(0,-9);r=9 find the equation for the circle

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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2. The range in individual stock prices within this mutual fund is 230.

3. An individual stock in the highest 25% of prices had a dollar value of at least Q3 = 344.68.

4. Individual stock prices in the middle 50% range between Q1 and Q3.

So, the prices are between 142.76 and 344.68.

5. This indicates a right-skewed distribution.

6. The median is a more appropriate measure of center for a right-skewed distribution.

7. We would expect the mean of the individual stock prices within this mutual fund to be greater than the median.

A financial tool called a mutual fund collects money from several investors. After that, the combined funds are invested in assets such as listed company stocks, corporate bonds, government bonds, and money market instruments.

To answer the questions about the DIA mutual fund based on the given information, let's refer to the five-number summary and boxplot:

Given:

Minimum: 100

First Quartile (Q1): 142.76

Median (Q2): 168.19

Third Quartile (Q3): 344.68

Maximum: 330

2. Range in individual stock prices within this mutual fund:

The range is calculated as the difference between the maximum and minimum values.

Range = Maximum - Minimum = 330 - 100 = 230

Therefore, the range in individual stock prices within this mutual fund is 230.

3. An individual stock in the highest 25% of prices:

To find the value of the individual stock in the highest 25% of prices, we need to find the value corresponding to the third quartile (Q3).

An individual stock in the highest 25% of prices had a dollar value of at least Q3 = 344.68.

4. Individual stock prices in the middle 50%:

The middle 50% of stock prices corresponds to the interquartile range (IQR), which is the difference between the first quartile (Q1) and the third quartile (Q3).

Individual stock prices in the middle 50% range between Q1 and Q3.

So, the prices are between 142.76 and 344.68.

5. Shape of the distribution of individual stock prices:

The shape of the distribution can be determined by analyzing the boxplot.

If the boxplot is approximately symmetric, the distribution is symmetric. If the boxplot has a longer tail on the left, it is left-skewed. If the boxplot has a longer tail on the right, it is right-skewed.

Based on the boxplot, we can see that the box (representing the interquartile range) is closer to the lower values, and the whisker on the right side is longer. This indicates a right-skewed distribution.

6. Appropriate measure of center for a right-skewed distribution:

In a right-skewed distribution, where the tail is longer on the right side, the mean is influenced by the outliers or extreme values, while the median is a more robust measure of center that is not affected by extreme values. Therefore, the median is a more appropriate measure of center for a right-skewed distribution.

7. Comparison of mean and median in this mutual fund:

For a right-skewed distribution, the mean tends to be greater than the median. This is because the presence of a few large values on the right side of the distribution pulls the mean towards higher values. In this case, we would expect the mean of the individual stock prices within this mutual fund to be greater than the median.

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0.578. is  the probability that the size of the family is at least 3.

What does the math term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.  

                                     Statistics describes the examination of events subject to probability.

P(X>=3) can be written as

= 1 - P(X<3)

= P(X<=2)

= 1-0.422

= 0.578

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Vector equation of the line tangent to the graph of r(t) at the point p0 on the curve r(t) = (3t - 1) i + 13t j + 4 k.

To find a vector equation of the line tangent to the graph of r(t) at the point P0 on the curve r(t) = (3t - 1) i + 13t j + 16 k, where P0 is given as (-1,4), we can use the following steps:

Step 1: Find the derivative of r(t) with respect to t:

r'(t) = 3 i + 13 j

Step 2: Evaluate the derivative at the point P0:

r'(-1) = 3 i + 13 j

Step 3: Use the point P0 and the vector r'(-1) to form the vector equation of the tangent line:

r(t) = P0 + r'(-1) t

where t is a scalar parameter.

Plugging in the values, we get:

r(t) = (-1)i + 4j + (3i + 13j)t

Simplifying, we get:

r(t) = (3t - 1) i + 13t j + 4 k

Therefore, the vector equation of the line tangent to the graph of r(t) at the point P0 on the curve

r(t) = (3t - 1) i + 13t j + 16 k  is

r(t) = (3t - 1) i + 13t j + 4 k.

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The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

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Answer:

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: \huge \color{green}{ \fbox \colorbox{black}{ \fbox{ \green {Answer} \: }}}\)

\( \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + 2 \cos(x) + 1} = 0\)

\( \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + \cos(x) + \cos(x) + 1} = 0\)

\( \longrightarrow \sf \color{teal}{ \cos {}^{} (x) ( \cos(x) + 1)+ 1(\cos(x) + 1} )= 0\)

\( \longrightarrow \sf \color{teal}{ ( \cos(x) + 1)(\cos(x) + 1} )= 0\)

\( \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{2} = 0\)

\( \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{} = 0\)

\( \longrightarrow \sf \color{teal}{ \cos(x) {}^{} }= - 1\)

\(\longrightarrow \sf \color{teal}{ x{}^{} }= \cos {}^{ - 1}( - 1)\)

\(\longrightarrow \sf \color{teal}{ x = (2n + 1) \pi \: \: \: \: rad}\)

where, \({ n \in \{whole \:\; number\}} \)

Principle value -

\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \cos {}^{ - 1} ( - 1) \)

\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2n + 1) \pi \: \: \: \: rad \: \)

put n = 0

\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2(0) + 1) \pi \: \: \: \: rad \: \)

\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (0 + 1) \pi \: \: \: \: rad \: \)

\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \pi \: \: \: \: rad \: = 180 \degree\)

Step-by-step explanation:

the surface areas are always the sum of the areas of the individual sides and base area.

so, all we need to do here is calculating the areas of triangles, rectangles (actually squares) and a hexagon.

the area of a triangle is

baseline × height / 2

or with Heron's formula when we have all sides

s = (a+b+c)/2

area = sqrt(s×(s-a)×(s-b)×(s-c))

the area of a rectangle is

length × width

for a square that is then

side × side = side²

and the area of a regular hexagon can be created again as sum of multiple sub-shapes. but ultimately it is

3 × sqrt(3) × side² / 2

1.

square base area : 10×10 = 100 cm²

lateral areas :

one triangle is 10×13/2 = 65 cm²

4 triangles are then 4×65 = 260 cm²

total surface area :

100 + 260 = 360 cm²

2a.

3 lateral triangles :

3 × 8×10/2 = 120 units²

base area (Heron's, as all 3 sides are 8 units) :

s = 3×8/2 = 12

area = sqrt(12×4×4×4) = sqrt(3×4×4×4×4) = 16×sqrt(3)

total surface area :

120 + 16×sqrt(3) = 147.7128129... units²

2b.

4 lateral triangles :

4 × 8×10/2 = 160 units²

base area : 8×8 = 64 units²

total surface area :

160 + 64 = 224 units²

2c.

6 lateral triangles :

6 × 8×20/2 = 480 units²

base area :

3×sqrt(3)×8²/2 = 96×sqrt(3)

total surface area :

480 + 96×sqrt(3) = 646.2768775... units²

2d.

base area : 16² = 256 units²

4 lateral triangles. but we need to get their height first.

Pythagoras :

(16/2)² + 24² = height²

8² + 24² = height²

64 + 576 = height²

height² = 640

height = sqrt(640) = sqrt(64×10) = 8×sqrt(10)

4 triangles are

4 × 16×8×sqrt(10)/2 = 256×sqrt(10) units²

total surface area :

256 + 256×sqrt(10) = 256×(1 + sqrt(10) = 1,065.543081... units²

Answer:

2/10 + 7/10

9/10

Step-by-step explanation:

I did the test.

Answer:

The expression written in equivalent form with common denominators is

✔ 2/10 + 7/10

The sum is

✔ 9/10

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Step 1: Find the sale price

First, we have to find the price it was sold for.

\(\longmapsto\) 5/4 of 800 = 5/4 * 800

\(\frac54 * 800 = \\\\\frac{4000}{4} = 1000\\\\\)

The article was sold for rs. 1000

Step 2: Finding the percentage

To find the percentage, we have to divide the sale price over the cost of the article

\(\frac{1000}{800} = \frac54 = 1.25 = 125percent\)

The cost of the article is 100% or 1

\(1.25 - 1 = 0.25 - or- 25percent\)

25%

-Chetan K

Answer:

The average rate of change of the function is 22.

Step-by-step explanation:

The given function is :

\(f(x)=x^4-5x\)

We need to find the average rate of change of the function on the closed interval (0, 3).

The average rate of change of a function in interval (a,b) is given by :

\(R=\dfrac{f(b)-f(a)}{b-a}\)

Here, a = 0 and b = 3

\(R=\dfrac{(3^4-5(3))-(0^4-5(0))}{3-0}\\\\=\dfrac{66}{3}\\\\=22\)

So, the average rate of change of the function is 22.

Answer:

22

Step-by-step explanation:

(f(3)-f(0))/3

=66/3

=22

The perimeter of the triangle ABC is 12 units. Hence, option (B) is correct.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given right angle triangle,

The vertices are A(-3, 2), B(-3, -1) and C(1, -1)

The distance between AB = 3,

And the distance between BC = 4

To find the distance of AC, use Pythagoreans theorem,

AC² = AB² + BC²

       = 3² + 4²

       = 9 + 16

AC² = 25

AC = 5

The perimeter of triangle ABC = AB + BC + AC

= 3 + 4 + 5

= 12

The perimeter of the triangle ABC is 12 unit.

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Answer:

12 boys

Step-by-step explanation:

Boys are 2 parts to girls 3 parts

   2 out of (2+3)  are boys   ====>  2/5 ths are boys

    2/5  * 30 = 12 boys

Answer:

12 boys

Step-by-step explanation:

The fraction of boys in the class are :

⇒ Ratio part of boys / Sum of ratio parts

⇒ 2 / 2 + 3

⇒ 2/5

Finding the number of boys :

⇒ Number of students × fraction of boys

⇒ 30 × 2/5

⇒ 6 × 2

⇒ 12 boys

Answer:

The player will be more likely to wear a yellow jersey because P(yellow) is more tha P(white).

Step-by-step explanation:

Get rid of the 0s. 35 is more than 20, therefore 0.35 will also be more than 0.20.

Hope this helps!

Answer:

2.0×10¹⁰

Step-by-step explanation:

....................

At the 0.1 level of significance, the conclusion we come up with is to reject the null hypothesis.

we are given that a random sample of 150 people was taken. 98 of the people in the sample favored the candidate, were it to determine whether or not the proportion of the population in favor of candidate a is significantly more than 57%.So we need to find the test statistic, which is 1.98  determined from the z score, here the rejection region is the number more than 1.28, and 1.98 is greater than 1.28, so it is better to simply reject the null hypothesis.

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Answer: Commutative Property of Addition

This property says that A+B = B+A. The order of addition doesn't matter.

As an example, 2+3 = 3+2 since both sides evaluate to 5.

Answer:B.

CR:4

10th term: 2,359,296

Step-by-step explanation:

I am not 100% sure but I think I will tell you this answer might be wrong I am not sure

The Laplace transform is applied to obtain the solution for y(t). In the second problem, the Laplace transform is used to solve for y(t), and in the third problem, to solve the system of differential equations for x(t) and y(t).

(a) To solve the initial value problem y" - 10y' + 9y = 5t, y(0) = -1, y'(0) = 2, we take the Laplace transform of both sides of the equation. Using the properties of the Laplace transform, we convert the differential equation into an algebraic equation in terms of the Laplace transform variable s. Solving for the Laplace transform of y(t), Y(s), we then apply the inverse Laplace transform to find the solution y(t).

(b) For the initial value problem y" - 6y + 5y = 3\(e^2\)t, y(0) = 2, y'(0) = 3, we follow a similar procedure. Taking the Laplace transform of both sides, we obtain an algebraic equation in terms of the Laplace transform variable s. Solving for Y(s), the Laplace transform of y(t), and applying the inverse Laplace transform, we find the solution y(t).

(c) The given system of differential equations dx/dt + 2dy/dt = 5\(e^t\) and dy/dt - 3x - 5 = 0 is solved using the Laplace transform. Taking the Laplace transform of both equations and applying the initial conditions, we obtain two equations in terms of the Laplace transform variables s and X(s), Y(s). Solving these equations simultaneously, we find the Laplace transform of x(t) and y(t). Finally, applying the inverse Laplace transform, we obtain the solutions x(t) and y(t).

In all three problems, the Laplace transform provides a powerful method to solve the given initial value problems and the system of differential equations by transforming them into algebraic equations that can be easily solved.

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============================================================

Explanation:

The area 81pi square meters leads to the radius 9 meters

Use the formula A = pi*r^2 to see why this is the case. You plug in A = 81pi and solve for r to get r = 9.

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

Once you know the radius, you can determine the circumference C

C = 2*pi*r

C = 2*pi*9

C = 2*9*pi

C = 18pi

The circumference is the perimeter, or distance, around the circle.

Answer:

47:59

Step-by-step explanation:

Answer: what is a and c

Step-by-step explanation:

We need a and c to solve for b.

Part (a)  K is a normal extension of E, but not of F.

Part (b) L is a normal extension of F, but L' is not.

Part (a)

Let E = KG(K,F). Since E is a field extension of F and K is a finite extension of F, then K is a normal extension of E. This is because F[K] is a finite separable extension and hence normal.

However, K is not a normal extension of any field F ⊆ E. This is because K is not a normal extension of F by assumption.

Part (b)

(a) L is a normal extension of F. This is because K is a normal extension of F (by assumption) and L is a splitting field of a polynomial over F, and so is a finite extension of K. Hence, L is a normal extension of F.

(b) Let L be any field such that K ⊆ L and L ≠ L'. Then L is not a normal extension of F. This is because K is a normal extension of F, and if L were a normal extension of F, then L' would also be a normal extension of F by transitivity. Because  L ≠ L', L is not a typical extension of F.

Complete Question:

Suppose that the characteristic of F is 0, and that K is a finite, but not normal, extension of F. (a) Let E = KG(K,F). Show that K s a normal extension of E, but not of any field F ES E. Solution. Proof (b) Suppose K -F(a) for some aE K. Let L be the splitting field of the minimal polynomial of a over F, with K C L. Prove that: (a) L is a normal extension of F Solution. Put your answer here... (b) For any field L, such that K L, Ç L, L' is not a normal extension of F. (L is called the normal closure of F in K.) Solution. Put your answer here...

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Answer:

Step-by-step explanation:

In first step, we just open the brackets and you should know that ++ = + and +- = - and -- = + and -+ is also equal to -

after opening the brackets we combine terms which are a like

then any order, any grouping you can write the answer in any order and you can also take - common and it will be written as      

-(5p-7a+6)

if you multiply the minus it will be the same.

The error in the work shown is in the second step of the calculation. Let's break down the incorrect step and identify the mistake:

3vx(y^12)/4^3 = 3vx^3(y^12)/3v4^3

The error occurs when simplifying the expression under the square root. The expression (y^12) is incorrectly simplified to (y^3)^4.

The correct simplification should be:

3vx^3(y^12)/3v4^3 = 3vx^3(y^3)^4/3v4^3

The mistake is that (y^12) cannot be simplified to (y^3)^4. In this step, the exponent should be divided by 3, not raised to the power of 4.

The correct simplification should be:

3vx^3(y^12)/3v4^3 = 3vx^3(y^4)/3v4^3

Therefore, the final simplified expression should be xy^4/4, instead of xy^3/4.

The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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Answer:

3; 6; 9; 12; 15; 18;

Step-by-step explanation:

Multiples of 3:

3*1=3

3*2=6

3*3=9

3*4=12

3*5=15

3*6=18

Answer:

3,6,9,12,15,18

Step-by-step explanation:

I think this might be correct I'm not sure

Problem 2, Part (a)

A = event elevator's 1st stop at the 2nd floor

P(A) = 3/4

Since the elevator needs to go up one floor

B = event elevator has its 2nd stop at the 3rd floor

P(B given A) = probability event B happens given event A happened

P(B given A) = 3/4

-----------

P(A and B) = P(A)*P(B given A)

P(A and B) = (3/4)*(3/4)

P(A and B) = 9/16

-----------

===============================================================

Problem 2, Part (b)

A = event elevator's 1st stop at the 2nd floor

P(A) = 3/4

B = event elevator has its 2nd stop at the 3rd floor

P(B given A) = 3/4

C = event elevator has its 3rd stop at 4th floor

P(C given (A and B)) = 3/4

-----------

P(A & B & C) = P(A)*P(B given A)*P(C given (A and B))

P(A & B & C) = (3/4)*(3/4)*(3/4)

P(A & B & C) = 27/64

-----------

===============================================================

Problem 2, Part (c)

A = event elevator's 1st stop at the 2nd floor

x = P(A) = 3/4

B = event elevator has its 2nd stop at the 3rd floor

y = P(B given A) = 3/4

C = event elevator has its 3rd stop at 2nd floor

z = P(C given (A and B)) = 1/4

D = event elevator has its 4th stop at 1st floor

w = P(D given (A & B & C)) = 1/4

-----------

P(A & B & C & D) = x*y*z*w

P(A & B & C & D) = (3/4)*(3/4)*(1/4)*(1/4)

P(A & B & C & D) = 9/256

-----------