One year, the population of a city was 252,000. Several years later it was 204,120. Find the percent decrease

The given complex numbers are 2 - 3i and -2 + 6i. We need to find the sum and product of the given complex numbers.

Sum of the complex numbers = (2 - 3i) + (-2 + 6i)

= 2 - 2 + (-3i + 6i)

= 4i

Therefore, the sum of the given complex numbers is 4i.

Now, let's find the product of the given complex numbers.

Product of the complex numbers = (2 - 3i) (-2 + 6i)

= -4 + 12i + 6i - 18i^2

= -4 + 18i + 18 (as i^2 = -1)

= 14 + 18i

Therefore, the product of the given complex numbers is 14 + 18i.

Hence, the sum of the given complex numbers is 4i and the product of the given complex numbers is 14 + 18i.

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A) the probability of winning a positive amount of money is approximately 0.000487.

B) the ticket would have to cost $0.0522 (or approximately $0.05) for this lottery to be fair, in the sense that the expected profit is $0.

(a) To calculate the probability of winning a positive amount of money, we need to add up the probabilities of winning each prize except for the $0 prize:

Probability of winning a positive amount
= Probability of winning $300,000 + Probability of winning $70,000 + Probability of winning $600 + Probability of winning $18 + Probability of winning $5 + Probability of winning $3

Probability of winning a positive amount

= 1/5,518,121 + 1/1,715,449 + 1/9,024 + 1/1,768 + 1/358 + 1/166

Probability of winning a positive amount

≈ 0.000487 (to two decimal places)

Thus, the probability of winning a positive amount of money is approximately 0.000487.

(b) To find the ticket cost that makes the lottery fair, we need to calculate the expected profit, which is the sum of the products of the probability of winning each prize and the amount of money won for that prize. Since there are six possible prizes, the expected profit can be written as:

Expected profit = (1/5,518,121)($300,000) + (1/1,715,449)($70,000) + (1/9,024)($600) + (1/1,768)($18) + (1/358)($5) + (1/166)($3) - Ticket cost

Simplifying the expression above, we get:

Expected profit
= $0.0522 - Ticket cost

For the lottery to be fair, the expected profit should be $0. Therefore, we can set the expected profit equal to $0 and solve for the ticket cost:

$0 = $0.0522 - Ticket cost

Ticket cost = $0.0522

Therefore, the ticket would have to cost $0.0522 (or approximately $0.05) for this lottery to be fair, in the sense that the expected profit is $0.

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Answer:[tex]180\pi[/tex]

Step-by-step explanation:

[tex]v=\pi rx^{2} h\\v=\pi 6^{2} 5\\\\v=180\pi[/tex]

The length of the tree house with a base of 7 ft on the model is given as follows:

1/3 ft.

The length of the model is obtained applying the proportions in the context of the problem.

The scale is a ratio that relates the size of a drawing or map to the actual size of the object or area being represented. It indicates how much the drawing or map has been reduced or enlarged in size from the actual object or area.

Hence the scale of 1:21 means that each ft on the drawing represents 21 ft of actual distance, hence the length of the drawing for an actual distance of 7 ft is given as follows:

1/21 x 7 = 1/3 ft.

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Answer:

-2°F

Step-by-step explanation:

Let M and S represent Monday and Sunday's low temperatures respectively. The given information relates M and S with the equation:

[tex]M = 6 + \frac{S}{2}[/tex]

We can rearrange the equation to solve for S.

[tex]S = 2(M-6)[/tex]

We can substitute 5 for M and find that S = -2.

∴The low temperature on Sunday was -2°F.

.

The first 5 terms of the sequence, whose general term is an = -9n - 9, would be the following: -18, -27, -36, -45, -54.

In mathematics, a sequence is an ordered list of numbers, called terms, that follow a particular pattern or rule. Each term in a sequence is identified by its position in the sequence, which is usually represented by an integer index or subscript.

To find the first 5 terms of the sequence with the general term an = -9n - 9, we can simply substitute the values of n from 1 to 5 into the formula and simplify:

a1 = -9(1) - 9 = -18

a2 = -9(2) - 9 = -27

a3 = -9(3) - 9 = -36

a4 = -9(4) - 9 = -45

a5 = -9(5) - 9 = -54

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Answer:

Ans: Rs 181.44.

Step-by-step explanation:

Looking at the corresponding probability in the distribution will allow you to determine the likelihood of selling a specific quantity of face masks each day.

Here is the probability distribution for the number of face masks sold per day:

X P(X)

10 0.2

12 0.1

14 0.2

15 0.3

20 0.1

25 0.1

To find the probability of selling a certain number of face masks per day, you look at the corresponding probability in the distribution. For example, the probability of selling 15 face masks per day is 0.3.

Note that the probabilities sum to 1, which is a requirement for any probability distribution.

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The inequality is t ≤ 28.

Inequalities serve as the defining characteristic οf the relatiοnship between twο values that are nοt equal. Equal dοes nοt imply inequality. Typically, we use the "nοt equal symbοl (≠)" tο indicate that twο values are nοt equal. But different inequalities are used tο cοmpare the values tο determine whether they are less than οr greater than.

Given that Deshaun runs each lap in 4 minutes. He will run at mοst 7 laps tοday.

Assume that t fοr the number οf minutes he will run tοday.

He will run at mοst 7×4 = 28 minutes.

The symbοl οf at mοst is ≤.

The inequality is t ≤ 28

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the height of the triangular pyramid is 13 units.

How to solve?

The formula for the volume of a pyramid is given by V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. In the case of a triangular pyramid, the base is a triangle, so the area of the base is given by A = (1/2)bh, where b is the base length and h is the height of the triangle.

Given that the volume of the triangular pyramid is 273 units³, we have:

V = (1/3)Bh = 273

We know that the base of the triangular pyramid has a base length of 14 units and a height of 9 units, so its area is:

A = (1/2)bh = (1/2)(14)(9) = 63

Substituting this value for B in the equation for the volume, we have:

(1/3)(63)h = 273

Multiplying both sides by 3, we get:

63h = 819

Dividing both sides by 63, we get:

h = 13

Therefore, the height of the triangular pyramid is 13 units.

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The solution to the linear system with repeated eigenvalues can be written in two forms: the exponential form and the Jordan form. In the Jordan form, the solution is written as:  [tex]x(t) = e^(J*t) * v_0[/tex]

In the exponential form, the solution is written as:
[tex]x(t) = e^(lambda*t) * (v + t*w)[/tex]
Where lambda is the repeated eigenvalue, v is the eigenvector, and w is the generalized eigenvector.

In the Jordan form, the solution is written as  :  [tex]x(t) = e^(J*t) * v_0[/tex]
Where J is the Jordan matrix, which is a matrix with the repeated eigenvalue lambda on the diagonal and a 1 on the superdiagonal, and v_0 is the initial condition vector.

Both forms of the solution give the same result, but the exponential form is simpler and easier to compute. The Jordan form is more general and can be used to find the solution for any linear system with repeated eigenvalues.

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Step-by-step explanation:

Your monthly payments with taxes and insurance included would be $2,903.71. This is calculated by taking the loan amount of $450,000 and multiplying it by the simple interest rate of 6.00%. The result is $27,000, which is then divided by the length of the loan, 30 years. This gives you

the principal and interest portion of your monthly payment, which is $2,033.33. To that, you add your yearly taxes of $2,000 and insurance of $1,500, divided by 12 months, to get an additional $416.67 and $125, respectively. Adding these two numbers together gives you your total monthly payment of $2,903.71.

Answer:

1. To expand the polynomial f(x) = (x-3)(x+2)(x+3), we can use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x+3) using FOIL again.

2. To expand the polynomial g(x) = (x-3)(x+2)(x-2), we can also use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x-2) using FOIL again.

3. The polynomial f(x) has three linear factors, and so the degree of the polynomial will be 3, since we will have to multiply three binomials together. The polynomial g(x) has four linear factors, and so the degree of the polynomial will be 4.

If we were to expand a polynomial with five linear factors, the degree of the polynomial would be 5, since we would have to multiply five binomials together.

4. The degree of a polynomial is determined by the highest power of x in the polynomial, which is determined by the number of terms in the expanded polynomial expression.

(6 sentences to use):

1. To expand the polynomial (x-3)(x+2)(x+3), we use the distributive property and multiply each term of the first binomial by each term of the second binomial, then multiply the resulting trinomial by the third binomial.

2. To expand the polynomial (x-3)(x+2)(x-2), we use the same strategy as in the previous example, multiplying each term of the first binomial by each term of the second binomial, and then multiplying the resulting trinomial by the third binomial.

3. The polynomial f(x) has three linear factors, so its degree is 3, which means the highest exponent in the polynomial is 3.

4. The polynomial g(x) has four linear factors, so its degree is 4, which means the highest exponent in the polynomial is 4.

5. If we were to expand a polynomial using five linear factors, we would again use the distributive property to multiply each term of each binomial together, resulting in a polynomial with a degree of 5, which means the highest exponent in the polynomial would be 5.

6. This strategy for multiplying three binomials is a useful tool in algebraic manipulation, allowing us to expand and simplify polynomial expressions.

Hope this helped! Sorry if it didn't. If you need more help, ask me! :]

Answer:

13 matches

Step-by-step explanation:

Notice 1st have 4 matches
then 2nd have 7 matches (since one is shared), this is 8-1

then 3rd have 10 matches (since two are shared) this is 12-2
Notice the pattern 4 matches per square minus one per aditional square from the first.
This give an equation
4n-1(n-1)= 3n+1
lets check
For n=1    matches= 3(1)+1=4

For n=2    matches= 3(2)+1=7

For n=3    matches= 3(3)+1=10
It works.
so

For n=4   matches= 3(4)+1=13

Step-by-step explanation:

The distributive property of multiplication over addition states that for any numbers a, b, and c, a × (b + c) = a × b + a × c.

Looking at Marta's work, we can see that the distributive property was used in line 1, where she distributed the 2 to both terms inside the parentheses:

2(x - 4) + 2x = x + 7

2x - 8 + 2x = x + 7

4x - 8 = x + 7

Therefore, the step in Marta's work that is justified by the distributive property is line 1, where she distributed the 2 to both terms inside the parentheses.

The value of the vehicle 5 years after purchase will be $12,500. After we predict the depreciation of car values as time progresses.

Due to use, wear, and tear, or becoming obsolete, an asset loses value over time. Depreciation is the measurement of this decrease.

Using the given linear model y = -1100x + 25,000, we can substitute x = 5 (since we want to find the value after 5 years of purchase) and solve for y:

y = -1100(5) + 25,000

y = -5500 + 25,000

y = 19,500

Therefore, the value of the vehicle 5 years after purchase will be $19,500.

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The conditional probability of drawing a heart on the fourth draw given that the first three cards are not hearts is 13/49.. The correct answer is D.

After drawing three cards without replacement, there are 52 - 3 = 49 cards remaining in the deck, of which 13 are hearts and 36 are not hearts.

If the first three cards are not hearts, then there are 36 cards remaining in the deck for the fourth draw, of which 13 are hearts and 23 are not hearts.

The conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, can be calculated using Bayes' theorem:

P(heart on 4th draw | first 3 not hearts) = P(heart on 4th draw and first 3 not hearts) / P(first 3 not hearts)

The probability of drawing a heart on the fourth draw and the first three not being hearts is:

P(heart on 4th draw and first 3 not hearts) = (36/52) * (35/51) * (34/50) * (13/49) = 0.0334

The probability of the first three cards not being hearts is:

P(first 3 not hearts) = (36/52) * (35/51) * (34/50) = 0.5764

Therefore, the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, is:

P(heart on 4th draw | first 3 not hearts) = 0.0334 / 0.5764 ≈ 0.058 or approximately 5.8%.

Therefore, the answer is 13/49. The correct answer is D.

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The percent of 25 doctors which is equivalent to 2 as required to be determined is; 8%.

As evident from the task content; the percent of 25 doctors which is equivalent to 2 is to be determined.

On this note, the percentage can be determined using the percent proportion formula as follows where x = the required percentage.

x / 100 = 2 / 25

25x = 200

x = 200 / 25

x = 8.

Hence, the equivalent percentage as required to be determined is; 8%.

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Answer:

(x-1)(x+6)

Step-by-step explanation:

The function f(x)= (x+4)(x-2)/(x+4)(x-2) passes through the origin with a constant slope of 1, and has two removable discontinuities at x=-4 and x=2.

The function that passes through the origin with a constant slope of 1 and has removable discontinuities at x=-4 and x=2 is given by:

f(x)= (x+4)(x-2)/(x+4)(x-2). This function can be written in its factored form as f(x)= 1.

The function has a constant slope of 1, which means that for any two points (x_1,y_1) and (x_2,y_2) the slope is given by

(y_2-y_1)/(x_2-x_1)=1.

The function has two removable discontinuities at x= -4 and x= 2. This means that at these points the function is undefined, and the derivative of the function is infinite.

Removable discontinuities can be resolved by factoring out a common factor from the numerator and denominator of the function. In the case of the given function, factoring out (x+4) and (x-2) resolves the discontinuities. The graph of the function is a straight line which passes through the origin. This is because the function is of the form y=mx, where m is the constant slope of 1, which makes the function pass through the origin.

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The Answer is approximately equal to 942.48 or 300π

(π=pi)

By using the speed fοrmula, the velοcity οf the wind is apprοximately 66.23 mph.

Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn. Mathematically, speed is calculated as fοllοws:

speed = distance/time

where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

Let's assume that the speed οf the wind is represented by the variable "v" (in mph). When the plane flies dοwnwind, the speed οf the plane relative tο the grοund is the sum οf its airspeed and the wind speed, οr (340 + v) mph. Similarly, when the plane flies upwind, the speed οf the plane relative tο the grοund is the difference between its airspeed and the wind speed, οr (340 - v) mph.

Nοw, lets use the fοrmula:

time = distance / speed

tο set up twο equatiοns and sοlve fοr the wind speed "v".

First, fοr the dοwnwind flight:

time = distance / speed

200 / (340 + v) = t

Secοnd, fοr the upwind flight:

time = distance / speed

140 / (340 - v) = t

Since the time taken fοr bοth flights is the same, we can equate the twο equatiοns:

200 / (340 + v) = 140 / (340 - v)

Nοw, we can sοlve fοr "v":

200(340 - v) = 140(340 + v)

68,000 - 200v = 47,600 + 140v

308v = 20,400

v ≈ 66.23

Therefοre, the velοcity οf the wind is apprοximately 66.23 mph.

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Yes, trigonometry only works on the right angled triangles.

The study of correlations between triangles' side lengths and angles is known as trigonometry.

Thus, the right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.

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The complete question is-

Right triangle and trigonometry:

Does trigonometry work on right triangles?

In response to the query, we can state that Salim thereby covered a total fraction distance of about 3.83 miles.

To represent a whole, any number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of the numerator to the denominator. They can all be expressed as simple fractions as integers. In the numerator or denominator of a complex fraction is a fraction. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.

Salim therefore walked a total of:

4/3 Plus 5/2 miles

We must identify a common denominator in order to add these fractions:

Six is the least frequent multiple of 3 and 2.

We may therefore rephrase the following fractions with denominators of 6:

4/3 = (4/3) x (2/2) = 8/6

5/2 = (5/2) x (3/3) = 15/6

We can now combine the fractions:

8/6 + 15/6 = 23/6

Salim covered a distance of 23/6 miles in all.

This fraction can be simplified by dividing both the numerator and denominator by their largest common factor, which is 1:

3.83 miles, or 23/6 miles (rounded to two decimal places)

Salim thereby covered a total distance of about 3.83 miles.

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As before, it follows that A3 is a maximal ideal of R, contradicting the fact that the chain is infinite. Therefore, R satisfies the ACC.

It is given that be an integral domain with a descending chain of ideals. Suppose that there exists an n such that for all i ≥ n, then ai = an. A ring satisfying this condition is said to satisfy the descending chain condition or DCC. Rings satisfying the DCC are called Artinian rings, after Emil Artin.

The statement to be proved is if R satisfies the descending chain condition, it must satisfy the ascending chain condition. Suppose, by contradiction, that R satisfies the DCC but does not satisfy the ACC. Then, there is an infinite ascending chain: A1 ⊂ A2 ⊂ A3 ⊂ A4 ⊂ ···.

Note that if R is an integral domain and if a ∈ R, then (a) is either (0) or is a maximal ideal in R. Hence, (0) is a minimal element in the collection of all proper ideals of R. Suppose A1 is a proper ideal of R that is maximal with respect to not being finitely generated. Since R satisfies the DCC, A1 cannot be infinite. Therefore, A1 is a finite set. Suppose A1 is not principal.

Then there exist two elements a, b ∈ A1 that do not belong to (a) and (b) respectively. This means that (a, b) is a proper ideal of R, properly containing A1, which contradicts the maximality of A1. Thus, A1 is a principal ideal generated by an element a1 ∈ A1.Suppose A2 = (a1, a2, a3, · · · , am) is a proper ideal properly containing A1. If A2 is finitely generated, then A2 ⊃ (a1) ⊃ (0) is a finite descending chain of ideals, which contradicts the DCC.

Thus, A2 is not finitely generated. By the maximality of A1, A2 must be principal, generated by an element a2 ∈ A2. It follows that a2 = c1a1 + c2a2 + · · · + cmam, where ci ∈ R for all i. Hence, (1 − c2)a2 = c1a1 + · · · + cmam, which means that a2 ∈ (a1). Therefore, (a1) = A1 = A2, and it follows that A2 is a maximal ideal of R.

Suppose A3 is a proper ideal properly containing A2. If A3 is finitely generated, then A3 ⊃ A2 ⊃ (0) is a finite ascending chain of ideals, which contradicts the ACC. Thus, A3 is not finitely generated. By the maximality of A2, A3 must be principal, generated by an element a3 ∈ A3.

As before, it follows that A3 is a maximal ideal of R, contradicting the fact that the chain is infinite. Therefore, R satisfies the ACC.

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The actual length and width of the swimming pool are 34 meters and 18 meters, respectively, based on a scale of 1 inch to 4 meters.

Based on the given information, we know that the scale of the drawing is 1 inch to 4 meters. This means that every 1 inch on the drawing represents 4 meters in actual length.

The length of the swimming pool on the drawing is given as 8.5 inches. To find the actual length of the swimming pool, we need to multiply the length on the drawing by the scale factor:

Actual length of the swimming pool = 8.5 inches x 4 meters/inch = 34 meters

Similarly, the width of the swimming pool on the drawing is given as 4.5 inches. To find the actual width of the swimming pool, we can use the same formula:

Actual width of the swimming pool = 4.5 inches x 4 meters/inch = 18 meters

Therefore, the actual length of the swimming pool is 34 meters and the actual width is 18 meters.

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Answer:

y = x/3 - 8/3 (OR) 3y = x - 8

Both of the above solutions are the same

Step-by-step explanation:

Using the form 'y=mx+c',

Since m = 1/3,

y = 1/3x + c

Substituting (5, -1) into the above equation:

-1  = 5/3 + c

c = -1 - 5/3

= -8/3

Hence,

y = x/3 - 8/3

(which is also the same as)

3y = x - 8

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Answer:

[tex]4\frac{8}9}[/tex]

Step-by-step explanation:

We can do this mathematically.

[tex]5-\frac{2}{18} = \frac{90}{18} - \frac{2}{18} = \frac{88}{18} = \frac{44}{9} = 4\frac{8}{9} \\[/tex]

We can also work this logically.

We know that [tex]\frac{2}{18}[/tex] is less than 1, so our answer should be (5-1) and a fraction.

Our answer should be 4 plus a fraction less than 1. To find what we need to add to [tex]\frac{2}{18}[/tex] to make 1, we ask ourself how many eighteenths make 1. So if we need to 18 parts and we have 2 already, we add 16 eighteens to make 1. The answer is [tex]4 \frac{16}{18}[/tex], or simplified, [tex]4\frac{8}9}[/tex].

The BEST choice for two perpendicular lines is: e) Their slopes are the reciprocal negatives of one another.

Perpendicular lines are those that cross at a correct angle when two separate lines share a plane. Vertical and horizontal lines, or the axes of a coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

If two lines intersect at the a right angle in Euclidean geometry, they are said to be parallel (90 degrees).

When two lines are parallel, their slopes are the reciprocal of each other's negative values. A slope of the second line would be "-1/m" if the curve of the initial line is "m."

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