2. Find the sum, S, for the arithmetic series described? Remember to use the formula

Answer:

Step-by-step explanation:

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

The monthly rent during the 8th year of living in the apartment will be $2510

The cost of the apartment per month in the first year is $1600

The rent is set to go up by $130 per year

The monthly rent during the 8th year of living in the apartment

This can be calculated by using arthimetic progression

here a = 1600

d = 130

We need to caluclate a₈

a₈th = a + (8-1)d

= 1600 + 7 x 130

1600 + 910

= 2510.

Therefore, the monthly rent during the 8th year of living in the apartment will be $2510

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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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Answer: 30

Step-by-step explanation:

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!

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 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 probability that a 3 will get any given times the dies is rolled is 0.17x

Total number of outcomes in one roll = 6

The favorable outcome = 3

The probability = Number of favorable outcomes / Total number of outcomes

Substitute the values in the equation

The probability of getting 3 in first roll= 1 / 6

Total number of times the die rolled = 11 times

The probability of getting 3 in all given times = (The probability of getting 3 in first roll )^ (Number of times the die rolled)

Consider the number of rolls as x

Substitute the values in the equation

The probability of getting 3 in all the given times = (1/6)^x

= 0.17x

Hence, the probability that a 3 will get any given times the dies is rolled is 0.17x

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The interest rate if the simple interest on ​$4000 for 5 years is ​$​1,200  is 30%

The formula for calculating the simple interest is expressed as;

I = PRT/ 100

Where;

Now, let's substitute the values into the formula, we have;

$1200 = $4000 × R × 5/ 100

cross multiply

$120000 = $4000 × R

Divide both sides by the coefficient of R

R = $120000/$4000

R = 30%

Hence, the value is 30%

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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

Using Marked recapature formula for estimation on population size we get,

the estimate for total population size is 1200.

Marked recaputure Method :

first step is to capture and mark a sample of individuals. The assumption behind mark-recapture methods is that the proportion of marked individuals recaptured in the second sample represents the proportion of marked individuals in the population as a whole. In algebraic terms,

R/S = M/N

where R --> second time marked

S---> size of sample second time

N --> estimate population size

M ---> Marked in start point

We have given that ,

Total marked turtles by researchers (M) = 800

Second time total sample size (S) = 300

second time marked turtles(R) = 200

we have to find out estimate for total population size .

For this , Mark -Recapture method is very efficient to calculate estimate for total population size.

putting all known values in above formula we get, R/S = N/M

=> 200/300 = 800/N

=> 800× 300 = N× 200

=> N × 200 = 240000

=> N = 240000/200

=> N = 1200

so, the estimate for total population size is 1200.

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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 prime multiples of 5 is number 5

The multiples of 5 are 1, 5.

The prime numbers are the numbers who can be divided only by 1 and itselves.

First we need the multiplies of 8

And then find their factors, if the number of factors is exactly two( that is 1 and the number itself) then it is prime.

The factors of 1 is 1

The factors of 5 are 1 and 5

The numbers which have only two factors are prime.

5 [s the prime multiples of 5

Therefore, the number 5 is the only prime number multiple of 5

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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]

The 95% confidence interval for the difference between the two population means is (-1,9).

The 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. As the sample size increases, the range of interval values will narrow, meaning that you know that mean with much more accuracy compared with a smaller sample.

We have given that,

the point estimate of the difference between the means = 4,

the standard error = 5

and we need to find 95% confidence level for the difference between the two population means.

We know the formula of confidence interval, that is

CI = difference in mean ± error

⇒ CI = 4 ± 5

CI = 4 + 5 = 9

CI = 4 - 5 = -1

Therefore confidence interval for the difference between the two population means is (-1 , 9).  

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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 gas used and miles are proportional for each scooter.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y = k x

for some constant k , called the constant of proportionality .

Therefore, let's check whether the scooter A and scooter B shows proportional relationships.

Hence,

For scooter A:

y = kx

where

Therefore,

2 = 150 k

k = 2  /150

k = 1 / 75

Hence,

y = 1 / 75 x

From the table of scooter A, the ratio is constant, therefore, the relationships of gas used and distance covered is proportional for scooter A.

For the Scooter B the graph is also proportional because the ratios of the variables are constant.

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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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Answer:

1st: 2/4 or simplified to 1/2, 7th: 65/256

Step-by-step explanation:

the amount the numerator increases by doubles every time.

like +1, +2, +4, +8, +16, +32, etc

the denominator also doubles

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

The planet that is closet to the sun is Mercury. Then it is Venus, Earth,Mars, Jupiter, Saturn, Uranus, Neptune.    

So likely it is 0% chance the earth is the closet planet to the sun.

The probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring.

The higher the probability number or percentage of an event the more likely is that the event will occur is known as likelihood of an outcome.

We can use the following steps to calculate the probability of an event.

Step 1:- Identify an event with one result.

Step 2:- Identify the total number of results or outcomes and favorable outcomes that can occur.

Step 3:- Divide the number of favorable outcomes by the total number of possible outcomes.

Give question is incomplete.

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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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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                                                                                                                                                                      

The circumference Of the circle with a radius is 70.336 inch

Describe circumference using an example.

A distance is covered by a boy if he starts jogging from point "A" and arrives at the same spot after going around the park once. The park's circumference, which is the length or limit that surrounds it and is shaped like a circle, is known. The boundary's length is its circumference.

What is the circumference measured in?

A circle's perimeter, or the distance encircling it, is known as its circumference. It has units of measurement like millimeters (mm), centimeters (cm), meters (m), or inches and is represented by the letter C in mathematical formulas. The following equations relate it to the radius,  , and pi: C = d. C = 2πr.

Given that:

Radius = 11.2 inch

Circumference = 2πr = 2 x 3.14 x 11.2 = 70.336 inch

Hence the Circumference is 70.336

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The graph is in the image uploaded.

Given equation:

y = 3x-7

compare this with standard equation y =mx+b

so slope m = 3

y-intercept b = -7

so the point is (0,-7)

Table:

x        y

1        -4

0       -7

we can plot the graph with two points.

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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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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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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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Excluding operation of division of nonzero rationals, all other binary operations i.e., subtraction of integers, function composition of polynomials with real coefficients, and multiplication of 2 X 2 matrices with integer entries are all associative.

Thus, option (a), (c), and (d) are associative while option (b) is not associative binary operation.

We have to find out which of the following binary operations are associative.

(a) Subtraction of integers

(b) Division of nonzero rationals

(c) Function composition of polynomials with real coefficients

(d) Multiplication of 2 X 2 matrices with integer entries

Firstly, let us understand what do we mean by the associative property of binary operations. The associative property of binary operations states that in an expression if we restructure the parentheses, then there will be no change in the final answer.

Let us look into each of the binary operations given to us individually.

(a) Subtraction of integers

Let us consider a subtraction operation such as -

a-(b-c) = a-b-c

Now, if we change the parentheses in the above operation like (a-b)-c then also the operation will be given as -

(a-b)-c = a-b-c

So, the subtraction of integers operation is associative.

(b) Division of nonzero rationals

Let us consider a division operation such as -

3/(9/3) = 1

Now, if we change the parentheses in the above operation like (3/9)/3 then the operation will be given as -

(3/9)/3 = (1/3)/3 = 1/9

So, we see that there is change in the final answer when the parentheses is rearranged in the operation of division of nonzero rationals. Thus, the division of nonzero rationals operation is not associative.

(c) Function composition of polynomials with real coefficients

Let us assume that we have polynomials given by -

f, q, s: R→R

This implies that -

(f · (q · s))(x) = f((q · s)(x)) = f(q(s(x)))

Similarly,

((f · q) · s)(x) = (f · q)(s(x)) = f(q(s(x)))

We see that both the final results are same even if the parentheses are rearranged. So, (f · q) · s = f · (q · s)

So, the operations of function composition of polynomials with real coefficients is associative.

(d) Multiplication of 2 X 2 matrices with integer entries

Let us say that P, Q, R are three matrices. This implies that for any entries in the matrices, we can say that -

P(QR) =  ΣP( ΣQR)

=> P(QR) =  ΣΣPQR

Similarly,

(PQ)R = Σ( ΣPQ)R

=>  (PQ)R = ΣΣPQR

So, we see that P(QR) = (PQ)R

Thus, the operation of multiplication of 2 X 2 matrices with integer entries is associative.

Therefore, excepting the operation of division of nonzero rationals, all other binary operations i.e., subtraction of integers, function composition of polynomials with real coefficients, and multiplication of 2 X 2 matrices with integer entries are all associative.

Thus, option (a), (c), and (d) are associative while option (b) is not associative binary operation.

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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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