Define the term drainage density

The total receipts after the end of 1,5,7 years are 124 , 604, 844 million respectively.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The function T(x)= 120x²+4

Thus after 1 year the receipts is T(1)=120×1+4

                                                          =124 million

After 5 years T(5)=120×5+4

                            =600+4

                            =604 million

Similarly for t=7 years T(7)=840+4

                                          =844 million

Hence, The total receipts after the end of 1,5,7 years are 124 , 604, 844 million respectively.

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Answer:

  y = 4

Step-by-step explanation:

You want the equation of the horizontal line containing the point (-1, 4).

On a horizontal line, the y-coordinates of every point are the same. The equation can be written ...

  y = constant

In order for the horizontal line to go through a point with y-coordinate 4, the constant must be 4. The equation is ...

  y = 4

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The regrouping column is used to carry numbers from the ones column to the tens column. In this case, there is a 1 that must be carried from the ones column to the tens column. The sum of 48 + 689 is 737.

A column is a vertical structure that acts as a support for a building or is used as a decorative object. It is commonly used in architecture and comes in many different styles, shapes, and sizes. Columns can be made from a variety of materials such as stone, marble, iron, and brass. They are often adorned with intricate carvings and detailed designs. Some ancient structures like the Parthenon in Athens, Greece, are famous for their impressive use of columns.

Hundreds

Tens

Regrouping

First Addend

Second Addend 6

Sum

4

8

Ones

7

7

The regrouping column is used to carry numbers from the ones column to the tens column. In this case, there is a 1 that must be carried from the ones column to the tens column. The sum of 48 + 689 is 737.

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The right side of the equation 9 - 3x +6+8 + 3x+7 can be simplified by combining like terms as: 30.

2(x - 5) can be simplified using the Distributive Property as: 2x - 10.

In Mathematics, the distributive property of multiplication states that when the sum of two or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Next, we would combining like terms in the right side of the equation as follows;

9 - 3x +6+8 + 3x+7 = (9 + 8 + 6 + 7) + (3x - 3x)

9 - 3x +6+8 + 3x+7 = 30.

By applying the distributive property of multiplication to left side of the equation, we have:

2(x - 5) = 2x - 10.

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1. The function is continuous everywhere because it is defined for all values of x, and there are no points where f(x) is undefined or where the limit as x approaches a specific value does not exist.

2. Interval of continuity: (-∞, ∞)

Discontinuities: None

Conditions of continuity not satisfied: None

Hence, option (d) is correct.

If and only if a function is continuous on every point in the open interval (a,b), it is continuous over that interval (a,b).

If and only if it is continuous on (a,b), then is continuous over the closed interval [a,b].

The right-sided limit of at x=a is (a), while the left-sided limit of at x=b is (b).

If a function is continuous across the whole open interval, it is said to be continuous over the interval. If it is continuous at each point in its interior and at both of its ends, it is continuous over a closed interval.

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twelve is two percent of six hundred

Slope intercept form is written as follows:

[tex]y=mx+b[/tex]

With this information, isolate y on the left side of the provided equation:

[tex]4y=10x-14[/tex]

Now, divide both sides of the equation by 4:

[tex]y=\frac{10}{4} x-\frac{7}{2}[/tex]

This equation cannot be simplified anymore, and is therefore the answer!

[tex]y=\frac{10}{4} x-\frac{7}{2}[/tex]

Answer:

y = (5/2)x - (7/2)

Step-by-step explanation:

–10x + 4y + 14 = 0

                 -14     -14

-----------------------------

-10x + 4y = -14

+10x                 + 10x

--------------------------------

4y = 10x - 14

÷4    ÷4     ÷4

----------------------

y = (10/4)x - (14/4)

simplified

y = (5/2)x - (7/2)

I hope this helps!

Therefore , the solution of the given problem of compound sentence's comes out to be { x|–2< x < 5}

Indicated by the conjunction "or," the compound sentence is true as long as either of the two statements is true. In other words, it is the union or combination of the solution sets for each unique assertion. The term "conjunction" refers to a compound inequality that contains the word "and". The words "and" and "or," which are considered to be variables of speech, have a different meaning in mathematics than they do in grammar.

Here,

Given :

=> On the number line

=> -5 to -2

and 5 to infinity .

So,

Both x| x > -2 and x < 5

The following is another method to state this solution set:

{ x|–2< x < 5}

It is assumed that the word "and" will always be used in compound inequality expressions when neither "and" nor "or" is explicitly used. You say, "x is more than  -2 and (reading to the right) x is less than 4," reading from the "x" position as "x|-2" "x," "x," and "x," respectively. This is the solution set's graph.

The Complete Question.

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For the given frequency distribution table the answer of the following questions are:

a. sample size is equal to n = 20.

b. Proportion , relative frequency , and the percentage are :

 f           Proportion                Relative frequency              Percentages

1                 0.05                        0.05                                     5

2               0.1                            0.1                                        10

3                0.15                           0.15                                    15

4                 0.2                            0.2                                    20

5                 0.25                         0.25                                   25

a. Sample size of the number of hours students slept before exam is :

n = 2+ 2 + 3+ 4+ 5 + 2+ 1+ 1

   = 20

b. Organization of the data in the form of frequency distribution table form is:

X       f           Proportion                Relative frequency              Percentages

8        2           2/20 = 0.1                   2/ 20 = 0.1                      0.1 × 100 = 10

7        2            2/20 = 0.1                   2/ 20 = 0.1                     0.1 × 100 = 10

6        3           3/20 = 0.15                   3/ 20 = 0.15                 0.15 × 100 =15

5        4           4/20 = 0.2                  4/ 20 = 0.2                     0.2 × 100 = 20

4        5          5/20 = 0.25                  5/ 20 = 0.25               0.25 × 100 = 25

3        2         2/20 = 0.1                   2/ 20 = 0.1                      0.1 × 100 = 10

2        1          1/20 = 0.05                   1/ 20 = 0.05                0.05 × 100 =5

1        1         1/20 = 0.05                   1/ 20 = 0.05                0.05 × 100 =5        

         20

Therefore, the sample size of the frequency distribution is 20 and the proportion , relative frequency ,and percentage are shown in the above table.

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The function represents an exponential decay, as it is a decreasing function.

A function is classified as exponential growth if it is an increasing function, that is, the function is increasing over it's entire domain.

A function is classified as exponential decay if it is an decreasing function, that is, the function is decreasing over it's entire domain.

As the function in this problem is decreasing, it is an exponential decay function.

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ABC has vertices A (0, -1), B (3,4), and C (3,1). The coordinates of the image after reflection over the x axis is

Reflection is a method of transformation that creates mirror image.

The transformation rule for reflection over the x axis is as below

(x, y) → (x, -y)

Applying the rule we have

A (0, -1), B (3, 4), and C (3, 1) will result to

A' (0, 1), B' (3, -4), and C' (3, -1)

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The equation in slope - intercept form would be y = 0.6x + 1.1.

Given is that Mr. Phan fills a portion of his pool with water on Monday. Then on Tuesday, he fills the pool with water coming from a hose at a constant rate. The table shows the number of feet of water in the pool as a function of time on Tuesday -

Time on Tuesday after 9 AM (hr) →   0    1      2

Amount of Water in Pool (ft) →          1.1   1.7   2.3​

Let the equation be -

y = mx + c

We can write the slope as -

{m} = (1.7 - 1.1)/(1 - 0)

{m} = 0.6

and

{c} = 1.1        

So, the equation in slope - intercept form would be -

y = 0.6x + 1.1

Therefore, the equation in slope - intercept form would be y = 0.6x + 1.1.

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Answer:

Step-by-step explanation:

i don't know convert

The method of moment estimators of a and b are [tex]\hat{a}=\bar{X}-\sqrt{3}S_x[/tex] and[tex]\hat{b}=\bar{X}+\sqrt{3}S_x[/tex] . And, the maximum likelihood estimators of a and b are  [tex]\hat{b}=x(n)[/tex] and [tex]\hat{a}=x(1)[/tex].

The random sample given is X₁, X₂, X₃,..........., Xₙ from the uniform distribution on [a, b]. The probability density function (pdf) of this is written as,

[tex]f(x)=\begin{cases} \frac{1}{b-a},&a < x < b\\0,&\text{otherwise} \end{cases}[/tex]

a) Now, let's calculate the expected value of X E(X). We get,

[tex]\begin{aligned}\mu _1=E(X)&=\int_a^b x\cdot\frac{1}{b-a}\;dx\\&=\frac{1}{b-a}\left[\frac{x^2}{2}\right]_a^b\\&=\frac{b+a}{2}\end{aligned}[/tex]

Let's calculate the second moment of X. We get,

[tex]\begin{aligned}\mu_2=E(X^2)&=\int^b_ax^2\cdot\frac{1}{b-a}\;dx\\&=\frac{1}{b-a}\left[\frac{x^3}{3}\right]_a^b\\&=\frac{b^3-a^3}{3(b-a)}\\&=\frac{b^2+a^2+ab}{3}\end{aligned}[/tex]

From the above values, variance is calculated as follows,

[tex]\begin{aligned}\mu_2-\mu_1^2=E(X)-E(X^2)&=\frac{b^2+a^2+ab}{3}-\frac{a^2+b^2+2ab}{4}\\&=\frac{4(b^2+a^2+ab)-3(a^2+b^2+2ab)}{12}\\&=\frac{b^2-2ab+a^2}{12}\\&=\frac{(b-a)^2}{12}\end{aligned}[/tex]

Now, using the method of moment, we denote [tex]E(X^2)=\mu_r[/tex] and [tex]M_n=\frac{1}{n}\sum_{i=1}^{n}X_i^2[/tex]. Then, [tex]\hat{\mu_r}=\frac{1}{n}\sum_{i=1}^{n}{X_i} ^r[/tex].

When [tex]\hat{a}[/tex] and [tex]\hat{b}[/tex] are the method of moment estimator of a and b, then, [tex]\hat{\mu_1}=\frac{\hat{a}+\hat{b}}{2}=\bar{X}[/tex] and [tex]\hat{\mu_2}=\frac{1}{n}\sum_{i=1}^{n}{X_i}^{2}[/tex].

Then,

[tex]\begin{aligned}\hat{\mu_2}-\hat{\mu_1^2}&=\left(\frac{1}{n}\sum_{i=1}^{n}({X_i}^{2}\right)-\bar{X}^2\\&=\frac{1}{n}\sum_{i=1}^{n}(X_i-\bar{X})^2\\&={S_x}^{2}\\\frac{(\hat{b}-\hat{a})^2}{12}&={S_x}^{2}\end{aligned}[/tex]

From [tex]\hat{b}+\hat{a}=2\bar{X}[/tex] and [tex]\hat{b}-\hat{a}=\sqrt{12{S_x}^{2}}=2\sqrt{3}S_x[/tex].

Then, the moment estimators of a and b are [tex]\hat{a}=\bar{X}-\sqrt{3}S_x[/tex] and[tex]\hat{b}=\bar{X}+\sqrt{3}S_x[/tex] .

b) Using the joint distribution of [tex]X=(X_1,........, X_n)[/tex] be

[tex]\begin{aligned}L(x_i\; a,b)&=\frac{1}{(b-a)^n}, a < x_i < b\\&=\frac{1}{(b-a)^n}, a < x(1) < x(n) < b\\&=\frac{1}{(b-a)^n}\cdot I\{x(n) < b\}\cdot I\{x(1) > a\}\end{aligned}[/tex]

where [tex]I_A=\begin{cases}1\;\text{if A is true}\\0\;\text{if not}\end{cases}[/tex]

The joint distribution of likelihood is maximum when b-a is minimum under the constraints b>x(n) and a<x(1). Then, [tex](b-a) > x(n)-x(1)[/tex]. So the minimum value is attained when [tex]b-a=x(n)-x(1)[/tex] that is [tex]\hat{b}=x(n)[/tex] and [tex]\hat{a}=x(1)[/tex]. Hence, the maximum likelihood estimate of a and b.

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Answer: The probability that vowels occupy even places in the word "jvuyojzrxccome" is 3/7.

Step-by-step explanation:

1) To find the probability that vowels occupy even places in the word "jvuyojzrxccome", we can use the following steps:

2) Break down the word into individual characters: "jvuyojzrxccome"

3) Identify the vowels in the word: "u, o, o, e"

4) Count the number of vowels in the word: 4

5) Count the number of even-positioned characters in the word: (1st, 3rd, 5th, 7th, 9th, 11th, 13th) 7

6) Identify the vowels in the even positions: "u, o, e"

7) Count the number of vowels in the even positions: 3

Use the formula for probability: P(vowels in even positions) = (number of favorable outcomes) / (number of total outcomes)

8) P(vowels in even positions) = 3/7

Therefore, the probability that vowels occupy even places in the word "jvuyojzrxccome" is 3/7.

Answer:

The radian measure of a central angle of a circle can be found using the formula:

Radian measure = Arc length / Radius

In this case, the radius is 22 centimeters, and the arc length is x. So,

Radian measure = x / 22

Step-by-step explanation:

Answer:

Step-by-step explanation:

d

The percentage multiplier to find 26% of an amount is, 0.26.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We know that;

Percentage multiplier calculates the percentage of an amount. It is also used to increase or decrease an amount by a percentage.

Now, In order to find the percentage multiplier of 26% of an amount we can multiply the number by a multiplier.

⇒ 26%

⇒ 26/100

⇒ 0.26

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The Gini coefficient for this nation cannot be calculated from the given information

From the question, we have the following parameters that can be used in our computation:

f(x) = 0.3x^4 +0.3x³ +0.4x²

The Gini coefficient for this nation cannot be calculated from the given information.

This is so because the Lorenz curve which is a graphical representation of the income distribution of a population is required

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Answer:

-3

Step-by-step explanation:

Write the equation in slope -intercept form: y = mx + b

where m is the slope.

       y - 5 = -3x

            y = -3x + 5

Slope = -3

[tex]y-5 =-3x[/tex]

[tex]y-5+5 =-3x+5\\ \\y=-3x+5[/tex]

The slope of a linear equation will always be the coefficient of the "x" variable when the equation is equalled to "y". The coefficient is just the number that multiplies the variable. Hence, the coefficient of this line is "-3". Check the attached image.

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A sample space the set of all the possible outcomes in a probability experiment.

The sample space in probability theory is the set of all possible outcomes of a random experiment.

It is the set of all possible results of an action, experiment, or random process. In other words, it is the set of all possible values that a random variable can take.

For example, in a coin flip experiment, the sample space could be defined as the set {heads, tails}.

In a dice roll experiment, the sample space could be defined as the set {1, 2, 3, 4, 5, 6}.

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Answer:

x = 11.5  This is the answer to the equation.

Step-by-step explanation:

2 · (x - 8) = 7  This is the equation as it is written.

x - 8 = 7/2

The class intervals would be:

Class 1: 2-10

Class 2: 11-19

Class 3: 20-28

Class 4: 29-37

Class 5: 38-46

Class interval can be determined by dividing the range of the data by the desired number of intervals (also known as classes).

First, we need to find the range of the data:

Maximum value: 47

Minimum value: 2

Range: 47 - 2 = 45

For this example, let's choose 5 classes.

Class interval = Range / Number of classes = 45 / 5 = 9

The class intervals would be:

Class 1: 2-10

Class 2: 11-19

Class 3: 20-28

Class 4: 29-37

Class 5: 38-46

Note: The upper limit of each class is always rounded up.

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The z-score for the male is more than the z-score for the female.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The z-score for males is given as,

z = (1600 - 3260.1) / 761.9

z = - 1660.1 / 761.9

z = - 2.179

The z-score for females is given as,

z = (1600 - 3080.7) / 523.1

z = - 1480.7 / 523.1

z = - 2.830

The z-score for the male is more than the z-score for the female.

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5+2+3+7+2=19:19 is the perimeter

In the weights of seven people, the 36th percentile is 135.

The following are the weights (in pounds) of seven people:

100, 115, 135, 140, 180, 197, 230

We have to determine the 36th percentile.

The term "percentile" describes how a score contrasts with other scores from the same collection. The percentage of values in a set of data scores that fall below a specific value is a typical way to represent percentile, despite the fact that there is no single meaning for this term.

The formula is:

= Percentile/100 × Total number of weights

There have total weights of 7 people and percentile is 36.

Now putting the value

= 36/100 × 7

= 2.52

= 3(approx)

To find the percentile value we count from left to right.

The 3rd number from left to right is 135.

So the 36th percentile is 135.

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The number of terms in the nth row is n + 1. The sum of the terms in the first n rows is equal to the sum of the first n + 1 triangular numbers, which is given by the formula n(n + 1)(n + 2)/6.

So to find m and n, we need to solve the following two equations simultaneously:

n(n + 1)(n + 2)/6 + m = 123000

n + 1 = 2m

Substituting the second equation into the first equation, we get:

m(2m + 1)(2m + 2)/6 = 123000

We can then solve for m using a numerical method, such as the bisection method or Newton-Raphson method. The solution is approximately m = 142.

So the values of m and n are 142 and 284, respectively.

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The solution for the equation 2cos4x - 1 = 0 is x = 3π/35.

For the values:

x = π/5 + 2kπ and also;

x = π/7 + kπ

then we can solve for k as follows:

π/5 + 2kπ = π/7 + kπ

collect like terms

2kπ - kπ = π/7 - π/5

kπ = (5π - 7π)/35 {simplifying the right hand side to a single fraction}

kπ = -2π/35

k = -2/35 {divide through by π}

put -2/35 for k in the equation x = π/7 + kπ to get the value of x;

x = π/7 - 2π/35 {simplifying the right hand side to a single fraction}

x = (5π - 2π)/35

x = 3π/35

Therefore, the solution for the equation 2cos4x - 1 = 0 is x = 3π/35.

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The grouping of all numbers with the formula a+bi is referred to as the complex number set. If b0, the number is also referred to as an imaginary number. The quantity is referred to be a real number if b=0.

A real number and an imaginary number added together is referred to by this phrase. It is symbolized by the letter z and has the formula a + bi.

Any number that is composed of both rational and irrational numbers is considered to be real. R is used to write these numbers, which may be native or positive.

Complex numbers are those that are expressed as a+ib, where a, b are actual numbers, and I is a fictitious number termed a "iota." I = (-1) is the value. A complex number, such as 2+3i, is one where the real number 2 (Re) and the imaginary number 3 I are both present (Im).

The number that is represented by the square root of a particular negative number is referred to by this phrase.

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