the incomes of all families in a particular suburb can be represented by a continuous random variable. it is known that the median income for all families in this suburb is $60,000 and that 40% of all families in the suburb have incomes above $72,000. (a) for a randomly chosen family, what is the probability that income will be between $60000 and $72000?

Answer:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

So, substituting the values given in the question, we get:

(x - 3)² + (y + 5)² = 3²

Simplifying, we get:

(x - 3)² + (y + 5)² = 9

Therefore, the correct option is A) (x - 3)² + (y + 5)² = 9.

Step-by-step explanation:

Answer:

9π

Step-by-step explanation:

circumference=6ft

radius=3ft

radius squared=9ft

area=9ft ×π

area=9π

Answer:

0

Step-by-step explanation:

Untuk menyelesaikan masalah ini, kita perlu menyelesaikan sistem persamaan linear dua variabel pertama dan sistem persamaan linear tiga variabel:

Sistem Persamaan Linear Dua Variabel:

2x + 3y = 8 ... (1)

-4x + 6y = 8 ... (2)

Untuk menyelesaikan sistem persamaan ini, kita dapat menggunakan metode eliminasi:

Langkah 1: Kalikan Persamaan (1) dengan 2 dan Persamaan (2) dengan 1. Kita memperoleh:

4x + 6y = 16 ... (3)

-4x + 6y = 8 ... (4)

Langkah 2: Tambahkan Persamaan (3) dan Persamaan (4). Kita memperoleh:

12y = 24

Langkah 3: Bagi kedua sisi dengan 12. Kita memperoleh:

y = 2

Langkah 4: Substitusikan y = 2 ke dalam Persamaan (1) atau (2). Kita memperoleh:

2x + 3(2) = 8

2x + 6 = 8

2x = 2

x = 1

Jadi, solusi dari sistem persamaan linear dua variabel adalah (x, y) = (1, 2).

Sistem Persamaan Linear Tiga Variabel:

x - z = -4 ... (5)

x + y + z = ?

2x + 3y = 8

Untuk menyelesaikan sistem persamaan ini, kita dapat menggunakan metode substitusi:

Langkah 1: Substitusikan x = 1 dan y = 2 dari sistem persamaan linear dua variabel ke dalam Persamaan (3). Kita memperoleh:

2(1) + 3(2) = 8

2 + 6 = 8

8 = 8

Langkah 2: Substitusikan x = 1 dari sistem persamaan linear dua variabel ke dalam Persamaan (5). Kita memperoleh:

1 - z = -4

z = 5

Langkah 3: Substitusikan x = 1 dan z = 5 ke dalam Persamaan (6). Kita memperoleh:

1 + y + 5 = ?

y = -6

Jadi, solusi dari sistem persamaan linear tiga variabel adalah (x, y, z) = (1, -6, 5).

Maka nilai x + y + z adalah:

x + y + z = 1 + (-6) + 5 = 0

Jadi, nilai x + y + z adalah 0

x = 3.375 and y = 5 provide the system of equations' answer.

The process of figuring out the unknown variables while keeping the equations balanced on both sides is known as the system of equations method. We solve an equation system by identifying the value of the variable that makes the condition of all the provided equations true. There are numerous methods for solving a system of equations.

Multiply the equation 4x+2y=23.50 by 2.

From the other equation, subtract.

Calculate y using a solution.

To find the value of x, substitute the value for y into one of the equations.

To eliminate one variable (either x or y) while utilising the elimination method, the equations are added or subtracted.

To start, we can multiply the first equation by 2 to get rid of the 2y term:

8x + 4y = 47

Next, we can subtract the second equation from this equation to eliminate the 8x term:

2y = 10

y = 5

Now that we have solved for y, we can substitute this value into one of the original equations (let's use the first one) to solve for x:

4x + 2(5) = 23.50

4x + 10 = 23.50

4x = 13.50

x = 3.375

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Answer:

-3

Step-by-step explanation:

5(y+2/5)=-13

5*y+5*2/5=-3

5y+2=-13

5y=-13-2

5y=-15

5y/5=-15/5

y=-3

Answer:

y = -3

Step-by-step explanation:

Now we have to,

→ Find the required value of y.

The equation is,

→ 5(y + (2/5)) = -13

Then the value of y will be,

→ 5(y + (2/5)) = -13

→ 5(y) + 5(2/5) = -13

→ 5y + (10/5) = -13

→ 5y + 2 = -13

→ 5y = -13 - 2

→ 5y = -15

→ y = (-15)/5

→ [ y = -3 ]

Hence, the value of y is -3.

The probability of X not occurring is 0.34.

What is Probability?

Probability is a branch of mathematics concerned with measuring the likelihood of events. It involves studying random phenomena, such as coin tosses, rolling dice, or weather patterns, and assigning numerical values to the likelihood of different outcomes .The formal definition of probability is based on the concept of equally likely outcomes, where the probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes

If P(X) = 0.66, then the probability of not X occurring (i.e., X complement or X bar) is:

P(X bar) = 1 - P(X)

P(X bar) = 1 - 0.66

P(X bar) = 0.34

Therefore, the probability of X not occurring is 0.34.

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The total monthly PITI of the mortgage loan, given the principal and the tax, would be $ 2, 512.08.

To find the monthly PITI, you first need to find the principal and interest portion by the formula :

= Amount financed / 1, 000 x factor for 8.75%, 15 years

= 188, 000 / 1, 000 x 10

= $ 1, 880

The monthly tax and insurance portion would be:

= ( Estimated property tax + Annual insurance ) / 12

= ( 5, 475 + 2, 110 ) / 12

= $ 632.08

The monthly PITI on the mortgage loan is therefore :

= 1, 880 + 632.08

= $ 2, 512.08

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The question is:

What is the total monthly PITI of the mortgage loan?

There are 24 different possible ways a resident can receive an advertisement in the mail.

The counting principle states that if there are "a" ways to do one thing, and "b" ways to do another thing, then there are "a × b" ways to do both things. In this case, we need to multiply the number of different types of advertisements for each week to find the total number of different possible ways a resident can receive an advertisement in the mail.

Week 1: 2 different types of advertisements (postcard or leaflet)
Week 2: 3 different types of advertisements (flyer, catalog, or calendar)
Week 3: 2 different types of advertisements (brochure or poster)
Week 4: 2 different types of advertisements (business card or coupon)

Total number of different possible ways = 2 × 3 × 2 × 2 = 24

Therefore, there are 24 different possible ways a resident can receive an advertisement in the mail.

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The initial fee per meter is $110.

Although the fundamentals of speed, time, and distance stay the same, the kind of problems posed in exams may vary.

Most of the time, applicants will be given 1-2 word problems based on Speed, Time, and Distance, but they should also be prepared for questions on data sufficiency and data interpretation based on the TDS (Time, Distance, and Speed) theme.

At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.

F(d) models the fee (in dollars) for climbing d meters.

F(d)=110+0.12d

To find the initial amount, substitute d=0 int the above function, and we get

F(0)=110+0.12(0)=110

Hence, the initial fee is $110.

The complete question is-

At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.F(d)models the fee (in dollars) for climbing d meters. F(d)=110+0.12d. What is the initial fee?

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The solution to the system of equations. is (x, y) = (-1, 6).

Simplifying this equation, we get:

6x + 6x + 18 = 6

12x + 18 = 6

Subtracting 18 from both sides:

12x = -12

Dividing both sides by 12:

x = -1

Now that we know x = -1, we can substitute this value into either equation to find y. We'll use the first equation:

y = 3x + 9

y = 3(-1) + 9

y = 6

Therefore, the solution to the system is (x, y) = (-1, 6).

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Will has 587 mins (9h 47m) of call time left for the month and used 791 mins (13h 11m) in the first 7 months. He has 4,909 mins (81h 49m) left for the remaining 5 months. His phone has 5,700 mins (95d 4h 20m) of call time in a year.

Will has 587 minutes of call time left for the rest of the month, which is 9 hours and 47 minutes (587/60). In the first 7 months, Will has used 791 minutes (113 minutes per month for 7 months), which is 13 hours and 11 minutes. He has 4,909 minutes (7 months x 700 minutes per month - 791 minutes used) or 81 hours and 49 minutes left for the remaining 5 months. In total, Will's phone has 5,700 minutes (12 months x 700 minutes per month) or 95 days, 4 hours and 20 minutes of call time in a year.

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Answer:

$0.10

Step-by-step explanation:

2 pound = 32 ounces

32 ounces = $3.20

What is the price per ounce?

3.20 / 32 = $0.10

So, the price per ounce is $0.10

The answer is 140 tamales would remain.

An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, among others. It is a mathematical phrase that represents a value or a set of values when evaluated.

We are given that Claudio made 300 tamales to give to pedestrians. Let the number of tamales Claudio passed out to pedestrians be represented by p.

If we assume that Claudio passed out p tamales, then the number of tamales remaining would be:

300 - p

If Claudio passed out samples to 160 pedestrians, then the number of tamales remaining would be:

300 - 160 = 140

Therefore, 140 tamales would remain.

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A. IQR or B. IQR is the correct response since Sunny Town is symmetrical or Sunny Town is asymmetrical.

The pattern of data distribution across various values or intervals is referred to as a distribution. The form, centre, and dispersion of a set of data can be described and examined in this manner.

We need to measure the fluctuation of the temperature data in both locations in order to decide which place has the most stable temperature. The interquartile range (IQR), which quantifies the spread of the middle 50% of the data, is the ideal measure of variability for this application.

As a result, depending on how the distributions are shaped, the answer is either A. IQR because Sunny Town is symmetric or B. IQR because Sunny Town is skewed. The IQR would be a suitable tool to gauge the data's spread if Sunny Town's temperature data were symmetric. The IQR would also be useful to measure the spread of the data if Sunny Town's temperature data were skewed. Therefore, the range would not be a suitable indicator of variability if the temperature data from either location were not skewed.

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The area of Mr. Denson's square-shaped patio that enclosed the fence is 324 m².

The area is represented as the number of unit squares that cover the surface of an enclosed figure or object, measured in square units like cm² and m².

The area is the product of the two sides (length and breadth).

The perimeter of a square = 4a, where a is one length of the square.

If 4a = 72 meters, a = 18 meters (72/4).

The area of the square-shaped patio = 324 m² (18 x 18).

Thus, Mr. Denson should know that his square-shaped patio has an area of 324 m².

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The value of the of your quarters incense is a function of and the number of quarters, then the output when input is 10 is 250.

Quarters:

In mathematical terms, quartering is the division of a whole into 4 equal parts, where 1 is the part referred to and 4 is the number of parts the whole is divided into.

Let the quarter be 25 cents then value(v) of quarter (cents) is functions of n then equation,

         v = 25n

Putting input (n =10)

   V =  25× 10

      = 250

The independent value is: n

The dependent value is : v

The equation is: v = 25n

And, the output when input is 10 is 250.

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Answer: 18d

Step-by-step explanation:

To find the greatest common factor (GCF) of the terms in the polynomial 18d^4e^2 − 45d^2 + 36d, we need to factor each term into its prime factors and then identify the common factors with the highest exponent for each variable.

The prime factors of each term are:

18d^4e^2 = 2 x 3^2 x d^4 x e^2

45d^2 = 3^2 x 5 x d^2

36d = 2^2 x 3^2 x d

To find the common factors, we need to look for factors that appear in all terms. The common factors with the highest exponent for each variable are:

2^1, 3^2, and d^1.

Therefore, the GCF of the terms in the polynomial is:

2 x 3^2 x d = 18d

Hence, the GCF of the terms in the polynomial 18d^4e^2 − 45d^2 + 36d is 18d.

To get the transformation's Jacobian, we must first compute the partial derivatives of each new variable with respect to each old variable: x/u = 0, x/v = 6 + 0 = 6, and x/w = 0 + 12w = 12w.

∂y/∂u = 8u ∂y/∂v = 0 ∂y/∂w = 8w + 0 = 8w z/u = 9 plus 0 = 9 z/v = 0 plus 18v = 18v z/w = 0 As a result, the transformation's Jacobian matrix is: [(x,y,z)/(u,v,w)] = J = \s[ 0 6 12w ] [ 8 0 8w ] [ 9 18v 0 ] A transformation's Jacobian is a matrix of partial derivatives that illustrates how changing the old variables impacts changing the new variables. We have three new variables x, y, and z in the provided transformation, which are functions of three old variables u, v, and w. To get the transformation's Jacobian, we must compute the partial derivatives of x, y, and z with respect to u, v, and w. We discover that x's partial derivative with respect to u is zero, x's partial derivative with respect to v is six, and x's partial derivative with respect to w is twelve. Likewise, y's partial derivative with regard to u.

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The length of the shaded arc is 68.71 metres squared.

The arc of a circle is defined as the part or segment of the circumference of a circle. Therefore, the length of the bolded arc can be found as follows:

length of an arc = ∅ / 360 × 2πr

where

Therefore,

r = 26 / 2 = 13 m

∅ = 360 - 57 = 303 degrees

length of an arc = 303 / 360 × 2 × 3.14 × 13

length of an arc =  24736.92 / 360

length of an arc = 68.7136666667

length of an arc = 68.71 metres squared

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The probability that a random sample of 55 students has a mean age of less than 19.2 age years is 0.3866 and the probability that a random sample of 55 students has a mean age between 18.8 and 23 years is 0.27808.

a. To find P(x < 19.2), we need to find the area under the normal distribution curve to the left of x = 19.2. We can use the formula for z-score to standardize the value of x:

z = (x - μ) / δ = (19.2 - 20.9) / 5.9 = -0.2881

Looking up the area to the left of z = -0.2881 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.3869. So P(x < 19.2) is 0.3866.

b. To find P(18.8 < x < 23.0), we need to find the area under the normal distribution curve between x = 18.8 and x = 23.0. Again, we can standardize the values of x and use a standard normal distribution table or calculator:

z1 = (18.8 - 20.9) / 5.9 = -0.3559

z2 = (23.0 - 20.9) / 5.9 = 0.3559

Looking up the area between z1 = -0.3559 and z2 = 0.3559 in a standard normal distribution table or using a calculator, we find that the probability is approximately0.27808. So P(18.8 < x < 23.0) is 0.27808.

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It would  take 5 people to paint the same wall is 1 hour and 20 minutes or 1:20.

It is clear that workers twice as fast as people when painting the same surface. This means that John will always draw twice as much area as people at any given time if they are working at the same time. So if they plan well and finish painting the room at the same time, John will paint twice as much area as people.

There is only one possibility:

3 people = 4 hours

Divide by 3.

1 person = 4/3 or 1 1/3 hours

There are 60 minutes in 1 hour. Multiply 1/3 by 60.

(1/3)× 60 = 60/3 = 20

1/3 of an hour is 20 minutes.

It would take 1 person 1 hour and 20 minutes to paint the wall

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Emila gοt a tοtal οf 2 + 7 = 9 marbles.

Let's first find οut which bags each friend gοt. Since each friend tοοk twο bags, we can subtract the marbles each friend gοt frοm the tοtal number οf marbles in the twο bags tο find οut the number οf marbles in the οther bag.

Amina gοt 5 marbles, sο the tοtal number οf marbles in her twο bags must be 1 + 4 οr 2 + 3. Let's assume she gοt bags with 1 and 4 marbles.

Then, the bags left fοr the οther friends are:

Bag 2: Breanna οr Chyna

Bag 5: Breanna οr Chyna

Bag 6: Deiοn οr Emila

Bag 7: Deiοn οr Emila

Bag 8: Available tο any friend

Bag 9: Available tο any friend

Bag 10: Available tο any friend

Breanna gοt 7 marbles, sο the tοtal number οf marbles in her twο bags must be 3 + 4. Therefοre, Chyna gοt bags with 2 and 5 marbles.

Chyna gοt 9 marbles, sο the tοtal number οf marbles in her twο bags must be 4 + 5. Therefοre, Deiοn gοt bags with 1 and 8 marbles.

Deiοn gοt 15 marbles, sο the tοtal number οf marbles in his twο bags must be 6 + 9. Therefοre, Emila gοt bags with 2 and 7 marbles.

Therefοre, Emila gοt a tοtal οf 2 + 7 = 9 marbles.

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[tex]\sin(15^o )=\cfrac{\stackrel{opposite}{7}}{\underset{hypotenuse}{h}}\implies h=\cfrac{7}{\sin(15^o )}\implies h\approx 27.05[/tex]

Make sure your calculator is in Degree mode.

Answer: W ≈ 16.6

Step-by-step explanation:

The Pythagorean Theorem equation is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] =[tex]c^{2}[/tex]

First do [tex]15^{2} +7^{2} =w^{2}[/tex]

Which equals [tex]274=w^{2}[/tex]

Then do[tex]\sqrt{274} =w[/tex]

so w ≈ 16.6

According to the trigonometric functions, the answer is A. StartFraction 12 Over 13 EndFraction.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of its sides. There are six primary trigonometric functions:

Sine (sin): the ratio of the opposite side to the hypotenuse of a right triangle.

Cosine (cos): the ratio of the adjacent side to the hypotenuse of a right triangle.

Tangent (tan): the ratio of the opposite side to the adjacent side of a right triangle.

Cosecant (csc): the reciprocal of the sine function, i.e. the ratio of the hypotenuse to the opposite side of a right triangle.

Secant (sec): the reciprocal of the cosine function, i.e. the ratio of the hypotenuse to the adjacent side of a right triangle.

Cotangent (cot): the reciprocal of the tangent function, i.e. the ratio of the adjacent side to the opposite side of a right triangle.

To find sin(K), we need to use the definition of sine which is the opposite side over the hypotenuse:

sin(K) = opposite / hypotenuse

In this case, the opposite side is LM and the hypotenuse is KM. We are given that KM = 13 and LM = 12, so we can plug these values into the formula:

sin(K) = 12/13

Therefore, the answer is A. StartFraction 12 Over 13 EndFraction.

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Answer:

Step-by-step explanation:

the error interval will be [15.29, 15.3).

What is error?

Error is the difference between an actual value and an estimate, or approximate, representation of that value in applied mathematics. The discrepancy between the population's average and the average of a sample taken from that population is a frequent example in statistics. The discrepancy between an irrational number's true value and the values of rational expressions like 22/7, 355/113, 3.14, or 3.14159 serves as an example of round-off error in numerical analysis. A truncation error happens when an infinite series is ignored for all but a small number of terms. For instance, the sum of the infinite series can be used to express the exponential function ex.

Find the error interval of 15.29:

[15.29, 15.3)

Hence the error interval will be [15.29, 15.3).

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The proportional relationship defined by the table is given as follows:

y = 2x.

A proportional relationship is defined according to the equation presented as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table, when the input variable x is increased by one, the output variable y is increased by 2, hence the constant of proportionality is given as follows:

k = 2.

Meaning that the equation is given as follows:

y = 2x.

The graph of the relation is given by the image presented at the end of the answer.

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Answer:

From the problem, we know that:

s + h = 137 (the total number of sodas and hot dogs sold is 137)

s = h + 49 (the number of sodas sold is 49 more than the number of hot dogs sold)

Now we can substitute the second equation into the first equation:

(h + 49) + h = 137

Simplifying this equation:

2h + 49 = 137

Subtracting 49 from both sides:

2h = 88

Dividing both sides by 2:

h = 44

Now we know that 44 hot dogs were sold. We can use the second equation to find the number of sodas sold:

s = h + 49

s = 44 + 49

s = 93

Therefore, 93 sodas were sold.

Number of sodas sold: 93

Number of hot dogs sold: 44

Step-by-step explanation:

Answer: Let's use variables to represent the number of sodas and hot dogs sold.

Let x be the number of hot dogs sold.

According to the problem, the number of sodas sold was 49 more than the number of hot dogs sold, so the number of sodas sold is x + 49.

The problem also tells us that the combined total of sodas and hot dogs sold was 137. So we can set up an equation:

x + (x + 49) = 137

Simplifying the left side:

2x + 49 = 137

Subtracting 49 from both sides:

2x = 88

Dividing both sides by 2:

x = 44

So the number of hot dogs sold was 44.

To find the number of sodas sold, we can use the expression we set up earlier:

x + 49

Substituting in our value for x:

44 + 49 = 93

So the number of sodas sold was 93.

Answer: Number of sodas sold: 93, Number of hot dogs sold: 44.

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