Subject: Add Maths
Pleasee helpp

x-2 is a factor of x^3-x^2-x-2

Show that x^3-x^2-x-2=0 has only one real root and state the value of this root

Answer:

4

Step-by-step explanation:

3/9 is the same as 1/3 so 1/3 or 12 is 4

Answer:

4

Step-by-step explanation:

Answer:

b. y-int: (0,0), same as x-int

c. increasing: [0, ♾ ).  decreasing: (-♾, 0].  constant: DNE.

d. even since when the x-values is going to - ♾ and ♾, the y-values go up to ♾.

Step-by-step explanation:

Given the fraction

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number. Therefore:

Answer:

Answer:

It is 24

Step-by-step explanation:

Use keep change flip, keep the 3 change the division to multiplication, and flip the 1/8 to 8/1 and 3 times 8/1 is 24

Answer:

A) 6x + 6y = 24, Yes, they have the same solution set

Step-by-step explanation:

Let's first start by multiplying the equation by 3:

(2*3)x + (2*3)y = 24

6x + 6y = 24

Now lets find the solution set for both:

6y = -6x + 24

y = -x +4

2y = -2x + 8

y = -x +4

Yes, they have the same solution set

Answer:

(a) (i) x + y ≤ 24

(ii) y ≥ 4 + x

(b) draw a graph with the coordinate given below:

* note that you must draw 2 lines in your graph as there are 2 linear inequalities

(i) (0,24) and (24,0)

(ii) (0,4) and (-4,0)

*when the sign is ≤ , shade below the drawen line on the graph.

*when the sign is ≥, shade above the drawen line on the graph.

(c) x=8

8 + y ≤ 24

y ≤ 16 ( maximum )

y ≥ 4+8

y ≥ 12 (minimum)

The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602

The repeated tossing of a coin follows a binomial distribution

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾

where,

n = No. of times the experiment was repeated

x = random variable defining the number of "successes"

p = probability of "success"

Here

"succeess" is the event of landing a head.

n = 20

x = no. of times heads should show, i.e 11

p = probability of landing a head in a single toss

= 1/2

Hence, putting all this in the formula above we get

P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾

= ²⁰C₁₁ 0.5¹¹ 0.5⁹

= ²⁰C₁₁ 0.5²⁰

= 20!/ 11! (20 - 11)! X 0.5²⁰

= a) 0.1602

Complete Question

An unbiased coin is tossed 20 times.

Find the probability that the coin lands heads exactly 11 times

a. 0.1602

b. 0.5731

c. 0.2941

d. 0.1527

e. 0.6374

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Answer:xxxxxxxxx

ggggggggxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Step-by-step explanation:

Juan is incorrect which means lines are are not perpendicular.

The lines y = (1/3)x and y = -3x cannot be both parallel and perpendicular. To determine if two lines are parallel, we compare their slopes. The first line has a slope of 1/3, while the second line has a slope of -3. Since the slopes are different, the lines are not parallel.

Roger is correct because the lines  y = (1/3)x and y = -3x are parallel not perpendicular. Therefore, Juan's statement that the lines are perpendicular is incorrect.

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Taylor Polynomial of degree 4 for the function `f(x) = ln x` centered at `x = 2` is:```
P(x) = ln 2 + (1/2)(x-2) - (1/8)(x-2)² + (1/32)(x-2)³ - (3/256)(x-2)⁴
```Hence, we have found the Taylor Polynomial of degree 4 for the function `f(x) = ln x` centered at `x = 2`.

Given the function `f(x) = ln x` and the center is at `x = 2`, we have to find the Taylor Polynomial of degree 4.

We have the Taylor Polynomial of degree `n` for `f(x)` is given by:

`P(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + (f'''(a)/3!)(x-a)^3 + ....... + (f^(n)(a))/n!(x-a)^n

`Let's find the first four derivatives of `f(x)`:```
f(x) = ln x
f'(x) = 1/x
f''(x) = -1/x²
f'''(x) = 2/x³
f''''(x) = -6/x⁴
```Now we substitute these derivatives in the Taylor Polynomial of degree 4 and simplify:```
P(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + (f'''(a)/3!)(x-a)^3 + (f''''(a))/4!(x-a)^4
f(2) = ln 2
f'(2) = 1/2
f''(2) = -1/4
f'''(2) = 2/8 = 1/4
f''''(2) = -6/16 = -3/8
```Therefore, the Taylor Polynomial of degree 4 for the function `f(x) = ln x` centered at `x = 2` is:```
P(x) = ln 2 + (1/2)(x-2) - (1/8)(x-2)² + (1/32)(x-2)³ - (3/256)(x-2)⁴
```Hence, we have found the Taylor Polynomial of degree 4 for the function `f(x) = ln x` centered at `x = 2`.

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Answer:

might be a diff answer

Step-by-step explanation:

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Answer:

3/2

Step-by-step explanation:

y=kx

use a point

3=k2

k=3/2

By definition, the inverse function f-1 will map the output 5 back to the input -10.

1. TRUE - If f(-10) = 5, it means that the input -10 maps to the output 5 under the function f.

2. FALSE - The statement is incorrect. The increasing or decreasing nature of a function and its inverse are not directly linked. For example, if f(x) = x^2, which is increasing, its inverse function f-1(x) = √x is also increasing.

3. Not clear - The statement seems incomplete and requires additional information or clarification to determine its validity.

4. FALSE - The statement is incorrect. The concavity of a function and its inverse are not directly related. For example, if f(x) = x^2, which is concave up, its inverse function f-1(x) = √x is concave down.

5. TRUE - The domain of the inverse function f-1 is indeed the range of the original function f. This is a fundamental property of inverse functions, where the roles of inputs and outputs are swapped.

Regarding the determination of where the function f(x) = 2x^2 ln(x/4) is increasing and decreasing, we need to analyze the sign of its derivative. Taking the derivative of f(x) and setting it equal to zero, we can find the critical points. Then, by examining the sign of the derivative on different intervals, we can determine where the function is increasing or decreasing.

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Answer:

m∠3 = 64°

Since angle 2 and 3 seem to be complementary angles, we know that the meaning of complementary angles is to add both angles to 90 degrees.

Subtract 90 by the known value to get the value of ∠3

90 - 26 = 64

Answer: 2,002 different 5-member committees of juniors

Step-by-step explanation:

       We can solve this question with the given formula for combinations (since all juniors have an equal chance of being selected):

➜ n is the number of juniors

➜ r is the number of juniors in the committee

\(\displaystyle _nC_r=\frac{n!}{r!(n-r)!}\)

       We will substitute our known values and solve. This formula is quite simple if you substitute all the known values and compute, however, I have written out each step below so you can see how this formula works.

\(\displaystyle _nC_r=\frac{n!}{r!(n-r)!}\)

\(\displaystyle _nC_r=\frac{14!}{5!(14-5)!}\)

\(\displaystyle _nC_r=\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{5!(9)!}\)

\(\displaystyle _nC_r=\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{(5*4*3*2*1)(9*8*7*6*5*4*3*2*1)}\)

\(\displaystyle _nC_r=\frac{87,178,291,200}{(120)(362,880)}\)

\(\displaystyle _nC_r=\frac{87,178,291,200}{43,545,600}\)

\(\displaystyle _nC_r=2,002\;\text{\;\;different\;\;committees}\)

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Answer: #4 = precipitation

               #3 = evaporation

           #2 clouds

           #1= sun

         #5= water

Step-by-step explanation:

Answer:

1: sun

2: clouds

3: Evaporation

4: Precipitation

5: Water

Step-by-step explanation:

The proportion of population having score between 65 to 110 is 81.85%.

We have-

Mean of population = 80

Standard deviation of population = 15

We are supposed to find the proportion of the population corresponding to scores between 65 and 110.

According to the formula of the Z-score.

z = (x-μ)/σ

X=interval, μ= population mean ,

σ= standard deviation

Here,x = 65,μ= 80,σ= 15 andz = (65-80)/15z = -1

For Z=-1, From the z-table, the area to the left is 0.1587

Now, we need to find the area in the right  It can be calculated as follows.

z = (110-80)/15 = 2.

Area to the left of Z=2.00 is 0.028

So, the area between Z= -1 and Z= 2 is

= Total Area - (area of population below 65 + area of population above 110)=1-(0.1587+0.0228)=0.8185

The proportion of the population corresponding to scores between 65 and 110 is 0.8185 or 81.85%.

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Every rectangle with four congruent sides is a square -> True

Every rhombus is a quadrilateral -> True

Every square is a parallelogram -> True

Every quadrilateral is a square -> False.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

here, we have,

we know that,

Every rectangle with four congruent sides is a square -> True

Every rhombus is a quadrilateral -> True

Every square is a parallelogram -> True

Every quadrilateral is a square -> False.

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The discriminant for the quadratic equation -8x^2 + 14x - 7 = 0 is 68, and this quadratic equation will have two distinct real solutions.

To find the discriminant, we use the formula D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. In this case, a = -8, b = 14, and c = -7. Plugging these values into the formula, we get D = (14)^2 - 4(-8)(-7) = 196 - 224 = -28. Since the discriminant is positive, there will be two distinct real solutions for this quadratic equation.

In general, the discriminant can help us determine the nature of the solutions of a quadratic equation. If the discriminant is positive, there are two distinct real solutions; if it's zero, there's exactly one real solution; and if it's negative, there are no real solutions, but two complex solutions.

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Step-by-step explanation:

The answer is A

Bcz In a race runs faster whoever does it in less time

Sofia has a rectangle poster that is 42 inches long and 30 inches wide.  The area of the poster is 1260 square inches.

The area of ​​a rectangle depends on its sides. Basically, the area formula is equal to the product of the length and width of a rectangle. When we talk about the perimeter of a rectangle, it is equal to the sum of its four sides. Therefore, we can say that the area bounded by the perimeter of a rectangle is its area. But in the case of a square, since all sides are equal, the area of ​​the square will be equal to the square of its length.

area of ​​rectangle = length x width

We know that :

Area of rectangle = Length × Breadth

                             = 42 × 30 inches

                             = 1260 square inches.

Therefore, the area of a rectangle is 1260 square inches.

Complete Question:

Sofia has a rectangular poster that is 42 inches long and 30 inches wide. What is the area of the poster in square inches? Do not round your answer. Be sure to include the correct unit in your answer.

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Answer: 75%

Step-by-step explanation:

common sense

Answer:

just be like im really trying to work on getting my grades up i fell off a little bit bc of some stuff at home and im busy sometimes but im serious about my work and it would mean the world to me if you could let me redo some assignents that i failed or that are locked i want my parents to be proud of me for once, thanks (they name)

Step-by-step explanation:

Let \(n=abcba\) be such a number. If 18 divides \(n\), then both 2 and 9 divide \(n\).

To be divisible by 2, we must have \(a\in\{2,4,6,8\}\). Meanwhile we can have \((b,c)\in\{0,1,2,\ldots,9\}^2\).

To be divisible by 9, we the sum of the digits of \(n\) must itself be divisible by 9, or

\(2a+2b+c=9k\)

for some integer \(k\).

The largest value of \(2a+2b+c\) is 2•8 + 2•9 + 9 = 43, so we must have \(k\in\{1,2,3,4\}\).

I'm not sure what the best way to get the final count may be, but there are 44 such numbers. It's rather tedious to do by hand.

• If \(k=1\), then \(2a+2b+c=9\), and we can do this in 4 ways.

For example,

2•2 + 2•0 + 5 = 9 \((n = 20502)\)

• If \(k=2\), then \(2a+2b+c=18\) and can be done in 16 ways.

2•2 + 2•3 + 8 = 18 \((n = 23832)\)

• If \(k=3\), then \(2a+2b+c=27\) and can be done in 18 ways.

2•2 + 2•7 + 9 = 27 \((n = 27972)\)

• If \(k=4\), then \(2a+2b+c=36\) and can be done in 6 ways.

2•6 + 2•8 + 8 = 36 \((n = 68886)\)

The general solution to the differential equation is:

\(xy = (1/3)e^{(-x)} + c|x|e^{(-4x)}\)

The given differential equation is:

\(x dy + (3x+1)y dx = e^{(-3x)dx}\)

We can see that this is not a homogeneous or exact differential equation.

We can try to solve it using an integrating factor.

The integrating factor for this differential equation is given by:

\(I(x) = e^{(a(3x+1)/x dx)}\)

\(I(x) = e^{(∫(3+1/x) dx)}\)

\(I(x) = e^{(3x + ln|x|)}\)

Multiplying both sides of the differential equation with the integrating

factor gives:

\(e^{(3x + ln|x|) } x dy + e^{(3x + ln|x|)(3x+1)y} dx = e^{(3x + ln|x|)} e^{(-3x)} dx\)

Simplifying this gives:

\(d(xy e^{(3x + ln|x|))} = e^{(3x)dx}\)

Integrating both sides gives:

\(xy e^{(3x + ln|x|) } = ∫e^{(3x)dx + c}\)

\(xy e^{(3x + ln|x|) } = (1/3)e^{(3x) + c}\)

\(xy e^{(4x)} = (1/3)e^{(3x) + c|x|}\)

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Randomized algorithms that guarantee exact solutions are named after the city of Las Vegas.

Las Vegas algorithms are a class of randomized algorithms that provide solutions that are guaranteed to be exact. These algorithms take advantage of randomness in their execution but ensure that the output is always correct. The name "Las Vegas" is derived from the concept of gambling in Las Vegas, where the outcomes are based on chance but the rules ensure fair play.

Las Vegas algorithms achieve their guaranteed exactness by employing techniques such as randomization, Monte Carlo methods, or probabilistic analysis. Despite the random components, these algorithms incorporate mechanisms that allow them to verify the correctness of the solution produced. If the initial random choices do not yield an exact solution, the algorithm may employ additional random iterations until it converges to an exact solution with a high probability.

By guaranteeing exact solutions, Las Vegas algorithms provide a valuable approach in solving certain computational problems where deterministic algorithms may be impractical or inefficient. These algorithms offer a balance between randomness and reliability, making them suitable for a wide range of applications in fields such as optimization, cryptography, and simulation.

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The function that they can use to determine how strongly related are two of the variables is equals to the cor() which stands for correlation. So, the correct choice for answer is option (c).

The function cor() returns the correlation between two variables. In R language, the cor() function is used to determine the correlation coefficient between two

vectors. Correlations may be generated

using the cor() function, while covariance

can be generated using the cov() function. In statistical, correlation shows us how strong the relationship is between two variables. It describes the degree to which two variables are linearly connected (meaning they change together at a constant rate). In case of symmetry, the correlation between A and B is the same as the correlation between B and A. The most used correlation coefficients are Pearson, Spearman, and Kendall.

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Complete question:

A data analyst is using statistical measures to get a better understanding of their data. What function can they use to determine how strongly related are two of the variables?

A) sd()

B) mean

C) cor()

D) bias()

The volume of a sphere with radius 8 units is 2143.57 units³

What is a Sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the volume of the sphere be represented as A

Now , the value of A is

Let the radius of the sphere be r

The value of r = 8

Now , the formula to calculate the volume of the sphere is

Volume of a Sphere = ( 4/3 ) πr³

Substituting the values in the equation , we get

Volume of a Sphere = ( 4/3 ) x 3.14 x 8 x 8 x 8

Volume of a Sphere = ( 4/3 ) x 3.14 x 512

Volume of a Sphere = ( 4/3 ) x 1607.68

Volume of a Sphere = 2143.57 units³

Therefore , the value of A is 2143.57 units³

Hence , the volume of the sphere is 2143.57 units³

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Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.

Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.

Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.

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