25% of what number is 9​

The solution of the differential equation would be [tex]r = \dfrac{(\theta - cos\theta) + C}{(sec\theta + tan\theta)}[/tex].

Using the concept of integration that states,

Integration in mathematics is a technique for integrating or adding up the parts to get the total. It involves a differentiation process in reverse.

Given that,

The differential equation is,

[tex]\dfrac{dr}{d\theta } + r sec(\theta ) = cos (\theta )[/tex]

Hence the auxiliary solution,

[tex]\mu (\theta ) = e^{\int\limits {sec\theta} \, d\theta}[/tex]

[tex]\mu (\theta ) = e^{ln |\limits {sec\theta + tan\theta|[/tex]

[tex]\mu (\theta ) = |sec\theta + tan\theta|[/tex]

Hence multiply both sides by [tex]\mu(\theta)[/tex],

[tex]({sec\theta + tan\theta)\dfrac{dr}{d\theta } + ({sec\theta + tan\theta) r sec(\theta ) = cos (\theta ) ({sec\theta + tan\theta)[/tex]

[tex]\dfrac{d}{d\theta} (r \times (sec\theta + tan\theta) = (1 + sin\theta)[/tex]

Integration on both sides,

[tex]r \times (sec\theta + tan\theta) = (\theta - cos\theta) + C[/tex]

Therefore, the solution is,

[tex]r = \dfrac{(\theta - cos\theta) + C}{(sec\theta + tan\theta)}[/tex]

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We divide the smaller number in HCF by the remaining after dividing the smaller number by the smaller number. Until there is no more remaining, we repeat the process.

For two or more numbers, HCF can be assessed. It is the most powerful factor for dividing any pair of numbers by either half or all of them. To illustrate: 15 is the biggest number that can divide both 60 and 75 perfectly, making it the highest common factor between those two numbers.

here

Step 1 is to divide the largest integer by the smallest number.

Step 2: Divide the first divisor by the first remainder, taking the divisor as the new dividend and the remainder as the new divisor.

Step 3: Continue until the remainder is 0 and the HCF of the given numbers is the last divisor.

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Answer:

The graph of g(x) = (3x+5) + 8 will be shifted 8 units up from the graph of f(x). Specifically, the graph of g(x) will be 8 units higher than the graph of f(x) for all x.

Step-by-step explanation:

The number of days the lizard that will be taken to reach the top will be 8 days .

Since we're given the information that the spider each day climbs five meters and slides back one meter, that means that it climbs for 4 meters daily .

Number of meters for each day = 5 - 1

= 4 meters

Therefore, since the spider is climbing up a 30 meter building, the number of days required will be :

= 30 / 4

= 15 / 2

= 7.5

= 8 days approximately.

Hence The number of days will be needed to reach the top is 8 days.

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Answer:

| AD | ≈ 48 m

Step-by-step explanation:

A line bisector divides a given line into two equal sections or parts. Thus the required proof to show that BC ≅ DF is stated below:

A given line is said to have been bisected if and only if it is divided into two equal parts by a constructed line. The line that divides a given line into two equal parts is termed a line bisector.

The appropriate proof is as stated below:

              STATEMENT                                                 REASON

1. AB ≅ FG                                                              Given

2. BF bisects AC and DG                                      Given

3. AB ≅ BC                                                             Definition of a bisector

4. DF ≅ FG                                                             Definition of a bisector

5. AC ≅ DG                                                         Property of two congruent lines

6. BC ≅ DF                                                         Property of two congruent lines

Therefore it can be deduced that BC ≅ DF  (property of two congruent lines)

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7 pens are obtained by adding 5 and 2. We receive 5 back after subtracting 7 pens and 2 pens. The procedures of addition and subtraction are reversed in this case.

Given,

Inverse operations;

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

Examples for inverse operations;

We get 7 pens when we mix 5 and 2. We now have 5 pens left after subtracting 7 pens and 2 pens. Addition and subtraction are inverse operations in this situation.

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The graph of the function h(x) is attached below.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is h(x) = √(x-2) + 3

The radical function is always positive.

Therefore,

x - 2 ≥ 0

x ≥ 2

The domain of the function is [2, ∞)

The value of h(x) is at the lowest value of x that is x = 2.

h(2) = √(2-2) + 3

h(2) = 3

The range of the function is [3, ∞)

The starting point of the function is (2,3).

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Answer:

Elga is 22 years old

Step-by-step explanation:

Let A = Alvin's age

Let E = Elga's age

We have the equations:

A = E - 11

A + E = 33

Substitute A = E - 11 from the first equation into the second equation and solve for E

So, we have

A + E = 33

(E - 11) + E = 33

2E - 11 = 33

2E = 44

E = 22 years old

So, Alvin is 11 years old and Elga is 22 years old

Answer:

No

Step-by-step explanation:

Consider the graphs of [tex]y=2^x[/tex] and [tex]y=3^x[/tex].

The median of 2/3 and 4 is 2.33.

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.

To arrange the data points in ascending order for a small data set, count the number of data points (n).

To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

Median = (2/3+4)/2 = 4.66/2 = 2.33

Thus, the median of 2/3 and 4 is 2.33.

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To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

Median = (2/3+4)/2 = 4.66/2 = 2.33

Thus, the median of 2/3 and 4 is 2.33.

AAA ( Angle - Angle - Angle) congruence rule is one of congruence postulate but not preferable, for showing the similarity in two triangles

Two triangles are said to be congruent if one can be superimposed on the other exactly by rigid body motion, and the congruence theorem gives the conditions under which this occurs.

AAA Congruence rule:

It is stands for angle-angle-angle Congruence rule. When all three angles of one triangle is equals to the corresponding angles of another triangle. but it is possible if and only if the corresponding sides of both triangles are equal and when all three sides of two triangles are equal to each other then we use SSS Congruence rule. So, it not considered as preferable congruence rule . For example, In ∆ABC and ∆PQR

all three angles of ∆ABC is equal to corresponding angles of ∆PQR. So,∆ABC and ∆PQR are congruent.

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The HCF of the polynomials x^6 -  3x^4+ 3x² - 1 and x³+ 3x^2+ 3x+ 1 is (x+1)^3.

Let us suppose the Polynomials to be f(x) = x^6 - 3x^4 + 3x^2 - 1  And polynomial g(x) = x^3 + 3x^2 + 3x + 1

Now,  According to the question,

we have f(x) = x^6 - 3x^4 + 3x^2 - 1  

Adding and subtracting 2^x2,

⇒ x^6 - x^4 - 2x^4 + 2^x2 + x^2 - 1

⇒ x^4(x^2 - 1) - 2x^2(x^2 - 1) +1(x^2 + 1)

⇒ (x^2 - 1)(x^4 - 2x^2 + 1)

⇒ (x + 1)(x - 1)(x^4 - 2x^2 + 1)

⇒ (x + 1)(x - 1)(x2 - 1)^2

⇒ (x + 1) (x - 1) (x + 1)^2 (x - 1)2

⇒ (x + 1)^3(x - 1)^3      ----(1)

And, g(x) = x^3 + 3x^2 + 3x + 1

⇒ x^3 + x^2 + 2x^2 + 2x + x + 1

⇒ x^2(x + 1) + 2x(x + 1) + 1(x + 1) ⇒ (x + 1)(x^2 + 2x + 1)

⇒ (x + 1) (x + 1)2 ⇒ (x + 1)3      ----(2)

Now, The HCF of f(x) and g(x) is the common factor of equations (1) and (2)

⇒ (x + 1)^3 .

∴ The HCF of the polynomials (x^6 - 3x^4 + 3x^2 - 1) and (x^3 + 3x^2 + 3x + 1) is (x + 1)^3.

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Answer: B )" AAS congruence theorem" an be used to prove that the triangles are congruent .

AAS congruence theorem tells that if two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle then the triangles are congruent.

Therefore option B is the correct answer. "AAS congruence" theorem an be used to prove that the triangles are congruent

The total number of combinations is given by the product between the numbers of options, so there are 8 combinations.

Here we have 3 variables and each can take two values:

x = {x₁, x₂}

y = {y₁, y₂}

z = {z₁, z₂}

The total number of combinations is equal to the product between the number of options that we have for each variable, then the number of combinations is:

C = 2*2*2 = 4*2 = 8

C = 8

There are 8 combinations.

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A. The mean of the data set is 71.09.

B. The median of the data set is the 12th term which is 74.

C. There is no mode value in the given data set.

D. Median value best represents the data.

A stem leaf method is used to represent discrete data.

The first column are the stem values and the second are the leaf values.

To find the mean of the data set we'll use the weightage average method

which is sum of all the values divided by the number of values.

∴ Mean = 71.09.

Total no. of data is 23 so the median is the 12th term which is 74.

There is no particular frequently occurring data hence no mode.

Median value best represents this data set as in the stem and leaf the most no. of data are in this row.

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Test value for a test of the difference between these two population proportions would be 2.44

What is Proportion?

A proportion in math is when two ratios are equivalent, that means they are equal to each other.

To calculate the test value for the difference between the two population proportions, you will need to first calculate the sample proportions for each group.

The sample proportion for the group of students attending 2-year colleges is 105/300 = 0.35.

The sample proportion for the group of students attending 4-year universities is 20/225 = 0.089.

Next, you can use these sample proportions to calculate the test value using the following formula:

      test value =  [tex]\frac{p1-p2}{\sqrt{[(p1(1-p1)/n1) + (p2(1-p2)/n2)]} }[/tex]

where p1 is the sample proportion for the first group, p2 is the sample proportion for the second group, n1 is the sample size for the first group, and n2 is the sample size for the second group.

Plugging in the values from the problem, we get:

test value = [tex]\frac{(0.35 - 0.089)}{\sqrt{[(0.35(1-0.35)/300) + (0.089(1-0.089)/225)]} }[/tex]

Simplifying this expression gives us a test value of approximately 2.44. This is the test value for the difference between the two population proportions.

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

The range() function outputs a list of numbers that starts at 0 by default, increases by 1 (by default), and ends before a given value .

The statistical range for a given data collection is the range of values between the highest and lowest values. Another way to show the range is to compare the top and lowest observation differences. The sample interval can be calculated by subtracting the highest number from the lowest. For continuous variables, the sample range is an essential measure of variability.

here ,

Python has a built-in method called range() that can be used to create a series of numbers.

The range() function accepts starting and ending values as inputs, which can be supplied by the user to construct a sequence .

The range() function outputs a list of numbers that starts at 0 by default, increases by 1 (by default), and ends before a given value .

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15 is the standard deviation of 225 .

What is explained by the standard deviation?

You can tell how skewed the data is by looking at the standard deviation. It gauges how far away from the mean each observed value is.

                      Any distribution will have roughly 95% of its values within two standard deviations of the mean. Think about the following data: 2, 1, 3, 2, 4. The average and the sum of squares representing the observations' variances from the mean will be 2.4 and 5.2, respectively.

Variance is simply the square of the standard deviation (v=σ2) .

          So if the variance is 225,

                        σ=√225 or 15.

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The y-intercept is (0, 5). Hence, the intercepts of the equation 5x + 3y = 15 are (3,0) and (0,5).

To find the x-intercept we have to substitute y = 0 into the equation, as follows:

9x - 7*0 = -63

9x = -63

Dividing by 9 at both sides of the equation:

9x/9 = -63/9

x = -7

To find the y-intercept we have to substitute x = 0 into the equation, as follows:

9*0 - 7y = -63

-7y = -63

Dividing by -7 at both sides of the equation:

-7y/(-7) = -63/(-7)

y = 9

x-intercept: −7; y-intercept: 9

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Answer: the tradition is to use (x, y) as the order of the coordinate pair locating a point on a plane

Step-by-step explanation: A two-axis system of east-west and north-south was defined using the algebra coordinate system created by mathematician René Descartes in the 1600s

Answer: 297492

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{10 [12^2 + (4 \times 2)] \div 8^2}[/tex]

[tex]\mathsf{= 10[12^2 + (8)] \div 8^2}[/tex]

[tex]\mathsf{= 10[12^2 + 8)] \div 8^2}[/tex]

[tex]\mathsf{= 10[12 \times 12 + 8] \div 8 \times 8}[/tex]

[tex]\mathsf{= 10[144 + 8] \div 64}[/tex]

[tex]\mathsf{= 10[152] \div 64}[/tex]

[tex]\mathsf{= 10(152) \div 64}[/tex]

[tex]\mathsf{= 1,520 \div 64}[/tex]

[tex]\mathsf{= \dfrac{1,520}{64}}[/tex]

[tex]\mathsf{= \dfrac{1,520 \div 16}{64 \div 16}}[/tex]

[tex]\mathsf{= \dfrac{95}{4}}[/tex]

[tex]\mathsf{= 23 \dfrac{3}{4}}[/tex]

[tex]\huge\text{Therefore, your answer is:}[/tex]

[tex]\huge\boxed{\mathsf{= \dfrac{95}{4}\ or \ 23 \dfrac{3}{4}\ or \ even\ 23.75}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Multiplicity of 3 is the number of times that the value 3 appears as a root of an equation  is the multiplicity of 3 is 3

Multiplicity of 3 (also known as a 3-fold root) is a mathematical concept used to describe the number of times a certain value appears as a root (or solution) of an equation. Specifically, it refers to the number of times a certain value appears as a root of a given equation when the equation is solved.

For example, the equation x2 = 9 has three solutions: x = 3, -3, and 0. This means that the multiplicity of 3 is 3, because 3 appears three times as a root of the equation. The general formula used to calculate the multiplicity of a given root is:

Multiplicity of x = Number of times x appears as a root of the equation

In this case, the multiplicity of 3 is 3, because 3 appears as a root of the equation three times. Similarly, if there are two solutions, x = -2 and x = 0, the multiplicity of -2 is 2, because -2 appears as a root of the equation twice.

In summary, multiplicity of 3 is the number of times that the value 3 appears as a root of an equation when the equation is solved. In the example above, the multiplicity of 3 is 3.

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Answer:

y = 5x + 10

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

We know slope 5 and y-intercept 10

So, our equation is

y = 5x + 10

By applying direct proportion, the value of y when x is 17 is equal to 68.

Mathematically, a direct proportion or direct variation can be represented the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

k = y/x

k = 156/39

k = 4

Now, we can calculate the value of y when x is 17;

y = kx

y = 4 × 17

y = 68.

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