Jean Paul is an interior designer who is working with a difficult client. Part of his design requires that he put 11 colored vases in a row on a shelf. He has 3 identical blue vases, 2 identical green vases, 4 identical red vases, a purple vase and a yellow vase. He has put up 4 different arrangements of the vases that his client complained about. As he begins to put up the fifth arrangement, he wonders how many different arrangements he might have to go through before his client complains about all of them. How many different arrangements could Jean Paul make

We are given the equations:

x - 3y = 2

3x - 4y = 0

writing the system as matrices

[tex]\left[\begin{array}{ccc}1&-3\\3&-4\end{array}\right][/tex][tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}2\\0\\\end{array}\right][/tex]

which is in the form:

AX = B

solving for X(the matrix holding the variables), we get:

X = (A⁻¹)B

Finding A⁻¹:

now, to do this, we need to find the inverse of A

[tex]\left[\begin{array}{ccc}w&x\\y&z\end{array}\right]^{-1} = \frac{1}{wz-xy}\left[\begin{array}{ccc}z&-x\\-y&w\end{array}\right][/tex]

using this formula to find the inverse of matrix A:

[tex]A^{-1} = \frac{1}{(1*-4)-(-3*3)}\left[\begin{array}{ccc}-4&3\\-3&1\end{array}\right][/tex]

[tex]A^{-1} = \frac{1}{5}\left[\begin{array}{ccc}-4&3\\-3&1\end{array}\right][/tex]

Matrix X:

We know that:

X = A⁻¹B

[tex]X = \frac{1}{5}\left[\begin{array}{ccc}-4&3\\-3&1\end{array}\right] * \left[\begin{array}{ccc}2\\0\end{array}\right][/tex]

[tex]X = \frac{1}{5}\left[\begin{array}{ccc}-8\\-6\end{array}\right][/tex]

since matrix X is just a matrix with the variables

[tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}\frac{-8}{5}\\\frac{-6}{5}\end{array}\right][/tex]

x = -8/5

y = -6/5

Answer:

see below

Step-by-step explanation:

We want where  both inequalities are true

y > -3

-2 >-3  this is true

y ≥ 2/3x -4

-2≥ 2/3*3 -4

-2 ≥ 2 -4

-2≥ -2

This is true

This is is the graph

Answer:

[tex]\boxed{\sf Option \ 3}[/tex]

Step-by-step explanation:

[tex]\sf The \ values \ must \ be \ true \ for \ both \ inequalities.[/tex]

[tex]x = 3\\y = -2[/tex]

[tex]y>-3\\-2>-3\\ \sf True[/tex]

[tex]y\geq \frac{2}{3}x-4 \\ -2\geq \frac{2}{3}(3)-4\\2\geq 2-4\\-2\geq-2 \\ \sf True[/tex]

given: [tex] Ac=\frac{vt2}r \quad vt=2 \quad r=2[/tex]

$\therefore Ac=\frac{(2)2}{2}=2$

The sequence is arithmetic, since the forward difference between consecutive terms is -9.

7 - 16 = -9

-2 - 7 = -9

etc.

This means the sequence has the formula

[tex]a_n=16-9(n-1)=25-9n[/tex]

The sum of the first 30 terms is

[tex]\displaystyle\sum_{n=1}^{30}a_n=25\sum_{n=1}^{30}1-9\sum_{n=1}^{30}n[/tex]

Recall the formulas,

[tex]\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n[/tex]

[tex]\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2[/tex]

Then the sum we want is

[tex]\displaystyle\sum_{n=1}^{30}a_n=25\cdot30-\frac{9\cdot30\cdot31}2=\boxed{-3435}[/tex]

Answer:

2.7 in²

Step-by-step explanation:

Since ∆BAC and ∆EDF are similar, therefore, the ratio of their area = square of the ratio of their corresponding side lengths.

Thus, if area of ∆EDF = x, area of ∆BAC = 6 in², EF = 2 in, BC = 3 in, therefore:

[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]

[tex] \frac{6}{x} = (1.5)^2 [/tex]

[tex] \frac{6}{x} = 2.25 [/tex]

[tex] \frac{6}{x}*x = 2.25*x [/tex]

[tex] 6 = 2.25x [/tex]

[tex] \frac{6}{2.25} = \frac{2.25x}{2.25} [/tex]

[tex] 2.67 = x [/tex]

[tex] x = 2.7 in^2 [/tex] (nearest tenth)

Answer:

x = 4

Step-by-step explanation:

6x + 3 = 2x + 19  ------ subtract 3 both sides

6x + 3 - 3 = 2x + 19 - 3   simplify

6x = 2x + 16         ------ subtract 2x both sides

6x - 2x = 2x + 16 - 2x      simplify

4x = 16

x = 16 / 4

x = 4

Answer: x = 4

Step-by-step explanation: If the variable appears on both sides of the equation, we put the variables together on one side of the equation and the numbers together on the other side of the equation.

So let's put our variables on the left side by first subtracting

2x from both sides of the equation to get 4x + 3 = 19.

Next, we subtract 3 from both sides to get 4x = 16.

Finally, we divide both sides by 4 to get x = 4.

Answer: C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello,

[tex]f(g(x))=\dfrac{8}{x^2}+4[/tex]

So if we take

[tex]f(x)=\dfrac{8}{x}+4 \ \ and \\\\g(x)=x^2\\ \\f(g(x))=\dfrac{8}{g(x)}+4=\dfrac{8}{x^2}+4[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Its a binomial

[tex]\\ \sf\longmapsto x^2-6x+5=0[/tex]

If zeros be alpha and beta

[tex]\\ \sf\longmapsto \alpha+\beta=\dfrac{-b}{a}[/tex]

[tex]\\ \sf\longmapsto \alpha+\beta=\dfrac{-(-6)}{1}[/tex]

[tex]\\ \sf\longmapsto \alpha+\beta=6[/tex]

the sum of the factors of the trinomial [tex]x^2-6x+5[/tex] is -6

Given :

A trinomial [tex]x^2-6x+5[/tex]

The given trinomial is in the form of [tex]ax^2+bx+c[/tex]

Compare the given trinomial with standard form and write the value of a,b,c

a=1, b=-6 and c=5

Sum of the factors of the trinomial is [tex]\frac{b}{a} =-\frac{-6}{1} =-6[/tex]

So, the sum of the factors of the trinomial is -6

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Answer:

Step-by-step explanation:

Given a plane passing through the point(1, 5,-1) and perpendicular to the vector (1, 5, 1), the equation of the plane can be expressed generally as;

a(x-x₀)+b(y-y₀)+c(z-z₀) = 0 where (x₀, y₀, z₀) is the point on the plane and (a, b,c) is the normal vector perpendicular to the plane i.e (1,5,1)

Given the point P (1, 5, -1) and the normal vector n(1, 5, 1)

x₀ = 1, y₀ =5, z₀ = -1, a = 1, b = 5 and c = 1

Substituting this point in the formula we will have;

a(x-x₀)+b(y-y₀)+c(z-z₀) = 0

1(x-1)+5(y-5)+1(z-(-1)) = 0

(x-1)+5(y-5)+(z+1) = 0

x-1+5y-25+z+1 = 0

x+5y+z-1-25+1 = 0

x+5y+z-25 = 0

x+5y+z = 25

The final expression gives the equation of the plane.

Answer:

the shorter side = 1526

the longer side = 763

area = 1164338

Step-by-step explanation:

lets say

a=length

b = width

a + 2b = 3052

this is the perimeter

such that

a = 3052 - 2b

the area of a rectangle is a*b

= (3052 - 2b)b

= 3052b - 2b²

we differentiate this to get:

= 3052 - 4b

such that

3052 = 4b

divide through by 4, to get b, the width

3052/4 = 763

b = 763

put the value of b into a

a = 3052 - 2b

a = 3052 - 2(763)

a = 3052 - 1526

a = 1526

therefore

the shorter side = 1526

the longer side = 763

area = a x b

area = 1526 x 763

area = 1526 x 763

= 1164338

Answer:

Jargon that they both understand will be used.

Step-by-step explanation:

Jargon that they both understand will be used.

Jargon is a literary term that is defined as the use of specific phrases and words in a particular situation, profession, or trade. The use of jargon becomes important in prose or verse or some technical pieces of writing, when the writer plans to convey something only to the readers who are aware of these terms. Some of such examples are:

Due diligence: This is a business term, which refers to the research that should be done before making an important business decision.

AWOL: Short for "absent without leave," AWOL is military jargon used to describe a person whose whereabouts is unknown.

Answer:

y=2(x-1)+5

Step-by-step explanation:

We know that it is 5 dollars for the first minute so we know the equation will start off with +5.

Than for the rest of the minutes, we have to make sure to subtract one from them, because the first number is worth 3 dollars more. Which is why it is x-1.

Then we multiply the new value times 2, because each additional minute is 2 dollars more.

Answer:

C

Step-by-step explanation:

3*3^2+8/2-(4+3)=27+4-7=24

Answer:

24

Step-by-step explanation:

Remember the order of operations: PEMDAS

P=Parenthesis  

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

(Now you break it down)

3x3(2)+8/2-(4+3)

3x3(2)+8/2-7

3x9+8/2-7

27+8/2-7

27+4-7

31-7

Then you get your answer! (24)

Answer:

what three options bro where are the options

Answer:

9 hours, 11 hours, 19 hours.

Step-by-step explanation:

Z will stay the same since the 2 will divide into 1

Refer to the attaachment

Answer:

[tex]106 \frac{3}{5}[/tex]

Explanation:

Convert any mixed numbers to fractions.

Reduce fractions where possible.

Then your initial equation becomes:

[tex]\frac{26}{5} \times \frac{-31}{3}[/tex]

Next, apply the fractions formula for multiplication. Formula below:

[tex]\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d}[/tex]

[tex]= \frac{26 \times -41}{5 \times 2}= \frac{-1066}{10}[/tex]

Simplifying -1066/10, (you can do this by using division) the answer is:  

[tex]106 \frac{3}{5}[/tex]

Answer:

-3 1/3

Step-by-step explanation:

5 2/10 x -10 1/3

10/10 x -10/3

1 x-10/3

-10/3

-3 1/3

your question is unclear. I think I understand it correctly

Answer:

The probability is  [tex]P(X > x ) = 0.19215[/tex]

Step-by-step explanation:

From the question we are told that

   Th The population mean [tex]\mu = \$ 1,999[/tex]

    The  standard deviation is  [tex]\sigma = \$ 574[/tex]

    The  values considered is  [tex]x = \$ 2,500[/tex]

Given that the distribution of the amounts spent follows the normal distribution then the  percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as

    [tex]P(X > x ) = P(\frac{ X - \mu}{\sigma } > \frac{ x - \mu}{\sigma } )[/tex]

Generally  

            [tex]X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

So

      [tex]P(X > x ) = P(Z > \frac{ x - \mu}{\sigma } )[/tex]

substituting values

      [tex]P(X > 2500 ) = P(Z > \frac{ 2500 - 1999}{574 } )[/tex]

      [tex]P(X > 2500 ) = P(Z >0.87 )[/tex]

From the normal distribution table the value of [tex]P(Z >0.87 )[/tex] is  

       [tex]P(Z >0.87 ) = 0.19215[/tex]

Thus  

       [tex]P(X > x ) = 0.19215[/tex]

Answer with explanation:

Sales    Commission(10% of sales)

$2,200      0.1×$2,200= $220  

$2,000       0.1× $2,000= $200

$3,134      0.1×$3,134=$313.4

$2,417         0.1×$2,417=$241.7                  

$2,579        0.1×$2,579 =$257.9

The completed table is given as follows

Day   Sales    Commission      Non-Sales pay        Earning

                    (10% of sales)                           (Commission +Non Sales pay)

Mon  $2,200      $220             $9.50                $220+ $9.50=$229.50

Tue   $2,000         $200                 $9.50                $200 +$9.50=$209.50

Thurs  $3,134      $313.4               $9.50                $313.4+ $9.50=$322.9  

Fri     $2,417         $241.7               $9.50                $241.7+$9.50= $251.2

Sat    $2,579        $257.9                 $9.50                $257.9+$9.50=$267.4

Answer:

The Variable has a coefficient.

Step-by-step explanation:

Answer: Negative sign

Adding two negative values results in another negative value.

-1.69 + (-1.69) = -3.38

It's like starting $1.69 in debt and then adding 1.69 dollars of more debt. You'll slide further into debt being $3.38 in debt total.

The sign is negative as the value of -1.69 + (-1.69) is -3.38.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-1.69 + (-1.69)

= -1.69 - 1.69

= -3.38

This means,

The sign is negative.

Thus,

The value of -1.69 + (-1.69) is -3.38.

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Answer:

1/256

Step-by-step explanation:

[tex]4^{-4}[/tex]

[tex](1/4)^{4}[/tex]

=> 1/256

Answer:

25x^2 + 40x + 16

Step-by-step explanation:

area = 5x * 5x + 5x * 4 + 5x * 4 + 4 * 4

area = 25x^2 + 40x + 16

25x² + 40x + 16 is the required equation in variable x.

What is mensuration ?

Mensuration is a branch of mathematics where we calculate length, width, area, volume, lateral surface area, total surface area.

The sum of the areas of the shaded rectangles is the total area.

By observation we can see that the four shaded rectangles together form a square.

We all know that the area of the square is (side)²

= (5x + 4)²

= 25x² + 40x + 16  this is the required equation.

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Answer:

Hello! I hope I am correct!

Step-by-step explanation:

295 feet will equal to 89.916 meters.

Steps in order to solve this problem:

First you have to multiply the length in feet by 0.3048.

295x 0.3048 or 295* 0.3048

(295 feet is equivalent to 89.916 meters!)

Will equal 89.916 meters.

Therefore, 295 feet = 89.916 meter

Hope this helps!

Brainliest would be appreciated!

By:BrainlyAnime

(Picture attached)

Answer:

[tex]5x + 2 = 100 \\ 5x = 100 - 2 \\ 5x = 98 \\ x = \frac{98}{5} \\ x = 19.6[/tex]

Answer: the answer would be x because that's the actual variable in the question then if 19.6 was not an option

Step-by-step explanation:

The value of function at x= -1 is f(-1) = 4.

We have the function as

f(x) = 2x² - 3x -1

To find the value of f(-1) when f(x) = 2x² - 3x -1, we substitute x = -1 into the expression:

f(-1) = 2(-1)² - 3(-1) - 1

      = 2(1) + 3 - 1

      = 2 + 3 - 1

      = 4.

Therefore, the value of function at x= -1 is f(-1) = 4.

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Answer:

683,280 hours is what I caculated. Is that right?

Step-by-step explanation:

Answer:

There are (365 x 24) hours for each year.

and 365 x 24 are 8760.

and 8760 x 78 are 683,280.

so, the average person does not live at least 1 Million hours, but they live more than 500 thousand hours, or 5 x 10^5 hours.

Hope it helps!

Bye!

P.S. Please give me Brainliest...

I desperately need one more Brainliest...

Answer: y=-2/3x-2/3

Step-by-step explanation:

concept to know: two lines that are perpendicular has opposite reciprocal slopes.

y=-2/3x+b

in order to find b or the y-intercept, we need to plug in a point

3=-2/3(-4)+b

3=8/3+b

b=-2/3

y=-2/3x-2/3

Hope this helps!! :)

Answer:

Step-by-step explanation:

step one :

Given that the equation of the circle is described as

[tex]x^2 + y^2 = 64[/tex]

To correctly identify the center of the circle we have to place the equation in the standard form.

the standard equation for a circle is

[tex](x-h)^2+(x-k)^2= r^2[/tex]

step two :

let us re-write the given equation so that we can compare it with the general equation of circle

[tex](x-0)^2+(x-0)^2= 8^2[/tex]

step three:

From this above equation in step two we can see that the circle has a radius of 8