Calculate how many different sequences can be formed that use the letters of the given word. Leave your answer as a product of terms of the form C(n, r). HINT [Decide where, for example, all the s's will go, rather than what will go in each position.]
georgianna
A) C(10, 7)
B) C(2, 10)C(1, 8)C(1, 7)C(1, 6)C(1, 5)C(2, 4)C(2, 2)
C) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 1)C(3, 1)C(2, 1)C(1, 1)
D) 10 · C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)

Answer:

6¹⁰×2³⁵

Step-by-step explanation:

he has 6 choices for the first multiple choice question.

and for each of those he had again 6 more choices to answer the second question. 6×6 = 36

so, for all 10 multiple choice questions he answer in

6¹⁰ different ways = 60466176 ways

then there are 35 true/false questions, which are Bausch again multiple choice questions but with only 2 options instead of 6.

so we get 2³⁵ different possibilities. a huge number.

and they're possible for each of the 60466176 ways of the multiple choice part.

so, in total we have

6¹⁰×2³⁵ different answer possibilities.

Answer: Vu is 15 years old now.

Step-by-step explanation:

Let present age of WU be x.

Then, the present age of Vu = 3x

Also, After 25 years

Age of Wu = x+25

According to the question:

[tex](x+25)=2(3x)\\\\\Rightarrow\ x+25=6x\\\\\Rightarrow\5x=25\\\\\Rightarrow\ x=5[/tex]

Present age of Vu = 3(5) = 15

Hence, Vu is 15 years old now.

Answer:

j

Step-by-step explanation:j

Answer:

the answers for x and y are both 12

Answer:

median and quartile deviation

3║54, 81

3║18, 27

3║9, 9

3║3, 3

3║1, 1

HCF = 27

Must click thanks and mark brainliest

Answer:

Hello,

Step-by-step explanation:

[tex]\begin{array}{c||c}\begin{array}{c|c}54&2\\27&3\\9&3\\3&3\\1\\\end{array}&\begin{array}{c|c}81&3\\27&3\\9&3\\3&3\\1\\\end{array}\end{array}\\\\54=2^1*3^3\\ 81=3^4\\\\\boxed{HCF(54,81)=3^3=27}\\[/tex]

Answer:

The  test is a two -tailed test

Step-by-step explanation:

From the question we are told that

    The  sample size is n  =  31

     The  sample mean is  [tex]\= x =11[/tex]

      The sample standard deviation is  [tex]\sigma = 3[/tex]

       The null hypothesis is  [tex]H_o: \mu \le 10[/tex]

         The  alternative hypothesis is  [tex]H_1 : \mu > 10[/tex]  

         The level of significance is [tex]\alpha = 0.05[/tex]

The test  statistics is mathematically represented as

       [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

      [tex]t = \frac{ 11 - 10 }{ \frac{3}{\sqrt{ 31} } }[/tex]

     [tex]t = 1.85[/tex]

The  p- value is mathematically represented as

       [tex]p-value = p( t > 1.856) = 0.0317[/tex]

Looking at the value of  [tex]p-value \ and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] hence we reject the null hypothesis

Given the that the p value is less than 0.05 it mean the this is a two-tailed test

You can put [tex]n[/tex] different elements in order in [tex]n![/tex] different ways.

So, you can visit 12 different cities in [tex]12!=479001600[/tex] different ways.

Answer: 479,001,600

Step-by-step explanation:

There are 12 ways to go to the first place, 11 for the second, ten for the third, and so on. So 12! Means 12x11x10x9x8x7x6x5x4x3x2x1.

Answer:

exact form: x=-56/3

mixed number form: -18 2/3

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

7/10 mi

Step-by-step explanation:

The total distance is 3 miles = 30/10 miles.

The other distances added gives 7/10+7/10+9/10 = 23/10

Therefore the last hop from Kingwood to Silvergrove is 30/10 - 23/10 = 7/10

Answer:

B

Step-by-step explanation:

x<15

There is an open circle at 15 and the line goes to the left

Answer:

a.    [tex]\mathbf{36 \sqrt{5}}[/tex]

b.   [tex]\mathbf{ \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]

Step-by-step explanation:

Evaluate integral _C x ds  where C is

a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)

i . e

[tex]\int \limits _c \ x \ ds[/tex]

where;

x = t   , y = t/2

the derivative of x with respect to t is:

[tex]\dfrac{dx}{dt}= 1[/tex]

the derivative of y with respect to t is:

[tex]\dfrac{dy}{dt}= \dfrac{1}{2}[/tex]

and t varies from 0 to 12.

we all know that:

[tex]ds=\sqrt{ (\dfrac{dx}{dt})^2 + ( \dfrac{dy}{dt} )^2}} \ \ dt[/tex]

∴

[tex]\int \limits _c \ x \ ds = \int \limits ^{12}_{t=0} \ t \ \sqrt{1+(\dfrac{1}{2})^2} \ dt[/tex]

[tex]= \int \limits ^{12}_{0} \ \dfrac{\sqrt{5}}{2}(\dfrac{t^2}{2}) \ dt[/tex]

[tex]= \dfrac{\sqrt{5}}{2} \ \ [\dfrac{t^2}{2}]^{12}_0[/tex]

[tex]= \dfrac{\sqrt{5}}{4}\times 144[/tex]

= [tex]\mathbf{36 \sqrt{5}}[/tex]

b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)

Given that:

x = t  ; y = 3t²

the derivative of  x with respect to t is:

[tex]\dfrac{dx}{dt}= 1[/tex]

the derivative of y with respect to t is:

[tex]\dfrac{dy}{dt} = 6t[/tex]

[tex]ds = \sqrt{1+36 \ t^2} \ dt[/tex]

Hence; the  integral _C x ds is:

[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]

Let consider u to be equal to  1 + 36t²

1 + 36t² = u

Then, the differential of t with respect to u is :

76 tdt = du

[tex]tdt = \dfrac{du}{76}[/tex]

The upper limit of the integral is = 1 + 36× 2² = 1 + 36×4= 145

Thus;

[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]

[tex]\mathtt{= \int \limits ^{145}_{0} \sqrt{u} \ \dfrac{1}{72} \ du}[/tex]

[tex]= \dfrac{1}{72} \times \dfrac{2}{3} \begin {pmatrix} u^{3/2} \end {pmatrix} ^{145}_{1}[/tex]

[tex]\mathtt{= \dfrac{2}{216} [ 145 \sqrt{145} - 1]}[/tex]

[tex]\mathbf{= \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]

Answer:

45

------

75

Step-by-step explanation:

Let x be the value of the numerator and x+30 be the value of the denominator

This is equal to 3/5

x             3

-------- = -------

x+30      5

Using cross products

5x = 3(x+30)

Distribute

5x = 3x+90

Subtract 3x from each side

2x = 90

Divide by 2

x = 45

The fraction is

45

-----

30+45

45

------

75

[tex]\dfrac{x}{x+30}=\dfrac{3}{5}\\\\5x=3(x+30)\\5x=3x+90\\2x=90\\x=45\\\\\dfrac{x}{x+30}=\dfrac{45}{45+30}=\dfrac{45}{75}[/tex]

Answer:

a.  the control limits should be set at (10.72, 11.28)

b. [tex]\mathbf{P(10.72<x<11.28) = 0.4526}[/tex]

c. [tex]\mathbf{P(10.72<x<11.28) = 0.0065}[/tex]

Step-by-step explanation:

Given that:

population mean μ = 11

standard deviation [tex]\sigma[/tex] = 1.0

sample size n = 35

5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.

Therefore, level of significance ∝ = 0.05+0.05 = 0.10

Critical value for [tex]z_{1-\alpha/2} =z_{1-0.10 /2}[/tex]

[tex]\implies z_{1-0.05} = z_{0.95}[/tex]

Using the EXCEL FORMULA: = NORMSINV (0.95)

z = 1.64

The lower control limit and the upper control limit can be determined by using the respective formulas:

Lower control limit = [tex]\mathtt{\mu - z_{1-\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}}[/tex]

Upper control limit = [tex]\mathtt{\mu + z_{1-\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}}[/tex]

For the lower control limit = [tex]11-1.64 \times \dfrac{1.0}{\sqrt{35}}[/tex]

For the lower control limit = [tex]11-0.27721[/tex]

For the lower control limit = 10.72279

For the lower control limit [tex]\simeq[/tex] 10.72

For the upper control limit = [tex]11+1.64 \times \dfrac{1.0}{\sqrt{35}}[/tex]

For the upper control limit = 11 + 0.27721

For the upper control limit = 11.27721

For the upper control limit  [tex]\simeq[/tex]  11.28

Therefore , the control limits should be set at (10.72, 11.28)

b. If the population mean shifts to 10.7, what is the probability that the change will be detected?

i.e

[tex]\mathtt{P(10.72<x<11.28) = P( \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}<z < \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}})[/tex]

[tex]\mathtt{P(10.72<x<11.28) = P( \dfrac{10.72- 10.7}{\dfrac{1.0}{\sqrt{35}}}<z < \dfrac{11.28- 10.7}{\dfrac{1.0}{\sqrt{35}}}})[/tex]

[tex]\mathtt{P(10.72<x<11.28) = P( \dfrac{0.02}{\dfrac{1.0}{5.916}}<z < \dfrac{0.58}{\dfrac{1.0}{5.916}}})[/tex]

[tex]\mathtt{P(10.72<x<11.28) = P(0.1183<z < 3.4313})[/tex]

[tex]\mathtt{P(10.72<x<11.28) = P(z< 3.4313) - P(z< 0.1183) }[/tex]

Using the EXCEL FORMULA: = NORMSDIST (3.4313) - NORMSDIST (0.118 ); we have:

[tex]\mathbf{P(10.72<x<11.28) = 0.4526}[/tex]

c If the population mean shifts to 11.7, what is the probability that the change will be detected?

i.e

[tex]\mathtt{P(10.72<x<11.28) = P( \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}<z < \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}})[/tex]

[tex]\mathtt{P(10.72<x<11.28) = P( \dfrac{10.72- 11.7}{\dfrac{1.0}{\sqrt{35}}}<z < \dfrac{11.28- 11.7}{\dfrac{1.0}{\sqrt{35}}}})[/tex]

[tex]\mathtt{P(10.72<x<11.28) = P( \dfrac{-0.98}{\dfrac{1.0}{5.916}}<z < \dfrac{-0.42}{\dfrac{1.0}{5.916}}})[/tex]

[tex]\mathtt{P(10.72<x<11.28) = P(-5.7978<z < -2.48472})[/tex]

[tex]\mathtt{P(10.72<x<11.28) = P(z< -2.48472) - P(z< -5.7978) }[/tex]

Using the EXCEL FORMULA: = NORMSDIST (-2.48472) - NORMSDIST (-5.7978); we have:

[tex]\mathbf{P(10.72<x<11.28) = 0.0065}[/tex]

Answer:

y+6=-1/2(x-3)

Step-by-step explanation:

Point slope form: y-y1=m(x-x1)

Given that:

m=-1/2 and point (3, -6), you just add these numbers into the equation, and this gives:

y+6=-1/2(x-3)

Hope this helped!

Have a nice day!

Answer:

1.84

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

7/6

Step-by-step explanation:

since the formula of area is length times width,you have to divide the area by the length to find the width

area=length×width

the width will be

width=area÷length

=7/8÷3/4

7/8×4/3

7/2×1/3

7/6

that's the width you can prove it by multiplying the length times the width to see if you will get 7/8..

I hope this helps

Answer:

It can be any two numbers that sum up to 36.

eg:18+18,30+6,15+21

Step-by-step explanation:

Given:

Let Benjamin's age be x and David's age y.

x+y=36

2x+2y=72

Solution:

As twice of 36=72, any two numbers that add up to 36 ,will give a sum of 72 after multiplying them with 2.Therefore ,Benjamin's and David's age can be any set of numbers that sum up to 36.

Answer:

8.8 pounds

Step-by-step explanation:

Given the following :

Combined weight loss which occurred within a week = 28 kg

Number of days in a week = 7 days

1 kilogram (kg) = 2.2 pounds

Combined weight loss in pounds that occurs within a week:

Weight loss in kg × 2.2

28kg * 2.2 = 61.6 pounds

Assume weight loss occurred at a constant rate :

Weight lost by the group per day :

(Total weight loss / number of days in a week)

(61.6 pounds / 7)

= 8.8 pounds daily

Answer:

88

Step-by-step explanation:

Found the answer and I am doing the quiz rn lel

Answer:

f-4

Step-by-step explanation:

f-4  cannot be simplified

This is the simplest form

Answer:

[tex]\large \boxed{f-4}[/tex]

Step-by-step explanation:

[tex]f-4[/tex]

[tex]\sf f \ is \ a \ nonzero \ number.[/tex]

[tex]\sf The \ expression \ cannot \ be \ simplified \ further.[/tex]

Answer:  4  inches

Step-by-step explanation:

1. We gonna find the the length of the right triangle legs using Phitagor theorem.

c²=a²+b²  (1)   , where c is triangle's  hypotenuse

a and b are the triangle's  legs.

Let the leg a =x,    so leg b=x+1 inches

Now we can write the equation using (1)

25=x²+(x+1)²

25=x²+x²+2*x+1

2*x²+2*x-24=0     ( divide by 2 both sides of the equation)

x²+x-12=0

Find the discriminant D=1+12*4=49

√D=7

x1= (-1+7)/2=3     x2=(-1-7)/2=-4 - x2=-4 not possible so length of the leg can not be negative.

So the shorter leg a=x= 3 inches

The longer leg b=x+1=4 inches

Answer:x ≤ 3

Step-by-step explanation:

Answer:

x ≥ -3

Step-by-step explanation:

x - 6 ≥ 15 + 8x

x - 8x ≥ 15 + 6

-7x ≥ 21

x ≥ 21/-7

x ≥ -3

x greater than equal to -3

check:

-3 - 6 ≥ 15 + 8*-3

-9 ≥ 15 - 24

Answer:

The straight time pay for $ 7.60 per hour and 40 work hours per week is $ 304.

Step-by-step explanation:

Let suppose that worker is suppose to work 8 hours per day, so that he must work 5 days weekly. The straight time is the suppose work time in a week, the pay is obtained after multiplying the hourly rate by the amount of hours per week. That is:

[tex]C = \left(\$\,7,60/hour\right)\cdot (40\,hours)[/tex]

[tex]C = \$\,304[/tex]

The straight time pay for $ 7.60 per hour and 40 work hours per week is $ 304.

Answer:

There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.

Step-by-step explanation:

Given:

There are 5 types of croissants:

plain croissants

cherry croissants

chocolate croissants

almond croissant

apple croissants

broccoli croissants

To find:

to choose 22 croissants with:

at least one plain croissant

at least two cherry croissants

at least three chocolate croissants

at least one almond croissant

at least two apple croissants

no more than three broccoli croissants

Solution:

First we select

At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants

So

1 + 2 + 3 + 1 + 2  = 9

Total croissants = 22  

So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.

n = 5

r = 13

C(n + r - 1, r)

= C(5 + 13 - 1, 13)

= C(17,13)

[tex]=\frac{17! }{13!(17-13)!}[/tex]

= 355687428096000 / 6227020800 ( 24 )

= 355687428096000 / 149448499200

= 2380

C(17,13) = 2380

C(n + r - 1, r)

= C(5 + 12 - 1, 12)

= C(16,12)

[tex]=\frac{16! }{12!(16-12)!}[/tex]

= 20922789888000 / 479001600 ( 24 )

= 20922789888000  / 11496038400

= 1820

C(16,12) = 1820

C(n + r - 1, r)

= C(5 + 11 - 1, 11)

= C(15,11)

[tex]=\frac{15! }{11!(15-11)!}[/tex]

= 1307674368000 / 39916800 (24)

= 1307674368000 / 958003200

= 1307674368000 / 958003200

= 1365

C(15,11) = 1365

C(n + r - 1, r)

= C(5 + 10 - 1, 10)

= C(14,10)

[tex]=\frac{14! }{10!(14-10)!}[/tex]

= 87178291200 / 3628800 ( 24 )

= 87178291200 / 87091200

= 1001

C(14,10) = 1001

Adding them:

2380 + 1820 + 1365 + 1001 = 6566 ways

Answer:

[tex] s = \sqrt{30} - 2\sqrt{5} m [/tex]

Step-by-step explanation:

Given:

Formula for side length of cube, [tex] s = \sqrt{\frac{SA}{6} [/tex]

Where, S.A = surface area of a cube, and s = side length.

Required:

Difference in side length between a cube with S.A of 180 m² and a cube with S.A of 120 m²

Solution:

Difference = (side length of cube with 180 m² S.A) - (side length of cube with 120 m² S.A)

[tex]s = (\sqrt{\frac{180}{6}}) - (\sqrt{\frac{120}{6}})[/tex]

[tex] s = (\sqrt{30}) - (\sqrt{20}) [/tex]

[tex] s = \sqrt{30} - \sqrt{4*5} [/tex]

[tex] s = \sqrt{30} - 2\sqrt{5} m [/tex]

Answer:

[tex]X=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]

Step-by-step explanation:

We are given the following matrix equation, from which we have to isolate X and simplify this value.

[tex]\begin{bmatrix}2&4\\ \:\:\:5&4\end{bmatrix}X\:+\:\begin{bmatrix}-8&-8\\ \:\:\:12&1\end{bmatrix}=\:\begin{bmatrix}-10&6\\ \:\:\:25&24\end{bmatrix}[/tex]

To isolate X, let us first subtract the second matrix, as demonstrated below, from either side. Further simplifying this equation we can multiply either side by the inverse of the matrix being the co - efficient of X, isolating it in the doing.

[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}[/tex] (Simplify second side of equation)

[tex]\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}=\begin{bmatrix}\left(-10\right)-\left(-8\right)&6-\left(-8\right)\\ 25-12&24-1\end{bmatrix}=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] (Multiply either side by inverse of matrix 1)

[tex]X=\begin{bmatrix}2&4\\ 5&4\end{bmatrix}^{-1}\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]

Our solution is hence option c

Answer:

Ok, as i understand it:

for a point P = (x, y)

The values of x and y can be randomly chosen from the set {1, 2, ..., 10}

We want to find the probability that the point P lies on the second quadrant:

First, what type of points are located in the second quadrant?

We should have a value negative for x, and positive for y.

But in our set;  {1, 2, ..., 10}, we have only positive values.

So x can not be negative, this means that the point can never be on the second quadrant.

So the probability is 0.

Answer:

The answer is

Step-by-step explanation:

To find the equation of the line that passes through two points , first find the slope and then use the formula

y - y1 = m(x - x1)

where m is the slope

(x1 , y1) are any of the points

To find the slope of the line using two points we use the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Slope of the line using points

(2, -7) and (8, -4) is

Now the equation of the line using point (2 , - 7) and slope 1/2 is

We have the final answer as

Hope this helps you

Answer:

False.

Step-by-step explanation:

Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The variance distribution is the squared value of each the difference by the mean. values of probability are squared and then their sum is taken to calculate variance deviation. The number of motorcycles greater than 1 has probability of 0.35 so the probability of x = 1 must also be 0.35.

Answer:

3/6 = 1/2 = 0.5

Step-by-step explanation:

3 / 6 = 1/2 = 0.5

Answer: 5.4

Step-by-step explanation: 27/5, so 5x5 makes 25 and 2 remaining so 5x0.4=2 so answer is 5+0.4 which equals to 5.4