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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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lateral area of the cylinder = 2πrh

What is lateral area of the cylinder ?

The lateral area of a cylinder is the area on the outside, meaning if you would cut open a cylinder longitudinally, and folded it open, the rectangle that remains is the lateral area of the cylinder.

Area of rectangle = Lateral area

length is the circumference of the circle = 2πr

and length can be consider as h.

Hence, lateral area of the cylinder = 2πrh.

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i didn't learn it.. so im not sure.. but i thimk 3

Answer:

d is the correct answer to your question

Answer:

9.2 units

Step-by-step explanation:

cause the last guy is right...

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 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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in a regression with 7 predictors and 62 observations,The degrees of freedom for a t-test for each coefficient would use 55 degrees of freedom (df = 62 - 7 = 55).

The degrees of freedom for a t-test for each coefficient is calculated by subtracting the number of predictors (7) from the number of observations (62) in a regression with 7 predictors and 62 observations,. This leaves us with 55 degrees of freedom (df = 62 - 7 = 55). Degrees of freedom measure the number of observations that are free to vary in estimating a parameter. In other words, they are the number of observations that are used to generate the estimate. In this case, there are 55 observations that can be used to estimate each coefficient.

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Answer: (2.4, -12.8)

Step-by-step explanation:

Answer:

putting more than question is against app rules but alr

Part A: The value of each of the houses after a fixed number of years can be described by a linear function. This is because the value of each house increases at a constant rate, with the same amount added each year.

Part B: The function for House 1 could be written as f(x) = 294,580 + 8,937.6x, and the function for House 2 could be written as f(x) = 295,000 + 9,000x.

Part C: After 25 years, the value of House 1 will be approximately $750,834.40, and the value of House 2 will be approximately $753,000. The difference in value between the two houses after 25 years will be approximately $2,165.60, which is not a significant difference in the overall value of the houses. Therefore, either house would be a good choice for Belinda to purchase.

Answer:

-7

*I think*

Step-by-step explanation:

3×(-5)=(-15)

(-15)+8=(-7)

The fundamental counting principal there will be 2*2*2*4*2 = 64 possible lunches.

What is fundamental counting principal ?

According to this concept, the sum of the outcomes of two or more independent events is equal to the product of the outcomes of each individual event. For instance, a youngster picking from a menu of six ice cream flavors and three types of cones will have a total of 6 x 3 = 18 options.

Here size has two types  say  2

Here cheese has two types say 2

Here type of bun has two types say 2

Here side order has four types say 4

Here fruit drink has two types say 2

So, according to the fundamental counting principal there will be 2*2*2*4*2 = 64 possible lunches.

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The number of years that the deposit was held for is 3 years.

From the information, Mr. Johnson deposited $2000 in an account that earns simple interest at an annual interest rate of 6%. and he received $360 as interest at the end of the tenure.

It should be noted that simple interest is Illustrated as:

I = PRT

Therefore, T = Interest / Principal × Rate

Time = 360 / (2000 × 6%)

Time = 360 / 120

Time = 3 years

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The equation of the line is y = 13/6x - 5

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

Points: (0, -5) and (6, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

c = -5

So, we have

y = mx - 5

Also, we have

(x, y) = (6, 8)

This means that

8 = m x 6 - 5

So, we have

6m = 13

This gives

m = 13/6

So, we have

y = 13/6x - 5

Hence, the equation is y = 13/6x - 5

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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.

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:-2,0

Step-by-step explanation:

you have to ether multiply or divide by an easy number

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!!!!!!

The best way to analyze their data for significance is to Conduct a two-way variable analysis.

As we can see, there is a 2x3 factorial design. Thus, we know that there will be a two level or two way analysis of variables, which is referred to as two way variables analysis. Factorial design is a research method that allows for the inquiry of a main and interaction effects of two or more independent variables on one or more outcome variables (s).

It has been argued that factorial designs represent the true beginning of modern behavioral research and have resulted in a significant paradigm shift in how social scientists conceptualize their research questions and produce objective results (Kerlinger & Lee, 2000).

Factorial design is an experimental methodology that goes beyond standard single-variable experimentation. Previously, social scientists were fixated on single independent variable experiments, foreshadowing the significance of extraneous variables that can attenuate or diminish research findings.

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Answer:

I'm not sure sorry sorry

The first three taylor polynomials of the function f(x) = e⁻ˣ at x = 0 is 1, 1 - x and 1 - x + x²/ 2.

Taylor polynomial of degree n for a function f(x) which is infinitely differentiable at a is

f(a) + f'(a)×(x - a)/ 1! + f''(a)×(x - a)²/ 2! + ... + (f⁽ⁿ⁾(a)×(x - a)ⁿ/ n! = ∑(i = 1 to n)(f⁽i⁾(a)×(x - a)^{i}/ i!)

where f⁽i⁾(a) denotes the ith derivative of f(x) at a

The first, second and nth derivative of the function f(x) = e⁻ˣ is

f'(x) = -e⁻ˣ

f''(x) = e⁻ˣ

f⁽ⁿ⁾x = (-1)ⁿe⁻ˣ

First Taylor polynomial, n = 1, here f(x) = e⁻ˣ and a = 0.

P₁(x) = f(0) = e⁻⁰ = 1

Similarly

P₂(x) = f(0) + f'(0)(x - 0)/ 1!

P₂(x) = 1 + -1×e⁻⁰×(x - 0)

P₂(x) = 1 - x

P₃(x) = f(0) + f'(0)(x - 0)/ 1! + f''(0)(x - 0)²/ 2!

P₃(x) = 1 - x + e⁻⁰×(x - 0)²/ 2

P₃(x) = 1 - x + x²/ 2

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It is about 24% of the students could be expected to score between 70 and 90 on the exam.

To find the percentage of students who score between 70 and 90 on the exam, we need to determine what proportion of the exam scores falls within that range. We can do this by converting the scores to standard units and using a table of the standard normal distribution.

First, we need to convert the scores to standard units. We do this by subtracting the mean of 100 from each score and then dividing by the standard deviation of 60. For a score of 70, the standard units would be (70 - 100)/60 = -1.67. For a score of 90, the standard units would be (90 - 100)/60 = -0.67.

Next, we can use a table of the standard normal distribution to find the proportion of scores that fall within that range. For example, a table of the standard normal distribution might tell us that the proportion of scores between -1.67 and -0.67 standard units is about 0.24

Percentage of scores within range = 8.64/36 * 100% = 24%

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Answer: 50%

Step-by-step explanation:

Take 2.62 divided by 5.24, then times 100 = 50%

Then take 100% - 50% = 50%

The percentage discount is 50%

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 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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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:

Square, rhombus, parralelogram

Step-by-step explanation:

Bro too much to type trust

Answer:

C) cos A = 15/17

cos A = adjacent/hypotenuse = 15/17

What is trigonometric ratio for right angle triangle?

The trigonometric ratios for a right angle triangle are sine, cosine, and tangent. The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

The following are the trigonometric ratios of a right angle triangle:

Sine (sin): Opposite Side/Hypotenuse

Cosine (cos): Adjacent Side/Hypotenuse

Tangent (tan): Opposite Side/Adjacent Side

Cosecant (csc): Hypotenuse/Opposite Side

Secant (sec): Hypotenuse/Adjacent Side

Cotangent (cot): Adjacent Side/Opposite Side

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Graph 3 - linear

Graph 4 - linear

The line does not touch the same x more than once.

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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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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