What Is the factored form of the polynomial
x^2-12x+27

Answer:

[tex]P(pink) = P(pink |\ female) = 0.6[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}{} & {Male} & {Female} & {Pink} & {156} & {72} \ \\ {Yellow} & {104} & {48} \ \end{array}[/tex]

Required

Why [tex]prefers\ pink\ lemonade[/tex] and [tex]female[/tex] are independent

First, calculate [tex]P(pink |\ female)[/tex]

This is calculated as:

[tex]P(pink |\ female) = \frac{n(pink\ \&\ female)}{n(female)}[/tex]

[tex]P(pink |\ female) = \frac{72}{48+72}[/tex]

[tex]P(pink |\ female) = \frac{72}{120}[/tex]

[tex]P(pink |\ female) = 0.6[/tex]

Next, calculate [tex]P(pink)[/tex]

[tex]P(pink) = \frac{n(pink)}{n(Total)}[/tex]

[tex]P(pink) = \frac{156 + 72}{156 + 72 + 104 + 48}[/tex]

[tex]P(pink) = \frac{228}{380}[/tex]

[tex]P(pink) = 0.6[/tex]

So, we have:

[tex]P(pink) = P(pink |\ female) = 0.6[/tex]

Hence, they are independent

Answer:

P(pink lemonade | female) = P(pink lemonade) = 0.6.

Step-by-step explanation:

A

Answer:

f(g(x)) =

[tex] {x}^{6} + 6 {x}^{4} + 8x^{2} + 2[/tex]

Step-by-step explanation:

put g(x) instead of any x in f(x)

[tex] {(x ^{2} + 2) }^{3} - 4( {x}^{2} + 2) + 2[/tex]

Answer:

0 zero

Step-by-step explanation:

you must find gf(x) first

g[ f(x) ] = g [ 2 + 1 ]

= 3-2+x which is you sub fx tu g

g [ f (-1) ] = 3-2-1

=0

Answer:

a) 83,b) -4,c) 48,d) 16,e) 8

Answer:

f(x) = (x + 4)^2 - 5

Step-by-step explanation:

Parent function: f(x) = x^2

To show this in a way that may look more familiar, f(x) = 1(x - 0)^2 + 0

Vertex form: f(x) = a(x - h)^2 + k

We know a = 1, because the slope is the same as the parent function.

Vertex: (h,k)

We can see that the vertex of the graph is (-4, -5)

So h = -4 and k = -5

Now all we need to do is plug the variables into our equation.

f(x) = a(x - h)^2 + k

f(x) = 1(x + 4)^2 - 5

f(x) = (x + 4)^2 - 5

Answer:

There is no actual question here, this is just a statement.

re-read the question .... i assume it says "what is the highest that she will get during a dive?"

highest point is at t = 33/32  

– 16(33/32)^2 + 33(33/32) + 4 =

62.015625

Step-by-step explanation:

Lindsey will be 30 feet in the air at approximately 1.09 seconds and 2.48 seconds.

To find the time at which Lindsey will be 30 feet in the air, we need to solve the quadratic equation y = -16x² + 33x + 45 for x when y = 30.

Setting y equal to 30, we have:

30 = -16x² + 33x + 45

Rearranging the equation, we have:

16x² - 33x - 15 = 0

To solve this quadratic equation, we can factor or use the quadratic formula. In this case, factoring might be more challenging, so we'll use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values from our equation, we have:

x = (-(-33) ± √((-33)² - 4(16)(-15))) / (2(16))

Simplifying, we get:

x = (33 ± √(1089 + 960)) / 32

x = (33 ± √(2049)) / 32

Calculating the square root of 2049, we have:

x = (33 ± √(2049)) / 32

x ≈ 1.09 or x ≈ 2.48

To learn more about quadratic equation click on,

https://brainly.com/question/27958207

#SPJ2

Complete question is:

Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x² + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.

At what time will Lindsey be 30 feet in air?

Answer:

Okay

Step-by-step explanation:

Answer:

yes is correct 6/6 = 1 / 3*2=6 =1

Answer:

nonsense. what's the difference between 6/6 or 1 .

Answer: B

Step-by-step explanation:

To find the values of x, we first need to write the function into an equation. We can derive 2 equations from the problem.

Equation 1: y=2|x+6|-4

Equation 2: y=6

Now, we can substitute.

2|x+6|-4=6

Let's solve for x.

2|x+6|-4=6        [add both sides by 4]

2|x+6|=10          [divide both sides by 2]

|x+6|=5              [subtract both sides by 6]

x=-1

Now that we know x=-1 is one of the solutions, we can eliminate C and D.

We know that the absolute value makes the number inside positive always. Therefore, let's solve for x with -5 instead.

|x+6|=-5              [subtract both sides by 6]

x=-11

Therefore, we know that B is the correct answer.

Answer:

29/20 or 1 9/20 or 1.45

Answer:

[tex]\frac{1}{5}+\frac{3}{4}+\frac{1}{2}[/tex]

lease common multiplier of 5,4,2 is 20

[tex]\frac{4}{20}+\frac{15}{20}+\frac{10}{20}[/tex]

[tex]Add\: 4+15+10= 29[/tex]

[tex]1/5+3/4+1/2=29/20[/tex]

[tex]Answer :\frac{29}{20}[/tex]

--------------------------

hope it helps

have a great day!!

Answer: I believe but not 100% sure

1) C

2) B

Step-by-step explanation:

The pH value of the apple juice is 3.5, option C) is the correct answer.

The pH value of the ammonia is 8.9, option D) is the correct answer.

The pH of a solution is defined as the logarithm of the reciprocal of the hydrogen ion concentration  [H+] of the given solution.

From the formular;

pH = -log[ H⁺ ]

Given the data in the question.

For the Apple juice;

pH = -log[ H⁺ ]

pH = -log[ 0.0003 ]

pH = 3.5

The pH value of the apple juice is 3.5

Option C) is the correct answer.

For the ammonia;

pH = -log[ H⁺ ]

pH = -log[ 1.3 × 10⁻⁹]

pH = 8.9

The pH value of the ammonia is 8.9

Option D) is the correct answer.

Learn more about pH & pOH here: brainly.com/question/17144456

#SPJ2

Answer:

74.8% approximately

Step-by-step explanation:

Area of circle is pi×r^2=pi×4^2=16pi=50.27 approximately

Area of pentagon (assumption regular pentagon)=5/2×apothem×side length=5/2(3.2)(4.7)=37.6

So the probability that it lands in the red is 37.6/50.27 approximately =74.8% approximately

Answer:

lâp bảng  

Step-by-step explanation:

X=0 thì xác suất lấy ra được sản phẩm tốt là 5*30%=1,5%

X =1 thì xác suất lấy ra được là 1* 70%*4*30%=0,84%

X=2 thì xác suất lấy ra được sản phẩm tốt là 2*70%*3*30%=1,26%

X=3 thì xác suất lấy ra được sản phẩm tốt là 3*70%*2*30%=1,26%

X=4 thì xác suất lấy ra được sản phẩm tốt là 4*70%*1*30%=0,84%

X=5 thì xác suất lấy ra được sản phẩm tốt là 5*70%=3,5%

X 0 1 2 3 4 5

P 1,5 0,84 1,26 1,26 0,84 3,5

b,

E(x)= 1,5*0+ 0,84*1+1,26*2+1,26*3+0,84*4+3,5*5=28

E(x^2)=1,5*0^2+0,84*1^2+1,26*2^2+1,26*3^2+0,84*4^2+3,5*5^2=118,16

===> V(x)= (E(x))^2-E(x^2)=28^2-118,16=665,84

Answer:

Step-by-step explanation:

Find the slope of QR. From that we can find the the slope of the line perpendicular to QR.

Q(-2, -5)   & R(8,1)

[tex]Slope \ = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-[-5]}{8-[-2]}\\\\=\frac{1+5}{8+2}\\\\=\frac{6}{10}\\\\=\frac{-3}{5}[/tex]

So, the slope of the line perpendicular to QR =  -1/m - 1÷ [tex]\frac{-5}{3} = -1*\frac{-3}{5}=\frac{3}{5}[/tex]

Bisector of QR divides the line QR to two half. We have find the midpoint of QR.

Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

               [tex]=(\frac{-2+8}{2},\frac{-5+1}{2})\\\\=(\frac{6}{2},\frac{-4}{2})\\\\=(3,-2)[/tex]

slope = 3/5  and the required line passes through (3 , -2)

y - y1 = m(x-x1)

[tex]y - [-2] = \frac{3}{5}(x - 3)\\\\y + 2 = \frac{3}{5}x-\frac{3}{5}*3\\\\y=\frac{3}{5}x-\frac{9}{5}-2\\\\y=\frac{3}{5}x-\frac{9}{5}-\frac{2*5}{1*5}\\\\y=\frac{3}{5}x-\frac{9}{5}-\frac{10}{5}\\\\y=\frac{3}{5}x-\frac{19}{5}[/tex]

Answer:

rs288

Step-by-step explanation:

MP of the article = 210×120100×10087.5= Rs.288210×120100×10087.5= Rs.288

Part of solved Discount questions and answers : >> Aptitude >> Discount

Answer:

not sure, sorry : p

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

I assume you want x, so I simply rearranged the terms, subtracted, and simplified.

Answer:

its to pixelated

Step-by-step explanation:

Answer:

6/4 or 1 1/2

Step-by-step explanation:

You have to use the Keep Change Flip technique.

Keep 3/4.

Change the division symbol to a multiplication one

Flipi 1/2 to 2/1

and when you multiply the answer is 6/4 = 1 1/2

Answer:

[tex]y\ =\ \ \tan\theta\ +2[/tex]

Step-by-step explanation:

Answer:

[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex]   or   [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]

Step-by-step explanation:

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

We have a = 3; b = -1; c = 4.

[tex] x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(4)}}{2(3)} [/tex]

[tex]x = \dfrac{1 \pm \sqrt{1 - 48}}{6}[/tex]

[tex]x = \dfrac{1 \pm \sqrt{-47}}{6}[/tex]

[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex]   or   [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]

Answer:

2x-y-1=0

Step-by-step explanation:

.

Answer:

no hablo inglés wey perdón corona y gracias

Answer:

3264:221

Step-by-step explanation:

If by last year there were 221 students and 12 teachers at Hilliard School, then;

221students = 12teachers

To find the equivalent ratio for 272students, we can say;

272students = x teachers

Divide both expressions

221/272 = 12/x

Cross multiply

221 * x = 272 * 12

221x = 3264

x = 3264/221

x = 3264:221

This gives the required proportion

A prime number has exactly two factors, 1 and itself. For example, 13 is a prime number because the only factors of 13 are 1 and 13. The number 8 is not prime because it has four factors: 1, 2, 4 and 8. The number 1 is not a prime number because it only has one factor (itself).

Hello,

let's assume a=the length and b the width.

[tex]\left\{\begin{array}{ccc}a&=&2*b\\2(a+b)&=&60\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&2*b\\a+b&=&30\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&2*b\\3b&=&30\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b&=&10\\a&=&20\\\end{array}\right.\\\\\\Area=10*20=200\ (ft^2)\\[/tex]

Answer:

[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z

Step-by-step explanation:

Given

[tex]$$A _ { 0 } = \{n \in \mathbf { Z } | n = 4 k$$,[/tex] for some integer k[tex]\}[/tex]

[tex]$$A _ { 1 } = \{ n \in \mathbf { Z } | n = 4 k + 1$$,[/tex] for some integer k},

[tex]$$A _ { 2 } = { n \in \mathbf { Z } | n = 4 k + 2$$,[/tex] for some integer k},

and

[tex]$$A _ { 3 } = { n \in \mathbf { Z } | n = 4 k + 3$$,[/tex]for some integer k}.

Required

Is [tex]\{0, 1, 2, 3\}[/tex] a partition of Z

Let

[tex]k = 0[/tex]

So:

[tex]$$A _ { 0 } = 4 k[/tex]

[tex]$$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0[/tex]

[tex]$$A _ { 1 } = 4 k + 1$$,[/tex]

[tex]A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1[/tex]

[tex]A _ { 2 } = 4 k + 2[/tex]

[tex]A _ { 2} = 4 *0 + 2$$ \to A_2 = 2[/tex]

[tex]A _ { 3 } = 4 k + 3[/tex]

[tex]A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3[/tex]

So, we have:

[tex]\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}[/tex]

Hence:

[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z