A box contains 8 white balls, 7 black balls, & 2 red balls.
a) how many red balls must be added to the box so that the probability of drawing a red ball is 8/9
b)how many black balls must be added to the original box so that the probability of drawing a white ball is 1/9?

Answers

Answer 1

Answer:

a) 118

b) 55

Step-by-step explanation:

a) Originally, there are 2 red balls and a total of 17 balls.

8/9 = (2 + x) / (17 + x)

8 (17 + x) = 9 (2 + x)

136 + 8x = 18 + 9x

x = 118

b) Originally, there are 8 white balls and a total of 17 balls.

1/9 = 8 / (17 + x)

17 + x = 72

x = 55


Related Questions

coeffecient of x in -7xyz2

Answers

☽------------❀-------------☾

Hi there!

~

The coefficient of x in -7xyz2 is -7.

❀Hope this helped you!❀

☽------------❀-------------☾

Classify the equation as a conditional equation, an identity, or a contradiction. 6x−10−8=9+4x−4x

Answers

Step-by-step explanation:

this is your answer.........

Answer:

conditional equation

Step-by-step explanation:

Collecting terms on both sides, we get

6x−10−86x−18=9+4x−4x=9

Adding 18 to both sides of the equation, we get

6x=27

This can be solved by dividing by 6 on both sides of the equation, which gives a unique solution of 92. So, this is a conditional equation.

Can someone help pls the question in the pic (geometry)

Answers

Answer:

Reflection over y axis, and translate right 1

Step-by-step explanation:

reflecting over the y-axis

Find the surface area of a square pyramid if the area of the base is 324 cm squared and the height is 40 cm.

Answers

Answer:

height h = 324 cm

slant height s = 324.61669704438 cm

side length a = 40 cm

lateral edge length e = 325.23222472566 cm

1/2 side length r = 20 cm

volume V = 172800 cm^3

lateral surface area L = 25969.33576355 cm^2

base surface area B = 1600 cm^2

total surface area A = 27569.33576355 cm^2

Step-by-step explanation:

Total Surface Area of a square pyramid:

A = L + B = a^2 + a√(a^2 + 4h^2))

A = a(a + √(a^2 + 4h^2))

Agenda:

h = height

s = slant height

a = side length

e = lateral edge length

r = a/2

V = volume

L = lateral surface area

B = base surface area

A = total surface area

Can someone explain aswell

Answers

Answer:

24 ft²

Step-by-step explanation:

find the length of the base of each triangle through a² + b² = c², c being hypotenuse.

after finding the length of each individual base, use A= 1/2bh (multiply base and height and then divide by 2) to calculate area of each triangle. then add and round. hope this helps

find the value of x so that f (x)=7

Answers

Answer:

i think its 24

Step-by-step explanation:


A club is choosing 2 members to serve on a committee. The club has
nominated 3 women and 3 men. Based on chance alone, what is the
probability no women are chosen to be on the committee?

Answers

Answer: The probability that no women are chosen to be in the committee is 2/5 or 0.40.

Step-by-step explanation:

We have two positions, and we have 6 options for those positions, 3 are men, and 3 are women.

If we want to see the probability where no women are chosen, then this means that in the first selection a man is chosen.

If all the 6 nominees have the same probability of being chosen, then the probability that in the first selection a man is chosen is equal to the number of men divided the total number of nominees, this is:

p1 = 3/6 = 1/2.

Now the same happens for the second selection, but now we have 5 total nominees and 2 are men, so the probability now is:

p2 = 2/5

And the joint probability will be the product of the individual probabilities, then we have:

P = p1*p2 = (1/2)*(2/5)  = 2/5.

The probability that no women are chosen to be in the committee is 2/5 or 0.40.

The probability that no woman is chosen to be on the committee is 0.40.

Given

A club is choosing 2 members to serve on a committee.

The club has nominated 3 women and 3 men.

The number of ways to select two persons from 6 will be:

[tex]\rm = ^6C_2[/tex]

Therefore,

The probability that no woman is chosen to be on the committee is;

[tex]= \dfrac{1}{2} \times \dfrac{2}{5}\\\\= \dfrac{1}{5}\\\\=0.40[/tex]

Hence, the probability that no woman is chosen to be on the committee is 0.40.

To know more about Probability click the link given below.

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Approximtely how many 27cubic volume cabinets will a container98,000cbic volume hold?

Answers

Answer: 3630

Step-by-step explanation:

Given that:

Volume of container = 98,000 cubic volume

Volume of cabinet = 27 cubic volume

The number of cabinets which the container will. Hold equals:

Volume of container / volume of cabinet

= 98000 cubic volume / 27 cubic volume

= 3629.6296

The container will hold approximately 3630 27 cubic volume of cabinet.

3x + 2(4x - 4) = 3
What’s the answer?

Answers

3x+2(4x-4)=3 - remove parentheses
3x+ 8x-8=3 - collect like terms
11x- 8 =3 - move the constant to the right
11x=3+8 - calculate
11x = 11 - divide both sides by 11
x= 1

make doubles. add 5+6

Answers

Answer:11

Step-by-step explanation:

What type of number is 3π+1?

Answers

Answer:

irrational

Step-by-step explanation:

I hope it helped you!!

Answer:

10.42478

Step-by-step explanation:

The expression that represents the area of this rectangle is . When b = 10, the area of the rectangle is square units.

Answers

Answer: 8b and 80

Step-by-step explanation: H3h3

The Area of Rectangle is 80 unit².

What is Area of rectangle?

The Area of rectangle is the product of its length to its width.

Area of rectangle = length x width

Given:

Expression that represents the area of this rectangle is 8b.

Now, b = 10

As, area of rectangle = l x w

area of rectangle = 8b

area of rectangle = 8 x 10

area of rectangle = 80 unit².

Hence, the area is 80 unit².

Learn more about Area of rectangle here:

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#SPJ2

Pls help with the explanation and answer ty!

Answers

I’m sorry, the text is too small. But I hope you find your answer soon.
Karen bought 16 boxes of pencil

Consider a situation that you might need to use your understanding of probability to make an informed decision.

Answers

When considering entering the lottery or paying to play a game at a carnival.

solve integers -32+ 10

Answers

Answer:

-22

Step-by-step explanation:

You have to add -32+10

and you will get the answer -22

Answer:

-22

Step-by-step explanation:

On a number line, negative numbers go left and posative numbers go right. So on a numberline, if you find -32 and jump ten spaces to the right, you land on -22

1-89. On graph paper, draw the quadrilateral with vertices A(–1, 3), B(4, 3), C(–1, –2), and D(4, –2). a. What kind of quadrilateral is this?

Answers

Answer:

it is a square

because

as we can see in the graph the

distance from A to B is 5 cm

distance from B to C is 5 cm

distance from C to D is 5 cm

distance from D to A is 5 cm

please mark me as the brainliest I really need it

A manufacturing company plans to progressively increase its production capacity over the next few quarters. (A quarter is a period of three months.) The increase in production can be modeled by the equation y = x6 − 25x4 + 199x2, where x is the number of quarters. What is the minimum duration required for the company to reach a production capacity of 4,975 units?

Answers

Answer:

  5 months

Step-by-step explanation:

We assume that y represents production capacity, rather than increase in production capacity. Then we want to solve the 6th-degree equation ...

  x^6 -25x^4 +199x^2 -4975 = 0

This can be factored in groups as ...

  x^4(x^2 -25) + 199(x^2 -25) = 0

  (x^4 +199)(x^2 -25) = 0

This has 4 complex solutions and 2 real solutions.

  x^2 = 25

  x = ±5

The duration required for capacity to reach 4975 units is 5 months.

Lila works 40 hours a week and earns $9 an hour . Her baby stays with a sitter during the hours Lila works . Lila pays the sitter $5 an hour . After paying the sitter , how much of her paycheck does Lila have left

Answers

Answer: $160

Step-by-step explanation: If she works 40 hours a week, than that is $360 a week, if she pays the sitter $5 a week, then that means she pays the sitter $200 a week.  Subtract and you get $160.  

How many terms of the series of - 3+0+3+6+9+...are needed to give a sum of 105?​

Answers

Answer:

10

Step-by-step explanation:

Remember that the formula for the sum of an arithmetic series is:

[tex]S=\frac{k}{2}(a+x_k)[/tex]

Where k is the number of terms, a is the initial term, and x_k is the last term of the series.

We essentially want to find k, the number of terms, given that the sum S is equal to 105. So, substitute 105 into our equation:

[tex]105=\frac{k}{2}(a+x_k)[/tex]

To do so, we need to final term x_k. We don't know what it is yet, but that doesn't matter. All we need to do is to write it in terms of k. First, remember that the standard form for the explicit formula of an arithmetic sequence is:

[tex]x_n=a+d(n-1)[/tex]

Where a is the first term, d is the common difference, and n is the nth term.

From our sequence, we can see that the first term is -3.

Also, we can determine that our common difference is +3, since each subsequent term is 3 more than the previous one. -3+3 is 0, 0+3 is 3, 3+3 is 6, and so on.

Therefore, our explicit formula is:

[tex]x_n=-3+3(n-1)[/tex]

Therefore, our final term, x_k, will be if we substitute k for n. So, we can acquire the equation:

[tex]x_k=-3+3(k-1)[/tex]

Now that we know what x_k is, we can substitute that into our original equation:

[tex]105=\frac{k}{2}(a+x_k)[/tex]

Substitute the equation into x_k. Also, let's substitute -3 (our first term) for a. So:

[tex]105=\frac{k}{2}(-3+(-3+3(k-1)))[/tex]

And now, all we have to do is to solve for k.

First, distribute the 3:

[tex]105=\frac{k}{2}(-3+(-3+3k-3))[/tex]

Add within the parentheses:

[tex]105=\frac{k}{2}(3k-9)[/tex]

Multiply both sides by 2. This removes the fraction on the right:

[tex]210=k(3k-9)[/tex]

Distribute. We will get a quadratic:

[tex]210=3k^2-9k[/tex]

So, let's solve for k. Let's divide everything by 3:

[tex]70=k^2-3k[/tex]

Subtract 70 from both sides:

[tex]0=k^2-3k-70[/tex]

Factor. We can use -10 and 7. So:

[tex]0=(k-10)(k+7)[/tex]

Zero Product Property:

[tex]k-10=0\text{ or } k+7=0[/tex]

Solve for k for each equation:

[tex]k=10\text{ or } k=-7[/tex]

-7 doesn't make sense (we can't have -7 terms). Remove that solution. So, we are left with:

[tex]k=10[/tex]

Therefore, the number of terms we have in our series for our sum to be 105 is 10.

And we're done!

Hi okay no question hello

Answers

hey how are you doing

Answer:

Hello

Step-by-step explanation:

yUh GeT iNtO iT

Graph the line with slope -1/2
passing through the point (-2, 4).

Answers

This image should help with that.                                                

A tourist information center is between a bus station and a train station. When mapped on a grid, the tourist information center is located at (1,4) and the bus is located at (-3,7) The train station is located at point

Answers

Answer: The train station is located at point (5,1).

Step-by-step explanation:

Given: On a grid, information center is located at (1,4) and the bus is located at (-3,7).

A tourist information center is between bus station and train station.

i.e.  tourist information center is a mid point  of line joining bus station and  train station.

Midpoint between (a,b) and (c,d) is given by :-

[tex](x,y)=(\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex]

Let (a,b) be the coordinates of train station , then

[tex](1,4)=(\dfrac{-3+a}{2},\dfrac{7+b}{2})\\\\\Rightarrow\ 1=\dfrac{-3+a}{2}\ \ \ , 4=\dfrac{7+b}{2}\\\\\Rightarrow\ 2=-3+a\ \ \ , 8=7+b\\\\\Rightarrow\ 2+3=a\ \ \ , 8-7=b\\\\\Rightarrow a= 5,\ \ b=1[/tex]

Hence, the train station is located at point (5,1).

Question 8
Solve the equation.
1/3x + 205
Your answer:
A.-9
B.13
C.9

Answers

Answer: none of thoses

Step-by-step explanation:

The answer actually is 1/3x(x+615)

Find the midpoint of the line segment with the given endpoints (-3,1 -2,8) (-4.92,-3.3)

Answers

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

Find the midpoint of the line segment with the given endpoints (-1,-6) (-6,5)

Answers

The correct answer is (-7/2,-1/2) or (-3.5,-0.5)  To find the midpoint of a segment, add both "x" coordinates, divide by 2.  Then add both "y" coordinates, and divide by 2

What is 15 x minus 3 y = 0 written in slope-intercept form? y = 5x y = negative 5 x x = one-fifth y x = 5 y

Answers

Answer:

y=5x

Step-by-step explanation:

Answer:

y=5x

Step-by-step explanation:

A rocket leaves the surface of Earth at time t=0 and travels straight up from the surface. The height, in feet, of the rocket above the surface of Earth is given by y(t), where t is measured in seconds for 0≤t≤600. Values of y(t) for selected values of t are given in the table above. Of the following values of t, at which value would the speed of the rocket most likely be greatest based on the data in the table?

(1) t=100

(2) t=200

(3)t=300

(4) t=400

Answers

Answer:

Remember that:

Speed = distance/time.

Then we can calculate the average speed in any segment,

Let's make a model where the average speed at t = t0 can be calculated as:

AS(t0) = (y(b) - y(a))/(b - a)

Where b is the next value of t0, and a is the previous value of t0. This is because t0 is the middle point in this segment.

Then:

if t0 = 100s

AS(100s) = (400ft - 0ft)/(200s - 0s) =   2ft/s

if t0 = 200s

AS(200s) = (1360ft - 50ft)/(300s - 100s) = 6.55 ft/s

if t0 = 300s

AS(300s) = (3200ft - 400ft)/(400s - 200s) =  14ft/s

if t0 = 400s

AS(400s) = (6250s - 1360s)/(500s - 300s) = 24.45 ft/s

So for the given options, t = 400s is the one where the velocity seems to be the biggest.

And this has a lot of sense, because while the distance between the values of time is constant (is always 100 seconds) we can see that the difference between consecutive values of y(t) is increasing.

Then we can conclude that the rocket is accelerating upwards, then as larger is the value of t, bigger will be the average velocity at that point.

Speed is simply the rate of change of distance over time.

The greatest speed is at [tex]t = 400[/tex]

To calculate the time of the greatest speed, we simply calculate the slope between each interval.

The slope (m) of a line is:

[tex]m = \frac{y_2 - y_1}{t_2 - t_1}[/tex]

When [tex]t = 100[/tex]

[tex](t_1,y_1) = (0,0)[/tex]

[tex](t_2,y_2) = (200,400)[/tex]

So, we have:

[tex]m = \frac{400-0}{200 -0}[/tex]

[tex]m= \frac{400}{200}[/tex]

[tex]m = 2[/tex]

When [tex]t = 200[/tex]

[tex](t_1,y_1) = (100,50)[/tex]

[tex](t_2,y_2) = (300,1360)[/tex]

So, we have:

[tex]m = \frac{1360-50}{300 -100}[/tex]

[tex]m = \frac{1310}{200}[/tex]

[tex]m = 6.55[/tex]

When [tex]t = 300[/tex]

[tex](t_1,y_1) = (200,400)[/tex]

[tex](t_2,y_2) = (400,3200)[/tex]

So, we have:

[tex]m = \frac{3200-400}{400 -200}[/tex]

[tex]m = \frac{2800}{200}[/tex]

[tex]m = 14[/tex]

When [tex]t = 400[/tex]

[tex](t_1,y_1) = (300,1360)[/tex]

[tex](t_2,y_2) = (500,6250)[/tex]

So, we have:

[tex]m = \frac{6250-1360}{500-300}[/tex]

[tex]m = \frac{4890}{200}[/tex]

[tex]m = 24.45[/tex]

From the above computation, the greatest speed (i.e. slope) is

[tex]m = 24.45[/tex]

The corresponding time at [tex]m = 24.45[/tex] is [tex]t = 400[/tex]

Hence, the greatest speed is at [tex]t = 400[/tex]

Read more about speed at:

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Is 7.0001 is terminating or repeating decimals

Answers

Answer:

it is terminating

Step-by-step explanation:

In 1970, a farmer using a two-row combine with a corn head could easily harvest 0.75 ha (1.85 acres) per hour and a typical corn yield was 5000 kg/ha (80 bu/acre). Before 1940, most corn was harvested by hand and a skilled person could harvest 250 kg/h (10 bu/h). Calculate the productivity ratio.

Answers

Answer:

The value is [tex]w = 6.7 \%[/tex]

Step-by-step explanation:

Generally the productivity rate is mathematically represented as

[tex]P_r = K * Z[/tex]

Here K is the ha the farmer could harvest in an hour and Z is a typical yield of corn in kg/ha

Now considering 1970

The productivity rate is

[tex]P_r = 0.75 *5000[/tex]

=> [tex]P_r = 3750 \ kg/h [/tex]

Now considering 1940

The productivity rate is given as [tex]P_R = 250 \ kg/h [/tex]

Generally the productivity ratio is mathematically ration is mathematically represented as

[tex]w = \frac{P_R}{P_r} * 100[/tex]

=> [tex]w =  \frac{250}{3750}  * 100[/tex]

=> [tex]w = 6.7 \%[/tex]

Which of the following sets are subspaces of R3 ?
A. {(x,y,z)|3x+8y-5z=2}
B. {(x,y,z)|-4x-9y+7z=0}
C. {(x,y,z)|x D. {(-4,y,z)|y,z arbitrary numbers}
E. {(x,0,0)|x arbitrary number}
F. {(-2x,-3x,-8x)|x arbitrary number}

Answers

Answer:

The following are the solution to the given points:

Step-by-step explanation:

for point A:

[tex]\to A={(x,y,z)|3x+8y-5z=2} \\\\\to for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)[/tex]

                                        [tex]=3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)[/tex]

The set A is not part of the subspace [tex]R^3[/tex]

for point B:

[tex]\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)[/tex]

                                             [tex]=-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0[/tex]

[tex]\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon B[/tex]

The set B is part of the subspace [tex]R^3[/tex]

for point C: [tex]\to C={(x,y,z)|x<y<z}[/tex]

In this, the scalar multiplication can't behold

[tex]\to for (-2,-1,2) \varepsilon C[/tex]

[tex]\to -1(-2,-1,2)= (2,1,-1)[/tex] ∉ C

this inequality is not hold

The set C is not a part of the subspace [tex]R^3[/tex]

for point D:

[tex]\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)[/tex]

The scalar multiplication s is not to hold

[tex]\to for (-4, 1,2)\varepsilon D\\\\\to -1(-4,1,2) = (4,-1,-2)[/tex] ∉ D

this is an inequality, which is not hold

The set D is not part of the subspace [tex]R^3[/tex]

For point E:

[tex]\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\[/tex]

The  [tex]x_1, x_2[/tex] is the arbitrary, in which [tex]ax_1+bx_2[/tex]is arbitrary  

[tex]\to a(x_1,0,0)+b(x_2,0,0) \varepsilon E[/tex]

The set E is the part of the subspace [tex]R^3[/tex]

For point F:

[tex]\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon F \\\\\to a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))[/tex]

The [tex]x_1, x_2[/tex] arbitrary so, they have [tex]ax_1+bx_2[/tex] as the arbitrary [tex]\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F[/tex]

The set F is the subspace of [tex]R^3[/tex]

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