One marble is randomly drawn and then replaced from a jar containing two white marbles and one
black marble. A second marble is drawn. What is the probability of drawing a white and then a
black?

[tex]y= 6x -4~~~~~~...(i)\\\\y = 5x -3~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~6x -4 = 5x -3\\\\\implies 6x -5x = -3 + 4\\\\\implies x = 1\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 6(1) -4 = 2\\\\\text{Hence,}~ (x,y) = (1,2)[/tex]

Since the paper representing her desk is 1 1/4 inches by 2 1/4 inches, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft

To answer the question, we need to know what scale is

A scale is the ratio of two dimension and it is given on a scale drawing.

Given that Chelsea makes a scale drawing of the room and cuts out pieces of paper to represent her furniture, and the paper representing her desk is 1 1/4 inches by 2 1/4 inches.

Since on the scale, we have 1/2 in = 1 foot ⇒ 1 in = 2 ft

So, the actual dimensions of her desk are

1 ¹/₄ in by 2 ¹/₄ in = 5/4 in by 9/4 in

= 5/4 × 1 in by 9/4 × 1 in

= 5/4 × 2 ft by 9/4 × 2 ft

= 5/2 ft by 9/2 ft

= 2 ¹/₂ ft by 4 ¹/₂ ft

So, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft

Learn more about scale here:

https://brainly.com/question/26467371

#SPJ1

The function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function that has vertex at (2, 6)

The options are:

f(x) = 2|x – 2| – 6

f(x) = 2|x – 2| + 6

f(x) = 2|x + 2| + 6

f(x) = 2|x + 2| – 6

As we know the vertex form of a quadratic function is given by:

f(x) = a(x - h)² + k

Similarly, mod function  can be expressed as:

m(x) = a|x - h| + k

Here (h, k) is the vertex of a function.

In the function:

f(x) = 2|x – 2| + 6

The vertex of the function is (2, 6)

Thus, the function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

Answer:

Can't see the problem. Send a picture of it.

Answer:

there are 75 colors of each candy

Step-by-step explanation:

300÷4=75

Answer: The ten thousand digit is 6.  And the millions digit is 4. So the answer is 10.

The scale factor of the dilation of line segment BA is 1/5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in the size of a figure.

From the diagram:

scale factor of BA = AC / CA' = 4 / (4 + 16) = 1/5

The scale factor of the dilation of line segment BA is 1/5.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

B

Step-by-step explanation:

I do believe

[tex]-3x^3 +12x^2 -15x +6\\\\=-3(x^3 -4x^2 +5x-2)\\\\=-3(x^3 -2x^2-2x^2 +4x+x-2)\\\\=-3\textbf{[} x^2(x-2) -2x(x-2)+ (x-2)\textbf{]}\\\\=-3(x-2)(x^2 -2x +1)\\\\=-3(x-2)(x-1)^2[/tex]

Answer:

-1

Step-by-step explanation:

Find the difference of each sequence

19 - 15 = 4

15 - 11 = 4

11 - 7 = 4

7- 3 = 4

3 - ? = 4

Subtract 4 from the 3

3 - 4 = -1

Therefore, the next term is -1

Answer:

1&32 2&16 4&8

Step-by-step explanation:

Factor Pair Pair Factorization

1 and 32       1 x 32 = 32

2 and 16         2 x 16 = 32

4 and 8      4 x 8 = 32

The sequence whose first term is - 4 and defined recursively by the formula f(n + 1) = f(n) + 3 have the element - 1 as the next term. (Correct choice: B)

In mathematics, sequences are sets whose elements observe at least a condition, which is represented by a recursion formula in this question:

f(n + 1) = f(n) + 3

Thus, the following term of the sequence is:

f(2) = f(1) + 3

f(2) = - 4 + 3

f(2) = - 1

The sequence whose first term is - 4 and defined recursively by the formula f(n + 1) = f(n) + 3 have the element - 1 as the next term. (Correct choice: B)

The statement is poorly formatted and reports typing mistakes. Correct statement is:

A sequence is defined recursively by the formula f(n + 1) = f(n) + 3. The first term of the sequence is - 4. What is the next term in the sequence? a) - 7, b) - 1, c) 1, d) 7

To learn more on sequences: https://brainly.com/question/21961097

#SPJ1

Answer:

θ = 0°

θ = 30°

θ = 150°

θ = 180°

Step-by-step explanation:

2sin² θ = sin θ

Then

2sin² θ - sin θ = 0

Then

sin θ (2sin θ - 1) = 0

Then

sin θ = 0  or  2sin θ - 1 = 0

Then

sin θ = 0  or  sin θ = 1/2

…………………………………………

We have sin θ = 0 and - 270° ≤ θ ≤180°

Then

θ = 0 or θ = π = 180°

On the other hand,

sin θ = 1/2 and - 270° ≤ θ ≤180°

Then

θ = π÷6 or θ = 5π÷6

π÷6 = 30° and 5π÷6 = 150°

The solution to the question is:

c is 6 = [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]

b is 5 = [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]

cosB is 2 = [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]

a is 4 = [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]

cosA is 3 = [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]

cosC is 1 = [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]

it is used to relate the three sides of a triangle with the angle facing one of its sides.

The square of the side facing the included angle is equal to the some of the squares of the other sides and the product of twice the other two sides and the cosine of the included angle.

Analysis:

If c is the side facing the included angle C, then

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] -2ab cos C-----------------1

then c =  [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]

if b is the side facing the included angle B, then

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2accosB-----------------2

b =  [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]

from equation 2, make cosB the subject of equation

2ac cosB =  [tex]a^{2}[/tex] +  [tex]c^{2}[/tex] - [tex]b^{2}[/tex]

cosB =  [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]

if a is the side facing the included angle A, then

[tex]a^{2}[/tex] = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] -2bccosA--------------------3

a =  [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]

from equation 3, making cosA subject of the equation

2bcosA =  [tex]b^{2}[/tex] +  [tex]c^{2}[/tex]  - [tex]a^{2}[/tex]

cosA =  [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]

from equation 1, making cos C the subject

2abcosC =  [tex]b^{2}[/tex] + [tex]a^{2}[/tex] -  [tex]c^{2}[/tex]

cos C =  [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]

In conclusion,

c is 6 = [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]

b is 5 = [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]

cosB is 2 = [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]

a is 4 = [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]

cosA is 3 = [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]

cosC is 1 = [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]

Learn more about cosine rule: brainly.com/question/4372174

$SPJ1

The average rate of change for this function for the interval from x = 1

to x = 3 will be 8. Therefore option B is correct.

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

where when

[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]

The average rate of change can be calculated as;

From x=1 to x=3,

y = 2 and y = 18

Therefore, based on the table, when:

[tex]x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18[/tex]

Then:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8[/tex]

Therefore option B is correct.

Learn more about average;

https://brainly.com/question/12424098

#SPJ1

A. Distance between A and B is: 5 units.

B. Triangle ABC is not an equilateral triangle because only two of its sides are equal.

An equilateral triangle has three sides that have the same length.

Given the vertices with their coordinate points as:

A (-3, 2)

B (-6, -2)

C (0, -2)

Use the distance formula, [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB, BC, and AC:

AB = √[(−6−(−3))² + (−2−2)²]

AB = √25

AB = 5 units

BC = √[(−6−0)² + (−2−(−2))²]

BC = √36

BC = 6 units

AC = √[(−3−0)² + (2−(−2))²]

AC = 25

AC = 5 units

Only two of the sides of the triangle, AB and AC, are equal. Therefore, it is not an equilateral triangle.

Learn more about equilateral triangle on:

https://brainly.com/question/15294703

#SPJ1

Answer:

x = 2

Step-by-step explanation:

This is a 45-45-90 special right triangle. The legs in this triangle are equal and the hypotenuse is leg multiplied with √2. Refer to the picture at the bottom.

One leg is x, the second leg is x and hypotenuse x√2.

[tex]x \sqrt{2} = 2 \sqrt{2} \\\\\text{Divide both sides with } \sqrt{2} \text{ to isolate } x.\\\frac{x \sqrt{2}}{\sqrt{2}} = \frac{2 \sqrt{2}}{\sqrt{2}}\\\\x = 2[/tex]

well, we know the discount is 4975 - 3781 = 1194.

if we take 4975 to be the 100%, what is 1194 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 4975 & 100\\ 1194& x \end{array} \implies \cfrac{4975}{1194}~~=~~\cfrac{100}{x}\implies \cfrac{26}{6}=\cfrac{100}{x} \\\\\\ 26x = 600\implies x=\cfrac{600}{26}\implies x\approx 23.08[/tex]

Answer:

0.76

Step-by-step explanation:

4975 × 0.76 = 3781

the discount percent given is .76%

Answer:

Use given values of h and j, and find the value of k:

The equation is now:

Find the value of g when h is 2 and j is 3:

Correct choice is D

Answer:

D. 144

Step-by-step explanation:

The possible dimension of the third side is 10 units.

A right triangle is a triangle that has three sides known as the opposite, adjacent and hypotenuse. The hypotenuse is the longest sides of the triangle. The opposite side is the side that faces an angle. The adjacent side is the third side.

If two side lengths are given, the third side can be determined using the Pythagoras theorem.

√a² + b ² = c

√6² + 8² = √36 + 64 = 10 units

To learn more about right angled triangle, please check: https://brainly.com/question/20694080

#SPJ1

The ratio of the area of sector abc to the area of sector dbe is 4/3

For sector abc, we have:

Angle = x

Radius  = 2r

For sector dbe, we have:

Angle = 3x

Radius = r

The area of a sector is:

[tex]Area =\frac{\theta}{360}* \pi r^2[/tex]

So, we have:

[tex]ABC =\frac{x}{360}* \pi (2r)^2[/tex]

Evaluate

[tex]ABC =\frac{x* \pi r^2}{90}[/tex]

For DBE, we have:

[tex]DBE =\frac{3x}{360}* \pi (r)^2[/tex]

Evaluate

[tex]DBE =\frac{x}{120}* \pi r^2[/tex]

The ratio of both areas is:

[tex]Ratio = \frac{x}{90}* \pi r^2 : \frac{x}{120}* \pi r^2[/tex]

Cancel out the common factors

[tex]Ratio = \frac{1}{90} : \frac{1}{120}[/tex]

Express as fraction

[tex]Ratio = \frac{120}{90}[/tex]

Divide

[tex]Ratio = \frac{4}{3}[/tex]

Hence, the ratio of the area of sector abc to the area of sector dbe is 4/3

Read more about sector areas at:

https://brainly.com/question/1582027

#SPJ4

4/3

its the answer edmentum

Step-by-step explanation:

Here is the solution...hope it helps:)

Answer:

$48

30/10 is equal to 3/1, 16 x 3 equals to 48.

Answer:$48

Step-by-step explanation:

$30/10p = $3 per person

3x6=18

18+30=48

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]5x-y=-7\implies 5x-y+7=0 \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{5} x+7=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so a line perpendicular to that one above will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{5\implies \cfrac{5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}[/tex]

Considering the definition of axis of symmetry, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

An axis of symmetry is an imaginary reference line that, when dividing any shape into two parts, its opposite points are equidistant from each other, that is, they are symmetrical.

In other words, the axis of symmetry is a vertical line that divides the parabola into two congruent halves.

The axis of symmetry is the line perpendicular to the "x" axis that contains the vertex of the function, that is, it always passes through the vertex of the parabola. So the x-coordinate of the vertex is the equation of the axis of symmetry.

That is, in a quadratic function that has the form:

f(x)= ax² + bx + c

the axis of symmetry is a vertical line and it is defined as [tex]x=\frac{-b}{2a}[/tex].

In this case, you know:

Replacing in the definition of axis of symmetry:

[tex]x=\frac{-12}{2x3}[/tex]

Solving:

[tex]x=\frac{-12}{6}[/tex]

x= -2

Finally, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

Learn more about axis of symmetry:

https://brainly.com/question/24737967

https://brainly.com/question/10473291

#SPJ1

Answer:

$43 + $6l

Step-by-step explanation:

Hello!

She spends $43 and bus several $6 laces.

We don't know how many she buys, but we know that we can represent that number using l.

That means she spends $43 + $6l.

The algebraic expression is $43 + $6l.

We can determine the price if we know the number of laces she buys. We can simply plug in the number of laces she bought, and we can plug it in for l in the equation.

Answer:

43= 6(x)

Explanation:

43 is the total,  and each of them are 6$ each. X is the variable that we don't know.

Answer:

ELA

Step-by-step explanation:

you add ela to a bonus points

Answer:

PLA + ELA = 90

Step-by-step explanation:

lol

The exponent for the expression, 5 × 5 × 5 × 5 × 5, would be expressed as: [tex]5^5[/tex].

An exponent can be defined as the power to which the base is to b e raised.

For example, a × a × a can be expressed in  exponent form as a³.

In the same vein, given the expression, 5 × 5 × 5 × 5 × 5, we would expressed this in exponent form as: [tex]5^5[/tex].

Learn more about exponent on:

https://brainly.com/question/11975096

#SPJ1

Answer:

B is true

C is false

D is false

Step-by-step explanation:

- B is true because two negative numbers are added together, the outcome is negative hence always less than 0

- C is false due to needing a negative number add to -1.5 to be less, a positive only makes the number greater

- D is false since you are adding 0.9 (9/10), anything less than this will m ake the sum be greater than 0

example: - 0.5 + 0.9 = 0.4 or - 0.8 + 0.9 = 0.1

Considering the definition of equation, the equation that represents the statement "Two times a number x increased by 8 is 20" is: 2x + 8= 20

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The unknown values represents the number (or numbers), if any, that make the equality true. This unknown number is the solution of the equation.

Considering that:

the equation that represents the statement "Two times a number x increased by 8 is 20" is:

2x + 8= 20

Learn more about equation with this similar problems:

https://brainly.com/question/12739262

https://brainly.com/question/3229223

https://brainly.com/question/13762189

#SPJ1

The equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.

The given statement is two times a number x increased by 8 is 20.

We need to write the equation to represent this statement.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, two times a number x=2x

Increased by 8 is 20=2x+8=20

Hence, the equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.

To learn more about equations visit:

https://brainly.com/question/2263981.

#SPJ1