Does Anybody know How P(A/B1) and P(A/B2) Comes? (highlighted one)

The dimensions of the original piece of cardboard are 24 inches by 12 inches

The given parameters are:

Length (l)= Width (w) + 12

Length of the square cut out = 6

Volume of box, V = 1728

The volume of the box is then calculated as

V = Length of squares * Length * Width

This gives

V = 6 * (w + 12) * w

So, we have:

6 * (w + 12) * w = 1728

Divide both sides by 6

(w + 12) * w = 288

Expand

w^2 + 12w - 288 = 0

Using a graphing calculator, we have:

w = 12

Substitute w = 12 in l = w + 12

Evaluate

l = 12 + 12

l = 24

Hence, the dimensions of the original piece of cardboard are 24 inches by 12 inches

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Complete question

Lorene plans to make a box from rectangular sheets of cardboard from which she cuts out 6 inches squares from each corner. The length of the original piece of cardboard is 12 inches more than the width. If the box is 1728 inches cubed, determine the dimensions of the original piece of cardboard.

Answer:

250 ounces of 40% percent copper alloy

Step-by-step explanation:

Let a be the number of ounces of 40% copper alloy.

[tex].4a + .7(500) = .6(500 + a)[/tex]

[tex].4a + 350 = 300 + .6a[/tex]

[tex].2a = 50[/tex]

[tex]2a = 500[/tex]

[tex]a = 250[/tex]

250 ounces of 40% copper alloy.

Answer:on the given cushion. We want to represent cost like 30 in terms of cost. Rita. Now by the identity sector tragical toe one by scientists. Now we know that science can't theta plus Costco Arteta is equal to one. So they get signed. Tetteh is equal to plus minus quite a tough one. Minus cause squared theta. So this will be a photo one by plus minus square wrote off one minus y squared theta.

Step-by-step explanation:

Answer:

Step-by-step explanation:for the triangle GIF, angle g = 80

angle f = 42 since angle FBA = 138

so angle i = 180 - 42 - 80

                 = 58

The value of

Domain(- ∞,∞), Range(- 16, ∞), Minimum Value = -16

Function is a quadratic function. x-intercepts are -4 and 4.

The function decreasing before vertex = (-∞,0)

The function increasing after vertex = (0, ∞)

y-intercept is -16.

Function is Positive(- ∞, - 4) ∪ (4, ∞) : , Function is negative : (- 4, 4)

Interval Increasing  Domain(0,∞),

Interval Decreasing  Range(- ∞, -16)

According to the data, equation  f(x) = [tex]x^{2}[/tex] – 16

It is an upward parabola because coefficient of  is positive.

The vertex form of a parabola is

f(x) = a[tex](x - h)^{2}[/tex] . . . (2)

where, a is constant and (h , k) is vertex.

From (1) and (2), we get

a = 1, h = 0, k = - 16

So, vertex of the parabola is (0,-16).

The given function is defined for all values of x. So,

Domain : (- ∞,∞)

The value of a function which is an upward parabola cannot be less than the y-coordinate of its vertex. So

Range : (- 16, ∞)

Minimum Value = y-coordinate of vertex = -16

Function is a quadratic function.

For f(x)=0

⇒ 0  = [tex]x^{2}[/tex] - 16

⇒ 16 =  [tex]x^{2}[/tex]

⇒ x = ± 4

So, x-intercepts are -4 and 4.

The function decreasing before vertex = (-∞,0)

The function increasing after vertex = (0, ∞)

For x=0,

f(0) = [tex](0)^{2}[/tex] - 16

⇒ - 16

So, y-intercept is -16.

Function is Positive : (- ∞, - 4) ∪ (4, ∞)

Function is negative : (- 4, 4)

Interval Increasing  Domain: (0,∞)

Interval Decreasing  Range: (- ∞, -16)

Following are the key features of functions

1. Domain and Range

2. x-intercept and y-intercept

3. Positive and Negative intervals

4. Intervals of increasing, decreasing and constant behavior

5. Parent Functions

6. Maxima and Minima

Domain and Range

Domain : The domain is the set of all possible inputs or x-values. To find the domain of a function, we have to look at the x-axis of the graph.

Determining Domain :

1. Start at the origin.

2. Move along the x-axis until you find the lowest possible x-value. This is your lower bound.

3. Return to the origin.

4. Move along the x-axis until you find your highest possible x-value. This is your upper bound.

Range :The range is the set of all possible outputs or y-values. To find the range of the graph, we have to look at the y-axis of the graph.

Determining Range :

For the range, do the same thing but move along the y-axis.

x-intercepts and y-intercepts

x-intercept :

1. This is where the graph crosses the x-axis.

2. To find it algebraically, set y = 0.

3. Have many names :

x-intercept

  -Roots

  -Zeros

  -y-intercept :

1. This is where the graph crosses the y-axis.

2. To find it algebraically, set x = 0.

Positive Interval :

In the diagram below, the graph of the function is above the x-axis in the following intervals.

(-3, -1) and (2, 4)

More precisely, y is positive when x ∈ (-3, -1) and (2, 4).

So, the positive intervals for the above graph are

(-3, -1) and (2, 4)

Negative Interval :

In the diagram above, the graph of the function is below the x-axis in the following intervals.

(-∞, -3), (-1, 2) and (4, +∞)

More precisely, y is negative when x ∈ (-∞, -3), (-1, 2) and (4, +∞).

So, the negative intervals for the above graph are

(-∞, -3), (-1, 2) and (4, +∞)

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Answer:

Step-by-step explanation:

Work done is transfer of energy...... but without complicating things a little further let's just consider the amount of work done while cleaning the backyard is the same regardless of who the doer is/ how many in number are the doers. So

So power is the time rate change of work done:

[tex]P=w/t\\[/tex]

let's say power of LeeAnn =L, Mandy=M

[tex]L=w/30 minutes\\M=w/25 minutes\\[/tex]

And if they worked together their power will add up to L+M

[tex]L+M=w/T\\[/tex], while T is the amount of time needed when they clean together.

[tex]L+M=w/T\\w/30min + w/25min =w/T\\1/30min+1/25min=1/T, w\neq 0\\1+(6/5)=30/T\\11/5=30/T\\11T=150\\T=150/11 min\\T=13.6 min[/tex]

Answer:7

Step-by-step explanation: the answer is 7

The graph is made and attached.

Given, the equation is x ₋ √x₊3 = 0

substitute values for x from the interval ₋1 to 5 and then graph the points.

for x = ₋1:

₋1 ₋ √₋1 ₊ 3 = 0

₋1 ₋ 1.42 = 0

₋2.42

for x = 0

0 ₋ √0₊3 = 0

₋1.74

for x=1

1 ₋ √1₊3 = 0

1 ₋ √4 = 0

1 ₋ 2 = 0

₋1

for x = 2

2 ₋ √2₊3 = 0

2 ₋ √5 = 0

2 ₋ 2.24 = 0

0.24

for x = 3

3 ₋ √3₊3 = 0

0.55

for x = 4

4 ₋ √4₊3 = 0

4 ₋ √7 = 0

1.25

for x = 5

5 ₋ √5₊3 = 0

2.17

hence we have the points (₋1,₋2.42) (0,₋1.74)(1,₋1)(2,0.24)(3,0.55)(4,1.25) and(5,2.17)

plot the above points on the graph.

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The expression is  negative one eighteenth times x plus 18.

The expression says "one sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x".

Therefore, the statement can be expressed as follows;

1 / 6 × 4 × x + 18 - 13 / 18 × x

Therefore, let's simplify it

1 / 6 × 4 × x + 18 - 13 / 18 × x

4x / 6 + 18 - 13 / 18 × x

4x / 6 + 18 - 13 / 18 x

combine like terms

4x / 6 + 18 - 13 / 18 x

4x / 6 - 13 / 18 x + 18

12x - 13x / 18 + 18

Therefore,

- 1 / 18 x + 18

Therefore, the expression is  negative one eighteenth times x plus 18.

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Answer: b) negative one eighteenth times x plus 3

Step-by-step explanation: :)

Answer:

1/8

Step-by-step explanation:

Hello,

[tex]4 = - 8 - \boxed{(-12)}[/tex]

Answer: the fourth choice, or y=-3x+18

Step-by-step explanation:

using the point-slope form, we can plug in the values:

y-0= -3(x-6)

distributing the right side we get

y-0=-3x+18

putting it into y=mx+b form we get y=-3x+18

The x-coordinate of point R from the given coordinates is -8

The formula for calculating the midpoint of coordinates is expressed according to the formula:

M(x, y) = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the coordinate points M (-3,4) and S (2, -3)

Substitute

-3 = (x₁+x₂)/2

-3 = 2+x₂/2

-6 = 2 + x₂

x₂ = -8

Similarly;

Substitute

4 = (-3+y₂)/2

4 = -3+x₂/2

8 = -3 + y₂

y₂ = 11

Hence the x-coordinate of point R from the given coordinates is -8

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Answer:

Step-by-step explanation:

a and b are integers

A number that can be written in the form a/b where a and b are integers. However, b cannot equal zero. Therefore a rational number

Answer:

2 and 17

Step-by-step explanation:

2 x 17= 34

hope it helps

Answer:

132 feet per second

Step-by-step explanation:

Answer:

96cm²

Step-by-step explanation:

1.) You can split the shape into 2: a rectangle and a triangle.

2.) The formula to find the area of the rectangle is:

length × width.

10 (length) × 8 (width) = 80cm²

3.) Then you can find the area of the triangle. The formula for finding the area of a triangle is:

½ × base × height.

½ × 4 (base) × 8 (height) = 16cm²

3.) Add the two answers together to give you the combined and total area of the shape.

80cm² + 16cm² = 96cm²

Interest earned by Mary is $ 3,745.92 which is more than the interest than Josh earned that is $ 3,600.

For Mary:

Principal = $ 30,000

Interest rate = 4 %

Compounded annually

t = 3 years

Amount = $ 30,000 ( 1 + 4 / 100 )³

A = 30,000 ( 1.04)³

A = 30,000 ( 1.124864 )

A = $ 33,745.92

Interest = A - P = 33,745.92 - 30,000 = $ 3745.92

For Josh:

Principal = $ 30,000

Simple interest

t = 3 years

Interest = 30,000 × 3 × 4 / 100

Interest = $ 3600

Therefore, interest earned by Mary is $ 3,745.92 which is more than the interest than Josh earned that is $ 3,600.

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Answer:

241.5 km

Step-by-step explanation:

The distance between London and Cardiff in kilometres is 241.5 km

Answer:

4.61x10^5

Step-by-step explanation:

You want the first number to be between 0 and 10, not equaling either. So you move the decimal place to the left. Then, you write the second half, which is that you multiply it by ten to the power of however many digits you moved to the left for, which is 5.

From the fig the Area model is, = 3/5(2/5 + 1/3)

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares.
Area of rectangle = l x b
given that, lets consider the fig as rectangle with one side 2/5+1/3 as breadth and another side 3/5

As we know , Area of rectangle = l x b

l=3/5

b=2/5+1/3

Area model= 3/5(2/5 + 1/3)

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Answer:

The Area model for the fig. is, = 3/5(2/5 + 1/3).

Step-by-step explanation:

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

Rectangle area = l x b

Given that, let's imagine the fig as a rectangle with a width of 2/5+1/3 and a length of 3/5.

As we know , Area of rectangle = l x b

l=3/5

b=2/5+1/3

Area model= 3/5(2/5 + 1/3)

Step-by-step explanation:

Divide by 4h, d=3f-g3/4h

Answer:

Angle 2 is 36 degrees because of Alternate Exterior Angle Theorem being that both of the angle outside and are alternate are Congruent.

The answer is X=11 because 2x+14=36, 2x=22, x=11. 2(11)+14=36

Answer:

I think the answer is A

Step-by-step explanation:

I'm not sure if it's correct or not but I chose the option because the atoms in substance are not chemically combined

Using a system of equations, the solution matrix that gives the weight of a fizgig and the weight of a whatsit is:

[x y] = [5 4]

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

Two fizgigs and three whatsits weigh 22 noozwhats, henec:

2x + 3y = 22.

Four fizgigs and two whatsits weigh 28 noozwhats, hence:

4x + 2y = 28.

Simplifying by 2:

2x + y = 14

y = 14 - 2x.

Replacing in the first equation:

2x + 3(14 - 2x) = 22

2x + 42 - 6x = 22

4x = 20

x = 20/4

x = 5 noozwhats.

y = 14 - 2(5) = 4 noozwhats.

Hence the solution matrix that gives the weight of a fizgig and the weight of a whatsit is:

[x y] = [5 4]

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Answer:

Step-by-step explanation:

meow meow its 99

Using it's concept, the mean test score is of 4.9.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

From the frequency table, the sum of the 30 observations is given by:

0 x 3 + 1 x 2 + 2 x 6 + 3 x 1 + 4 x 1 + 5 x 3 + 6 x 2 + 7 x 4 + 8 x 4 + 9 x 2 + 10 x 2 = 146.

Hence the mean test score is given as follows:

M = 146/30 = 4.9.

The mean test score is of 4.9.

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Answer:

point A and point B

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

I think it’s B. because it has negative 3 and negative 2 but for C., it is between negative 2 and negative 1 which can’t be correct since it would end at negative 2 and this is why it is b.