Two bags contain 10 balls each. Every round, you choose with equal probability one of the 2 bags and pick out a ball. After a while, you choose an empty bag. What is the probability for the other bag to contain exactly 4 balls at that time?
a. 2.90%
b. 6.10%
c. 10.80%
d. 12.20%

first lets collect the x's so -12x + x is -11x (think about a number line if you are not sure) then we minus 3x so we get  -14x

-9 + 5 is -4 then if we minus 1 we get -5 so

- 14x - 5

Answer: Combine each like term. Any number in this expression with the variable x is a like term. -12x+1x-3x=-14x. The numbers with no variable are like terms. -9+5-1=-5. The simplified expression is -14x-5.

Step-by-step explanation:

Answer:

A length of a ray cannot be measured therefore it's refferd to as infinite. same

Answer: 161/13

Step-by-step explanation: 1. Multiply the denominator by The number

2. add the answer from step one to the numerator

3. Write the answer from step 2 over the denominator

Answer:

3 ones

2 tenths

8 hundredths

I'm sorry if I misunderstood.

Good luck though! :)

Please add Brainliest if you'd like, not that it matters.

[tex]\bf \underline{ \underline{Given : }}[/tex]

[tex]\bf \underline{ \underline{To \: be \: calculated : }}[/tex]

Calculate the curved surface area of the cone .

[tex]\bf \underline{ \underline{Formula \: applied : }}[/tex]

Curved surface area of cone = πrl

[tex]\bf \underline{ \underline{Solution : }}[/tex]

First of all,

Radius = Diameter/2

=> Radius,r = 14/2

=> Radius,r = 7 cm

Now,

[tex] \sf{Curved \: surface \: area \: of \: cone =\pi rl}[/tex]

[tex] \sf \: \implies \: \dfrac{22}{ \cancel7} \times \cancel7 \times 8.45[/tex]

[tex] \sf\implies22 \times 8.45[/tex]

[tex] \sf \implies 185.9 \: {cm}^{2} [/tex]

Hence,the Curved surface area of cone is 185.9 cm².

Answer:[tex]S(t)=12-0.75t[/tex]

Step-by-step explanation:

Given: The snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours  after the storm ended, after the storm ended, the depth of snow was down to 9 inches.

Snow melted in 4 hours = [tex]0.75\times4 =3\text{ inches}[/tex]

Initial depth of snow = 9 + 3 inches = 12 inches.

Now, depth of snow on Tristan's lawn = Initial depth -0.75(Number of hours)

Let S(t) be the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling.

Then, [tex]S(t)=12-0.75t[/tex]

The linear equation that represents the depth of snow on Tristan's lawn, in inches, t hours  after the snow stopped falling is:

[tex]S(t) = 12 - 0.75t[/tex]

A linear function in the model will have the following format:

[tex]S(t) = S(0) - mt[/tex]

In which:

The snow melts at a rate of 0.75 inches per hour, thus [tex]m = 0.75[/tex] and:

[tex]S(t) = S(0) - 0.75t[/tex]

After 4 hours, there were 9 inches, that is, when [tex]t = 4, S(t) = 9[/tex], and this is used to find S(0).

[tex]S(t) = S(0) - 0.75t[/tex]

[tex]9 = S(0) - 0.75(4)[/tex]

[tex]S(0) = 9 + 0.75(4)[/tex]

[tex]S(0) = 12[/tex]

Hence, the equation is:

[tex]S(t) = 12 - 0.75t[/tex]

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Taking any number x, and adding on its opposite -x, leads to x+(-x) = x-x = 0

This is the inverse property of addition.

A numeric example would be 7 + (-7) = 7-7 = 0

Going back to x-x = 0, we can replace x with any expression (whether simple or complicated) we want.

So in this case, we replace each 'x' with 'x+3' to get (x+3)-(x+3) = 0

The equation (x+3)-(x+3) = 0 has infinitely many solutions. The solution set is the set of all real numbers. We can replace x with any number and the original equation will simplify to a true statement.

Answer: $160.18

Step-by-step explanation:    

Answer:

$160.18

Step-by-step explanation:

The cabinet's sale price (or in this case, sub-total) is $149. The sales tax is 7.5%, which means you must multiply 149 x 7.5% to get 11.175. After you do this, you must add the 11.175 (which we will round to $11.18 for your tax) to your subtotal ($149). Since $149 + $11.18 = $160.18, you will have to pay a total of $160.18 for the cabinet.

Answer:

divide both sides by 23

making it to be 0.26

The value of x from the equation 23x =6 is x= 6/23.

To solve for the value of x in the equation 23x = 6, we need to isolate x on one side of the equation.

Divide both sides of the equation by 23:

(23x) / 23 = 6 / 23

Simplifying:

x = 6 / 23

Therefore, the value of x is 6 divided by 23, which can be left as a fraction or decimal depending on the desired form.

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Answer:

C

Step-by-step explanation:

3-(-5=8

3+5=8

They are on the same x axis so all you have to do is add 3 and 5 together.

Answer:

c) Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.

Step-by-step explanation:

a) Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.

b) Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.

c) Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.

d) Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=√8

Answer:

Difference = 3x² + 3x + 1

See Explanation

Step-by-step explanation:

Required: How changes in sides of a cube affects its volume.

Take for instance the side of the cube is x.

The initial volume would be:

Volume = x * x * x

Volume = x³

When then dimension is increased by 1 unit, the new volume would be

Volume = (x + 1) * (x + 1) * (x + 1)

Expand the brackets

New Volume = (x² + 2x + 1)(x + 1)

New Volume = x³ + 3x² + 3x + 1

[Calculate the difference between both volumes]

Difference = New Volume - Initial Volume

Difference = x³ + 3x² + 3x + 1 - x³

[Collect like terms]

Difference = x³ - x³ + 3x² + 3x + 1

Difference = 3x² + 3x + 1

So, there will be a difference of 3x² + 3x + 1 when the dimension is increased from x to x + 1

Take for instance: a dimension of 2 units is increased to 3 units

Initial Volume = 2³ = 8

New Volume = 3³ = 27

Difference = 27 - 8

Difference = 19

Using the derived formula (x = 2)

Difference = 3x² + 3x + 1

Substitute 2 for x

Difference = 3 * 2² + 3 * 2 + 1

Difference = 3 * 4 + 6 + 1

Difference = 12 + 6 + 1

Difference = 19

Answer: 7+0.7+0.05

Since 7 is in the ones place it goes in front of the decimal. .7 is in the tenth place because it's behind the decimal. .05 is also behind the decimal so it's in the hundredths place.

Answer:

341.5 because it makes the most sense

Answer:

340.511

Step-by-step explanation:

The five in the tenths place would make you round up.

Hope this helps! Can I get Brainliest? I’ve never had it before.

Answer:

[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

cross simplify

[tex]\frac{1}{8}[/tex] • [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{2}[/tex] • [tex]\frac{1}{5}[/tex]

multiply

[tex]\frac{1}{2}[/tex] • [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{10}[/tex]

Answer:

83, 97, 111 i think that is what you are asking

Answer:

83, 97,111

Step-by-step explanation:

Answer:8^20

Step-by-step explanation:

I just say 10x2=20 lol

Answer:

[tex]8^{20}[/tex]

Step-by-step explanation:

8^10*2

8^20

Answer:

12

Step-by-step explanation:

The number of shells collected by Paula is 12 shells

The correct answer is B.

The given expression:

total number of shells collected by the friends, t = 43 shells

number of shells collected by Paula = x

number of shell collected by Bethany = 2x - 3

number of shell collected by Jerrell = [tex]\frac{x}{2} + 2[/tex]

To find:

The number of shells collected by Paula is calculated as follows:

[tex]x + (2x-3 ) + (\frac{x}{2} + 2) = 43\\\\3x + \frac{x}{2} - 1 = 43\\\\\frac{6x + x}{2} = 43 + 1\\\\\frac{7x}{2} = 44\\\\7x = 88\\\\x = \frac{88}{7} \\\\x \approx 12 \ shells[/tex]

Thus, the number of shells collected by Paula is 12 shells

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Answer:

a

mean [tex]\mu = 10[/tex] variance [tex]\sigma^2 = 6[/tex]

b

The binomial random variable x fall into this interval ranges from

     - 5  to  5

c

[tex]P(6 \le x \le 14) = 0.8969[/tex]  

Step-by-step explanation:

From the question we are told that

  The sample size is  [tex]n = 25[/tex]

   The  percentage that look for gas stations and food outlets that are close to or visible from the highway is  [tex]p = 0.40[/tex]

Generally the mean is mathematically represented as

       [tex]\mu = n * p[/tex]

=>     [tex]\mu = 0.40 * 25[/tex]

=>    [tex]\mu = 10[/tex]

The variance is mathematically represented as

      [tex]\sigma^2 = np(1- p )[/tex]

=>   [tex]\sigma^2 = 25 * 0.40(1- 0.40 )[/tex]

=>    [tex]\sigma^2 = 6[/tex]

The  standard deviation is mathematically evaluated as

     [tex]\sigma = \sqrt{\sigma^2}[/tex]

     [tex]\sigma = \sqrt{6}[/tex]

    [tex]\sigma = 2.45[/tex]

The  interval is evaluated as

       [tex]p\pm 2 \sigma[/tex]

=>   [tex]p - 2 \sigma\ \ \ , \ \ \ p + 2\sigma[/tex]

=>   [tex]0.40 - 2 *2.45\ \ \ , \ \ \ 0.40 + 2* 2.45[/tex]

=>   [tex]-4.5\ \ \ , \ \ \ 5.3[/tex]

The binomial random variable x fall into this interval ranges from

     - 5  to  5

Generally

    [tex]P(6 \le x \le 14) = P(\frac{ x - \mu }{\sigma } \le \frac{14 - 10}{{2.45}} ]-P[ \frac{ x - \mu }{\sigma } \le \frac{6 - 10}{2.45 } ][/tex]

     [tex]P(6 \le x \le 14) = P(Z \le 1.63 ]-P[ Z \le -1.63 ][/tex]

     [tex]P(6 \le x \le 14) = [1- P(Z > 1.63 ]] -[1- P[ Z > -1.63 ]][/tex]      

From the z-table  

                 [tex]P(Z > 1.63 ) = 0.051551[/tex]

And

                [tex]P(Z >- 1.63 ) =0.94845[/tex]

=>        [tex]P(6 \le x \le 14) = [1-0.051551] -[1-0.94845][/tex]      

=>        [tex]P(6 \le x \le 14) = 0.8969[/tex]  

To solve this polynomial equation, we will need to factor the left side.

On the left, we have a a trinomial in a special form that

can be factored as the product of two binomials.

The trinomial on the left can be factored which makes life easier.

This factors as (x + 11)(x - 2) = 0.

This means that either x + 11 = 0 or x - 2 = 0.

Solving each equation from here, we get x = -11 or x = 2.

So the solution is {-11, 2}.

Answer:

2 and -11

Step-by-step explanation:

Step 1: Use the quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^{2-4ac} } }{2a} \\x=\frac{-9+-\sqrt{9^{2}-4(1) (-22)} }{2(1)} \\x=\frac{-9+-\sqrt{169} }{2(1)}\\x=\frac{-9+-13 }{2}\\x1=\frac{-9+13 }{2}\\x1=\frac{4}{2} \\x1 = 2\\x2 = \frac{-9-13 }{2}\\x2 = \frac{-22 }{2}\\x2 = -11\\[/tex]

Therefore the values of 'x' that make the equation true is 2 and -11

Answer:

There is an accident ahead, which often causes traffic to slow.

Step-by-step explanation:

Looking at the question closely, we understand that the traffic jam occurred at a time that is not generally regarded as a rush hour.

A traffic jam due to road repair is not really an option because roads are closed during repairs. Shop malls announce their special sales days ahead of time so that many people will hear about it.

However, it is likely that an accident occurred. An road accident may suddenly occur on an otherwise less busy road. This often leads to an unusual delay in traffic irrespective of the hour of the day when it occurs.

Answer:

x=20

Step-by-step explanation:

<2 = <3 when the lines are parallel

3x-10 = x+30

Subtract x from each side

3x-10 -x = x+30-x

2x-10 = 30

Add 10 to each side

2x-10 +10 = 30+10

2x = 40

Divide by 2

2x/2= 40/2

x =20

Answer:

Total Earnings = 18,160

1) 1.07 * principal1 *  + 1.06  * principal2= 18,160

2) principal1 + principal2 = 17,000

We'll multiply equation 2) by -1.06

2) -1.06*principal1 -1.06*principal2 = -18,020 then adding equation 1)

1) 1.07 * principal1 *  + 1.06  * principal2= 18,160

.01*principal1 = 140

principal 1 = 14,000

and therefore principal 2 = 3,000

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

first you plug in 4 for x and -3 for y. then you solve

Answer: 50 and 5, respectively

Step-by-step explanation:

For this problem, we are given x and y. With the x and y value given, all we have to do is to plug them into the expressions and solve.

5(x-2y)                        [plug in x=4 and y=-3]

5((4)-2(-3))                 [combine like terms by using order of operations]

5(4+6)

5(10)=50

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

2x+y                            [plug in x=4 and y=-3]

2(4)+(-3)                     [combine like terms by using order of operations]

8-3=5

Now that we have plugged in x=4 and y=-3 into the two expressions, we get 50 for the first expression and 5 for the second equation.

Answer:

1) yes ; 2) 1/36 ; 3) 1/36 ; 4) 1/18

Step-by-step explanation:

Given the following :

Two fair dice : 1 green ; 1 red

A) Are the outcomes on the dice independent:

Yes, becomes the outcome of the green dice does not have any effect on the outcome of the red dice.

B) Find P(1 on green die and 5 on red die).

Probability = (number of required outcome) / (total possible outcomes)

Total outcomes of a dice = 6

P(1 on green) = 1 / 6

P(5 on red) = 1/6

P(1 on green die and 5 on red die) :

(1/ 6) × (1/6) = 1/36

C) Find P(5 on green die and 1 on red die)

P(5 on green) = 1/6

P(1 on red) = 1/6

Find P(5 on green die and 1 on red die):

1/6 × 1/6 = 1/36

D) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die))

P(5 on green die and 1 on red die) = 1/36

P(1 on green die and 5 on red die) = 1/36

P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) =

P(5 on green die and 1 on red die) + P(1 on green die and 5 on red die)

= (1/36 + 1/36) = 2 /36 = 1/18

Answer:

Step-by-step explanation:

Represent the equation as follows:

[tex]a * b = c[/tex]

Where a,b and c are decimal numbers

To solve further, we make use of trial by error method

Let

[tex]a = 2.52[/tex]

[tex]b = 0.6[/tex]

Such that

[tex]2.5 * 0.6 = c[/tex]

[tex]1.512 = c[/tex]

[tex]c = 1.512[/tex]

This set of digits do not follow the rule in the question

Let

[tex]a = 2.55[/tex]

[tex]b = 1.6[/tex]

[tex]2.55 * 1.6 = c[/tex]

[tex]4.08 = c[/tex]

[tex]c = 4.08[/tex]

The result has only 2 non zeros (4 and 8)

Hence

[tex]2.55 * 1.6 = 4.08[/tex] answers the question.

However, there are other set of numbers that can be used too

One of the equation which illustrates and meets the conditions given is :

First number, x = 1.25

First number, x = 1.25 Second number, y = 0.2

Result = first Number × second number

Result = 1.25 × 0.2

Result = 1.25 × 0.2 Result = 0.25

Evaluating the result : 0.25

Number of digits = 3

Non - zero digits = 2

There are several values of x and y which will satisfy the 3 conditions given.

Therefore, the product of the values 1.25 and 0.2 gives the required output.

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Answer: x=-6

Step-by-step explanation:

Undefined slopes are vertical lines, so there's no y variable in the equation. so you look at the point (-6, -8) and take out the y, which is negative eight. So your answer is negative six.

The equation of the line that passes through the point (-6, -8) and has an undefined slope will be y + 8 = m (x + 6).

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Then the equation of the line that passes through the point (-6, -8) and has an undefined slope will be

y + 8 = m (x + 6)

The equation of the line that passes through the point (-6, -8) and has an undefined slope will be y + 8 = m (x + 6).

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Answer:

a) 1/11 (b) 7/22 (c) 5/11 (d) 0 (e) 19/66

Step-by-step explanation:

Given the following :

Number of Blue socks = n(B) = 4

Number of Gray socks = n(G) =5

Number of black socks = n(Bl) = 3

Total number of socks = (4 + 5 + 3) = 12

Probability = ( number of required outcomes / number of total possible outcomes)

Picking 2 socks at random:

A) probability of two blue socks :

Ist pick = p(B) = (4/12) = 1/3

Number of Blue socks left = (4 - 1) =3

Total socks left = 12 - 1 = 11

2nd pick = p(B) = (3/11)

P(2 blue socks) = (1/3 * 3/11) = 3 /33 = 1/11

B) No gray socks :

Number of non - gray socks = (4 + 3) = 7

1st pick = 7/12

After 1st pick non-gray socks left = 6

Total socks left = 11

2nd pick = 6 / 11

P(non-gray) = (7/12 × 6/11) = 42/132 = 7/22

C.) Atleast one black socks = (1 - P(no black))

Number of non-black socks = (4 +5) = 9

1st pick = 9/12 = 3/4

After 1st pick, non-black left = 8, total = 11

2nd pick = 8/11

P(non - black) = (3/4 × 8/11) = 24/44 = 6/11

P(atleast 1 black) = (1 - 6/11) = 5 /11

D.) A green socks

Number of green socks = 0

P(green) = 0

E.) A matching socks :

1) matching black socks :

Ist pick = p(Bl) = (3/12) = 1/4

Number of Black socks left = (3 - 1) =2

Total socks left = 12 - 1 = 11

2nd pick = p(Bl) = (2/11)

P(matching black socks) = (1/4 * 2/11) = 2 /44 = 1/22

11) matching blue socks:

Ist pick = p(B) = (4/12) = 1/3

Number of Blue socks left = (4 - 1) =3

Total socks left = 12 - 1 = 11

2nd pick = p(B) = (3/11)

P(matching blue socks) = (1/3 * 3/11) = 3 /33 = 1/11

111) matching gray socks :

Ist pick = p(B) = (5/12) = 5/12

Number of Blue socks left = (5 - 1) =4

Total socks left = 12 - 1 = 11

2nd pick = p(B) = (4/11)

P(matching gray socks) = (5/12 * 4/11) = 20/132 = 5 /33

Summing the probabilities :

(1/22 + 1/11 + 5/33) = (3 + 6 + 10) / 66 = 19/66

Using the hypergeometric distribution, it is found that there is a:

a) 0.0909 = 9.09% probability that you end up with 2 blue socks.

b) 0.3182 = 31.82% probability that you end up with no gray socks.

c) 0.4545 = 45.45% probability that you end up with at least 1 black sock.

d) 0% probability that you end up with a green sock.

e) 0.2879 = 28.79% probability that you end up with matching socks.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

Item a:

The probability is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,12,2,4) = \frac{C_{4,2}C_{8,0}}{C_{12,2}} = 0.0909[/tex]

0.0909 = 9.09% probability that you end up with 2 blue socks.

Item b:

The probability is P(X = 0), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,12,2,5) = \frac{C_{5,0}C_{7,2}}{C_{12,2}} = 0.3182[/tex]

0.3182 = 31.82% probability that you end up with no gray socks.

Item c:

The probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,12,2,3) = \frac{C_{3,0}C_{9,2}}{C_{12,2}} = 0.5455[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.5455 = 0.4545[/tex]

0.4545 = 45.45% probability that you end up with at least 1 black sock.

Item d:

There are no green socks, hence 0% probability that you end up with a green sock.

Item e:

Hence, for two gray:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,12,2,5) = \frac{C_{5,2}C_{7,0}}{C_{12,2}} = 0.1515[/tex]

Then, for two black:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,12,2,3) = \frac{C_{3,2}C_{9,0}}{C_{12,2}} = 0.0455[/tex]

Then, the probability of matching socks is:

[tex]p = 0.0909 + 0.1515 + 0.0455 = 0.2879[/tex]

0.2879 = 28.79% probability that you end up with matching socks.

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

Work Shown:

cos(angle) = adjacent/hypotenuse

cos(x) = 5/12

x = arccos(5/12)

x = 65.375681647836 which is approximate

x = 65.4 after rounding to one decimal place

Make sure your calculator is in degree mode. The arccosine function is the same as the inverse cosine function (shortened to [tex]\cos^{-1}[/tex] ).

Answer:

c)

The distribution is skewed down the middle,

Therefore it is symmetric.