You have a bag which contains only red and green marbles. In this bag with $x^{2} 5$ marbles total, $x 1$ are red. Also, $x-3$ marbles have a scratch on them. The probability of drawing a red marble from the original bag is equal to that of drawing a marble with a scratch from the marbles left in the bag after twenty scratch-free marbles are taken out of the full bag. How many marbles were originally in the bag?

Answers

Answer 1

The original number of marbles in the bag is 30.

The given parameters are:

[tex]Red = x + 1[/tex]

[tex]Total = x^2 + 5[/tex]

The probability of red is:

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

[tex]P(Red) = \frac{x+1}{x^2 + 5}[/tex]

When 20 marbles were removed, the marbles left are:

[tex]Marbles =Total - 20[/tex]

This gives:

[tex]Marbles =x^2 + 5 - 20[/tex]

[tex]Marbles =x^2 -15[/tex]

The probability of selecting a scratched marble at this point is:

[tex]P(Scratch) = \frac{Scratch}{Marbles}[/tex]

[tex]P(Scratch) = \frac{x -3}{x^2 - 15}[/tex]

This probability equals the probability of red.

i.e.

[tex]P(Red) = P(Scratch)[/tex]

So, we have:

[tex]\frac{x +1}{x^2 + 5} = \frac{x -3}{x^2 - 15}[/tex]

Cross multiply

[tex](x + 1)(x^2 - 15) = (x - 3)(x^2 + 5)[/tex]

Expand

[tex]x^3 - 15x + x^2 - 15 = x^3 + 5x - 3x^2 - 15[/tex]

Subtract [tex]x^3[/tex] from both sides

[tex]- 15x + x^2 - 15 = 5x - 3x^2 - 15[/tex]

Add 15 to both sides

[tex]- 15x + x^2 = 5x - 3x^2[/tex]

Collect like terms

[tex]3x^2 + x^2 - 15x - 5x = 0[/tex]

[tex]4x^2 - 20x = 0[/tex]

Divide through by 4

[tex]x^2 - 5x = 0[/tex]

Expand

[tex]x(x - 5) = 0[/tex]

Split

[tex]x = 0[/tex] or [tex]x - 5 = 0[/tex]

[tex]x = 0[/tex] or [tex]x = 5[/tex]

x can't be 0.

So: [tex]x = 5[/tex]

The number of marbles initially is:

[tex]Total = x^2 + 5[/tex]

[tex]Total = 5^2 + 5[/tex]

[tex]Total = 30[/tex]

Hence, the original number of marbles in the bag is 30.

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Related Questions

A coffee pot holds 6 quarts of coffee. How much is this in cups?

Answers

Answer:

24 cups

Step-by-step explanation:

1 quart = 4 cups

6x4= 24 cups

Answer:

24 cups.

Step-by-step explanation:

Each quart is equal to 4 cups. This means you have to do 6x4 to find the answer.

FURNITURE A modern table is constructed with four legs made
of concrete cubes with cube-shaped notches.
a. Define one or more variables and write an expression that
represents the volume of one table leg.

b. Marisol determined that she will use 12,636 cubic inches of
concrete to construct the four table legs. If the sides of the
notches are 40% of the sides of the legs, how long are the sides of the legs?

Answers

The volume of a shape is the amount of space in it.

The expression that represents the volume of one table leg is: [tex]V = l^3 + n^3[/tex]The sides of the legs is 14.37 inches long

(a) The volume of one table leg

Represent the side length of the leg with l, and the side length of the notch with n.

So, the expression that represents the volume of one table leg is:

[tex]V = l^3 + n^3[/tex]

(b) The length of the sides

From the question, we have:

[tex]n = 40\% \times l[/tex]

Express 40% as decimal

[tex]n = 0.40 \times l[/tex]

[tex]n = 0.4l[/tex]

Substitute 0.4l for n in [tex]V = l^3 + n^3[/tex]

[tex]V =l^3 + (0.4l)^3[/tex]

[tex]V =l^3 + 0.064l^3[/tex]

[tex]V =1.064l^3[/tex]

The volume of the 4 legs is given as: 12636

So, the volume of one leg would be 12636/4

So, we have:

[tex]1.064l^3 = \frac{12636}{4}[/tex]

[tex]1.064l^3 = 3159[/tex]

Divide both sides by 1.064

[tex]l^3 = 2968.985[/tex]

Take cube roots of both sides

[tex]l = 14.37[/tex]

Hence, the sides of the legs is 14.37 inches long

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HELP MEEEEEEEEEEEEEEEE!!!

Answers

Answer:

enlargement: >1reduction: <11: same size

Step-by-step explanation:

The scale factor of an enlargement is greater than 1.

The scale factor of a reduction is less than 1.

A scale factor of 1 will produce a congruent figure, one the same size as the original.

_____

A longer way to say it

A figure is enlarged when its dimensions are greater than those of the original. Then the ratio of dimensions will be ...

  (greater than original)/(original) = greater than 1

Similarly, a figure is reduced when its dimensions are less than those of the original:

  (less than original)/(original) = less than 1

Multiplying dimensions by a scale factor of 1 does not change them. The scaled figure is the same size as the original.

what is the perimeter of rectangle INA
9.10
10 units
10 unite
18 unita
unite

Answers

Answer:P=2(l+w)

Step-by-step explanation: its easy


Will mark brainliest

Answers

Answer:

Quadrant 3     or aka     Quadrant III

Step-by-step explanation:

The top right quadrant is the first quadrant. Aka Quardant 1

The top left quadrant is the second qudrant. Aka Quadrant 2

The bottom left quadrant is the third quadrant. Aka Quadrant 3

The bottom left quadrant is the fourth quadrtant. Aka Quadrant 4

The heart is located in the bottom left quadrant. Meaning, it is the third quadrant. Aka Quadrant 3

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Send me a message on it and I'll follow you right back

Two fractions in the middle of 1/4 and 3/4

Answers

2/4 and 2.5/4 this is my answer
The right answer is 2/4 and 3/5
2/4 = 0.5 and 3/5 = 0.6 and both these numbers are in between 1/4 = 0.25 and 3/4 = 0.75

one yard is the same as A.12 inchs. B.24 inches. C.3 feet. D.1 foot​

Answers

Answer: C. 3 feet

Step-by-step explanation:

1 yard is equivalent to 3 feet.

triangle ABC rotated 90 degress clockwise about point P to create triangle DEF. Determine the correct orientation and location of triangle DEF

Answers

When a triangle is rotated, it must be rotated through a center.

The location of the triangle would be above point P, and the orientation is triangle DEF (the first triangle)

The triangle is given as: triangle ABC.

And the degree of rotation is 90 degrees clockwise.

Given that the triangle is rotated about point P, then the new location after 90 degrees rotation would be above point P.

And the orientation would point to the right of point P.

Hence, the location of the triangle would be above point P, and the orientation is triangle DEF (the first triangle).

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simplify 3^2 x 3^4 x 3^6 A3^10 B3^12 C3^48 D3^0​

Answers

Answer:

[tex]\boxed{\sf\: B)\:3^{12}}[/tex]

Step-by-step explanation:

[tex]\sf 3^2\times \:3^4\times \:3^6[/tex]

Apply exponent rule:

[tex]\hookrightarrow \boxed{\sf a^b\times \:a^c=a^{b+c}}[/tex]

[tex]\sf 3^2\times \:3^4\times \:3^6[/tex][tex]\sf 3^{2+4+6}[/tex]

Add the numbers:

[tex]\sf 2+4+6=12[/tex][tex]\sf \:3^{12}[/tex]

________________________________

find the interval in which the function is negative.

f(x) = x^2 - 3x - 4

I. (- infinite, -1)

II. (-1, 4)

III. (4, infinite)

A. III only

B. II only

C. I, II

D. I, III​

Answers

Answer:

  B. II only . . . (-1, 4)

Step-by-step explanation:

The function factors as ...

  f(x) = (x +1)(x -4)

The factors are zero when x=-1 and x=4. The value of the function will be negative when one of these factors is negative, between x=-1 and x=4. In interval notation, that interval is ...

  (-1, 4) . . . interval for f(x) < 0 . . . . . . interval description II (only)

Solve using elimination 5x+7y=9
2x-3y=-37

Answers

Answer:

x = -8

y = 7

Step-by-step explanation:

5x + 7y = 9

2x - 3y = -37

1.) First, multiply each side to match either y-values or x-values. (In this example, we'll use match x-values)

10x + 14y = 18 (multiplied by 2)

10x - 15y = -185 (multiplied by 5)

2.) Then, subtract the entirety of one equation to isolate the y-value.

10x + 14y = 18

-10x + 15y = 185

3.) Add and subtract values and divide to find y.

29y = 203

y = 7

4.) Plug-in y to solve for x into one equation, or repeat steps 1-3.

15x + 21y = 27

14x - 21y = -259

29x = -232

x = -8

Mr.Wedmore works at a car dealership and earns a monthly salary of $2,000. He also earns 25% commission on the gross profit of the car sales. If Mr.Wedmore brought in $10,000 worth of profit, for the dealership, how much would he earn this month

Answers

Answer:

25% of 2000= 500

25% of 10000= 2500

Step-by-step explanation:

26. Dy Aminah arrived at her office at 07 45h. The journey to her office was 50 minutes. At what time did she leave her house?​

Answers

Answer:

6 55

Step-by-step explanation:

Hassan surveyed 120 of the students in his school about their favorite color. 114 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was purple?

Answers

Answer:

95%

i think it should be that

5% because you take the 6 that was the difference and then you divide it by the whole and then you multiply the decimal by 100 to get 5%

Manolo and Annalisa make handbags. Manolo made 16 handbags the first day and 12 each day after
that. Annalisa made 8 the first day and 12 each day after that.

Answers

Based on the amount being made by Manolo and Annalisa every day, the amount both made on the various days were:

Annalisa made 8 bags on Day 1Manolo had made 40 bags by Day 3

Annalisa is said to have made 8 bags on the first day so this is the number of bags that should be put in the table for having been made in the first day.

Manolo made 16 bags on the first day and then 12 bags each day after that. The total number of bags made by the third day by Manolo would be:

= 16 + 12 + 12

= 40 bags

In conclusion, Annalisa made 8 bags on Day 1 and Manolo had made 40 bags on the 3rd day.

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help pls i don't know how to do it

Answers

Answer:

y=5x-8

Step-by-step explanation:

Slope=m=(7-3)/(3-2)

y=5x+b=>2=5*2+c=>c=-8

So y=5x-8

[tex]\text{Given that,}\\\\(x_1,y_1) = (2,2), ~ \text{and}~ (x_2,y_2) = (3,7)\\\\\text{Slope, m =} \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{7-2}{3-2} = \dfrac 51 = 5\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y-2= 5(x-2)\\\\\implies y -2 = 5x-10\\\\\implies y = 5x -10 +2\\\\\implies y = 5x -8\\\\\\\text{It is now in a form of y = mx +c}[/tex]

To find the surface area, Brad splits the figure into two pieces, the rectangular prism and
the triangular prism.
He finds the total surface area of the rectangular prism by finding the area of each face
to get 1,104 cm
He then finds the total surface area of the triangular prism by finding the area of each
face to get 1,008 cm
Finally, he adds the surface areas together to get 2,112 cm.
Is Brad's solution correct? Why or why not?
Select the option that correctly answers both questions.
No, he did not find the correct total surface area for the triangular prism.
O No, he did not find the correct total surface area for the rectangular prism.
No, he needs to subtract the areas of the faces where the two prisms are
attached
Yes, he correctly found the sum of the surface areas for each prism.

Answers

The surface area of the figure is the amount of area covered by the figure.

The figure is not given, so I will give a general solution.

The method followed by Brad to calculate the surface area of the prism is correct.

However, whether Brad correctly calculates the areas of the rectangular prism and the triangular prism cannot be determined.

So, the conclusion is that:

If Brad's calculation of the surface areas of the prisms is correct, then the surface area of the figure is correct because 1104 + 1008 = 2112.If otherwise, then the solution is incorrect

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Write, in slope-intercept-form, the inequality shown in the graph.
Two points which the boundary line intersects are shown?

Answers

Answer:

y > 3x - 4

Step-by-step explanation:

lmk if you want an explanation

A driver travels for 2 hours at 90 miles per hour, during which her car gets 30 miles per galoon of gasoline. She is paid $0.70 per mile, and her only expense is gasoline at $4 per gallon. What is her net rate of pay, in dollars per hour, after this expense?

Answers

Answer:

Her net rate of pay in dollars per hour after the expense = $26

Step-by-step explanation:

Given:

Driver travels for 2 hours.

Speed = 60 miles per hour

Her car runs at the rate of 30 miles per gallon of gasoline.

She is paid $0.50 per mile.

Expenses is price of gasoline at the rate of $2.00 per gallon.

To find her net rate of pay in dollars per hour.

Solution:

In one hour the driver travels = 60 miles

For each mile she is paid = $0.50

So, for 60 miles she will be paid =

In a gallon of gasoline the car travels = 30 miles

So, to travel 60 miles, the car would require = gallons of gasoline

1 gallon of gasoline cost = $2.00

Expenses for 2 gallons of gasoline =

So, in one hour she gets paid =$30 and her expenses for an hour drive = $4.

Thus, her net rate of pay in dollars per hour after the expense =

Brainlist please

The net rate of pay is $122 for the two hours journey.

The driver travels for 2 hours at 90 miles per hour.

Total distance travelled = 2 hours * 90 miles per hour = 180 miles

Money paid to driver = $0.70 per mile * 180 miles = $126

Fuel consumption = 30 miles per gallon, hence:

Total fuel consumption = 180 miles / (30 miles per gallon) = 6 gallon

Total expense = $4 per gallon * 6 gallon = $24

Net rate of pay = $126 - $24 = $122

The net rate of pay is $122 for the two hours journey.

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Which graph represents an function

Answers

we kind of need to see the graphs to decide.
but the function is any graph that is completely straight and goes through the center (0,0)

Help please please!!!

Answers

i is 900, j is 6, k is 8, l is 1. Please give me brainliest

Tell whether the ordered pair is a solution to the equation. Please show how you solved it.


(4, 4); y = -x + 8

Answers

Answer:

The ordered pair is a solution to the equation

Step-by-step explanation:

Plug the ordered pair into the equation as (x,y):

y = -x + 8

4 = -4 + 8

4 = 4

Since both sides are equal to each other, then the ordered pair is a solution to the equation.

Yes, it is a solution to the equation.

Plug in the values 4, for y, and 4, for x. Since there is a negative sign next to x, it turns 4 into -4. So, the equation will look like this: 4 = -4 + 8, add 8 to -4, and you get 4. 4 = 4. 4 = 4 is a true statement, so the pair IS a solution to the equation. Hope this helps!

how to solve for x (proportions)

Answers

Answer:

16/3 or 5 1/3

Step-by-step explanation:

Cross Multiply

4×4

3×x

16=3x

Divide 3 from 16

x=16/3 or 5 1/3

2. Name 3 points that are collinear*
2
s
S
R
O points T, Q, and R
O points T, Q, and S
O points S, Q, and R

Answers

Answer:

T, Q, and R

Step-by-step explanation:

These points are all on the same line, making them collinear.

I hope this helps!!

The length of a rectangle is 6 inches more than 4 times its width. A similar
rectangle has a length of 18 inches and a width of 4 inches. What is the area of the
first rectangle??

Answers

Answer:

18 × 4 is 72...

so.. the area of rectangle is 72inches²

Step-by-step explanation:

to find the area of rectangle is Lenght multiple with its Width

Solve for x. I need help understanding my math.

Answers

Answer:

x = 33

Step-by-step explanation:

11 - 4 = 7

You need to make that fraction equal 11

33/3 = 11

I hope this helps!

Q.

[tex] \frac{9}{6} + \frac{6}{9} = [/tex]

#use method
#good luck​

Answers

Answer:

The answer is 13/6

Step-by-step explanation:

9/6 + 6/9

9/6 = 3/2

6/9 = 2/3

Now,

3/2 + 2/3

Cross Multiply

3 × 3 + 2 × 2/2 × 3

9 + 4/6 = 13/6

Thus, The answer is 13/6

-TheUnknownScientist 72

[tex]\large\huge\green{\sf{Answer:-}}[/tex]

[tex] = \frac{9}{6} + \frac{6}{9} \\ = \frac{27 + 12}{18} \\ = \frac{39}{18} \\ = \frac{13}{6} [/tex]

is h(x) = 6 a linear function and why

Answers

Answer:

yes, absolutely. specifically it's a horizontal line at 6.

whats the rate of change

Answers

The line needs to start at the 0 it can’t be off the 0

What should the IUPAC name for a binary covalent compound lack? prefixes Roman numerals an -ide ending the name of a nonmetal.​

Answers

The  IUPAC name for a binary covalent compound lack prefixes such as mono, di, tri tetra etc.

A binary compound is a compound that is composed of only two elements. Many binary compounds could be made up of a metal and a nonmetal or even two nonmetals as the case may be. Examples of binary compounds include; SO2, NaH, K2S etc.

We must note that a binary covalent compound uses Roman numerals to indicate the oxidation state of the central atom in the compound. For instance, SO2 is called Sulfur IV oxide.

Hence, the  IUPAC name for a binary covalent compound lack prefixes such as mono, di, tri tetra etc.

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