Find f. f"(x) = -2 + 24x - 12x², f(0) = 6, f(0) = 14
f(x) = ...

Answer:

0.7>0.54

Step-by-step explanation:

An example that shows the closure property for polynomials failing to work is:

5x^2 + 2x + 1 / (2x - 1)

This fails to demonstrate the closure property for polynomials because polynomial division is not included in the basic arithmetic operations (addition, subtraction, multiplication) used when discussing the closure property for polynomials. Polynomial division requires a quotient, which is not necessarily a polynomial. For example, the quotient when performing the division above is:

2.5x + 3 / (2x -1) + 0.5

The 0.5 in the quotient is a constant term, not a polynomial, so the result of this division is not a polynomial. Therefore, polynomial division breaks the closure property of polynomials.

The closure property for polynomials states that when any two polynomials are combined using the basic arithmetic operations (addition, subtraction, multiplication), the result will always be a polynomial. Division is not one of these basic operations, so examples involving polynomial division, like the one shown, do not demonstrate closure of polynomials.

The volume of a rectangular prism with a square base is given by the formula V = S^2 * H, where S represents the side length of the square base and H represents the height of the prism.

In this case, the refrigerator box is shaped like a rectangular prism with a square base of 3-foot sides and a height of 6 feet. To find the volume, we substitute the given values into the formula:

V = (3 ft)^2 * 6 ft

= 9 ft^2 * 6 ft

= 54 ft^3

Therefore, the volume of the refrigerator box is 54 cubic feet.

In the explanation, we used the formula for the volume of a rectangular prism with a square base, which states that the volume is equal to the square of the side length of the base multiplied by the height of the prism. By substituting the given values into the formula, we calculated the volume of the refrigerator box to be 54 cubic feet.

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Answer:

PM = 8

Step-by-step explanation:

P is the Centroid of the triangle JLN.

Centroid of a triangle divide the medians in the ratio 2 : 1

Therefore,

JP : PM = 2 : 1

Let JP = 2x & PM = x

So, 2x = 16 (JP = 16)

x = 16/2

x = 8

PM = 8 ( PM =x)

The COUNTIF function is used to compute the number of times a particular condition is satisfied within a given range of cells.

It is an excel statistical function, which is used to count the number of cells that meet a criterion. To determine how many cells in the worksheet contain a number higher than or less than the one specified, the countif formula is used.

It is typed =COUNTIF

1. Select a cell

2. Type =COUNTIF

3. Double-click the COUNTIF command

4. Select a range

5. Type

,6. Select a cell (the criteria, the value that you want to count)7.

Hit enter Hence the answer is COUNTIF

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Answer:

My username is

Step-by-step explanation:

IloveSatorisamam

Answer: My xbox gamertag is...

Bubbles5306

Step-by-step explanation:

Given logistic differential equation of population of meerkats, dP/dt = -0.002P^2 + 6P,Let us solve the differential prism equation for dP/dt to find the population of the meerkats when it is growing the fastest:At maximum, dP/dt = 0

Therefore, 0 = -0.002P^2 + 6PPutting 0 on one side,6P = 0.002P^2Divide both sides by P,6 = 0.002PTherefore, P = 3000 (population of meerkats when it is growing the fastest)Now, let us find the limit P(t) as t approaches infinity; that is, when the population stops growinglim P(t) = limit as t approaches infinity of the population P(t)Solving the logistic differential equation for P(t) by separation of variables,We get,∫(1/(K - P) dP) = ∫(-0.002 dt)Solving the integration,log(K - P) = -0.002t + C,where C is the constant of integration.At t = 0, P = P0

Then, C = log(K - P0)Therefore,log(K - P) = -0.002t + log(K - P0)log((K - P)/(K - P0)) = -0.002tTaking the antilog of both sides of the equation,(K - P)/(K - P0) = e^(-0.002t)Therefore, K - P = (K - P0) e^(-0.002t)Solving for P,We get,P = K - (K - P0) e^(-0.002t)As t approaches infinity, e^(-0.002t) approaches 0Hence, P approaches KTherefore, lim P(t) = K = 2000The value of the dt constant k for the logistic differential equation of the termite population dP/dt = KP - 0.0001P^2 with carrying capacity K = 2000 is given by dP/dt = KP - 0.0001P^2Given, K = 2000Also, dP/dt = KP - 0.0001P^2,So, dP/dt = K (1 - 0.0001(P/K)^2) = KP (1 - (P/20,000)^2)Therefore, the value of the constant k is 0.02 (option B).

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Relative frequency for the class with lower class limit 27 is 20.0%.

To find the relative frequency for the class with lower class limit 27, we must first find the total frequency of the data set. The total frequency is 28 (2+7+5+5+6+3=28). Since the class with lower class limit 27 has a frequency of 5, we can calculate the relative frequency of this class by dividing the frequency of the class by the total frequency.

Formula:

Relative Frequency = (Number of Students in the Class)/(Total Number of Students in the Group) x 100

Relative Frequency = (5)/(28) x 100

Relative Frequency = 0.1786 x 100

Relative Frequency = 17.86%

Rounded to one decimal place, Relative Frequency = 20.0%.

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Answer:

\(I(n)=113.5n+125\)

Step-by-step explanation:

Given functions:

\(\begin{cases}A(n)=40.75n+125\\B(n)=70.55n \end{cases}\)

If function I(n) is the total of both functions combined then:

\(\begin{aligned}\implies I(n) & = A(n) + B(n)\\& = (40.75n+125)+(70.55n)\\& = 40.75n+125+70.55n\\& = 40.75n+70.55n+125\\& = 111.3n+125\end{aligned}\)

The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

N is the number of observations in the data set.

It is given that:

The data set:

45, 76, 30, 22, 51, 40, 63, 66, 41

From the formula:

∑(x(i) - X)² = 2463.55

N = 9

SD = √(2463.55/9)

SD = 16.54

Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

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The answer is:Option (F) Box (iii) is the best and Box (i) is worst, for the given one hundred draws will be made at random with replacement from one of the following boxes based on expected-probability.

Given the three boxes:

(i) 1 9(ii) 4 6(iii) 5 5

One hundred draws will be made at random with replacement from one of the above boxes.

Let us now calculate the expected value of the sum for each of the boxes:

(i) Expected value of sum = (1+9)/2 × 100

                                          = 500.

(ii) Expected value of sum = (4+6)/2 × 100

                                           = 500.

(iii) Expected value of sum = (5+5)/2 × 100

                                            = 500.

Box (i) and (ii) have the same expected value, so we can choose either of them.

However, it is important to note that in Box (ii) the numbers are closer together than in Box (i),

so the sum is more likely to be near the expected value.

This makes Box (ii) the best option.

Box (iii) is the worst option as it has a smaller range than the other two boxes,

Which means that it is less likely to produce a sum close to the expected value.

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The volume of the given solid, with the boundaries, is given as follows:

661.5 cubic units.

The volume of the solid is obtained using a double integral.

The equation for the solid is given as follows:

7x + 9y + z = 63.

z = 63 - 7x - 9y.

The coordinate planes bound the plane, hence:

Hence the double integral that is used to obtain the volume of the solid is given as follows:

\(V = \int_{0}^{9}\int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dydx\)

The inner integral is given as follows:

\(I = \int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dy\)

Which, applying the Fundamental Theorem of Calculus, has the result given as follows:

\(I = -98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441\)

Then the volume of the solid is given by the outer integral as follows:

\(V = \int_{0}^{9} \left(-98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441\right) dx\)

Which has a numeric value of:

661.5 cubic units.

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Answer:

\(y=2x\)

Step-by-step explanation:

We want to write an equation in slope-intercept form that passes through the points (2, 4) and (3, 6).

So, we will first find the slope. Let (2, 4) be (x₁, y₁) an let (3, 6) be (x₂, y₂).

The slope formula is given by:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

So, by substitution, our slope is:

\(\displaystyle m=\frac{6-4}{3-2}=\frac{2}{1}=2\)

Now, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

By substitution:

\(y-(4)=2(x-(2))\)

Distribute:

\(y-4=2x-4\)

Adding 4 to both sides yields:

\(y=2x\)

And we have our equation.

In this case, the y-intercept is 0.

The below mentioned are the factors of given equations

Factorization:

In mathematics, factorization or factoring is the method of expressing a quantity or another numerical component as a product of many factors, typically small or easier components of the same kind.

In the case of integers, ancient Greek mathematicians were the first to consider factorization. They demonstrated the fundamental theorem of arithmetic, which states that any positive integer can be taken account into a prime number product , which cannot be factored into integers greater than 1. Furthermore, this factorization is unique until the order of the factors is changed.

1)\(9a^{2}-18a=9a(a-2)\)

2)\(16a^{3}b^{3} +32ab=16ab((ab)^{2} +2)\)

3) inappropriate question

4)\(3x^{5} +4x^{4} -5x^{2} =x^{2} (3x^{3} +4x^{2} -5)\)

5)\(2x^{3} -x=2(x-1)(x+1)\)

Therefore,The above mentioned are the factors of the given questions.

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Answer:

The square root of 31 is 5.5 (not including numbers after that, just those two work) therefore it's in between the two numbers of 5 and 6.

Answer:

5.56776436283

Step-by-step explanation:

i googled it

Answer:

I think this is how you use it.

Use the side lengths to classify the triangle as acute, right, or obtuse. Classify the triangle as acute, right, or obtuse. Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides. Compare c2 with a2 b2.

Answer:

Use the side lengths to classify the triangle as acute, right, or obtuse. Classify the triangle as acute, right, or obtuse. Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides. Compare c2 with a2 b2.

In order to caculate the perimeter of the given polygon, you first determine the length of each side of the polygon, just as follow:

side RS = 2 - (-2) = 2 + 2 = 4

side ST = 1 - (-3) = 1 + 4 = 5

side TQ = 2 - (-2) = 2 + 2 = 4

side QR = 1 - (-3) = 1 + 4 = 5

finally you sume all lengths:

4 + 5 + 4 + 5 = 18

Hence, the perimeters of the given polygon is 18 units

Answer:

m/1   <   m/6

m/3 + m/5 < m/7 + m/8

Step-by-step explanation:

hope this helped!

(a) Is this an observational study or an experiment?

ans=Observational study – no treatment was imposed

(b) What are the explanatory and response variables?

ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior

d) Does this study show that child care causes children to be more aggressive? Explain.

No. Observational studies cannot show cause-and-effect

Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.

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Answer:

no solution

Step-by-step explanation:

Given

3(x - 3) = 3x + 4 ← distribute parenthesis on left side

3x - 9 = 3x + 4 ( add 9 to both sides )

3x = 3x + 13 ( subtract 3x from both sides )

0 = 13 ← not possible

This indicates the equation has no solution

Answer:

She must read more than 5 hours

Step-by-step explanation:

equation 12h+10>70

12h>60

h>5

So she must read more than 5 hours

(can I get brainliest now)

Answer:

12x5=60+10=70 pages.

She reads 12 pages per hour, so if she read for 5 hours, she would have read 60 pages. She has already read 10 pages, so that would equal 70 Pages.

The total present value of these payments at the time the first payment is made is 1,735.85 (747.26 + 988.59).

To calculate the present value of these payments, we need to use the formula for the present value of an annuity:

\(PV = (P/i) x [1 - (1+i)^-n]\)

Where:
P = payment amount
i = annual effective rate
n = number of payments

Using this formula, we can calculate the present value of the first 10 payments:

\(PV = (100/0.07) x [1 - (1+0.07)^-10] = 747.26\)

To calculate the present value of the remaining 10 payments, we need to first calculate the payment amounts. To do

this, we can use the following formula:

\(Pn = P1 x (1 + g)^n\)

Where:
Pn = payment in year n
P1 = first payment amount
g = growth rate
n = number of years since first payment

For the 11th payment:

\(P11 = 105 x (1 + 0.05)^1 = 110.25\)

For the 12th payment:

\(P12 = 110.25 x (1 + 0.05)^1 = 115.76\)

And so on, until the 20th payment:

\(P20 = 163.32 x (1 - 0.05)^8 = 79.24\)

Now we can calculate the present value of these payments:

PV = \((110.25/0.07) x [1 - (1+0.07)^-10] + (115.76/0.07) x [1 - (1+0.07)^-9] + ... + (79.24/0.07) x [1 - (1+0.07)^-1]\)

PV = 988.59

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Step-by-step explanation:

<2+<3=180° because they are on a staright line.

Mathematically this will be

(5x+9)°+(4x+19)°=180°

9x+28°=180°

9x=180°-28°

9x=152°

\( \frac{9x}{9} = \frac{152}{9} \\ x = \frac{152}{9} \)

We are not done yet we found the value kf x now we can find the value of <2 GIVEN BY 5X+9 BU PLUGGING IN THE VALUE OF X

\( < 2 = 5(\frac{159}{9} ) + 9 \\ < 2 = \frac{841}{9} \\ = 93.44444444\)

Rounded is 93.44

The Laplace Transform is defined by the following formula:

\(\[F(s) = \int_{0}^{\infty} f(t) e^{-st} \, dt\]\)

Let's use this formula to determine the Laplace transform of \(F(s)\).

\(\[F(s) = 0 \text{ for } t < -5\]\)

\(\[F(s) = t \text{ for } -5 \leq t < 5\]\)

\(\[F(s) = 0 \text{ for } t \geq 5\]\)

Using the above definition of the Laplace transform, we have:

\(\[F(s) = \int_{0}^{5} t \, e^{-st} \, dt\]\)

This can be solved using integration by parts:

\(\[F(s) = \left[ -\frac{t}{s} e^{-st} \right]_{0}^{5} + \frac{1}{s} \int_{0}^{5} e^{-st} \, dt\]\)

Evaluating the first term gives\(\(-\frac{5}{s} e^{-5s} + \frac{1}{s^2} (e^{-5s} - 1)\)\)

Thus, the Laplace transform of \(F(s)\) is given by:

\(\[F(s) = -\frac{5}{s} e^{-5s} + \frac{1}{s^2} (e^{-5s} - 1)\]\)

The Laplace Transform is a powerful tool used in the analysis of linear time-invariant systems and differential equations. It can be used to convert a time-domain function into a frequency-domain function, making it easier to analyze.

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One car travel South at 64 mi/h and the other travels west at 48 mi/h. The distance between the cars increases with rate at 80 mi/h.

To find the rate of change, we need to find the derivative of the variables with respect to time.

Let:

p = distance between 2 cars

q = distance between car 1 and the start point

r = distance between car 2 and the start point

Using the Pythagorean Theorem:

p² = q² + r²

Take the derivative with respect to time:

2p dp/dt = 2q dq/dt + 2r dr/dt

dq/dt = speed of car 1 = 64 mi/h

dr/dt = speed of car 2 = 48 mi/h

The distance of car 1 and car 2 from the start point after 4 hours:

q = 64 x 4 = 256 miles

r = 48 x 4 = 192 miles

Using the Pythagorean theorem:

p² =256² + 192²

p = 320 miles

Hence,

2p dp/dt = 2q dq/dt + 2r dr/dt

p dp/dt = q dq/dt + r dr/dt

320  x dp/dt = 256 x 64 + 192  x 48

dp/dt = 80

Hence, the distance between the cars increases with rate at 80 mi/h

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Given the following question:

Where the trapezoid is...

6ft by 9ft

Find the area:

Answer:

2 stickers will be left over

Step-by-step explanation:

To answer the question, all you need to do is figure out at what value of stickers would the remaining stickers be equal to 2 if the piles are made up of either 3 to a set or 4 to a set. To do this, we need to figure out the size of the whole set of stickers.

Lets assume that the total number of stickers is 14. Lets test the 2 given conditions. If we divide it in piles of 3 then we will have a pile of 12 stickers (4 piles of 3 stickers each) with 2 stickers remaining.

Lets test the second condition. If we divide it in piles of 4, we will again have 12 stickers (3 piles of 4 stickers each) with 2 stickers remaining.

Now that both conditions have been satisfied, all we have to do is see how many stickers are left if we make a pile of 12 stickers. In this case, we will have just one pile of 12 stickers and, again, we will be left with 2 stickers.

Therefore, the answer is 2 stickers

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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The highest point on a bell-shaped curve represents the peak or maximum value of the distribution. This point is known as the mode of the distribution.

In a bell-shaped curve, also known as a normal distribution or Gaussian distribution, the data is symmetrically distributed around the mean. The curve is characterized by a central peak, and the highest point on this peak corresponds to the mode.

The mode represents the most frequently occurring value or the value that has the highest frequency in the dataset. It is the point of highest density in the distribution.

The bell-shaped curve is often used to model naturally occurring phenomena and is widely applied in statistics and probability theory. The mode provides information about the most common or typical value in the dataset and is useful for understanding the central tendency of the distribution.

While the mean and median also have significance in a normal distribution, the highest point on the bell-shaped curve specifically represents the mode, indicating the value with the highest occurrence in the dataset.

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