Factor this polynomial expression.
3x^2 - 12x+ 12

A. (3x - 2)(x-6)
B. 3(x-2)(x + 2)
C. 3(x-2)(x-2)
D. 3(x + 2)(x + 2)

Answer:

The standard error of a proportion p in a sample of size n is given by: [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

The standard error of a proportion p in a sample of size n is given by: [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Answer:

27 by 27

Step-by-step explanation:

Let the sides be x and y. The problem is essentially asking:

Given 2(x+y)=108, maximize xy.

We know that x+y=54. By the Arithmetic Mean - Geometric Mean inequality, we can see that [tex]\frac{x+y}{2} \ge \sqrt{xy[/tex]. Substituting in x+y=54, we get [tex]27\ge\sqrt{xy}[/tex], meaning that [tex]729 \ge xy[/tex]. Equality will only be obtained when x=y (in this case it will generate the maximum for xy), so setting x = y, we can see that x = y = 27. Hence, 27 is the answer you are looking for.

Answer: Because [tex]\frac{\pi }{3} =\frac{180\°}{3} =60\°[/tex], therefore [tex]\frac{\pi }{3} =60\°[/tex].

Answer:

y=-\frac{2}{3}\approx -0.666666667

Answer:

Not very sure what you mean,

But in the provided set, 8 is the greatest number, and 1 is the smallest.

Hope this helps!!

Answer:

1/120

Step-by-step explanation:

For the first letter, you have a 1/5 chance of getting w

On the second you have a 1/4 chance to get the r

Then 1/3 and 1/2

Next you just multiply the bottom numbers

That gives you how many diffrent outcomes there can be. Put that over 1 and you have your answer.

Hope this helps <3

Answer:

90

Step-by-step explanation:

5x – 2y + (7x – y)

Combine like terms

12x -3y

Let x = 7 and y = -2

12(7) -3(-2)

84 +6

90

Answer:

90

Step-by-step explanation:

Hi there!

We are given this expression:

5x-2y+(7x-y) and we want to evaluate it if x=7 and y=-2

First, let's combine like terms, as that will make it easier for when we substitute the values into the expression

Open up the parentheses

5x-2y+7x-y

Combine like terms

12x-3y

Now substitute 7 as x and -2 as y into the expression

12(7)-3(-2)

Multiply

84+6

Add

90

Hope this helps!

I'll be referring to each of these numbers as x and y.

x + y = 4

(x^2) + (y^2) - 3(x)(y) = 76

x = 4 - y

(4 - y)^2 + (y^2) - 3(4 - y)(y) = 76

(4 - y)(4 - y) + y^2 - (3y)(4 - y) = 76

16 - 4y - 4y + y^2 + y^2 - 12y + 3y^2 = 76

16 - 20y + 5y^2 = 76

5y^2 - 20y - 60 = 0

y^2 - 4y - 12y = 0

(y - 6)(y + 2) = 0

y = 6 or -2

x = 4 - 6 = -2

x = 4 - - 2 = 6

As you can see, we got the same numbers for both x and y, -2 and 6. Therefore, the two numbers are -2 and 6. But, we can check our work to ensure that the answer is correct.

x = -2

y = 6

6 - 2 = 4

4 = 4

(-2)^2 + (6^2) - 3(-2)(6) = 76

4 + 36 - 3(-12) = 76

40 + 36 = 76

76 = 76

Hope this helps!

Answer:

X and y = -2 or 6

Step-by-step explanation:

Answer:

[tex]{ \tt{y = 3x + 7}}[/tex]

Step-by-step explanation:

General equation of a line:

[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]

m is the slope, and c is the y-intercept:

m = 3, and c = 7

Answer:

The height is 20 meters

Step-by-step explanation:

First set up the equation (Area)80=bh/2 then set up another equation, (height) h=4+2b (base). After this you can substitute h in the equation to end up with 80=(b(2b+4))/2 simplify it to get 80=b^2+2b then solve. The base is 8 meters, plug into the formula that we made before and you find the height is 20 meters.

Answer:

[tex] \frac{x}{5} [/tex]

Step-by-step explanation:

[tex]f {}^{ - 1} (x)[/tex]

means inverse.

Find the inverse of the function.

[tex]f(x) = 5x[/tex]

Replace y with and vice versa.

[tex]x = {5y}[/tex]

Solve for y

[tex] \frac{x}{5} = y[/tex]

The inverse function is

[tex] \frac{x}{5} [/tex]

JWL = JWI + IWL

87 = (2x + 24) + (3x - 12)

87 = 5x + 12

5x = 75

x = 15

Hope this helps!

The value of the variable x will be 15. Then the correct option is A.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

The measure of the angle ∠JWL will be 87°.

The angle ∠JWI and angle ∠IWL will be the linear angle.

Then the sum of the angle ∠JWI and angle ∠IWL is equal to the angle ∠JWI.

          ∠JWI + ∠IWL = 87°

(2x + 24) + (3x – 12) = 87

                    5x + 12 = 87

                           5x = 87 – 12

                           5x = 75

                             x = 75 / 5

                             x = 15

Thus, the value of the variable x will be 15.

Then the correct option is A.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ5

9514 1404 393

Answer:

  a) 2.038 seconds

  b) 5.918 meters

  c) 1.076 seconds

Step-by-step explanation:

For the purpose of answering these questions, it is convenient to put the given equation into vertex form.

  h = -4.9t² +9.2t +1.6

  = -4.9(t² -(9.2/4.9)t) +1.6

  = -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²

  = -4.9(t -46/49)² +290/49

__

a) To find h = 0, we solve ...

  0 = -4.9(t -46/49)² +290/49

  290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9

  √(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds

The ball takes about 2.038 seconds to fall to the ground.

__

b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:

  290/49 m ≈ 5.918 m

The maximum height of the ball is about 5.918 m.

__

c) We want to find t for h ≥ 4.5.

  h ≥ 4.5

  -4.9(t -46/49)² +290/49 ≥ 4.5

Subtracting 290/49 and dividing by -4.9, we have ...

  (t -46/49)² ≥ 695/2401

Taking the square root, and adding 46/49, we find the time interval to be ...

  -√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49

The difference between the interval end points is the time above 4.5 meters. That difference is ...

  2√(695/2401) ≈ 1.076 . . . . seconds

The ball is at or above 4.5 meters for about 1.076 seconds.

__

I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.

_____

Additional comment

I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.

"Vertex form" for a quadratic is ...

  y = a(x -h)² +k . . . .  where the vertex is (h, k) and 'a' is a vertical scale factor.

In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)

Answer:

the 3rd, 4th, and 5th one

Step-by-step explanation:

Answer:

Step-by-step explanation:

:)

Answer:

False

Step-by-step explanation:

You first need to distribute the -4 to (x+4).

Answer:

(x - 3/8)^2 = x^2 - 3/4x + 9/64

Step-by-step explanation:

Step-by-step explanation:

divide the number with x by 2 and get the square of that number and add that number to this given equation

number with x = -3/4

= x^2 - 3/4 x + 9/64

= (x -3/8) ^2

Answer:

1. $11747.083

2. $29,253

3. $24222.04

4. $1542.23

Step-by-step explanation:

Message for explanation if you want.

Answer:

2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

See the photo for the steps. :)

Answer:

24feet

Step-by-step explanation:

the first rope well give it letter X and the longer rope we'll give it 2x since it's twice then we add the two unknown numbers which must lead to a total of 36feet when we add the unknown digits we'll get 3x then simply the unknown digit with the total and u'll get 12 replace the X from the first letters with 12by multiplying

Answer:

you have 38 friends

Step-by-step explanation:

because you have to add I think so

Answer:

38 friends

Step-by-step explanation:

Answer: This quadratic equation has two real solutions.

Step-by-step explanation:

[tex]y=x^{2} -11x+7\\\\D=(-11)^{2} -4 \cdot 7=121-28=93 \: > 0\\\\x=\dfrac{11 \pm \sqrt{93} }{2}[/tex]

Answer:

The correct answer is "Test 20%, Service 10%".

Step-by-step explanation:

As we know,

The coefficient of variation (CV) is:

⇒ [tex]CV=\frac{Standard \ deviation}{Mean}\times 100[/tex]

Now,

CV of test will be:

= [tex]\frac{40}{200}\times 100[/tex]

= [tex]20[/tex] (%)

CV of service will be:

= [tex]\frac{2}{20}\times 100[/tex]

= [tex]10[/tex] (%)

Answer:

[tex](f-g)(4) = -59[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=4x-3\text{ and } g(x) = x^3 +2x[/tex]

And we want to find the value of:

[tex](f-g)(4)[/tex]

Recall that this is equivalent to:

[tex](f-g)(4) = f(4) - g(4)[/tex]

Find f(4):

[tex]f(4) = 4(4)-3 = 13[/tex]

And find g(4):

[tex]g(4) = (4)^3 + 2(4) =72[/tex]

Substitute:

[tex](f-g)(4) = (13)-(72)[/tex]

And subtract. Hence:

[tex](f-g)(4) = -59[/tex]

Step-by-step explanation:

I love this question!

So there are a couple different ways of solving this. You feel free to ignore whichever one makes less sense.

Subtracting First

The first option is taking f(x) and g(x) and subtracting them, then introducing the number.

The calculation:

f(x) - g(x)

Substitute.

4x - 3 - (x^3 + 2x)

Multiply out the negative.

4x - 3 - x^3 - 2x

Rewrite.

-x^3 + 4x - 2x - 3

Simplify.

-x^3 + 2x - 3

Then, replace x with 4.

-(4)^3 + 2(4) - 3

Simplify.

-64 + 8 - 3

Add.

-59

Making x = 4 first

Here, we'll do what's on the tin. Find f(4) and g(4), then subtract them.

f(x) = 4x - 3

f(4) = 4(4) - 3

f(4) = 16 - 3

f(4) = 13

Then find g(4):

g(x) = x^3 + 2x

g(4) = (4)^3 + 2(4)

g(4) = 64 + 8

g(4) = 72

Then, subtract these two:

f(4) - g(4) = 13 - 72

f(4) - g(4) = -59

Answer:

Either way, the answer is -59

Answer:

A) -3/2

Step-by-step explanation:

You pick the difference between the two points and divide them.

y-axis: 2-(-1)= 3

x-axis: -3-(-1) = -2

So slope is -3/2

Answer:

x=2

y=1.732

Step-by-step explanation:

we use the formulae.....

SOHCAHTOA

where..Cos 60°=1/x

cos60=0.5

0.5=1/1

X=2

0.8660=y/2

y= 1.732

lim ( sinx-1)/(x-1)

x=>0

apply x=0

(sin(0)-1)/(0-1)

(0-1)/(-1)

=1