Which of these equations have no solution? Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1

[tex]\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y=-2(x-\stackrel{h}{3})^2+\stackrel{k}{4}\qquad\qquad \stackrel{vertex}{(\underline{3},4)}\qquad \qquad \stackrel{\textit{axis of symmetry}}{x=\underline{3}}[/tex]

From the equation of the parabola in vertex-form, it's line of symmetry is given by:

[tex]l: x = 3[/tex]

The equation of a parabola of vertex (h,k) is given by:

[tex]y = a(x - h)^2 + k[/tex]

The line of symmetry is given by:

[tex]l: x = h[/tex]

In this problem, the parabola is modeled by the following equation:

[tex]y = -2(x - 3)^2 + 4[/tex]

Hence, the coefficients of the vertex are [tex]h = 3, k = 4[/tex], and the line of symmetry is:

[tex]l: x = 3[/tex]

A similar problem is given at https://brainly.com/question/24737967

Answer:

-2

Step-by-step explanation:

The equation is in the form

y = mx + b where m is the slope and b is the y intercept

The y intercept is where x = 0

In the table the value where x=0 is y=-2

So the equation becomes

y =-4x +-2

Answer:-2

Step-by-step explanation:

Substitute the given numbers for their letters in the equation:

N = NOe^kt

N - amount after t years

No = Original amount

K = 0.0001

t = number of years

Substitute the given numbers for their letters in the equation:

0.70 = 1 * e^-0.0001t

Take the logarithm of both sides:

log0.70 = loge^-0.0001t

-0.1549 = -0.0001t * 0.43429

t = -0.1549 / (-0.0001 * 0.43429)

t = 3566.74

Rounded to the nearest year = 3,567 years old.

The age of the mammal hide is  3,567 years old.

Given,

N = NOe^kt

Here

N - amount after t years

No = Original amount

K = 0.0001

t = number of years

Now

[tex]0.70 = 1 \times e^{-0.0001}t[/tex]

Now Take the logarithm of both sides:

[tex]log0.70 = loge^{-0.0001}t\\\\-0.1549 = -0.0001t \times 0.43429\\\\t = -0.1549 \div (-0.0001 \times 0.43429)[/tex]

t = 3566.74

Learn more about the age here: https://brainly.com/question/17880579

Transform M to the standard normally distributed random variable Z via

[tex]Z=\dfrac{M-\mu_M}{\sigma_M}[/tex]

where [tex]\mu_M[/tex] and [tex]\sigma_M[/tex] are the mean and standard deviation for [tex]M[/tex], respectively. Then

[tex]P(236.5<M<236.7)=P(-0.2308<Z<-0.0769)\approx\boxed{0.0606}[/tex]

Answer:

0.0606.                        .                

hope this helps

Answer:

Area of triangle = 73.1 m²

Step-by-step explanation:

Points to remember

Area of triangle = bh/2

Where b - base and h - height

To find the height of triangle

Let 'h' be the height of triangle

Sin 35 = h/17

h = 17 * Sin 35

 = 17 * 0.5736

 = 9.75 m

To find the area of triangle

Here b = 15 m and h = 9.75

Area = bh/2

 = (15 * 9.75)/2

 = 73.125 ≈73.1 m²

Answer:

[tex]A = 73.1\ m^2[/tex]

Step-by-step explanation:

We calculate the height of the triangle using the function [tex]sin(\theta)[/tex]

By definition:

[tex]sin(\theta) =\frac{h}{hypotenuse}[/tex]

Where h is the height of the triangle

In this case we have that:

[tex]\theta=35\°[/tex]

[tex]hypotenuse=17[/tex]

Then:

[tex]sin(35) =\frac{h}{17}[/tex]

[tex]h=sin(35)*17\\\\\\h =9.75[/tex]

Then the area of a triangle is calculated as:

[tex]A = 0.5 * b * h[/tex]

Where b is the length of the base of the triangle and h is its height

In this case

[tex]b=15[/tex]

So

[tex]A = 0.5 *15*9.75[/tex]

[tex]A = 73.1\ m^2[/tex]

Answer:

[tex]-10ms^{-1}[/tex]

Step-by-step explanation:

The position function is [tex]s(t)=1-10t[/tex].

The instantaneous velocity at t=10 is given by:

[tex]s'(10)[/tex].

We first of all find the derivative of the position function to get:

[tex]s'(t)=-10[/tex]

We now substitute t=10 to get:

[tex]s'(10)=-10[/tex]

Therefore the instantaneous velocity at t=10 is -10m/s

Answer:

The vehicle will get 25 mpg at speeds of approximately  22 mph and 101 mph.

Step-by-step explanation:

Given, the equation that is used to determine the gas mileage for a certain vehicle is,

[tex]m=-0.03x^2+3.7x-43----(1)[/tex]

If the mileage is 25 mpg.

That is, m = 25 mpg,

From equation (1),

[tex]-0.03x^2+3.7x-43=25[/tex]

By the quadratic formula,

[tex]x=\frac{-3.7\pm \sqrt{3.7^2-4\times -0.03\times -43}}{2\times -0.03}[/tex]

[tex]x=\frac{-3.7\pm \sqrt{8.53}}{-0.06}[/tex]

[tex]\implies x=\frac{-3.7+ \sqrt{8.53}}{-0.06}\text{ or }x=\frac{-3.7- \sqrt{8.53}}{-0.06}[/tex]

[tex]\implies x\approx 22\text{ or }x\approx 101[/tex]

Hence, the speed of the vehicle of the vehicle are approximately 22 mph and 101 mph.

To find the speed at which the car gets 25 mpg, the equation -0.03x^2 +3.7x-43 is set equal to 25 and then solved. Using the quadratic formula, the speeds are approximately 30 mph and 76 mph when rounded to the nearest whole number.

The question requires you to find the speed(s) at which the vehicle gets 25 miles per gallon (mpg). To do this, you'll need to equate the given quadratic equation (-0.03x^2 +3.7x-43) to 25 and then solve for x (representing speed in mph). So, the equation becomes:

-0.03x^2 +3.7x-43 = 25

This simplifies to:

-0.03x^2 +3.7x - 68 = 0

This quadratic equation can be solved by factoring, completing the square or using the quadratic formula. In this case, the quadratic formula is the best solution:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

By substituting a = -0.03, b = 3.7, and c = -68 into the formula, the calculated speeds are approximately 30 mph and 76 mph.

Please keep in mind that the answers were rounded to the nearest whole number (mph). Hence, the vehicle will get 25 mpg at speeds of approximately 30 mph and 76 mph.

https://brainly.com/question/30398551

#SPJ3

Answer:

$9,220,000(0.888)^t

Step-by-step explanation:

Model this using the following formula:

Value = (Present Value)*(1 - rate of decay)^(number of years)

Here, Value after t years = $9,220,000(1 -0.112)^t

          Value after t years =  $9,220,000(0.888)^t

Answer:

  0.6 km

Step-by-step explanation:

(3 km)/(5 friends) = 0.6 km/friend

Each person should lead for 0.6 km.

Answer:

3/5

Step-by-step explanation:

3 divided by 5 equals to 3/5 or 0.6

Answer:

5:4

Step-by-step explanation:

If point B divides the segment AC in the ratio 2:1, then

AB=2x units and BC=x units.

If point D divides the segment AB in the ratio 3:2, then

AD=3y units and DB=2y units.

Since AD+DB=AB, then

[tex]3y+2y=2x\\ \\5y=2x\\ \\y=\dfrac{2}{5}x[/tex]

Now,

[tex]AD=3y\\ \\DC=DB+BC=2y+x=2y+\dfrac{2}{5}y=\dfrac{12}{5}y[/tex]

So,

[tex]AD:DC=3y:\dfrac{12}{5}y=15:12=5:4[/tex]

Answer:

AD:DC=6:9

Step-by-step explanation:

We know that:

AB:BC=2:1

AD:DB=3:2

We can conclude that:

AB+BC=AC

Then:

AB=2/3AC

BC=1/3AC

AD+DB=AB

Then

AD=3/5AB

DB=2/5AB

From the above we can replace:

AD=(3/5)(2/3AC)=6/15AC

On the other hand:

DC= DB+BC

DC=2/5AB+1/3AC

In terms of AC

DC=((2/5)(2/3AC))+1/3AC=4/15AC+1/3AC

DC=27/45AC=9/15AC

From:

AD=6/15AC

DC=9/15AC

we can say that:

AD:DC=6:9

Answer:

  66°59'57.4379"

Step-by-step explanation:

A suitable calculator can find the angle whose sine is 0.9205 and convert that angle to degrees, minutes, and seconds

  θ = arcsin(0.9205) ≈ 66.999288° ≈ 66°59'57.4379"

___

Multiplying the fractional part of the degree measure by 60 minutes per degree gives the minutes measure:

  0.999288° ≈ 59.95730'

And multiplying the fractional part of that by 60 seconds per minute gives the seconds measure:

  0.95730' = 57.4379"

In total, we have 66°59'57.4379"

Answer:

Graph the two points (0,1) and (2,-1) then connect them with a straight edge.

Step-by-step explanation:

The transformed graph is still a line since the parent is a line.

[tex]g(x)=\frac{-1}{2}f(x+2)[/tex]

Identify two points that cross nicely on your curve for f:

(2,-2) and (4,2)

So I'm going to replace x in x+2 so that x+2 is 2 and then do it also for when x+2 is 4.

x+2=2 when x=0 since 0+2=2.

x+2=4 when x=2 since 2+2=4.

So plugging in x=0:

[tex]g(x)=\frac{-1}{2}f(x+2)[/tex]

[tex]g(0)=\frac{-1}{2}f(0+2)[/tex]

[tex]g(0)=\frac{-1}{2}f(2)[/tex]

[tex]g(0)=\frac{-1}{2}(-2)[/tex] since we had the point (2,-2) on line f.

[tex]g(0)=1[/tex] so g contains the point (0,1).

So plugging in the other value we had for x, x=2:

[tex]g(x)=\frac{-1}{2}f(x+2)[/tex]

[tex]g(2)=\frac{-1}{2}f(2+2)[/tex]

[tex]g(2)=\frac{-1}{2}f(4)[/tex]

[tex]g(2)=\frac{-1}{2}(2)[/tex] since we had the point (4,2) on the line f.

[tex]g(2)=-1[/tex] so g contains the point (2,-1).

Graph the two points (0,1) and (2,-1) then connect them with a straight edge.

Answer:

The third choice down

Step-by-step explanation:

Plotting the point (-2, 9) has us in QII.  We connect the point to the origin and then drop the altitude to the negative x-axis, creating a right triangle.  The side adjacent to the reference angle theta is |-2| and the alltitude (height) is 9.  The sin of the angle is found in the side opposite the angle (got it as 9) over the hypotenuse (don't have it).  We solve for the hypotenuse using Pythagorean's Theorem:

[tex]c^2=2^2+9^2[/tex] so

[tex]c^2=85[/tex] and

[tex]c=\sqrt{85}[/tex]

Now we can find the sin of theta:

[tex]sin\theta=\frac{9}{\sqrt{85} }[/tex]

We have to rationalize the denominator now.  Multiply the fraction by

[tex]\frac{\sqrt{85} }{\sqrt{85} }[/tex]

Doing that gives us the final

[tex]\frac{9\sqrt{85} }{85}[/tex]

third choice from the top

For this case we have that by definition, it is called arcsine (arcsin) from a number to the angle that has that number as its sine.

We must find the [tex]arcsin (\frac {\sqrt {2}} {2})[/tex]. Then, we look for the angle whose sine is [tex]\frac {\sqrt {2}} {2}[/tex].

We have to, by definition:

[tex]Sin (45) = \frac {\sqrt {2}} {2}[/tex]

So, we have to:

[tex]arcsin (\frac {\sqrt {2}} {2}) = 45[/tex]

Answer:

Option B

Answer:

Choice B

Step-by-step explanation:

An option is to find the the square root of 2 in decimals is [tex]\frac{1.414213562}{2} ≈ 0.7071067812[/tex]

Now we can use the arc sine, which is the inverse of a sin.

To do this we must use a scientific calculator. By pressing the arc sin button and entering in 0.7071067812, we can find the arc sin, which is 45°.

Question 9:

Answer: False

Step-by-step explanation: False. These sides will not create a triangle because the longest side equals the two other sides combined. 10=7+3. This will just be a line.

Question 10:

Answer: False

Step-by-step explanation: False. These sides will not create a triangle because the longest side equals the two other sides combined. 7=2+5. This will just be a line.

Answer with explanation:

We know that the formula for binomial probability :-

[tex]P(x)=^nC_xp^x\ q^{n-x}[/tex], where P(x) is the probability of getting success in x trials , n is the total number of trials and p is the probability of getting success in each trial.

Given : The probability that consumers are comfortable having drones deliver their purchases = 0.28

The total number of consumers selected = 5

To find the probability that when five consumers are randomly​ selected, exactly three of them are comfortable with delivery by drones , we substitute

n=5, x=3 , p=0.28 and q=1-0.28=0.72 in the above formula.

[tex]P(3)=^5C_3(0.28)^3\ (0.72)^{2}\\\\10(0.28)^3(0.72)^{2}\approx0.1138[/tex]

Thus, the probability that when five consumers are randomly​ selected, exactly three of them are comfortable with delivery by drones = 0.1138

The student's question concerns finding the probability of getting exactly three successes in five binomial trials. The values are: n = 5, X = 3, p = 0.28, and q = 0.72. The random variables X represents the number of consumers comfortable with drone delivery, and p' the proportion of such consumers.

The student is asking about a probability problem involving a binomial distribution, which is a common topic in high school mathematics. In the scenario provided, we have the following information: the number of trials (n), which is 5 (being the number of consumers randomly selected); the number of successes (X), which is 3 (being the number of consumers comfortable with drone delivery); the probability of success (p), which is 0.28 (given that 28% of consumers are comfortable with drone delivery); and the probability of failure (q), which is 1 - p = 0.72.

To find the probability that exactly three out of five consumers are comfortable with drone delivery, we would use the binomial distribution formula:

P(X = x) = C(n, x) * px * qn-x

Where C(n, x) is the number of combinations of n items taken x at a time. This would give us the probability that when five consumers are randomly selected, exactly three are comfortable with drone delivery. As this problem involves a binomial distribution, defining the random variable X as 'the number of consumers comfortable with drone delivery' and p' as 'the sample proportion of consumers comfortable with drone delivery' makes it clearer.

Answer:

A = 676πcm²

Step-by-step explanation:

According to given data:

GY = 10 cm

XY = 16 cm

The formula for finding the area of the circle is:

A = πr²

Since we have two radius. By adding the two radius we get:

GY+XY=10+16

=26

Now put the value in the formula:

A=πr²

A = π(26cm)²

A = 676πcm²

Thus the correct option is 676....

Answer: Option D

[tex](9x^2+1)(3x+1)(3x-1)[/tex]

Step-by-step explanation:

We have the following expression

[tex]81x^4-1[/tex]

We can rewrite the expression in the following way:

[tex](9x^2)^2-1^2[/tex]

Remember the following property

[tex](a+b)(a-b) = a^2 -b^2[/tex]

Then in this case [tex]a=(9x^2)[/tex] and [tex]b=1[/tex]

So we have that

[tex](9x^2)^2-1^2[/tex]

[tex](9x^2+1)(9x^2-1)[/tex]

Now we can rewrite the expression  [tex]9x^2[/tex] as follows

[tex](3x)^2[/tex]

So

[tex](9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)[/tex]

Then in this case [tex]a=(3x)[/tex] and [tex]b=1[/tex]

So we have that

[tex](9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)[/tex]

[tex](9x^2+1)(9x^2-1) =(9x^2+1)(3x+1)(3x-1)[/tex]

finally the factored expression is:

[tex](9x^2+1)(3x+1)(3x-1)[/tex]

Answer:

Step-by-step explanation:

.

Answer:

  $3195

Step-by-step explanation:

The fraction remaining was ...

  1 - 1/3 -1/5 = 15/15 -5/15 -3/15 = 7/15

The given amount is 7/15 of Tom' salary, ...

  $1491 = (7/15)×salary

  $1491×(15/7) = salary = $3195 . . . . . . . . . multiply by the inverse of the coefficient of salary

Tom's monthly salary was $3195.

Final Answer:

To equal the triathlon record of 2 hours and 46 minutes, Mr. B must run at a speed of approximately 3.33 meters per second.

Explanation:

To find out how fast Mr. B must run in meters per second to equal the triathlon record, we first need to calculate the total time he spent on the swim and bike ride. Then, we can subtract that total time from the record time to find the remaining time available for the run. Finally, we can use this remaining time to calculate Mr. B's required running speed.

1.Total time spent on swim and bike ride:

  - Swim time: 25 minutes and 10 seconds

  - Bike ride time: 1 hour, 30 minutes, and 50 seconds

  Convert both times to seconds:

  - Swim time = 25 minutes * 60 seconds/minute + 10 seconds = 1510 seconds

  - Bike ride time = 1 hour * 60 minutes/hour * 60 seconds/minute + 30 minutes * 60 seconds/minute + 50 seconds = 5450 seconds

  Total time = Swim time + Bike ride time = 1510 seconds + 5450 seconds = 6960 seconds

2.Remaining time available for the run:

  Triathlon record time = 2 hours * 60 minutes/hour + 46 minutes = 2 hours * 60 minutes/hour + 46 * 60 seconds/minute = 7200 seconds + 2760 seconds = 9960 seconds

  Remaining time for the run = Triathlon record time - Total time spent on swim and bike ride = 9960 seconds - 6960 seconds = 3000 seconds

3.Calculating Mr. B's required running speed:

  Distance of the run = 10 km = 10000 meters

  Running speed = Distance / Time = 10000 meters / 3000 seconds ≈ 3.33 meters/second

So, Mr. B must run at a speed of approximately 3.33 meters per second to equal the triathlon record.

Answer:

  500%

Step-by-step explanation:

The percentage change is given by ...

  percent change = ((new value)/(old value) -1) × 100% = (180/30 -1)×100%

  = (6 -1)×100% = 500%

Mobile device sales increased 500% from 1998 to 2007.

Answer:

Number of mobiles sold in the year 1998=30 million

Number of mobiles sold in the year 2007=180 million

Percentage increase in mobile sale from year 1998 to 2007 will be

           [tex]=\frac{\text{final}-\text{Initial}}{\text{Initial}}\\\\=\frac{180-30}{30}\times100\\\\=\frac{150}{30} \times 100\\\\=\frac{15000}{30}\\\\=500\text{Percent}[/tex]

 =500%

Answer:

  see below

Step-by-step explanation:

The sum is irrational, so can only be indicated or approximated.

[tex]\dfrac{1}{6}+\sqrt{6}=\dfrac{1+6\sqrt{6}}{6}\approx 2.61615\,64094\,49844\,76486\,39507\,4137\dots[/tex]

For this case we must find the sum of the following expression:

[tex]\frac {1} {6} + \sqrt {6}[/tex]

We have that when entering [tex]\sqrt {6}[/tex] in a calculator we obtain:

[tex]\sqrt {6} = 2.45[/tex]

On the other hand:

[tex]\frac {1} {6} = 0.16[/tex]periodic number

So, the expression is:

[tex]\frac {1} {6} + \sqrt {6} = 2.62[/tex]

Answer:

2.62

Answer:

  3x² -4x +12

Step-by-step explanation:

This involves straightforward application of the distributive property

x(2x+3)+(x-3)(x-4)

= 2x² +3x +x(x -4) -3(x -4)

= 2x² +3x +x² -4x -3x +12

= 3x² -4x +12

Answer:

f(x) = 3x^2 - 4x + 12

Step-by-step explanation:

First, let's label the expression and do a little housekeeping:

X(2x+3)+(x-3)(x-4) should be f(x) = x(2x+3)+(x-3)(x-4).

If we perform the indicated multiplication, we get:

f(x) = 2x^2 + 3x + (x^2 - 7x + 12), or

f(x) = 2x^2 + 3x + x^2 - 7x + 12.  Combine like terms to obtain:

f(x) = 3x^2 - 4x + 12

Answer:

$ 1,965,334

Step-by-step explanation:

Annual sales of company in 1999 = $ 1,200,000

Geometric mean growth rate = 10.37 % = 0.1037

In order to forecast we have to use the concept of Geometric sequence. The annual sales of company in 1999 constitute the first term of the sequence, so:

[tex]a_{1}=1,200,000[/tex]

The growth rate is 10.37% more, this means compared to previous year the growth factor will be

r =1 + 0.1037 = 1.1037

We have to forecast the sales in 2004 which will be the 6th term of the sequence with 1999 being the first term. The general formula for n-th term of the sequence is given as:

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

So, for 6th term or the year 2004, the forecast will be:

[tex]a_{6}=1,200,000(1.1037)^{6-1}\\\\ a_{6}=1,965,334[/tex]

Thus, the forecasted sales for 2004 are $ 1,965,334

Answer:

Total length after 33 days will be 117 miles

Step-by-step explanation:

A construction crew is lengthening a road. The road started with a length of 51 miles.

Average addition of the road is = 2 miles per day

Let the number of days crew has worked are D and length of the road is L, then length of the road can represented by the equation

L = 2D + 51

If the number of days worked by the crew is = 33 days

Then total length of the road will be L = 2×33 + 51

L = 66 + 51

L = 117 miles

Total length of the road after 33 days of the construction will be 117 miles.

Answer:

Step-by-step explanation:

That a and b are actually h and k, the coordinates of the vertex of the parabola.  There is a formula to find h:

[tex]h=\frac{-b}{2a}[/tex]

then when you find h, sub it back into the original equation to find k.  For us, a = 1, b = -5, and c = 8:

[tex]h=\frac{-(-5)}{2(1)}=\frac{5}{2}[/tex]

so h (or a) = 5/2

Now we sub that value in for x to find k (or b):

[tex]k=1(\frac{5}{2})^2-5(\frac{5}{2})+8[/tex]

and k (or b) = 7/4.

Rewriting in vertex form:

[tex](x-\frac{5}{2})^2+\frac{7}{4}[/tex]

The expression x^2 - 5x + 8 can be written as (x - 5/2)^2 + 1.75 by the process of completing the square, where a = 5/2, and b = 1.75.

To express

x^2-5x+8

in the form

(x-a)^2+b

, we need to complete the square.

First, let's divide the coefficient of x, -5, by 2 to get -5/2 and square that to get 6.25. So, we add and subtract this inside the expression.

Therefore, x^2 - 5x + 8 becomes x^2 - 5x + 6.25 - 6.25 + 8.

This can be rewritten as (x - 5/2)^2 - 6.25 + 8 or (x - 5/2)^2 + 1.75.

Hence, the expression x^2 - 5x + 8 can be written in the form (x - a) ^2 + b where a = 5/2 and b = 1.75.

https://brainly.com/question/36246034

#SPJ3

Answer: Part a) [tex]P(a)=\frac{1}{\binom{r+w}{r}}[/tex]

part b)[tex]P(b)=\frac{1}{\binom{r+w}{r}}+\frac{r}{\binom{r+w}{r}}[/tex]

Step-by-step explanation:

The probability is calculated as follows:

We have proability of any event E = [tex]P(E)=\frac{Favourablecases}{TotalCases}[/tex]

For part a)

Probability that a red ball is drawn in first attempt = [tex]P(E_{1})=\frac{r}{r+w}[/tex]

Probability that a red ball is drawn in second attempt=[tex]P(E_{2})=\frac{r-1}{r+w-1}[/tex]

Probability that a red ball is drawn in third attempt = [tex]P(E_{3})=\frac{r-2}{r+w-1}[/tex]

Generalising this result

Probability that a red ball is drawn in [tex}i^{th}[/tex] attempt = [tex]P(E_{i})=\frac{r-i}{r+w-i}[/tex]

Thus the probability that events [tex]E_{1},E_{2}....E_{i}[/tex] occur in succession is

[tex]P(E)=P(E_{1})\times P(E_{2})\times P(E_{3})\times ...[/tex]

Thus [tex]P(E)[/tex]=[tex]\frac{r}{r+w}\times \frac{r-1}{r+w-1}\times \frac{r-2}{r+w-2}\times ...\times \frac{1}{w}\\\\P(E)=\frac{r!}{(r+w)!}\times (w-1)![/tex]

Thus our probability becomes

[tex]P(E)=\frac{1}{\binom{r+w}{r}}[/tex]

Part b)

The event " r red balls are drawn before 2 whites are drawn" can happen in 2 ways

1) 'r' red balls are drawn before 2 white balls are drawn with probability same as calculated for part a.

2) exactly 1 white ball is drawn in between 'r' draws then a red ball again at [tex](r+1)^{th}[/tex] draw

We have to calculate probability of part 2 as we have already calculated probability of part 1.

For part 2 we have to figure out how many ways are there to draw a white ball among (r) red balls which is obtained by permutations of 1 white ball among (r) red balls which equals [tex]\binom{r}{r-1}[/tex]

Thus the probability becomes [tex]P(E_i)=\frac{\binom{r}{r-1}}{\binom{r+w}{r}}=\frac{r}{\binom{r+w}{r}}[/tex]

Thus required probability of case b becomes [tex]P(E)+ P(E_{i})[/tex]

= [tex]P(b)=\frac{1}{\binom{r+w}{r}}+\frac{r}{\binom{r+w}{r}}\\\\[/tex]

The probability that all r red balls will be obtained before any white balls are obtained is 1. Before two white balls are obtained, all red balls must be drawn, so the probability is 1/w. This is based on the assumption that the draws are random.

The subject of this question is probability theory, which falls under the broad subject of Mathematics. The first part of the question asks for the probability that all r red balls will be obtained before a white ball is obtained. The second part asks for the probability that all r red balls will be obtained before two white balls are obtained.

For part (a), the probability that all r red balls will be obtained before any white balls are obtained is 1 because the balls are drawn without replacement and we are considering r draws. Therefore, every draw will be a red ball before a white ball.

For part (b), as for drawing one white ball after obtaining all r red balls, the first white ball can be the (r+1)th draw. But before drawing the second white ball, all the red balls have to be obtained. Because the balls are drawn without replacement, the probability that all r red balls will be obtained before two white balls are obtained is 1/w, where w is the total white balls.

The main assumption here is that the draws are random. So the probability of drawing a red or white ball does not change after each draw. This question is at a High School level because it involves basic probability theory and combinatorial principles.

https://brainly.com/question/31469353

#SPJ3

Answer:

5

Step-by-step explanation:

The nth term of a geometric series is:

a_n = a₁ (r)^(n-1)

where a₁ is the first term and r is the common ratio.

Here, we have:

40 = a₁ (r)^(4-1)

160 = a₁ (r)^(6-1)

40 = a₁ (r)^3

160 = a₁ (r)^5

If we divide the two equations:

4 = r^2

r = 2

Now substitute into either equation to find a₁:

40 = a₁ (2)^3

40 = 8 a₁

a₁ = 5

Answer:

Step-by-step explanation:

The absolute value function graph is shifted to the right by some unknown amount. That is, the parent function p(x) = |x| has become f(x) = p(x-a) = |x-a|, a right-shift of "a" units.

The grid squares are not marked, so we cannot say exactly what the right-shift is. The only two answer choices having the correct form are ...

  f(x) = |x-7|

  f(x) = |x -23|

_____

Anything that looks like |x+a| will be left-shifted by "a" units.

Anything that looks like |x| +a will be shifted up by "a" units. If "a" is negative, the actual shift is downward.

Answer:

f(x) = |x – 23|

f(x) = |x – 7|

Step-by-step explanation:

Right on edge