A computer programming team has 17 members. (a) How many ways can a group of nine be chosen to work on a project? As in Example 9.5.4, since the set of people in a group is a subset of the set of people on the team, the answer is (b) Suppose nine team members are women and eight are men. (1) How many groups of nine can be chosen that contain five women and four men? As in Example 9.5.7a, think of forming the group as a two-step process, where step 1 is to choose the women and step 2 is to choose the men. The answer is (ii) How many groups of nine can be chosen that contain at least one man? As in Example 9.5.7b, consider the relationship between the set of groups that consist entirely of women and the set of groups with at least one man. This thinking leads to the conclusion that the number of groups with at least on man is (iii) How many groups of nine can be chosen that contain at most three women? A group of nine that contains at most three women can contain no women, one woman, two women, or three women. So, the number of groups of nine that contain at most three women is (c) Suppose two team members refuse to work together on projects. How many groups of nine can be chosen to work on a project? In a similar way as in Example 9.5.6, let A and B be the two team members who refuse to work together in a group. Thinking about the number of groups that contain A and not B, B and not A, and neither A nor B leads to the conclusion that the total number of groups of that can be chosen to work on the project is (d) Suppose two team members insist on either working together or not at all on projects. How many groups of nine can be chosen to work on a project? As in Example 9.5.5, let A and B be the two team members who insist on working in a group together or not at all. How many groups contain both A and B? How many groups contain neither A nor B?

One way governments try to encourage growth is, the government can only promote growth by raising unemployment compensation.

Increased output of products and services is referred to as economic growth. Economic growth can be influenced by changes in capital goods, labour force, technology, and human capital. In general, there are two main factors that contribute to economic growth: an increase in the workforce's size and an increase in that workforce's productivity (output per hour worked). Both can expand the economy's total size, but only robust productivity growth can raise per capita GDP and income.

Given,

One way governments try to encourage growth is,

Out of the available alternatives, the government can only promote growth by raising unemployment compensation. Increased unemployment benefits will boost aggregate demand by giving laid-off workers their spending power back.

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The probability of getting the fewer than four twos is 0.5665.

       P(X = x) = C(n,x). p ˣ .(1 - p)ⁿ⁻ˣ

        C(n,x) = n!/x!(n-x)!

For the given question-

p is the likelihood that X will occur.

20 times of a die are rolled;

This indicates that; n = 20.

Six sides, one of which is two:

This indicates that; p = 1/6 = 0.1667.

Probability of having three or fewer twos:

Such is:

P(X < 4) = P(X = 0) +  P(X = 1) + P(X = 2) +  P(X = 3)

So,

P(X < 4) = C(n,x).  p ˣ .(1 - p)ⁿ⁻ˣ

P(X = 0) = C(20,0).  0.1667⁰ .(0.8333)²⁰

P(X = 0) = 0.0261

P(X = 1) = C(20,1).  0.1667¹ .(0.8333)¹⁹

P(X = 1) = 0.1043

P(X = 2) = C(20,2).  0.1667 ² .(0.8333)¹⁸

P(X = 2) = 0.1982

P(X = 3) = C(20,3).  0.1667³ .(0.8333)¹⁷

P(X = 3) = 0.2379

P(X < 4) = P(X = 0) +  P(X = 1) + P(X = 2) +  P(X = 3)

P(X < 4) = 0.0261 +  0.1043 + 0.1982 + 0.2379

P(X < 4) = 0.5665

Thus, the probability of getting the fewer than four twos is 0.5665.

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The five things when two parallel lines are cut by a transversal are the corresponding angle, alternate interior angle, alternate exterior angle, consecutive interior angles, and alternate angle.

Here we have to find the five things that happen when two parallel lines are cut by a transversal.

When two parallel lines are cut by the transversal line it will form five angles.

Corresponding angle, alternate interior angle, alternate exterior angle, consecutive interior angles, and alternate angle.

From the given figure:

Corresponding angle:

∠1 and ∠5

∠2 and ∠6

∠3 and ∠7

∠4 and ∠8

consecutive angle:

∠3 and ∠6

∠4 and ∠5

alternate interior angle:

∠3 and ∠5

∠4 and ∠6

alternate exterior angle:

∠2 and ∠8

∠1 and ∠7

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Answer:

  x +2y = -2

Step-by-step explanation:

You want the line perpendicular to 2x-y = 5 that passes through (6, -4).

The slopes of perpendicular lines are opposite reciprocals. This means the equation of the perpendicular line can be formed by swapping the coefficients of x and y, and negating one of them. We want the leading coefficient to be positive, so we choose our line's equation to be ...

  2x -y = constant . . . . . . . . . . original line

  x +2y = <some constant>

The constant must be chosen so the equation is true at the given point:

  x + 2y = (6) +2(-4) = -2

An equation for the perpendicular line is ...

  x +2y = -2

There are three main key terms here - Physical determinism, elitist-populist dilemma, and urban planning. They can be defined as done below.

First, we have at hand the term Physical determination which can be defined as the belief that physical objects and all physical causes can be described using terms and models of the physical sciences.

Secondly, the elitist-populist dilemma is a disagreement between two political factions. elitists are, of course, the socially and economically well-off sections of the population. The populist factions are the ones that cater to the general public and are at odds with the previous group.

Lastly, urban planning is the process of planning for development in urban areas.

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Answer: 1 1/6

Step-by-step explanation:

(P.S: Everthing in italics are either fractions. mixed numbers, or numbers.

And there ya' go! The answer is 1 1/6! You're welcome!

Transition matrix is called a doubly stochastic matrix (if sum of each rows and columns is 1 ).

We can see that the distribution of doubly stochastic matrix for all finite dimensional has Uniform stationary distribution.

Doubly Stochastic Matrix

A transition random matrix P is defined as a dual random matrix if the sum of the rows and columns is one.

Therefore, for each column j of the doubly random matrix, let ∑ ipᵢⱼ = 1. Suppose the distribution π on S also has π₁ = π if the Markov chain starts with the initial distribution π₀ = π. That is, if the distribution at time 0 is π, the distribution of π remains 1, and this π is said to be stationary.

Example: A uniform distribution [[π(i) = 1/N for all i]] is stationary if the N × N stochastic transition matrix P is symmetric. More generally, the uniform distribution is stationary if the matrix P is doubly stochastic, i.e. the columns of P sum to 1 (we already know that the rows of P sum to all 1). are available). It is easy to see that when πn approaches a limiting distribution as n → ∞, this limiting distribution must be stationary. To see this, assuming lim n→∞ πn = π' , and n → ∞ in the equation πₙ₊₁ = πₙP, we get π = π'P. This shows that π' is stationary. So , the arguments given pass clearly and simply when the state space is finite.Hence, the required results is achieved .

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49.07 is the mean and standard deviation of the waiting time .

What is standard deviation in math?

Your dataset's average level of variability is represented by the standard deviation. It reveals, on average, how far away from the mean each value is.

                                A low standard deviation means that values are clustered close to the mean, whereas a high standard deviation means that values are typically far from the mean.

Let X shows the waiting time. So mean

μ = E(x) = a + b/2 =  30 + 200/2  = 115

Standard deviaiton

 σ = [tex]\sqrt{\frac{(b - a )^{2} }{12} }[/tex]

     = [tex]\sqrt{\frac{(200 -30)^{2} }{12} }[/tex]

     = 49.07

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The answers to all subquestions would be

Part A: [tex]P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}[/tex], x= 0, 1, 2, 3, ..., 15.

Part B: P(X = 1) = 0.2312

Part C: P(X = 2) = 0.2656

Part D: P(X ≥ 2) = 0.6814

Part E: P(X = 0) = 0.0874

What is a binomial distribution?

The binomial distribution with parameters n and p in probability theory and statistics is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own Boolean-valued outcome: success or failure.

Let X be the random variable.

The number of trials n = 15, P=0.15

X ~ Bin(n, p)

Part A:

      [tex]P(X=x)= {n \choose x} (p)^{x} (1-p)^{n-x}[/tex]

      [tex]P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}[/tex], x=0, 1, 2, 3,..., 15.

Part B:

    [tex]P(X=1)= {15 \choose 1} (0.15)^{1} (0.85)^{15-1}\\\\P(X=1)= {(15)} (0.15) (0.85)^{14}\\\\P(X=1)=0.2312[/tex]

Part C:

     [tex]P(X=2)= {15 \choose 2} (0.15)^{2} (0.85)^{15-2}\\\\P(X=2)= {(105)} (0.15)^2 (0.85)^{13}\\\\P(X=2)=0.2856[/tex]

Part D:

 [tex]P(X\geq 2)= 1-P(X < 2)\\\\P(X\geq 2)=1-P(X=0)-P(X=1)\\\\P(X\geq 2)=1-0.0873-0.3212\\\\P(X\geq2)=0.6814[/tex]

Part E:

  The probability of none of the children getting the disease will be

             [tex]P(X=0)= {15 \choose 0} (0.15)^{0} (0.85)^{15-0}\\\\P(X=0)= {(1)} (1) (0.85)^{15}\\\\P(X=1)=0.8734[/tex]

Hence,

Part A: [tex]P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}[/tex], x= 0, 1, 2, 3, ..., 15.

Part B: P(X = 1) = 0.2312

Part C: P(X = 2) = 0.2656

Part D: P(X ≥ 2) = 0.6814

Part E: P(X = 0) = 0.0874

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There are four common types of transformations -

translation

rotation

reflection

 dilation.

Using Magnetic field,

a) Magnetic force acting on loop is 2.59 ×10⁻⁴ N

b) Torque acting on loop is zero.

We have given that,

Each side of square loop wire , L = 2.00 cm

Square loop carring current , I₂ = 0.230 A

Solenoid , has n= 30 turns/cm

Current Carrying in solenoid, I₁ = 15.0 A

Magnetic field inside solenoid , B = μ₀ n I₁

where, μ₀---> susceptibility of free space

μ₀ = 4π×10⁻⁷A/m

pulgging all known values in above formula,

B = (4π×10⁻⁷ A/m) 30 turn/cm × 100cm /1m (15.0 A)

= 5.6 ×10⁻² T

Now, the magnitude of magnetic force on one side of loop , F = B× L× I₂× sinθ

=> F = ( 5.6 ×10⁻² T )(0.02 m)(0.230 A) sin90°

=> F = 0.02599 × 10⁻² N

=> F = 2.59 ×10⁻⁴ N

The force acting on one side of loop lie in the plane of loop, are prependicular to the all sides and directed away from interior of the loop. Thus, these force strech the loop do tends to rotate it.

So, if loop is not rotate then there is not torque associated. Hence, Torque acing on loop is zero.

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Complete question:

A single-turn square loop of wire, 2.00 cm on each edge, carries a clockwise current of 0.230A. The loop is inside a solenoid, with the plane of the loop perpendicular to the magnetic field of the solenoid. The solenoid has 30.0 turns/cm and carries a clockwise current of 15.0 A. Find (a) the force on each side of the loop and (b) the torque acting on the loop.

The present age of the son is 12 years and the present age of the father is 36 years.

What is the age problem?

Age problems are algebra word problems that deal with the ages of people currently, in the past, or in the future.

Let the present age of the son be 'x'

Then, the present age of the father will be '3x'

According to the question,

The age of the son after 12 years = (x+12) years

And the age of the father after 12 years = 2(x+12) years

Therefore,

or, 3x+12=2(x+12)

or, 3x+12=2x+24

or, x=12

And, the father's age = 3*12 = 36 years

Hence, the present age of the son is 12 years and the present age of the father is 36 years.

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Answer:

y = 3/4x + 2

Step-by-step explanation:

Not sure if you wrote your answer choices incorrectly, but if B is y=3/4x + 2 then the answer is B

Answer:

The speed of the plane is 200 mph

Step-by-step explanation:

distance = rate x time

The times are equal.

Car:

150 = rt

[tex]\frac{150}{r}[/tex] = t

Plane:

600 = (r+ 150)t

[tex]\frac{600}{(r+ 150)}[/tex] = t

Set the two equation equal to each other and solve for r:

[tex]\frac{150}{r}[/tex] = [tex]\frac{600}{(r+150)}[/tex]  Multiple both sides by r(r+ 150)  to clear the fraction

[tex]\frac{r(r+150)}{1}[/tex] ([tex]\frac{150}{r}[/tex]) = [tex]\frac{r(r + 150)}{1 }[/tex] ([tex]\frac{600}{(r+ 150)}[/tex])

(r+150)(150) =  600r

150r + 22500 = 600r  Subtract 150r from both sides

22500 = 450r  Divide both sides by 450

50 = r  This is the rate of the car.        

The plane is 50 + 150 = 200                                                                                                                                                                      

Answer:

$189

Step-by-step explanation:

Calculate a unit rate (dollars per hour) then times by 9 hours. OR use a proportion. You will get the same answer.

dollars/hour

= $252/12hours

= $21/1hour

= 21 $/hr

21 × 9 = 189

Yoko will make $189 for 9 hours.

OR use a proportion.

$/hour = $/hour

252/12 = x/9

cross-multiply

12x = 252(9)

12x = 2268

divide by 12

x = 2268/12

x = 189

same answer!

to find the percentage we divide the number with the other number which wew take it as base and multiply with 100

let us under stande this with an example

we want to know what percentage is 5 of 10

so we divide 5 by 10 and multiply it with 100

i.e. (5/10)*100 = 0.5*100 = 50%

hence we can say that 5 is 50% of 10

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We divide a number by another number, using that other number as the base, then multiply the result by 100 to get the percentage that one number is of another.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

We place the percent symbol (%) next to the number to indicate that the number is a percentage.

For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

To get what percentage one number is of another:

We divide the number by another number, use that other number as the base, and multiply the result by 100 to determine the percentage.

Let's use an example to further understand this:

We're curious about what proportion makes up 5 of 10.

Consequently, we increase it by 100 and divide 5 by 10.

That is (5/10) × 100 = 0.5 × 100 = 50%

So, we can say that 5 is equal to 10 / 50%.

Therefore, we divide a number by another number, using that other number as the base, then multiply the result by 100 to get the percentage that one number is of another.

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On a 30-years mortgage, the monthly payment is $686.39, total cost of mortgage is $100,000 and total interest paid is $122,100.4.

By using formula, M =  [[tex]\frac{P [i(1+i)^{n} ]}{[(1+i)^{n-1} ] }[/tex]

Where, M is the monthly payment

P is the principal amount

i is the interest rate

n is the number of payments

As per question,

1) Months in 30 years (n) =30x12= 360

i = 5.2%

P = $125,000

By using the formula mentioned above,

monthly payment = $686.39

2) total cost of mortgage = home price - down payment

= 125,000 - 25000

= $100,000

3) total interest paid = (M x n) - P

= (686.39 x 360) - 125,000

= $122,100.4

If you don't repay the loaned money for the purchase or refinancing of a home, the lender has the right to seize your property under the terms of a mortgage, which is a contract between you and the lender. The standard four components of a mortgage payment are principal, interest, taxes, and insurance. The primary component is the sum that is subtracted from your outstanding loan balance.

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The hypotheses are:

Null hypothesis: the average test scores are the same for the different teaching methods.

Alternative hypothesis: the average test scores are different for the different teaching methods.

To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample.

Hence we get the required answer.

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The correct option for the t test for the difference between the means of 2 independent populations is sample variances are equal.

The Autonomous samples t Test analyzes the method for two free gatherings to decide if there is factual proof that the related populace implies are essentially unique. The Free samples t Test is a parametric test. This test is otherwise called: Free t Test.

The t test for the difference between the means of 2 independent populations when standard deviations are unknown, we must assume that sample variances are equal.

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Using disk scheduling algorithm,

Total distance ( head movement) for following algorithms is 120.

Disk Scheduling Algorithm

Disk scheduling is performed by the operating system to schedule I/O requests to arrive at the disk. Disk scheduling is also called I/O scheduling.

we have given that

Total cylinders on a disk drive = 100 , numbered from 0 to 99.

The queue order is 10, 20, 50, 70, 80 .

Current disk position = cylinder 40

Starting from current head position.

We have to calculate the total distance (head movement) for the following algorithm.

Since, disk moving towards zero.

Now , Total distance = |40-10| + | 10-0| + |0-20| +

|20-50| + |50-70| + |70-80|

= 30 + 10 + 20 + 30 + 20 + 10

= 120

Hence, the required distance is 120.

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The time of depreciation is 3.3 year

From the question, we have the following parameters:

Initial value = $27,300

Final value = $22,100

Rate of depreciation = 6.1% per year

These parameters can be represented using the following exponential equation

A(n) = A *(1 - r)ⁿ

Where

n = number of years

A  = Initial value = 27300

A(n) = Final value = 22100

r = rate of decay = 6.1%

Substitute the known values in the above equation, so, we have the following representation

27300*(1 - 6.1%)ⁿ = 22100

Divide

(1 - 6.1%)ⁿ = 0.81

0.939ⁿ = 0.81

Take the logarithm

n = log(0.81)/log(0.939)

Evaluate

n = 3.3

Hence, the number of years is 3.3 year

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The inequality for the given situation is 10b+7u≥1400.

Given that, Kevin works as a busboy making $10 per hour and as a theater usher making $7 per hour.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let b be the number of hours he works as a busboy this month, and let u be the number of hours he works as an usher.

His goal this month is to earn at least $1400 total.

So, the given inequality is 10b+7u≥1400

Therefore, the inequality for the given situation is 10b+7u≥1400.

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The equation represents the line that passes through (- 6, 7) and (- 3, 6) is  y = -1/3x +5

The slope-intercept form is just a means of formulating a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are clearly visible. This form is frequently referred to as the y = mx + b form. This line form is one of the most prevalent in algebra classes.

A line's slope-intercept form is y = mx + b, where m is its slope and b is its y-intercept.

The equation of the line which is passing through two points is:

y₂-y₁ / x₂-x₁

(6-7)/(-3+6)=-1/3

A line's slope-intercept form is y =mx +b, where m is the slope and b is the y intercept.

y = -1/3 x +b. We must now calculate b, the y intercept. To find b, plug one of the given points into the previous equation and solve for b.

6 = -1/3(-3) + b

b = 5

y = -1/3x +5

Therefore, the equation represents the line that passes through (- 6, 7) and (- 3, 6) is  y = -1/3x +5

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The inequality could be used to determine the number of subscriptions that Jennifer needs to sell is 2x+x≥90.

In mathematics, an inequality is a relationship that results from a non-equal comparison of two integers or other mathematical expressions. It is most typically used on a number line to compare the sizes of two numbers. There are several notations for various sorts of inequalities:

The symbol a < b indicates that an is less than b.

The symbol a > b indicates that an is greater than b.

These are known as strict inequalities, because an is strictly less than or strictly bigger than b. Equivalence is not allowed.

Given,

Carol intends to sell twice the number of magazine subscriptions as Jennifer..

And also given that,

Carol and Jennifer needs to sell at least 90 subscriptions in all

Let Carol sell 2x magazines then Jennifer sell x

So, they need to sell at least 90

x+2x ≥ 90

∴2x+x ≥ 90

Hence, the answer is  option 4

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The probability of selling more than radios is 0.07 when the probability of selling radios is from 0 to 5.

Given that,

In the picture we can see the full question.

We have to find what is the probability of selling more than 3 radios.

We know that,

In the picture there is a table

We have to first find the table then we get the probability of selling more than 3 radios.

First,

Given data is 100 weeks of sales data

Probability is number of weeks/ 100 weeks

x=0, number of weeks is 3

P=3/100=0.03

x=1, number of weeks is 20

P=20/100=0.2

x=2, number of weeks is 50

P=50/100=0.5

x=3, number of weeks is 20

P=20/100=0.2

x=4, number of weeks is 5

P=5/100=0.05

x=5, number of weeks is 2

P=2/100=0.02

The probability table we get,

x term are 0,1,2,3,4,5

P(x)    |0.03 | 0.2 |  0.5 |  0.2 |0.05| 0.02|

The probability of selling more than 3 radios is sum of the probability of selling 4 radios and 5 radios

P(x>3)=P(x=4)+P(x=5)

P(x>3)= 0.05+0.02

P(x>3)= 0.07

Therefore, The probability of selling more than radios is 0.07 when the probability of selling radios is from 0 to 5.

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let m be the vector space of all 3x3 matrices, and let h be its subspace consisting of all a satisfying. The dimension of h will be  0 ≤ h ≤ 3

If m be the vector space , a subset h ⊆ m is a subspace of m if the ten axioms (L₁ , L₂ , L₃ , . . . . L₁₀) of m are satisfied on h but it suffices only two axioms to hold on h for h that are axioms of closure of h under two linear operations : the sum of vectors and their multiplication by scalars in the field F.

Let m is a vector space over a field F,  a subset h which is closed under the two linear operation of m : the vector addition and multiplication of vector by scalar .

L₁ (∀x , y ∈m) , x+ y∈ m ---------(1)

L₂ (∀λ ∈ F) ( ∀ x∈ m ) λx ∈m -------(2)

A subset h⊆ m which satisfy (1) and (2) is a subspace of v

Dimension of Vector space and a subspace :

According to linear algebra theorem,

The number of vectors in all the basis if finitely generated vector space m is the same. This number is just the dimension of subspace m : dim m .

If m is spanned then here, dim m = 3

h ⊆ subs m <===> dim h < dim m

If h is subspace of m and dim m = 3 then,

dim h = h with 0≤ h ≤3

If h is zero, the dimension of improper subspace , h = {0}

If dim h = dim m = 3 the h = m since any basis A of h is a basis of m too and conversely,

Hence , any vector m of all 3×3 matrices and h be its subspace , the dim h will be 0 ≤ h ≤ 3

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Yes , on degeneracy of an optimal basic feasible solution in one problem (primal) implies uniqueness of optimal solutions for the other(dual).

Degenerate Elementary Feasible Solutions:

Elementary feasible solutions where one or more of the elementary variables are zero.

Discrete Variable: A decision variable that can only accept integer values.

Feasible Solution: A solution that satisfies all constraints.

Yes, a linear programming optimization problem can have a degenerate optimal solution, but a dual problem has a unique optimal solution, but only if instead of the optimal solution there is a degenerate optimal solution.

Example: Suppose the main problem depends on

max (z) = x₁+x₂

x₁≤1

x₁+x₂≤1

x₁, x₂≥0.

The solution (1,0) is optimal and degenerate, but all solutions (a,1−a) for 0≤a≤1 are also optimal.

dual is min(z)= y₁+y₂

subject to

y₁+y₂≥1,

y₂≥1,

y₁,y₂≥0.

dual has a unique (degenerate) optimal solution (0,1). So, there are situations where there are mostly degenerate optima, but unique dual optima.

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The required area is 10.3 square units.

Area of triangle= 12 /(a* b)

Area of a triangle using trigonometric area formula = 1/2( a * b) sin(c)

here, base = a , height = b*sin(c)

Given ,

Only the sine of the included angle, whose two side lengths are specified, can be used despite the two angle measurements that have been provided. The EF and DF sides of our triangle's angle, which measures 31 degrees, are also provided.

On putting the values given in the formula we get,

Area = 1/2* 8 * 5sin(31)

        = 20 * 0.51503807491

         ≈ 10.3

Therefore, the area of the triangle DEF is 10.3 square units.

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Answer:

Step-by-step explanation:

Yes it is possible because of the working man solution of indigineous triangles in the diameter of a ml

Answer: 92°

Step-by-step explanation:

The triangle is an isosceles triangle, since two sides are equal. That means the two opposite angles are also equal. Hence m∠N = m∠M = 44°.

Since all interior angles of a triangle adds up to 180°, m∠L can be calculated as:

[tex]180-2(44)=180-88=92[/tex]