc intersects the arc from M at point Q

4. Join YQ which is the bisector of angle XYZ

* Now lets compare these steps by the steps of the question

∵ The vertex of the angle ABC is A represented by Y

∵ The rays of the angle AC and AB represented by YX and YZ

∵ Points D , E represented by points M , N

∴ The construction is " Bisecting an angle "

7 0

3 years ago

Eduardo has purchased a home with an assessed value of $179,000. The property tax rate in his area is 2.3%. What is his monthly

ad-work [718]

Answer:

C. 343.08

Step-by-step explanation:

Convert the tax rate into a decimal and multiply by the house price:

.023(179,000) = 4,117

Divide by 12 (to get monthly rate):

4,117/12 ≈ 343.08

Option C should be the correct answer.

7 0

3 years ago

Colton wrote a ratio comparing the number of sports video games that he owns to the number of driving video games that he owns a

alina1380 [7]

Answer:

there are no other ratios shown but 8:6,12:9,16:12,20:15,and 24:18 are all equivalent

Step-by-step explanation:

smile time

8 0

3 years ago