Answer both question

Answer:

x<2

Step-by-step explanation:

x- 2 <0

x < 2

Answer:

\(0<x<2\)

Step-by-step explanation:

Hi there!

\(x(x-2)<0\)

Set x(x-2) equal to 0:

\(x(x-2)=0\)

Solve for x by using the zero product property:

\(x(x-2)=0\)

\(x=0\) and \(x=2\)

Now, we know that for the inequality \(x(x-2)<0\), one of the following must be true:

1) \(0<x<2\)

2) \(x<0\) or \(x>2\)

To find out which one it is, 1) or 2), we can substitute a value into \(x(x-2)<0\) to see if the inequality is true.

For example, 1 takes place in between 0 and 2. If 1 satisfies \(x(x-2)<0\), then \(0<x<2\) must be true. If it does not, then \(x<0\) or \(x>2\) must be true:

\(1(1-2)<0\\1(-1)<0\\-1<0\)

This inequality is true. Thus, \(0<x<2\).

I hope this helps!

Answer:

-24

Step-by-step explanation:

-2×4= -8

-8×3= -24

-24×1= -24

I hope this helps ^-^

Intermediate models of integration differ from the enemies and allies models due to their approach in fostering collaboration and cooperation between different entities while maintaining a certain degree of autonomy and independence.

Intermediate models of integration, in contrast to enemies and allies models, aim to establish a framework where entities can work together while retaining their individual identities and interests. These models recognize that complete integration or isolation may not be the most optimal or feasible approaches. Instead, they emphasize the importance of collaboration and cooperation between different entities, such as organizations or countries, while respecting their autonomy.

In intermediate models of integration, entities seek to identify shared goals and interests, leading to mutually beneficial outcomes. They acknowledge the value of diversity and differences in perspectives, considering them as assets rather than obstacles. This approach encourages open communication, negotiation, and compromise to bridge gaps and find common ground. Rather than viewing other entities as adversaries or allies, the emphasis is on building relationships based on trust, transparency, and shared values.

Intermediate models of integration often involve the establishment of frameworks, agreements, or platforms that facilitate collaboration while allowing for flexibility and adaptation to changing circumstances. These models promote inclusivity, recognizing that integration can be a complex process that requires active participation from all involved entities. By combining the strengths and resources of different entities, intermediate models of integration strive to achieve collective progress and shared prosperity while acknowledging the importance of maintaining individual identities and interests.

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Answer: hope it helps!

Step-by-step explanation:

g/3 + 11=25

             - 11

g/3 = 14/3

g= 4.66666666667 (rounded to 5)

a. The PDF of X is f(x) = (1 / (3 * √(6π))) * exp(-(x - 2)² / 18)

b.

c. Using the Markov inequality, we can bound P(X ≥ 3) as 2/3 or less.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

a. To determine the Probability Density Function (PDF) of X, we need to use the characteristics of a Gaussian distribution. The PDF of a Gaussian distribution with mean μ and standard deviation σ is given by:

f(x) = (1 / (σ * √(2π))) * exp(-(x - μ)² / (2σ²))

In this case, the mean μ is 2 and the RMS value is o=3, which is equivalent to the standard deviation σ.

Therefore, substituting these values into the equation, we get:

f(x) = (1 / (3 * √(2π))) * exp(-(x - 2)² / (2 * 3²))

Simplifying further, we have:

f(x) = (1 / (3 * √(6π))) * exp(-(x - 2)² / 18)

So, this is the PDF of X.

b. To find P(X ≥ 3) using the PDF derived in part (a), we need to integrate the PDF from 3 to infinity:

P(X ≥ 3) = ∫[3, ∞] f(x) dx

P(X ≥ 3) = ∫[3, ∞] (1 / (3 * √(6π))) * exp(-(x - 2)² / 18) dx

Unfortunately, the integral cannot be solved analytically. However, it can be approximated using numerical methods or software.

c. The Markov inequality provides an upper bound for the probability of a random variable being greater than or equal to a positive constant. The inequality states:

P(X ≥ a) ≤ E(X) / a

Where P(X ≥ a) is the probability that X is greater than or equal to a, and E(X) is the expected value of X.

In this case, we want to find an upper bound for P(X ≥ 3). Since X is a Gaussian distribution with mean μ = 2, we have:

E(X) = μ = 2

Using the Markov inequality, we can bound P(X ≥ 3) as follows:

P(X ≥ 3) ≤ E(X) / 3

P(X ≥ 3) ≤ 2 / 3

Therefore, using the Markov inequality, we can bound P(X ≥ 3) as 2/3 or less.

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The solution to the recurrence relation is:

\(Qn = (1/2)(2^n) - (1/2)\)

To find an explicit formula for the Fibonacci sequence, we first write out the first few terms:

\(f0 = 0\)

\(f1 = 1\)

\(f2 = 1\)

\(f3 = 2\)

\(f4 = 3\)

\(f5 = 5\)

\(f6 = 8\)

...

We notice that each term is the sum of the two preceding terms. Therefore, we can write:

\(fn = fn-1 + fn-2\)

Let's solve this recurrence relation to find an explicit formula for the nth term. First, we write out the first few terms in terms of f1 and f0:

\(f2 = f1 + f0\)

\(f3 = f2 + f1 = f1 + f0 + f1 = 2f1 + f0\)

\(f4 = f3 + f2 = 3f1 + 2f0\)

\(f5 = f4 + f3 = 5f1 + 3f0\)

\(f6 = f5 + f4 = 8f1 + 5f0\)

We can see that the coefficients of f1 and f0 are the Fibonacci numbers themselves (1, 1, 2, 3, 5, 8, ...). Therefore, we can write the explicit formula:

\(fn = (1/√5) [(1+√5)/2]^n - (1/√5) [(1-√5)/2]^n\)

(a) To solve the recurrence relation \(On = 7On-1 - 10On-2\), we first find the roots of the characteristic equation:

\(r^2 = 7r - 10\)

\(r = (7 ± √(7^2 + 40))/2\)

\(r1 = 5, r2 = -2\)

Therefore, the general solution to the recurrence relation is:

\(On = c1(5^n) + c2(-2^n)\)

We can find the values of c1 and c2 by using the initial conditions:

\(O0 = 1, O1 = 5\)

\(c1 + c2 = 1\)

\(5c1 - 2c2 = 5\)

Solving these equations, we get:

\(c1 = 1, c2 = -1/3\)

Therefore, the solution to the recurrence relation is:

On = 5^n - (1/3)(-2)^n

(b) To solve the recurrence relation Qn \(= 2Qn-1 + 1\), we first find the root of the characteristic equation:

\(r - 2 = 0\)

\(r = 2\)

Therefore, the general solution to the recurrence relation is:

Qn = c(2^n) + d

We can find the values of c and d using the initial conditions:

\(Q0 = 0, Q1 = 1\)

\(c + d = 0\)

\(2c + d = 1\)

Solving these equations, we get:

\(c = 1/2, d = -1/2\)

Therefore, the solution to the recurrence relation is:

Qn \(= (1/2)(2^n) - (1/2)\)

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The series is divergent and we conclude that by using ratio test.

The ratio test is a mathematical test used to determine the convergence or divergence of an infinite series. It involves taking the ratio of the absolute values of consecutive terms in the series and taking the limit as the number of terms approaches infinity. If the limit is less than 1, the series converges; if the limit is greater than 1, the series diverges; and if the limit is equal to 1, the test is inconclusive and other tests may be needed.

To use the ratio test to determine the convergence of the series we need to calculate the limit of the ratio of successive terms:

lim as n approaches infinity of \(|(-1)^(n+1) * 4^(n+1) * (7(n+1)-3) / (n+1)!| / |(-1)^n * 4^n * (7n-3) / n!|\)
Simplifying this expression, we get:

lim as n approaches infinity of \(|4 * (7n + 4) / (n + 1)|\)

Using L'Hopital's rule, we can find that this limit is equal to 28. Therefore, since the limit is greater than 1, the series diverges by the ratio test.

Therefore, the series is divergent.

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Answer:

10 repeats 1 time

6 repeats 2 times

4 repeats 3 times

1 repeats 1 time

so 4 is the mod

hope this helps

have a good day :)

Step-by-step explanation:

Answer: 4

Step-by-step explanation: The number 4 is being repeated the most out of the other numbers.

Hey there! :)

Answer:

A. \(f(x) = (x - 2)^{4}\)

Step-by-step explanation:

Recall that the transformation form of a polynomial with degree four is:

\(f(x) =\) ±\(a(b(x-h))^{4} +k\)

In this instance, we will need to use the h value, or the horizontal shift.

It is given that there is only a horizontal shift of 2 units to the right, or h = 2. Plug this into the equation:

\(f(x) = (x - 2)^{4}\)

Answer:

No solutions or ∅

Step-by-step explanation:

Do the algebra:

\(-\frac{1}{3}+\frac{2}{3}m=\frac2 3 m - \frac 2 3 \\\\\frac 2 3 m = \frac 2 3 m - \frac 2 3\\\\0=-\frac 2 3\)

Since 0 ≠ -2/3, this equation has no solutions.

Hope this helped :)

Answer:

rebecca increased the length by 3 and the width by 2

Step-by-step explanation:

First we need to find the length and width by factorizing the expressio ofr the area;

A = 2w^2+7w+6

A = 2w^2+4w+3w+6

A = 2w(w+2)+3(w+2)

A = (2w+3)(w+2)

Since l = 2w

Length = 2w+3

width = w+2

This shows that rebecca increased the length by 3 and the width by 2

The hw return by using the given input vector < 4, -6, 4 > will be  -67.

The given weights for a linear regression model (non-linear classifier) are as follows:

w0=1w1=-10w2=6w3=2

Given the input vector < 4, -6, 4 >, we are to find what will hw return. In order to find hw, we need to calculate the weighted sum of the input vector and the given weights as shown below.

hw = w0 + w1x1 + w2x2 + w3x3

where x1, x2, and x3 are the values of the input vector < 4, -6, 4 >.

Substituting the values of the input vector and the given weights in the above equation, we get;hw = 1 - 10(4) + 6(-6) + 2(4) = 1 - 40 - 36 + 8 = -67

Therefore, the value of hw will be -67.

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Answer:

12.5%

Step-by-step explanation:

So, Mika did do the division right. So we can get that out of the way. In order to convert to a percent, you just simply move the decimal point over two times. In this case, we have 0.125. We move it over twice to get 12.5. Now, we just plop the percentage next to it to get: 12.5%.

May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

12.5%

(can also be written as:)12\(\frac{1}{2}\)%

Step-by-step explanation:

She should bring the decimal point over two places to the right.

To convert decimals to percents ALWAYS bring the decimal point two places to the right and and a percentage sign.

Answer:

top left is 2x²

top right -6x

bottom left -1

bottom right 3

Answer:

4x^3+12x^2-x-3=0

Take the GCF of the groups. By groups, I mean the 1st two coefficients and variables.

4x^2(x-3) -1(x+3) =0

Then equal everything to the big 0.

4x^2=0

x+3=0

Then they're one step equations

x= -3, -1, 0

Answer:

Part A - \(l_{1} + l_{2} = 5\cdot x^{2} + 7\cdot x -4\), Part B - Polynomial of second degree and formed by 3 monomials, Part C - \(l_{3} = 5\cdot x^{3} -x^{2}-8\cdot x +1\)

Step-by-step explanation:

Part A - The total length of the sides 1 and 2 is equal to the addition between respective polynomials:

\(l_{1} + l_{2} = (3\cdot x^{2} - 2\cdot x - 1) + (9\cdot x + 2\cdot x^{2} - 3)\)

\(l_{1} + l_{2} = (3\cdot x^{2} + 2\cdot x^{2}) + (9\cdot x - 2\cdot x) +[(-1) + (-3)]\)

\(l_{1} + l_{2} = 5\cdot x^{2} + 7\cdot x -4\)

Part B - The degree is the highest exponent of the polynomial and the classification is related to the number of monomial that make part of the algebraic expression. In this case, we conclude that resulting expression is a polynomial of second degree and formed by 3 monomials.

Part C - The length of the third side of the triangle by subtracting the expression found in part A from the polynomial of the perimeter of the triangle:

\(l_{3} = p - l_{1} - l_{2}\)

\(l_{3} = (5\cdot x^{3}+4\cdot x^{2}-x-3) -(5\cdot x^{2}+7\cdot x -4)\)

\(l_{3} = 5\cdot x^{3} + [4+(-5)]\cdot x^{2}+[(-1)+(-7)]\cdot x +[(-3)+ 4]\)

\(l_{3} = 5\cdot x^{3} -x^{2}-8\cdot x +1\)

Answer:

Part A; Total length of side 1 and 2  = 5·x² + 7·x - 4

Part B; The degree of the polynomial is 2

The classification of the polynomial is a trinomial quadratic equation

Part C; 5·x³ - 4·x² - 6·x + 2

Step-by-step explanation:

The length of the sides of the rectangle are;

Side 1: 3·x² - 2·x - 1

Side 2: 9·x + 2·x² - 3

The perimeter of the rectangle is 5·x³ + 4·x² - x - 3

Part A

The given expression for the sides of the rectangle are;

Side 1: 3·x² - 2·x - 1

Side 2: 9·x + 2·x² - 3

The total length of side 1 and side 2 is given by add ing the given expressions as follows;

Total length of side 1 and 2  = 3·x² - 2·x - 1 + 9·x + 2·x² - 3 = 5·x² + 7·x - 4

Part B

The degree of the polynomial is 2 and the classification of the polynomial is a trinomial quadratic equation

Part C

Given that a rectangle rectangle consists of two pairs of equal opposite sides, we have;

The length of the third side = The perimeter - (2 × The length of side 1 + The length of side 2)

The length of the third side = 5·x³ + 4·x² - x - 3 - (2 × (3·x² - 2·x - 1) + 9·x + 2·x² - 3)

The length of the third side = 5·x³ + 4·x² - x - 3 - (8·x² + 5·x - 5)

The length of the third side = 5·x³ - 4·x² - 6·x + 2

Answer:

she ate 2 ice creams per hour

Step-by-step explanation:

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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Answer:

75 yards makes 30 sweatshirts

x yards makes 1 sweatshirt

cross multiply

x = 75/30

2.5 yards

Step-by-step explanation:

the rate of change is officially

(f(x2) - f(x1)) / (x2 - x1)

but for a line function (as we have here) this is totally easy : it is the slope of the line.

and that means it is the factor of x.

in our case this is -3/2.

because the slope of a line is the ratio "y coordinate change / x coordinate change". and that is exactly corresponding to the general rate of change definition above.

Answer: (f(x2) - f(x1)) / (x2 - x1)

because the slope of a line is the ratio "y coordinate change / x coordinate change".

Step-by-step explanation: HOPE IT HELPS YOU .THANKS .

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

Answer:

x = 8

Step-by-step explanation:

2x + 12 = 3x + 6

-6         =      -6

2x + 6  = 3x

Not exactly sure how to explain the rest but:

Multiples of 2:2,4,6,8,10,12,14,16,18,20,22,24

Multiples of 3: 3,6,9,12,15,18,21,24

So what plus 6 will give you a multiple of 3?

(a) The probability that the letter E is first is 1/5.

(b) The probability that the letter E is chosen is 2/5.

(c) The probability that both vowels are chosen is 1/10.

(d) If both vowels are chosen, and they are next to each other, the probability is 1/10.

(a) To find the probability that the letter E is first, we need to determine the total number of possible arrangements of three letters chosen from the word EXACT. Since there are five distinct letters in the word, the total number of possible arrangements is 5P3, which equals 60. Out of these 60 arrangements, only 12 will have E as the first letter (ECA, ECT, EXA, EXC, and EXT). Therefore, the probability is 12/60, which simplifies to 1/5.

(b) The probability that the letter E is chosen can be calculated by considering the total number of possibilities where E appears in the arrangement. Out of the 60 possible arrangements, 24 will have E in them (ECA, ECT, EXA, EXC, and EXT, as well as CEA, CET, CXA, CXT, XEA, XEC, and XET, and their corresponding permutations). Therefore, the probability is 24/60, which simplifies to 2/5.

(c) To determine the probability that both vowels are chosen, we need to count the number of arrangements where both E and A are included. Out of the 60 possible arrangements, there are six that satisfy this condition (ECA, EXA, EAC, EXA, AEC, and AXE). Hence, the probability is 6/60, which simplifies to 1/10.

(d) Lastly, if both vowels are chosen and they must be next to each other, we only need to consider the arrangements where E and A are adjacent. There are two such arrangements (EAC and AEC) out of the 60 total arrangements. Therefore, the probability is 2/60, which also simplifies to 1/10.

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Answer(s):

\(\displaystyle y = 4sin\:(x + \frac{\pi}{2}) \\ y = -4cos\:(x \pm \pi) \\ y = 4cos\:x\)

Step-by-step explanation:

\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 4\)

OR

\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 4\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = 4sin\:x,\)in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{2}\:unit\)to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD \(\displaystyle \frac{\pi}{2}\:unit,\)which means the C-term will be negative, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1}.\)So, the sine graph of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = 4sin\:(x + \frac{\pi}{2}).\)Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit \(\displaystyle [-3\pi, -4],\)from there to \(\displaystyle [-\pi, -4],\)they are obviously \(\displaystyle 2\pi\:units\)apart, telling you that the period of the graph is \(\displaystyle 2\pi.\)Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\)in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

To show that the points (7, -2), (5, 1), and (3, 4) are collinear, we need to verify that they lie on the same straight line.

We can use the slope formula to calculate the slope of the line that passes through (7, -2) and (5, 1):

m = (y2 - y1) / (x2 - x1)

m = (1 - (-2)) / (5 - 7) = -3/2

Now we can use the point-slope form of a line to write the equation of the line that passes through (7, -2) and has slope -3/2:

y - (-2) = (-3/2)(x - 7)

Simplifying this equation, we get:

y + 2 = (-3/2)x + 21/2

y = (-3/2)x + 17/2

Next, we can verify if the third point (3, 4) lies on this line. We can substitute x = 3 and y = 4 into the equation of the line:

4 = (-3/2)(3) + 17/2

4 = -9/2 + 17/2

4 = 8/2

Since this equation is true, the point (3, 4) lies on the line that passes through (7, -2) and (5, 1). Therefore, the points (7, -2), (5, 1), and (3, 4) are collinear.

Hence , the 6th term of the sequence is 24

It is given that first term is 4 and nth term is a(n)  = a(n-1) + 4   ......(1)

Putting n = 6  in equation (2) , we get sixth term

  a(6) = 4(6-1) +4

  a(6) =   4(5) + 4

  a(6) =  20 + 4

   a(6) = 24

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Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

B. Multiplying by  is the same as multiplying by 80%.

Step-by-step explanation:

probably to late but idc