There is a bag with only red marbles and blue marbles. The probability of randomly choosing a blue marble is 2/9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.

Let the original fraction be

[tex]\dfrac{n-1}{n}[/tex]

Now let's increase both numerator and denominator by 2:

[tex]\dfrac{n+1}{n+2}[/tex]

This produces a 1/12 increase:

[tex]\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}[/tex]

The left hand side can be rearranged as

[tex]\dfrac{2}{n^2+2n}=\dfrac{1}{12}[/tex]

Invert both sides:

[tex]\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24[/tex]

Solve the quadratic equation:

[tex]n^2+2n-24=0 \iff n=-6 \lor n=4[/tex]

So, in the first case, the original fraction is

[tex]\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}[/tex]

In the second case, we have

[tex]\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}[/tex]

The number [tex]\log_9(81)[/tex] means: which exponent we have to give to 9 in order to get 81?

Since [tex]81=9^2[/tex], the answer is 2.

Answer:

oop xc

Step-by-step explanation:

You can simplify fractions between powers of the same base as follows:

[tex]\dfrac{a^x}{a^y}=a^{x-y}[/tex]

So, in your case, you have

[tex]\dfrac{3^4}{3^2}=3^{4-2}=3^2=9[/tex]

Answer:

15

Step-by-step explanation:

First do, 30% + 45% = 75%. Then do, 100-75=25.

Lastly,

proportions:

   x/60 = 25/100

So your answer is, 15.

Answer:

Answer is D)14

Step-by-step explanation:

if u convert 3 1/2 into an improper fraction then it should look lie 7/2 the multiply that by 4 which equal 28/2 then divide that and it will equal 14

Answer: 10

Step-by-step explanation:

Well i got 10 if your asking what i think u are

7 1/2 divided by 3/4 = 10

Answer:

The correct option is (d) a student needs to take 10 dance classes to learn the routine. Step-by-step explanation: Given that each dance class is hour and a student takes hours to learn a dance routine. We are to select the TRUE statement. Thus, a student needs 10 dance classes to learn the dance routine.

Step-by-step explanation:

The correct option is (d) a student needs to take 10 dance classes to learn the routine. Step-by-step explanation: Given that each dance class is hour and a student takes hours to learn a dance routine. We are to select the TRUE statement. Thus, a student needs 10 dance classes to learn the dance routine.

Answer:

[tex]m=\frac{-3}{5}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (4, 3)

Point (-1, 6)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

[tex]m=-\frac{3}{5}[/tex]

Step-by-step explanation:

Answer:

x-9

Step-by-step explanation:

HOPE THIS HELP -_-

Answer:

x=2/3

Step-by-step explanation:

6x=3x+2

3x=2

x=2/3

Answer:

Speed = 25miles per hour

Step-by-step explanation:

Represent the time with x and the distance with y

So, from the attachment; we have the following details:

[tex](x_1,y_1) = (0.5,12.5)[/tex]

[tex](x_2,y_2) = (1,25)[/tex]

[tex](x_3,y_3) = (1.5,37.5)[/tex]

Required

Determine the constant speed

Because the train travelled at a constant speed, the speed can be calculated using:

[tex]Speed = \frac{y_3}{x_3}=\frac{y_2}{x_2}=\frac{y_1}{x_1}[/tex]

[tex]Speed = \frac{12.5}{0.5}=\frac{25}{1}=\frac{37.5}{1.5}[/tex]

[tex]Speed = 25=25=25[/tex]

Notice that the result of each division is the same.

Hence, the constant speed is:

Speed = 25miles per hour

Answer:

The price of one pretzel is $-10.75

Step-by-step explanation:

I'm not really sure why the pretzel would be negative dollars, but I checked my answer multiple times and it's right. For this problem you need a system of equations. The system will be 3d+2p=16 (since 3 drinks and 2 pretzels is 16 dollars) and 6d+5p=21.25 (since 6 drinks and 5 pretzels is 21.25 dollars). To solve this system, the first thing we're going to do is multiply the first system by -2 so that we can cancel the d variable. This will leave you with

-6d-4p=-32. Now, you can add this to the other equation. Since the -6 and 6 cancel, we only have the p variable now (that's why we multiplied by -2, to cancel out the d variable when we added later). Now we have -4p=-32 and 5p=21.25. Add these two equations together and you'll get 1p=-10.75, or p=-10.75. If you needed to solve for the drinks, you could plug -10.75 back into one of the first two equations, but for this problem we don't so -10.75 is your answer.

Step-by-step explanation:

There are 40 DuBois students going on a field trip.

Each one pays their teacher $8.75 to cover admission to the museum and lunch.

Admission for the students is $120 and each one gets an equal amount to spend on lunch.

To Find :

How much will each DuBois student be able to spend on lunch.

Solution :

Amount they paid for admission :

\begin{gathered}P =\$ \dfrac{120}{40}\\\\P=\$3\end{gathered}P=$40120P=$3

Now, amount of money to spend on lunch is 8.75 -8.75−3 = $5.75 .

Hence, this is the required solution.

Answer:

Each GT student gets $3 for lunch

Step-by-step explanation:

40 GT student gave teacher $8.75 so you multiply 40 by 8.75= $350.00

To find how much they need to spend for lunch you divide $120 by 40 student because they paid for it. And you get $3!

I hope this helps!

Answer:

The y intercept is the b in y = mx + b

Step-by-step explanation:

Answer:

It has a thick atmosphere which causes extremely high temperatures.

Step-by-step explanation:

venus's atmosphere is almost entirely carbon dioxide, and is also about 90x heavier than earth's atmosphere, which is similar to diving 3,000 feet below the ocean.

In conclusion, the answer would be "It has a thick atmosphere which causes extremely high temperatures."

Answer:

Equation- 50+40h=210

Answer- h=4

Step-by-step explanation:

Just simplify the equation :)

50+40h=210

40h=160

h=4

The electrician worked for 4 hours.

Happy holidays!

Answer:

The answer is 200.

Step-by-step explanation:

The steps are :

[tex] \sqrt[3]{8 \times {10}^{6} } [/tex]

[tex] = \sqrt[3]{8} \times \sqrt[3]{ {10}^{6} } [/tex]

[tex] = {8}^{ \frac{1}{3} } \times {10}^{(6 \times \frac{1}{3} )} [/tex]

[tex] = 2 \times {10}^{2} [/tex]

[tex] = 200[/tex]

Answer:

D. 60

Step-by-step explanation:

Since the question stated that the number of marbles given out to his 6 friends were equal, we are certain that the total number of marbles is a factor or multiple of 6.

The only other assumption here is the number of marbles given has to be whole number. This means we just have to go through the answer choices and pick the one that is a multiple of 6.

A. 15 - This is wrong as 15 is not a multiple of 6.

B. 33 - This is wrong as 33 is not a multiple of 6.

C. 56 - This is wrong as 56 is not a multiple of 6.

D. 60 - This is CORRECT as 60 is a multiple of 6.

If Jorge gives each of his friends 10 marbles each, it would bring the total number of marbles to be 60.

Answer:

15

Step-by-step explanation:

5x3=15

Answer:

I agree buster. I can't even run that far.

Step-by-step explanation:

Answer:

"With the high level of interest in our 45-70

Step-by-step explanation:

Graph shows the solution set for the inequality which is the correct answer would be options (A).

Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Given the system of inequalities as

y>2x-6 and y<2x +4

To determine the solutions, you first have to graph both of the lines in the problem.

y=2x-6 and y=2x +4. Then, to shift them to inequality, you have to shade the half-plane that they represent.

The solution is the space that they have in common. In this case, it will be on the right side of the graph.

Learn more about inequalities here:

brainly.com/question/20383699

#SPJ2

Answer:

Hi :)

Step-by-step explanation:

Answer:

I think the answer is 11 because 2x + 3x=5 and 1 + 10=11

Answer:

he saved about 2300$

Step-by-step explanation:

Answer:

Decimal Places

1.6962 = 1.70 (2 d.p)

0.4247 = 0.425 to 3 d.p

0.007395 = 0.007 to 3 d.p

0.007395 = 0.0074 (4 d.p)

Significant Figures

32 549 = 32 500 (3 s.f)

32 549 = 32 550 (4 s.f)

909 520 = 910 000 (3 s.f)

909 520 = 909 500 (4 s.f)

Hope this helps :)

for the first one it is the second option because of one property of logarithms:

log(a)-log(b)=log[tex]\frac{a}{b}[/tex]

for the second one using the same property we can say that we third option is correct and not the second one but we use one more property of the logarithm

loga(b)^x=xloga(b) the power of the logarithm becomes a fator and [tex]\sqrt[3]{x}[/tex] is equal to [tex]x^{\frac{1}{3}}[/tex]

Answer:

x<6

Step-by-step explanation:

You divide by 6 then change the inequality sign.

Answer:

It might help u , plz Brain-list it

Step-by-step explanation:

The option is not given but still its clear from the graph

That its slope intercept form will be ,

X=0  (the point where it intersect x axis) and Y=0  (the point where it intersect y axis)  

Answer:

y = 8x

Step-by-step explanation:

Hope this helps

(From k12)

Answer:

your answer should be x = -3

Answer:

x=-3

Step-by-step explanation:

7-2x-11+9-3x=20

5-5x=20

-5x=15

x=-3

Answer:

Step-by-step explanation:

Given points:

Ratio of partitioning:

Use of formula:

Substitute values:

Answer:

To combine like terms, add the variable terms together and then add the constants together. When you combine the variable terms, you have 1w + 1w, which is 2w. When you combine the constants, you have 10 – 4, which is 6. The equivalent expression is 2w + 6.

Step-by-step explanation:

Answer:

add both "w" which equals 2w. Then add 10 and -4 which is 6. So the answer is 2w+6... I'm pretty that's the answer make sure to double-check though

Step-by-step explanation:

Hope this helps!!