1) f(x) = 3x2+ 5x -2
a) Write an equation that can be used to find the zeros of the function.
b) What are the zeros of the function?

a)  f(0) = 4, f(1) = 0, f(2) = 3, f(3) = 3, and f(4) = 0. Since f covers all elements of R5, f is a surjection.

b) g(x) = 5. This means that g does not cover all elements of Ro, so it is not a surjection.

c) F(0) = 4, F(1) = 0, F(2) = 3, F(3) = 2, and F(4) = 3. Since F covers all elements of R5, F is a surjection.

(a) The function f(x) = x^2 + 4 (mod 5) maps each element of R5 to a unique element in R5. Therefore, f is an injection. To show that f is a surjection, we need to show that for every y in R5, there exists an x in R5 such that f(x) = y. We can do this by computing f(x) for all x in R5 and checking if it covers all elements of R5. In this case, f(0) = 4, f(1) = 0, f(2) = 3, f(3) = 3, and f(4) = 0. Since f covers all elements of R5, f is a surjection.

(b) The function g(x) = x^2 + 4 (mod 6) maps each element of R6 to a unique element in Ro. Therefore, g is an injection. However, g is not a surjection because there is no x in R6 such that g(x) = 5. This means that g does not cover all elements of Ro, so it is not a surjection.

(c) The function F(x) = x^3 + 4 (mod 5) maps each element of R5 to a unique element in R5. Therefore, F is an injection. To show that F is a surjection, we can again compute F(x) for all x in R5 and check if it covers all elements of R5. In this case, F(0) = 4, F(1) = 0, F(2) = 3, F(3) = 2, and F(4) = 3. Since F covers all elements of R5, F is a surjection.

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Answer:

1: 3, 1/3

2: 9, 1/9

3: 27, 1/27

4: 81, 1/81

We are given the function to differentiate:

\({\quad \qquad \sf \rightarrow y=x^{e^x}}\)

Do take natural log on both sides, then we will be having

\({:\implies \quad \sf ln(y)=ln(x^{e^{x}})}\)

\({:\implies \quad \sf ln(y)=e^{x}ln(x)\quad \qquad \{\because ln(a^b)=bln(a)\}}\)

Now, differentiate both sides by using so called chain rule and the product rule

\({:\implies \quad \sf \dfrac{1}{y}\dfrac{dy}{dx}=e^{x}ln(x)+\dfrac{e^x}{x}}\)

\({:\implies \quad \boxed{\bf{\dfrac{dy}{dx}=x^{e^x}\bigg\{\dfrac{e^x}{x}+ln(x)e^{x}\bigg\}}}}\)

Hence, Option B) is correct

Product rule of differentiation:

Where, u and v are functions of x

The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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The series ∑ e^n / n^2, where n starts from 1 and goes to infinity, diverges. This means that the series does not have a finite sum and keeps growing indefinitely.

To determine the convergence or divergence of the series ∑ e^n / n^2, we can use various tests. One commonly used test is the comparison test.

When we compare the given series to a known series, such as the harmonic series or geometric series, we can see that the terms of the given series do not decrease or approach zero as n increases. In fact, the exponential term e^n grows exponentially, and the denominator n^2 increases at a much slower rate.

As a result, the terms of the series do not tend to zero, and we can conclude that the series diverges. In other words, the sum of the series goes to infinity as n approaches infinity. This indicates that the series does not have a finite sum and keeps growing indefinitely.

Therefore, the series ∑ e^n / n^2 diverges.

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The vοlume οf the sοlid generated by revοlving the regiοn bοunded by y = 3√sin(x) and y = 0

The area οr vοlume that a cοne takes up is referred tο as its vοlume. Cοnes are measured by their vοlume in cubic units such as cm3, m3, in3, etc. By rοtating a triangle at any οf its vertices, a cοne can be created. A cοne is a rοbust, spherical, three-dimensiοnal geοmetric figure.. Its surface area is curved.

The perpendicular height is measured frοm base tο vertex. Right circular cοnes and οblique cοnes are twο different types οf cοnes. While the vertex οf an οblique cοne is nοt vertically abοve the center οf the base, it is in the right circular cοne where it is vertically abοve the base.

We can simplify this integral using a u-substitutiοn, letting u = sin(x) and du = cοs(x) dx:

V = ∫(1/2 tο √2/2) 2π(3√u) (1/√u) du

= 6π ∫(1/2 tο √2/2)\(u^{(-1/2) du\)

= 12π [\(u^{(1/2)\)](1/2 tο √2/2)c

= 12π (√2 - 1)

Therefοre, the vοlume οf the sοlid generated by revοlving the regiοn bοunded by y = 3√sin(x) and y = 0, fοr π/6 ≤ x ≤ 3π/4, abοut the x-axis is 12π(√2 - 1) cubic units.

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Answer:

cherry= 4ft

maple = 2ft

Step-by-step explanation:

5.80c + 4.20m = 31.60

when we set this equation to the side of page we see

31.60 / 6 = 5.2

if he used 6ft then we can see that 5.2 is the equation

5.8cn  + 4.2mn = 5.2

4(5.8c) + 2(4.2m) = 31.60

proves the 5.2 was a higher distribution than the 4.2  

= 4 cherry and 2 maple

The given histogram is right skewed type.

A histogram is a graphic representation of data in a grouped frequency distribution with continuous classes.

They are similar to a bar graphs, but there are no gaps between the consecutive rectangles.

Histograms are widely used for ranging data into groups. It is a highly practical graph due to its clarity and simplicity.

Histogram :-

It is a collection of rectangles next to one another, where each bar represents a different type of data.

In this context, frequency refers to the number of times a number appears in statistical data.

It is known as a frequency distribution when shown in a table.

Here, the distribution here is skewed to the left. Therefore, it is also referred to as a negatively skewed histogram graph.

Hence, the given histogram is right skewed type.

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Answer:

f

Step-by-step explanation:

fgbdf

Answer:

x=3

Step-by-step explanation:

They are isosceles triangles and angle 2=56.  

56=53+x

x=3

Answer:

The length of the curtain is 10.625 feet

Step-by-step explanation:

The length of the curtain to cover one side of the room depends on the shape of the room

Given a room shape of a square, we have;

Perimeter = 4 × Side length of the room

Length of the curtain = Side length of the room

Therefore;

Perimeter = 4 × Length of the curtain

42.5 feet = 4 × Length of the curtain

Length of the curtain = (42.5 feet)/4 = 10.625 feet

The length of the curtain = 10.625 feet.

Answer: 75° is the smallest amount you need to rotate the image for it to look the same.

Step-by-step explanation: I hope it can be correct :))

Using the Pigeonhole Principle, it can be shown that in a set of n positive integers, none exceeding 2n, there is at least one integer that divides another integer.

We can prove this statement by contradiction using the Pigeonhole Principle.

Suppose we have a set of n positive integers, none of which exceed 2n, and assume that no integer in the set divides another integer.

Consider the prime factorization of each integer in the set. Since each integer is at most 2n, the largest prime factor in the prime factorization of any integer is at most 2n.

Now, let's consider the possible prime factors of the integers in the set. There are only n possible prime factors, namely 2, 3, 5, ..., and 2n (the largest prime factor).

By the Pigeonhole Principle, if we have n+1 distinct integers, and we distribute them into n pigeonholes (corresponding to the n possible prime factors), at least two integers must share the same pigeonhole (prime factor).

This means that there exist two integers in the set with the same prime factor. Let's call these integers a and b, where a ≠ b. Since they have the same prime factor, one integer must divide the other.

This contradicts our initial assumption that no integer in the set divides another integer.

Therefore, our assumption must be false, and there must be at least one integer in the set that divides another integer.

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Answer:

it is an rigjt angle triangle you shoult pythogores therom if you will know it it will be easy to you to understand this question

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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1. Consider a series that changes deterministically: AYt = a. Given initial value of Yo, write the general solution of the difference equation. A difference equation of the form Ay(t) = a has a general solution of y(t) = A + at, where A is a constant of integration. Therefore, the general solution for the difference equation in question is y(t) = Yo + at.

2. In a trend stationary process, the trend is deterministic. Therefore, it is stationary after removing the trend. In a stochastic trend, the trend is stochastic, and the process is non-stationary even after the trend is removed. Since the process above has a deterministic trend, it is a trend stationary process.

3. The first difference of the series should be taken to remove the trend from the series. The first difference is calculated as y(t) - y(t-1).

4. Consider now a series with the following motion: AY₁ = a + et. Given the initial value of Yo, write the general solution of the difference equation. The difference equation Ay(t) = a + et has a general solution of y(t) = (a/e) + A + Bt + ut, where u(t) is a stationary noise term with zero mean and constant variance. Therefore, the general solution to the difference equation in question is y(t) = a/e + Yo + Bt + ut.

5. Explain whether the process above is trend stationary or stochastic trend. Since the process above has a stochastic trend, it is a non-stationary process.

6. The first difference of the series should be taken to remove the trend from the series. The first difference is calculated as y(t) - y(t-1).

7. The hypothesis for a unit root test is that a series has a unit root, meaning it is non-stationary. The Dickey-Fuller test can be used to test for unit roots by regressing the first difference of the series on the lagged level of the series and testing whether the coefficient on the lagged level is significantly different from zero

8. The Augmented Dickey-Fuller test can be used to test for unit roots by regressing the first difference of the series on the lagged level of the series and the lagged first difference of the series and testing whether the coefficient on the lagged level is significantly different from zero.

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If a = [a₁, a₂, ···, aₙ] and b = [b₁, b₂, ···, \(\text{b}_{p}\)], suppose that the last column of ab is 0, but no column of b is 0. The set {a₁, . . ., aₙ} must be linearly dependent because there must be at least one linear combination of a₁, a₂, ..., aₙ that results in a column of b that is zero. This implies that a₁, a₂, ..., aₙ are linearly dependent.

A linearly dependent set is a set of vectors in which there is at least one vector that can be expressed as a linear combination of the other vectors in the set. For example, the set {v₁, v₂, v₃} is linearly dependent if v₁ = a × v₂ + b × v₃ for some constants a and b.

A linear combination set of vectors is a set of vectors that can be combined together to create a single vector. It is the sum of the vectors multiplied by scalar coefficients. For example, if you have three vectors A, B, and C, a linear combination of these vectors is defined as:

A + k₁B + k₂C

where k₁ and k₂ are scalar coefficients.

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Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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1. The scatter plot has a positive linear association

2. The scatter plot here has a negative association

3. The scatter plot has a positive association

4. The scatter plot has a negative association

1. This is a positive linear association because as one of the variable increases, the other variable also increases as well. The increase is in the same proportion.

2. This is negative because as the tempretaure is rising, the same of the hot drinks are declining instead. When temperature was 20 degrees, that was when the highest amount of hot drinks was sold. That was the coldest temperature. The hotter it got, the less it was needed.

3. This is linear because the increase in one variable shows increase in another variable as well.

4. This is negative because as variable B falls, there is a rise in the variable A

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Answer:

(i) 5/2 mod 6

5/2 = x

( cross multiply )

2x = 5

( Find the smallest multiple of 5 that can go in both 2 and 5)

The number = 10

2x = 10

(divide both sides by 2 to make x the subject)

x = 5

Ans: 5 mod 6

(ii) 9/7 mod 7

9/7 = x

( cross multiply )

7x = 9

( Find the smallest multiple of 9 that can go in both 7 and 9)

That no = 63

7x = 63

Divide both sides by 7 to make x the subject)

x = 9

Ans: 9 mod 7

(iii) 6/5 mod 7

6/5 = x

( cross multiply )

5x= 6

( Find the smallest multiple of 5 that can go in both 6 and 5)

No: 30

5x = 30

(D.B.S by 6 to make x subject of the formula)

x = 6

Ans: 6 mod 7

Answer:

I'm not sure, but I'll try

Step-by-step explanation:

(Side)^2 = (Hypotenuse)^2 - (Side)^2

(Side)^2 = (9)^2 - ( √ 65 )^2

(Side)^2 = (81) - (65)

(Side)^2 = 16

Take root of answer

Side = √16

Side = 4

Answer = 4

_________

\( \: \)

a² = c² - b²

a² = 9² - (√65)²

a² = 81 - 65

a² = 16

a = √16

a = 4

Answer:

y=1 1/2x

Step-by-step explanation:

y= mx+c

1st point : (2,3)

2nd point : (4,6)

m= 3-6/2-4

= -3/-2

= 1 1/2

y=1 1/2x

Answer: Yes

Step-by-step explanation: can be written as 6 17/50

Answer: yes because its a terminating number

Answer:

You divide the smaller number by the bigger, or the received points out of the total, so you would divide 99 by 150 giving you 66%

Answer : 66%

Explanation : 33 ÷ 50  Or 99 ÷ 150

Answer:

398

Step-by-step explanation:

She will have to score exactly 398 to tie the score with Anne

Answer:

298 points

Step-by-step explanation:

First, I added 245, 672 and 437 for 1,454.

\(245+672+437=1454\)

Then, multiply 438 (Anne's average) by 4 for 1,752.

\(4(438)=1752\)

After that, subtract 1454 from 1752 for 298 points in game 4.

\(1752-1454=298\)

(A strategy for that you could use is subract the larger ending two digits from the smaller one, then subtract that from 100. Then subtract the front digits of the second number from the front digits of the first number minus one.

So here, 54 - 52 = 2

100 - 2 - 98, so that's the last two digits.

(17 - 1) - 14 = f

16 - 14 = 2 = f, so that's the front digit.

Check the picture below.

\(\tan(38^o )=\cfrac{\stackrel{opposite}{42}}{\underset{adjacent}{x}} \implies x=\cfrac{42}{\tan(38^o)}\implies x\approx 53.76 \\\\[-0.35em] ~\dotfill\\\\ \sin( 38^o )=\cfrac{\stackrel{opposite}{42}}{\underset{hypotenuse}{y}} \implies y=\cfrac{42}{\sin(38^o)}\implies y\approx 68.22\)

Make sure your calculator is in Degree mode.

now as far as the ∡z goes, well, is really a complementary angle with 38°, so ∡z=52°, and of course the angle at the water level is a right-angle.

By the way, the "y" distance is less than 150 feet, so might as well, let the captain know, he's down below playing bingo.

hmmm let's get the functions for the 38° angle.

\(\sin(38 )\approx \cfrac{\stackrel{opposite}{42}}{\underset{hypotenuse}{68.22}}~\hfill \cos(38 )\approx \cfrac{\stackrel{adjacent}{53.76}}{\underset{hypotenuse}{68.22}}~\hfill \tan(38 )\approx \cfrac{\stackrel{opposite}{42}}{\underset{adjacent}{53.76}} \\\\\\ \cot(38 )\approx \cfrac{\stackrel{adjacent}{53.76}}{\underset{opposite}{42}}~\hfill \sec(38 )\approx \cfrac{\stackrel{hypotenuse}{68.22}}{\underset{adjacent}{53.76}}~\hfill \csc(38 )\approx \cfrac{\stackrel{hypotenuse}{68.22}}{\underset{opposite}{42}}\)

Answer: \(4.016\ hr\)

Step-by-step explanation:

Given

Train A has speed of \(v_a=75\ mph\)

Train B has speed of \(v_b=50\ mph\)

If Paris and Pisa is 500 miles apart

If they meet x hours after the start

The sum of the distances traveled by Train A and B is 500 miles

\(\Rightarrow 75\times x+50\times x=500\\\Rightarrow 125x=500\\\Rightarrow x=4.016\ hr\)

So, after \(4.016\ hr\) they will pass each other.

The expressions formed are,

Formation of expressions in 1, 2 and 3:

In 1, twelve times f is, 12f

Taking away 5, it becomes (12f-5)

In 2, sum of k and 6 is, (k+6)

One-half of the above quantity is, (k+6)/2

In 3, sum of 5 with x is, (x+5)

Now, x squared minus the above expression indicates (x²-x+5)

Formation of expressions in 4 and 5:

In 4, product of a and b, is ab and 3 times c is 3c

Sum of the expressions evaluated in the previous statement = ab+3c

In 5, 24 times the product of x and y is, 24xy

Adding, g in the above computed expression, we get, 24xy+g

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Answer:

Step-by-step explanation:

Vertical lines have a slope value of 0 - FALSE

Vertical lines have the slope undefined

The ordered pairs that lie along the same vertical line have identical c-coordinates. (I do not have enough info of what c-coordinate represents )

The ordered pairs that lie along the same vertical line have identical x-coordinates, yet they have different y-coordinate.

Vertical lines increase as you read them from left to right. FALSE

Vertical lines extent upwards and downwards, not left to right.

The ordered pairs that lie along the same vertical line have increasing e-coordinates. (I do not have enough info of what e-coordinate represents)

The value of y coordinates increases if we move upwards along the vertical line.