There are 3 students on a team for a relay race. How many teams can be made from 32 students?

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y,  λ) = x + y +  λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx =  λ*y + 1

dL/dy =  λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate  λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

Answer:

Quadratic

Step-by-step explanation:

It looks like it’s forming a very wide arch so quadratic formulas are arches

The equation of the regression line model for the data plot determines a quadratic equation

The connection between the independent (x) and dependent (y) variables in the graph can be graphically represented using regression lines.

In a linear model, the terms are added rather than multiplied, divided, or provided as a non-algebraic function, as has been the case thus far in this section. Analysis of experimental, monetary, and biological data as well as complex system prediction are both possible using linear modelling.

A statistical technique used to build a linear model is called linear regression. The model explains how one or more independent variables Xi relate to a dependent variable y (also known as the response) (called the predictors). The distance between each data point and the regression line is called a residual.

Given data ,

Let the linear regression line be represented as A

Now , the value of A is

Let the first coordinate on the graph be P ( 1 , 5.5 )

Let the second coordinate on the graph be Q ( 2 , 6 )

And , the data plots on the graph represents a curve or parabolic equation

So , it is a quadratic equation

Hence , the data plot of the regression line is quadratic

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Answer:

x=10

Step-by-step explanation:

since there are 3 zeroes in 1,000

x is 10

because 10^3=1000

Answer:

10

Step-by-step explanation:

Answer:   10°

__________________________________________________________

We are given:

Sin(6θ)  = Cos(3θ)

Solving for θ:

Simplifying Cos(3θ):

We know that:  

Cos(θ) = Sin(90-θ)

So, we can say that:

Cos(3θ) = Sin(90 - 3θ)

Finding the value of θ:

Sin(6θ) = Cos(3θ)

Sin(6θ) = Sin(90 - 3θ)                             [Since Cos(3θ) = Sin(90 - 3θ)]

6θ = 90 - 3θ                                            [If Sin(θ) = Sin(A) ; θ = A]

9θ = 90                                                   [adding 3θ on both sides]

θ = 10°                                                     [dividing both sides by 9]

Answer:

0.0475 or 4% professional language translators get paid less than $250 per hour

Step-by-step explanation:

Mean = 320

Standard Deviation = 41.75

We need to find proportion of professional language translators get paid less than $250 per hour i.e P(x<250)

First we will find value of z

Using formula: [tex]z=\frac{x-\mu}{\sigma}[/tex]

We have x=250, finding z

[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{250-320}{41.75}\\z=-1.67[/tex]

Now we will find P(z<-1.67) by looking into the normal distribution table

[tex]P(z<-1.67)=0.0475\\[/tex]

So,0.0475 or 4% professional language translators get paid less than $250 per hour

Answer:

1.44

Step-by-step explanation:

Answer:

the answer is 1.44

Step-by-step explanation:

Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.

                      Your welcome

Answer:

$40.23

Step-by-step explanation:

Answer:

40.23

Step-by-step explanation:

easy just do 13.5*2.98

Answer:

$36.52

you're welcome :)

Answer:

Step-by-step explanation:

hi

Answer:

B

Step-by-step explanation:

Answer:

1.7

Step-by-step explanation:

2.5÷1.5

5/3

1.66666

1.7

The divisions of 2.5 divided by 1.5 gives to 5/3 or 1.6667.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Given:

2.5 divided by 1.5

So, 2.5 / 1.5

= 25 x 10 / 15 x 10

= 25/15

= 5 x 5 / 5 x 3

= 5/3

Hence, the divisions results to 5/3 or 1.6667

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Answer:

1. 4

2. 20

3. 80

Step-by-step explanation:

Answer:

-2

Hope this helps,

PumpkinSpice1

The slope of the line will be ( -1 / 2 ). The correct option is C.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The two points are (0,3) and ( 6,0). The slope of the line will be calculated by using the formula below;-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 0 - 3 ) / ( 6 - 0 )

Slope = -3 / 6 = -1 / 2

Therefore, the slope of the line will be ( -1 / 2 ). The correct option is C.

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Answer:

112

the answer is 112 :)))))

Answer:

-2

or

-2/1

Explanation:

**Slope = rise/run**

By counting the distance between the points, from (0,3) to (1,1) , it went down 2 units and right by 1 unit

Answer:

m= -2

Step-by-step explanation:

Pick two points and subtract the y coordinates, then subtract the x coordinates, (0,3) and (1,1)  or (1,1) and (2,-1)

[tex]m = \frac{y_{2_ } - y_{1} }{x_{2} -x_{1} } = \frac{1-3}{1-0} = \frac{-2}{1} = -2[/tex]      [tex]\frac{-1-1}{2-1} = \frac{-2}{1} = -2[/tex]

Answer:

(C / n) + 2

Step-by-step explanation:

Amount spent (C) = 42

Number of friends (n) = 6

Coupon on ticket = $2

Original price of ticket will be :

Cost per coupon ticket = (Total amount spent / number of friends)

(Total amount spent / number of friends) + coupon on ticket

= (C / n) + 2

= (42 /6) + 2

= 7 + 2

= 9

Answer:

9 boys 9 girls

Step-by-step explanation:

18 = 2x

9

Answer:

It's C

Step-by-step explanation:

Answer:

-$14.50

Step-by-step explanation:

This is easily solved on a calculator.

-34.50 + 20.00 = -14.50

Answer:

41/200

This is solved and put in standard form

Answer:

Using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]

Step-by-step explanation:

We need to used distributive property to solve (x+12)8

The distributive property of multiplication or addition states that: [tex]a(b+c)=ab+ac[/tex]

Using the property:

[tex](x+12)8\\=8x+8*12\\=8x+96[/tex]

So, using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]

Answer:

DE, BC, BA, CA

Step-by-step explanation:

basically just find the ones that do not cross and those are parellel.

Answer:

Um so then what is the question???

Step-by-step explanation:

Answer:

`She grew 5.75?

Step-by-step explanation:

I don't really know what the full question is, but if I saw that in a test and nothing else than I would put what the answer says lol

Answer and step-by-step explanation:

cos = adj/hyp (in a right triangle)

cos0 = 3/5

adj = 3

hyp = 5

opp = sqrt( 5^2 - 3^2) = sqrt( 25-9) = sqrt(16) = 4 (Pythogorean theorem)

tan0 = opp/adj = 4/3

Answer:

[tex]\boxed {\boxed {\sf tan( \theta)=4/3}}[/tex]

Step-by-step explanation:

Cosine is equal to adjacent over hypotenuse.

We are given: cosθ=3/5

We want to find tanθ. Tangent is equal to opposite over adjacent.

We need to find the other leg of the triangle, which is the "opposite". Use Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

The hypotenuse (c) is 5.

[tex]a^2+b^2=5^2[/tex]

One leg (a) is 3, the other (b) is unknown.

[tex]3^2+b^2=5^2[/tex]

Evaluate all the exponents.

[tex]9+b^2=25[/tex]

Subtract 9 from both sides of the equation.

[tex]9-9+b^2=25-9[/tex]

[tex]b^2=16[/tex]

Take the square root of both sides.

[tex]\sqrt{b^2} =\sqrt{16}[/tex]

[tex]b=4[/tex]

Now we know the "opposite" is 4. We can find the tangent now.

[tex]tan(x)=opposite/adjacent[/tex] (opposite=4, adjacent=3)

[tex]tan( \theta)=4/3[/tex]

The tangent of theta is 4/3

Answer:

3.73

Step-by-step explanation:

56/15

3 11/15

3.73

Answer:

1. x>-1

2. x<4

3. x<-1

4. x>-2

5. x<-3

6. x<7

Step-by-step explanation:

1. 2x>-2  Divide both sides by 2.

  /2   /2

x>-1

2. 4x<16  Divide both sides by 4.

   /4   /4

x<4

3. x+4<3 Subtract both sides by 4.

      -4  -4

x<-1

4. 5x>-10  Divide both sides by 5.

  /5     /5

x>-2

5. 3x<-9   Divide both sides by 3.

   /3   /3

x<-3

6. x-4<3  Add 4 to both sides.

    +4 +4

x<7

Hope this helps you out...next time, try to figure it out yourself without asking a lot of questions. By looking at one example, you can probably apply what to do for the other inequalities.