if the nth term of a number sequence is n^2+1 find the first three terms and the tenth term

The factor is  [tex](t^4+rs^5)(t^8-rs^5t^4+r^2s^{10})[/tex].

Option (D) is correct.

What is factorization?

Factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors.

Given:

[tex]t^{12}-r^{3}s^{15}[/tex]

For factorizing the above expression is

now, using the formula

(a³ - b³) = ( a+ b)( a² -ab + b²)

Then,

[tex]=(t^4)^{3}-(rs^{5})^{3}\\=(t^4+rs^5)((t^4)^2-(t^4\timesrs^5)+(rs^5)^2)\\=(t^4+rs^5)(t^8-rs^5t^4+r^2s^{10})[/tex]

Hence, the correct factorization is [tex](t^4+rs^5)(t^8-rs^5t^4+r^2s^{10})[/tex].

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Answer:

B

Step-by-step explanation:

2ab is the area of the greatest rectangle that can be inscribed in an ecllipse [tex]\frac{x^2}{a^2} + \frac{x^2}{b^2} = 1[/tex].

The reactangle with the greatest area that can be inscribed in an ecllipse is symmetry with respect to x axis .

we know that (a cos θ ,bsin θ) is the general point on the ecllipse so the others points is (- a cos θ ,bsin θ) , (a cos θ ,-bsin θ)  and (-a cos θ ,- bsin θ)

so the length of the rectangle is 2a cos θ  and the breadth of the rectangle is 2b sin θ

to area of rectangle = length * breadth

=> 2a cos θ  * 2b sin θ

=>4ab sin θ *cos θ

=> 4ab sin 2θ

so area of rectangle (A) = 4ab sin 2θ   -----(i)

so get the maximum area dA/dθ =0

=> 4ab *2 cos 2θ =0

=> 8ab cos 2θ=0

=> cos 2θ =0

=> 2θ = π/2

=> θ =π/4

putting the value of θ in equation (i) we get

A = 4ab cos π/4 *sin π/4

A = 4ab *[tex]\frac{1}{\sqrt{2} }[/tex]  *[tex]\frac{1}{\sqrt{2} }[/tex]

=> 2ab

so rectangle with largest area inside the ecllipse = 2ab

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The complete factorization of the polynomial  x³ + 2x² + 4x + 8 is  

(x² + 4)(x + 2).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A cubic polynomial x³ + 2x² + 4x + 8.

Now, Factoring this polynomial,

= x³ + 4x + 2x² + 8.

= x(x² + 4) + 2(x² + 4).

= (x² + 4)(x + 2).

Now, (x² + 4) can not be factored anymore.

So, The factor of  x³ + 2x² + 4x + 8 is  (x² + 4)(x + 2).

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In order to estimate the mean height of all bears in the Smokies within 4 inches of the actual height with a 99% confidence level, you would need a sample size of 25 bears.

You must calculate the sample size using the formula below in order to estimate the mean bear height in the Smokies within 4 inches of the actual height at a 99% confidence level:

n = [tex](\frac{2 X SD}{E})^2[/tex]

Where,

n = sample size

SD = standard deviation of the population (which you have estimated to be 10 inches)

E = margin of error (which you want to be 4 inches)

Putting these values into the formula, we get:

n = [tex](\frac{2 X 10}{4})^2[/tex]

= 25

In order to estimate the mean height of all bears in the Smokies within 4 inches of the actual height with a 99% confidence level, you would need a sample size of 25 bears.

It's important to note that this is only a rough estimate, and the exact sample size may change depending on the population's real characteristics and the level of precision you require. To enhance the accuracy of your estimate, it's also critical to select a sample that is typical of the total population.

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Answer:

9

Step-by-step explanation:

Answer:

The answer is 44. 10% more than 40 is 40 + 4 = 44.

Step-by-step explanation:

To find 10% more of a number, you can simply multiply the number by 10%. In this case, 10% of 40 is 40 * 0.1 = 4. Therefore, 10% more than 40 is 40 + 4 = 44.

Answer:

110/100 × 40 = 44 ( remember this is not the only ans)

all numbers must be greater than 44

The average number of children in a family under the age of 1818 is 0.76, which is the predicted value of this distribution.

The product of each potential result and its associated probability yields the anticipated value of a probability distribution. The probable outcomes in this scenario are 0, 1, 2, 3, & 4 minors, with the associated probability shown in the table.

We may add the products of each result and its probability to determine the estimated return of this distribution:

Expected value = (0)(0.58) + (1)(0.18) + (2)(0.16) + (3)(0.06) + (4)(0.02)

= 0 + 0.18 + 0.32 + 0.18 + 0.08

= 0.76

Therefore, 0.76 children below the age of 18 per household are the anticipated value of this distribution.

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Answer: If Lin sells b boxes of cookies, she will earn 3.75b dollars. Therefore, the inequality that will be true whenever Lin makes her goal is:

3.75b > 30

This inequality can be read as "the total amount of money Lin earns selling cookies is greater than $30."

Step-by-step explanation:

Answer:

I am not sure which form you want.

Points slope: y -2  = 3(x -4)

Slope intercept:  y = 3x -10

Step-by-step explanation:

Point slope form for the line

y- y = m(x -x)  

slope of 3 and the point (4,2)  Use 4 for x and 2 for y

y -2  = 3(x -4)

Slope intercept form of a line

y = mx + b

2 = 3(4) + b

2 = 12 + b  Subtract 12 from both sides

2 - 12 = 12 - 12 + b

-10 = b

y = mx + b

y = 3x -10

The line l and line m are parallel.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

Given that, transversal t cuts line l and line m.

∠2≅∠7

Transversal t cuts line l and line m (Given)

∠2≅∠7 (Given)

∠2≅∠3 (Vertical angles theorem)

∠3≅∠7 (Converse of corresponding angles postulates)

l║m proved

Hence, the line l and line m are parallel.

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The required explanation of null hypothesis and alternate hypothesis for given question is below.

What is hypothesis test?

Hypothesis testing is a type of measurable derivation that utilizes information from an example to make inferences about a populace boundary or a populace likelihood circulation. Initial, a speculative supposition that is made about the boundary or dissemination.

According to question:

Connection is a factual measure that communicates the degree to which two factors are directly related (meaning they change together at a consistent rate).

It's a typical device for portraying basic connections without saying something about circumstances and logical results.

As indicated by the inquiry,

A gathering of researcher haphazardly chose 20 Piknits from the ocean bottom and estimated their particular loads in grams.

Likewise, They were curious as to whether the weight of the Piknits can be utilized to foresee the quantity of Gogles.

From the given data,

Null hypothesis : H0 : There is no direct connection between the heaviness of piknits and the quantity of gogles

Alternative hypothesis : Ha: There is a direct connection between the heaviness of piknits and the quantity of gogles

Choice 4 is right about Null hypothesis and Alternative hypothesis.

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81.3 marks is obtained by the student in psycology course

percentage of marks of  test that count for final marks =45 %

percentage of marks of quizzes that count for final marks =35 %

percentage of marks of papers that count for final marks =10 %

percentage of marks of final project that count for final marks =10 %

marks obtained by student in test = 75

marks obtained by student in quizzes = 85

marks obtained by student in papers =  88

marks obtained by student in final project = 90

Total marks obtained = [tex]\frac{45}{100} * 75 + \frac{35}{100} *85 + \frac{10}{100} * 88 +\frac{10}{100} *90[/tex]

Total marks obtained = 33.75 + 29.75 + 8.8 + 9 = 81.3

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Answer:

Step-by-step explanation:

(-1 - 3)/(3 - 0) = -4/3

y - 3 = -4/3(x - 0)

y - 3 = -4/3x + 0

y = -4/3x + 3

Answer:

(1,5)

Step-by-step explanation:

when x = 1

[tex]y \geq -4 + 3 (1)\\y \geq -1\\[/tex]

when x = 5

[tex]y \geq -4 + 3(5)\\y \geq 11\\[/tex]

Only (1,5) pair is a solution.

Answer:

-7

*I think*

Step-by-step explanation:

3×(-5)=(-15)

(-15)+8=(-7)

When n is large the distribution of the sample means will approach a normal distribution.

The central limit theorem (CLT) is a statistical theory that predicts that given a large enough sample size from a population with a certain level of variation, the mean of all the samples from that population will be close to the population mean.

To put it another way, the central limit theorem predicts with absolute certainty the form of the distribution of means when we take repeated samples from a certain population. In particular, the distribution of means derived from repeated sampling will tend toward normality as sample sizes increase.

In other words, when n is large, the distribution of the sample means will resemble a normal distribution if we continually pick independent, random samples of size n from any population.

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The measure of the diagonal MP is 66 cm.

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, Parallelogram MNPR has diagonals that intersect at E. In the parallelogram, ME = (7x - 30) cm and PE = (5x-12) cm.

We know that, diagonals of a parallelogram bisects each other,

Therefore, ME = PE

(7x - 30) = (5x-12)

2x = 18

x = 9

ME = PE = 33

MP = ME + PE

MP = 33+33

MP = 66

Hence, The value of MP is 66 cm

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Answer:

first option

Step-by-step explanation:

inequalities of the type | x | > a have solutions of the form

x < - a or x > a

given

| 7 + m | - 4 > 8 ( add 4 to both sides )

| 7 + m | > 12

then

7 + m < - 12 (subtract 7 from both sides )

m < - 19

OR

7 + m > 12 ( subtract 7 from both sides )

m > 5

solution is m > 5 or m < - 19

The expression simplify value is [tex]48x ^{-9} * y^{10}[/tex]

Simple Rules and Procedures for Any Algebraic Expression

Remove brackets and parentheses by multiplying the appropriate factors.

If the words have exponents, use the exponent rule to eliminate grouping.

By adding or removing coefficients, combine like terms.

Add the constants together.

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Simplify and Multiply the numbers.

[tex]6x ^{-9} * 8y^{10} \\48x ^{-9} * y^{10}[/tex]

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Answer: (2.4, -12.8)

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem to find the height of the balloon. In particular, we can consider the right triangle formed by the stake, the top of the balloon, and the part of the string that is attached to the stake.

[asy]

unitsize(2 cm);

pair A, B, C, D, E;

A = (0,0);

B = (0,15);

C = extension(A,B,A+(1,0),B+(1,0));

D = extension(A,C,A+(0,1),C+(0,1));

E = extension(B,D,B+(0,-1),D+(0,-1));

draw(A--B--C--cycle);

draw(A--D--E--cycle);

draw(rightanglemark(A,D,C,2));

label("$A$", A, S);

label("$B$", B, N);

label("$C$", C, E);

label("$D$", D, E);

label("$E$", E, W);

[/asy]

Let $a$ be the distance from the stake to the top of the balloon, $b$ be the height of the balloon, and $c$ be the length of the string. We know that $a = 15$ feet and $c = 15$ feet, so we can use the Pythagorean theorem to find $b$:

$a^2 + b^2 = c^2$

$15^2 + b^2 = 15^2$

$225 + b^2 = 225$

$b^2 = 0$

$b = \sqrt{0} = 0$ feet

Therefore, the height of the balloon is 0 feet. This is because the balloon has been pulled up by the wind so that its top is directly above the stake, and therefore its height is 0 feet.

Linearly because the table shows a constant percentage increase in temperature each month.

A graph is a diagram that depicts the relationship or connection between two or more quantities. Linear implies straight. The x and y coordinates of two points are connected by a straight line, or straight graph, to form a linear graph. Everyday life involves the utilization of linear relations, which can be graphed in a plane to produce a straight line.

In the first month it is 5

In the second month it is 7.2 so the increment in temperature is 7.2 - 5 = 2.2

In the third month it is 9.4 and the increment in temperature is 9.4 - 7.2 = 2.2

In the fourth month it is 11.6 and the increment in temperatue is 11.6 - 9.4 = 2.2

In the fifth month it is 13.8 and the increment in temperature is 13.8 - 11.6 = 2.2

So the increment is happening linearly

The equation which depicts this is y = (2.2)x+5 where x is the no.of month.

Linearly because the table shows a constant percentage increase in temperature each month.

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The value of the Confidence interval will be 3.787

The number of standard deviations from the t-mean distribution is equal to a t-score. The test statistic used in t-tests and regression testing is the t-score. When the data follow a t-distribution, it may also be used to represent how distant an observation is from the mean.

The t-score formula is written as follows:t=¯¯¯x−μS√n t = x ¯ − μ S n , where ¯¯¯x, is the sample mean, is the population mean, S n is the sample size, and x is the standard deviation of the sample. Square root n must be included in the formula.

using tables of t distribution we have

t-score for 99.8%

Confidence Interval (alpha) =1-0.998=0.002

Sample size (n)=15

df=n-1=14

t-score for a 99.8% Confidence Interval will be

t(0.002,14)=3.787

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Answer:

A. 113 degree

Step-by-step explanation:

These are Alternate Interior Angles, which means the 113-degree angles and the? are equal. So, the answer is A

The positive integers that would make (3²)ⁿ greater than 39 are any positive integers greater than 1.

An integer means the number zero (0), a positive natural number or a negative integer with a minus sign (−1, −2, −3, etc.).

To see this, we can simply plug in different values for the positive integer and see when(3²)ⁿ becomes greater than 39.

If we plug in 1, we get (3²)ⁿ = 9, which is not greater than 39.

If we plug in 2, we get (3²)ⁿ = 81, which is greater than 39.

Therefore, any positive integer greater than 1 would make (3²)ⁿ greater than 39.

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Possible Question

Describe all the positive integers that would make (3²)ⁿ greater than 39. Explain your reasoning

Answer: 10 cm

Step-by-step explanation:

Given, length=8cm

breadth=6 cm

Pythagoras theorem states that sum of square of base and square of perpendicular height is equal to square of hypotnyse.

Thus, we can write:

Considering, base=length=8cm

Perpendicular=breadth=6cm

Therefore, length of diagonal =√(length∧2+breadth∧2)

                                                 =√(8∧2+6∧2) cm

                                                = 10 cm

Therefore the length of diagonal = 10cm.

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Answer:

Step-by-step explanation:

x - 3 = 5

(x -3) +3 = 5+3

x - 3 + 3 = 8

so,

x = 8

Liza will pass Ralph after 5 hours, and they each will have traveled 325 miles.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The situation is modeled by this system,

⇒ y = 60x + 25

⇒ y = 65x

Where, x is the number of hour after Liza leaves and y is the distance each will travel.

Now,

Since, The situation is modeled by this system,

⇒ y = 60x + 25

⇒ y = 65x

To equate both equation, we get;

⇒ 65x = 60x + 25

⇒ 5x = 25

⇒ x = 5

Thus, Liza will pass Ralph after 5 hours.

And, The distance will they each have traveled is,

⇒ y = 60x + 25

⇒ y = 60 × 5 + 25

⇒ y = 300 + 25

⇒ y = 325 miles

Thus, They each will have traveled 325 miles.

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1:

The mean is 14.8

The median is 14 (11+17)/2=14  

The mode is 10

2:

15, 21, 23, 26, 28, 30, 36, 38, 40, 43, 45, 49

3:

The mean is 91.6666666667

4:

The cost of the 5th child is $7850

IM SO SORRY IF I GOT ANY WRONG!!!!!!

Answer:

It costs $0.49 for each avocado and $0.36 for each tomato.

Step-by-step explanation:

This is a system of equations problem.

Let x represent the avocados and y represent tomatoes:

4x + 5y = 3.76  <--- scenario 1

6x + 3y = 4.02 <---- scenario 2

If we graph these out on a graphing calculator, the lines will intersept at point (0.49,0.36)

The x coordinate represents how much it costs for each avacado and the y coordinate represents how much it costs for each tomato