Using polynomial long division how can you determine if x-3 is a factor of x^3+4x^2-12x+24

Considering the given probabilities, it is found that the correct option about whether the events are independent is given as follows:

p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).

Two events, A and B are independent, if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Researching this problem on the internet, the probabilities are given as follows:

[tex]P(X) = \frac{4}{5}, P(Y) = \frac{1}{4}, P(X \cap Y) = \frac{1}{5}[/tex]

Hence:

[tex]P(X)P(Y) = \frac{4}{5} \times \frac{1}{4} = \frac{1}{5} = P(X \cap Y)[/tex]

Hence the events are independent and the correct option is given by:

p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).

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Answer:The answer iis 1810.3cm^2

Step-by-step explanation:

Question :-

Answer :-

[tex] \rule{180pt}{3pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{12 \: cm}}\end{picture}[/tex]

Solution :-

As per the provided information in the given question, we have been given that the radius of the sphere is 12 cm. We have been asked to find or calculate the surface area of the sphere.

To calculate the surface area of the sphere, we will use the formula below :-

[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]

Substitute the given values into the above formula and solve for surface area:

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(12 \: cm)^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(144 \: cm^2)[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(452.16 \: cm^2)[/tex]

[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 1809 \: cm^2}[/tex]

Therefore :-

[tex]\\[/tex]

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Have a great day! <33

Answer:

x > 9

The graph is a half-plane. (All the points with their abscissa (their value on the x-axis) greater than 9

Step-by-step explanation:

6 +x > 15

x > 15 - 6

x > 9

Answer:

X>9

Step-by-step explanation:

the other guy has the graph

Answer:

c. 22

Step-by-step explanation:

Let x = Tata's age and y = Kaka's age.

x - 10 = y

x+3 + y+3 = 40

Now, we can substitute in x - 10 for y.

x + 3 + (x - 10) + 3 = 40

so 2x = 44

x = 22

Therefore, Tata's current age is 22.

The volume of a pyramid that fits exactly inside a cube is 9 cubic feet is 3 cubic feet

The formula for calculating the volume of a pyramid is expressed as:

V = Base area. * height/3

Since it is a cube with a volume of  9 cubic feet, the length of the cube will be:

l = ∛9
l = 2.08

Determine the volume of the pyramid

V = 9/3

V = 3 cubic feet

Hence the volume of a pyramid that fits exactly inside a cube is 9 cubic feet is 3 cubic feet

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point-slope form

y - y₁ = m(x - x₁)

[tex]y-1=-\frac{1}{2}(x-8)\\\\y-1=-\frac{1}{2}x+4\\\\y=-\frac{1}{2}x+5[/tex]

The answer is A) Choice A.

Based on the height of the pyramid and the dimensions of the square base, the space that Maria has inside the pop-up net is 1,280 in³.

This can be found as the volume of a pyramid which is:

= (Length x Width x Height) / 3

Solving gives:

= (16 x 16 x 15) / 3

= 3,840 / 3

= 1,280 in³

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Answer:

153.86 in²

Step-by-step explanation:

The area of a circle is:

A = π r²

Radius is just half of the diameter so r = 7.

Substitute 3.14 for π.

Restate the equation:

A = 3.14 x 7² = 3.14 x 49

A = 153.86

Answer:

10.533

Step-by-step explanation:

Have a great rest of your day
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Answer:

it will be 30% in the highlighted cell

Step-by-step explanation:

hope this helps

Answer:

63 quizzes= 7 weeks

90 quizzes= x weeks

63x = (7)(90)

x= (7)(90)/63

x= 10 weeks

Answer:

Step-by-step explanation:

Answer:

y=-1/3x

Step-by-step explanation:

if it’s going down by one there should be one on top on since it’s going over by 3 it should be 3 on the bottom

Answer: 4

Step-by-step explanation:

x - 2y =10

x = 10 + 2y

[tex]\frac{2x)}{y + 5}[/tex]

[tex]\frac{2(10+2y)}{y+5}[/tex]

[tex]\frac{20+4y}{y+5}[/tex]

[tex]\frac{4(5+y)}{y+5}[/tex] ... cancel like terms (y + 5)

= 4

The range, standard deviation, and variance say about gas prices in 2018 discussed below

Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.

As the variance in 2018 is 0.0121.

A model with low variance means sampled data is close to where the model predicted it would be.

As the standard deviation in 2018 is 0.1098.

Low standard deviation means data are clustered around the mean

A small range means low variability in a distribution.

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Answer:

The probability of a certain event is 1 or 100%

The probability of an impossible event is 0 or 0%

Answer:

See below ~

Step-by-step explanation:

Answer:

46 hours do the students play video games per week

Answer:

Step-by-step explanation:

Refer the attachment

Answer:

752.5 in³

Step-by-step explanation:

  Rectangular prism:

            l = 10 in ; w = 7 in ; h = 8 in

   [tex]\boxed{\text{Volume of rectangular prism=l*w*h}}[/tex]

                                                = 10 * 7 * 8

                                                = 560 in³

Half cylinder:

Diameter of the cylinder will be equal to the width of the rectangular prism.

       r = 7/2 = 3.5 inches ; h = 10 in

[tex]\boxed{\text{Volume of half cylinder =$\dfrac{1}{2}\pi r^2h$}}[/tex]

                                       [tex]\sf =\dfrac{1}{2}*3.14*3.5*3.510\\\\ = 192.5 \ in^3[/tex]

Volume of composite figure = 560 - 192.5

                                               = 752.5 in³

Answer:

15 lbs of onions.

Step-by-step explanation:

23 lbs divided by $46 = 0.5 lbs per $1

0.5 lbs times $30

15 lbs

=============================================================

Work Shown:

(23 pounds)/(46 dollars) = (x pounds)/(30 dollars)

23/46 = x/30

1/2 = x/30

1*30 = 2*x

30 = 2x

2x = 30

x = 30/2

x = 15

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

Another approach:

Divide the cost over the number of pounds to find the unit price

46/23 = 2

The onions cost $2 per pound.

If x is the number of pounds, and we pay $30, then

2x = 30

x = 30/2

x = 15

Meaning 15 pounds of onions cost $30.

Answer:

The volume of the cylinder is equal to 70.65 cm³.

General Formulas and Concepts:
Geometry

Volume Formula [Cylinder]: V = πr²h

Step-by-step explanation:

Step 1: Define

Identify given variables from diagram.

r = 3 cm

h = 2.5 cm

Step 2: Find Volume

∴ we found the volume of the cylinder to be 70.65 cm³.

---

Topic: Geometry

Answer:

LCM of 8, 9, and 12 is 72.

Step-by-step explanation:

The LCM of three non-zero integers, a(8), b(9), and c(12), is the smallest positive integer m(72) that is divisible by a(8), b(9), and c(12) without any remainder.

appreciate it if someone will follow me.

Answer:

72

Step-by-step explanation:

To find the Lowest Common Multiple (LCM), prime factorize the included terms, and multiply the factors of each number of the highest power together.

Prime factorizing

LCM (8, 12, 9)

= 2³ x 3²

= 8 x 9

= 72

The probability that exactly four of the students were been born on a weekday (i.e. Monday through Friday) is 0.2125.

To determine the probability, we need to first find the probability of having a student being born on a weekday.

[tex]=\mathbf{\dfrac{5}{7}}[/tex]

The probability of having 4 students born on a weekday is:

[tex]=\mathbf{(\dfrac{5}{7})^4}[/tex]

Since we have 4 students, we also need to find the probability of the students that are not being born, which is:

[tex]=\mathbf{(\dfrac{2}{7})^3}[/tex]

Also, there are [tex](^7_4)[/tex] = 35 ways to get four students out of seven students.

Therefore, we have the probability as:

[tex]\mathbf{P = 35 \times (\dfrac{5}{7})^4 \times (\dfrac{2}{7})^3}[/tex]

P = 0.2125  

Therefore, we can conclude that the probability that exactly four of the students were born on a weekday is 0.2125.

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The number of gigabytes of data can she use while staying within her budget should be less than 4.3 gigabytes.

Linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

Under her cell phone plan, Ella pays a flat cost of $37.50 per month and $5 per gigabyte.

She wants to keep her bill at $59 per month.

Then the number of the gigabytes of data can she use while staying within her budget will be

Let x be the number of the gigabytes. Then the equation will be

5x + 37.5 < 59

          5x < 21.5

            x < 4.3

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Answer:

vertex = (4, - 37 )

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = 2x² - 16x - 5 ← factor 2 out of the first 2 terms

    = 2(x² - 8x) - 5

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

f(x) = 2(x² + 2(- 4)x + 16 - 16) - 5

    = 2(x - 4)² - 32 - 5

   = 2(x - 4)² - 37 ← in vertex form

with vertex = (4, - 37 )

Answer:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (3, 5) and r = , hence

(x - 3)² + (y - 5)² = (  )², that is

(x - 3)² + (y - 5)² =  ← equation of circle

Step-by-step explanation:

Answer:

last option (x-2)(x+1)/3

Step-by-step explanation:

(x^2-4)/(x-7) ÷ (3x+6)/(x^2-6x+7)

(x^2-4)/(x-7) * (x^2-6x+7)/(3x+6)

(x+2)(x-2)/(x-7) * (x-7)(x+1)/3(x+2)

(x-2)/1 * (x+1)/3

(x-2)(x+1)/3

Answer:

28.27

Step-by-step explanation: used to do acellus too

Answer:

Step-by-step explanation:

AB = altitude = 2.7 miles

BC =  8.3 miles

[tex]\sf tan \ \theta = \dfrac{opposite \ side \ of \ \theta}{adjacent \ side \ of \ \theta}\\\\Tan \ \theta = \dfrac{AB}{BC}=\dfrac{2.7}{8.3}\\\\Tan \ \theta = 0.33\\\\\theta = tan^{-1} \ 0.33[/tex]

[tex]\boxed{\theta = 18.3}[/tex]