Can anyone help me with these 3 questions having trouble understanding

The conjecture we can use is that the sum of all even numbers is an even number.

We are given the sum of two even numbers as follows;

12 = 4 + 8

26 = 6 + 20

48 = 16 + 32

72 = 24 + 48

88 = 36 x 52

From the above, we see that they are all even numbers and as such the conjecture we can use is that the sum of all even numbers is an even number.

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I assume [tex]m,n[/tex] are integers to avoid (ir)rational powers of -1.

If [tex]m,n[/tex] are both even, or if [tex]m=n[/tex], then

[tex]\displaystyle \lim_{n\to-1} \frac{x^m+1}{x^n+1} = \frac{1+1}{1+1} = 1[/tex]

If [tex]m,n[/tex] are both odd and [tex]m\neq n[/tex], then we can factorize

[tex]\dfrac{x^m+1}{x^n+1} = \dfrac{(x+1)(x^{m-1} - x^{m-2} + \cdots - x + 1)}{(x+1)(x^{n-1}-x^{n-2}+\cdots-x+1)}[/tex]

Note that there are [tex]m[/tex] terms in the numerator and [tex]n[/tex] terms in the denominator.

In the limit, the factors of [tex]x+1[/tex] cancel and

[tex]\displaystyle \lim_{x\to-1} \frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{x^{m-1} - x^{m-2} + \cdots - x + 1}{x^{n-1}-x^{n-2}+\cdots-x+1} \\\\ ~~~~~~~~~~~~~~~~~~= \dfrac{1-(-1)+1-(-1)+\cdots-(-1)+1}{1-(-1)+1-(-1)+\cdots-(-1)+1} \\\\ ~~~~~~~~~~~~~~~~~~=\frac{1+1+\cdots+1}{1+1+\cdots+1} = \dfrac mn[/tex]

If [tex]m[/tex] is even and [tex]n[/tex] is odd, then we can only factorize the denominator and the discontinuity at [tex]x=-1[/tex] is nonremovable, so

[tex]\displaystyle \lim_{x\to-1}\frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{x^m+1}{(x+1)(x^{n-1}-x^{n-2}+\cdots-x+1)} \\\\ ~~~~~~~~~~~~~~~~~~= \frac2m \lim_{x\to-1} \frac1{x+1}[/tex]

which does not exist.

If [tex]m[/tex] is odd and [tex]n[/tex] is even, then we can factorize the numerator so that

[tex]\displaystyle \lim_{x\to-1}\frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{(x+1)(x^{m-1}-x^{m-2} +\cdots -x+1)}{x^n+1} \\\\ ~~~~~~~~~~~~~~~~~~= \frac{0m}2 = 0[/tex]

The roots of the equation is x = 4.56 OR x = 0.44

From the question, we are to determine the roots of the given equation

The given equation is

x² -5x +2 = 0

Using the formula method,

[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]

In the given equation,

a = 1, b = -5, c = 2

Putting the values into the formula,

[tex]x =\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(2) } }{2(1)}[/tex]

[tex]x =\frac{5 \pm \sqrt{25-8} }{2}[/tex]

[tex]x =\frac{5 \pm \sqrt{17} }{2}[/tex]

[tex]x =\frac{5 + \sqrt{17} }{2}[/tex] OR [tex]x =\frac{5 - \sqrt{17} }{2}[/tex]

[tex]x =\frac{5 + 4.12}{2}[/tex] OR [tex]x =\frac{5 - 4.12}{2}[/tex]

[tex]x =\frac{9.12}{2}[/tex] OR [tex]x =\frac{0.88}{2}[/tex]

x = 4.56 OR x = 0.44

Hence, the roots of the equation is x = 4.56 OR x = 0.44

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In accordance with the graph of the cubic function, the roots are - 2, - 1, 3.

In this question we have a graph of a cubic equation, the roots are the points of the curve that pass through the x-axis. Cubic equations have at least a real root and at most three. In accordance with the graph of the cubic equation, the roots are - 2, - 1, 3.

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Answer:

35 and 7

Step-by-step explanation:

5x + 1x =42

6x=42

x=7

Answer:

Greater number: 35

Smaller number: 7

Step-by-step explanation:

1) Set up system of equations.

Let x = greater number

Let y = smaller number

----------------------------------------------

x + y = 42

x = 5y

2) Solve them using elimination or substitution.

x + y = 42

x - 5y = 0

----------------

6y = 42

y = 42/6

y = 7

3) Substitute the found answer into one of the two equations to find the value of x.

x = 5(7)

x = 35

Therefore, the greater number is 35, and the smaller number is 7.

The height of the cylinder is 3.82 m

2. The surface area is 316.5 ft²

The volume is 406.5 ft³

The volume of a cylinder is given by the formula,

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

V = 300 m³

r = 5 m

h = ?

Putting the parameters into the formula, we get

300 = π × 5² × h

300 = π × 25× h

∴ h = 300/25π

h = 3.82 m

Hence, the height of the cylinder is 3.82 m

2.

Diameter = 6 feet 6 inches = 6.5 feet

∴ Radius = 3.25 feet

Height = 12 feet 3 inches = 12.25 feet

Surface area of a cylinder is given by

Surface area = 2πr(r + h)

Where r is the radius

and h is the height

Surface area = 2π×3.25(3.25 + 12.25)

Surface area = 316.5 ft²

For the volume

V = πr²h

V = π × 3.25² × 12.25

V = 406.5 ft³

Hence, the volume is 406.5 ft³

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The distance d is 9 ft and the height is 12ft.

Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.

The height is one cathetus and the distance is the other catheti.

Let's define:

We know that the height of the tower is 3 ft larger than the distance, then:

h = d + 3ft

Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.

Then:

[tex]d^2 + (d + 3ft)^2 = (15ft)^2[/tex]

Now we can solve this equation for d:

[tex]d^2 + d^2 + 6ft*d + 9ft^2 = (15ft)^2\\\\2d^2 + 6ft*d - 216 ft^2 = 0\\\\d^2 + 3ft*d - 108ft^2 = 0[/tex]

Then the solutions are:

[tex]d = \frac{-3ft \pm \sqrt{(3ft)^2 - 4*(-108ft^2)} }{2} \\\\d = \frac{-3ft \pm 21ft }{2}[/tex]

We only take the positive solution:

d = (-3ft + 21ft)/2 = 9ft

And the height is 3 ft more than that, so:

h = 9ft + 3ft = 12ft

The distance d is 9 ft and the height is 12ft.

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Answer: [tex](-2, 5)[/tex]

Step-by-step explanation:

The graphs are shown in the attached image.

The solution is where they intersect.

The solution to the system of equations is x = -2 and y = 5.

i.e

The solution is = (-2, 5)

We have,

To find the solutions, you need to set the two equations equal to each other because they both represent the same variable "y."

So, you'll have:

(-7/2)x - 2 = -2x + 1

Now, let's solve for x:

Step 1:

Get rid of the fractions by multiplying both sides by 2:

2 * ((-7/2)x - 2) = 2 * (-2x + 1)

This simplifies to:

-7x - 4 = -4x + 2

Step 2:

Isolate the x terms on one side of the equation.

Let's move the -4x to the left side by adding 4x to both sides:

-7x - 4 + 4x = -4x + 4x + 2

This simplifies to:

-3x - 4 = 2

Step 3:

Now, isolate the constant term by moving the -4 to the right side by adding 4 to both sides:

-3x - 4 + 4 = 2 + 4

This simplifies to:

-3x = 6

Step 4:

Finally, solve for x by dividing both sides by -3:

x = 6 / -3

x = -2

Now that you've found the value of x, plug it back into either of the original equations to find the corresponding y value.

Let's use the first equation y = (-7/2)x - 2:

y = (-7/2) * (-2) - 2

y = 7 - 2

y = 5

Thus,

The solution to the system of equations is x = -2 and y = 5.

i.e

(-2, 5)

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Reason:

Set A = {0,1,2,3,4,5,6,7,8,9}

Set B = {0,1,2,3,4,5,6,7}

The probability of getting a "2" from set A is 1/10 since there is one copy of "2" that we want out of ten values total.

The probability of getting a "2" from set B is 1/8 for similar reasoning. This time there are eight numbers in this set.

Multiply those fractions mentioned (1/10)*(1/8) = 1/80

This fraction converts to the exact decimal value of 0.0125, meaning there's exactly a 1.25% chance of getting "2" twice in a row.

Area

Answer:

1725 ft²

Step-by-step explanation:

The formula to find the area of a trapezoid is :

Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height

Let us solve it now.

Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height

Area = [tex]\frac{1}{2}[/tex] × ( 65 + 50 ) × 30

Area = [tex]\frac{1}{2}[/tex] × ( 115 ) × 30

Area = [tex]\frac{1}{2}[/tex] × 3450

Area = 1725 ft²

The graph isn't bipartite because it isn't possible to assign either Blue or Red to each vertex, without having connected vertices with the same color.

The bipartite graph theorem states that a graph is considered to be bipartite only if it's possible to assign either Blue or Red to all the vertex, such that no two (2) connected vertices would have the same color.

By critically observing the image after assigning the colors to each vertices (see attachment), we can logically deduce that the graph isn't bipartite because it isn't possible to assign either Blue or Red to all the vertex, without having connected vertices with the same color.

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I would be better to purchase whole onions at $1.99 per pound, and cut them yourself

Number of bowls = 50

Weight of each bowl = 8

Total weight of the onion soup = 8 x 50 = 400 ounces

Note that:

1 pound = 16 ounces

Total weight in pounds = 400/16

Total weight in pounds = 25 pounds

If you buy the whole onions and purchase at $1.99 per pound

Total cost = 25 x 1.99 = $49.75

If you purchase pre-sliced onions at $2.99 per pound

Total cost = 25 x $2.99 = $74.75

Since it is cheaper to purchase whole onions at $1.99 per pound, it is the better choice

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h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.

Given,

h(x) = -0.017x² + 1.08x + 5.8

Put h = 24,

h(24) = -0.017(24)² + 1.08(24) + 5.8

h(24) = -9.792 + 25.92 + 5.8

h(24) = 21.93

The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.

Vertical intercept, x = 0

h(0) = -0.017(0)² + 1.08(0) + 5.8

h(0) = 5.8

The height of the shot put above the ground is 5.8 feet at the start.

vertex coordinates,

(h,k) = [(-b/2a),-(b²- 4ac)/4a]

(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]

(h,k) = [(1.08/0.034),(1.5608)/0.068)]

(h,k) = (31.76,22.95)

The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.

Put h(x) = 0,

-0.017x² + 1.08x + 5.8 = 0

Use quadratic formula for solving x,

x = (-b±√b²- 4ac)/2a

Here a = -0.017, b=1.08, c=5.8

x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)

x = [-1.08±√1.5608]/-0.034

x =  [-1.08-1.2493]/-0.034 and x =  [-1.08+1.2493]/-0.034

x = 68.509 and x = - 4.98

Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²

                                                                        = √73.49²

                                                                        = 73.49 feet              

Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.

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Using it's concept, a radical equation is given as follows:

[tex]\sqrt{x} + 3 = 13[/tex].

A radical equation is an equation in which the variable is inside the radical.

Hence, among the equations given, the radical equation is:

[tex]\sqrt{x} + 3 = 13[/tex].

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Answer:

C

Step-by-step explanation:

took edge test and got 100

The complex conjugate roots exists A = -1 - 4i or A = -1 + 12i.

If one of the roots exists w = B + 2i, then the other root exists its conjugate w = B - 2i. So we can factorize the quadratic to

[tex]z^2+4z+20+iz(A+1) = (z-(B+2i))(z-(B-2i))[/tex]

Expand the right side and collect all the coefficients.

[tex]z^2+(4+(A+1)i)z+20 = z^2-2Bz+B^2+4[/tex]

From the z and constant terms, we have

[tex]$\left \{ {{4+(A+1)i = -2B} \atop {20 = B^2+4}} \right.[/tex]

From the second equation, we get

[tex]B^2 = 16[/tex]

B = ± 4

Then 4+(A+1)i = ± 8

(A + 1)i = 4 or (A + 1)i = -12

Since [tex]$\frac{1}{i} = -i[/tex], we have

[tex]$\frac{-A+1}{i} =4[/tex] or [tex]$\frac{-A+1}{i} =-12[/tex]

A+1 = -4i or A+1 = 12i

A = -1-4i or A = -1+12i

Therefore, the complex conjugate roots exists A = -1-4i or A = -1+12i.

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The solution to the given polynomial in their degree are:

2a + 4a³ - 5a² - 1

= 4a³ - 5a² + 2a - 1

The leading coefficient is 4a³

4z - 2z² - 5z⁴

= -5z⁴ - 2z² + 4z

The leading coefficient is -5z⁴

(-3d² - 8 + 2d) + (4d - 12 + d²)

= -3d² - 8 + 2d + 4d - 12 + d²

= -2d² + 6d - 20

(y + 5) + (2y + 4y² - 2)

= y + 5 + 2y + 4y² - 2

= 4y² + 3y + 3

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Using the binomial distribution, there is a 0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, there is a fixed number of independent trials, each with only two possible outcomes, hence the binomial distribution is used. The values of the parameters are:

n = 15, p = 0.36.

The probability is P(X = 5), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{15,5}.(0.36)^{5}.(0.64)^{10} = 0.2094[/tex]

0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.

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The two bottom graphs demonstrate translations.

We will have a translation only if:

The images where the figures are only moved a little bit are the ones that demonstrate just a translation, and these are the two lower ones.

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Answer: x>2

Step-by-step explanation:

[tex]8(x-1) > 12-2x\\\\8x-8 > 12-2x\\\\10x-8 > 12\\\\10x > 20\\\\x > 2[/tex]

1. The preparation of the adjusting entries as of December 31 for Arnez Company is as follows:

1. Debit Office Supplies Expenses $16,363

Credit Office Supplies $16.363

2. Debit Insurance Expenses $7,740

Credit Prepaid Insurance $7,740

3. Debit Salaries Expenses $54,000

Credit Salaries Payable $54,000

4. Debit Rent Receivable $3,400

Credit Rent Revenue $3,400

5. Debit Unearned Rent Revenue $6,160

Credit Rent Revenue $6,160

2. The preparation of the journal entries to record the first subsequent cash transactions in January of the next year for Arnez Company is as follows:

Debit Salaries Payable $54,000

Credit Cash $54,000

Debit Cash $6,800

Credit Rent Receivable $3,400

Credit Rent Revenue $3,400

1. Office Supplies Expenses $16,363 Office Supplies $16.363 ($3,850 + $15,901 - $3,388)

2. Insurance Expenses $7,740 Prepaid Insurance $7,740 ($27,744 - $20,004)

3. Salaries Expenses $54,000 Salaries Payable $54,000 ($1,800 x 15 x 2)

4. Rent Receivable $3,400 Rent Revenue $3,400

5. Unearned Rent Revenue $6,160 Rent Revenue $6,160 ($3,080 x 2)

Salaries Payable $54,000 Cash $54,000

Cash $6,800 Rent Receivable $3,400  Rent Revenue $3,400

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Using a discrete distribution, the expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Considering the situation described in this problem, the distribution for the earnings is given as follows:

Hence the expected value is given as follows:

[tex]E(X) = 700\frac{1}{1000} - 2\frac{999}{1000} = \frac{700 - 2(999)}{1000} = -1.298[/tex]

The expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.

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Answer:

1.894

3.169

2.064

3.690

Step-by-step explanation: 90% ; sample size = 8

Degree of freedom, df = n - 1

t(1 - α/2, 7) = t0.05, 7 = 1.894

[tex]m = \frac{f(5) - f(0)}{5 - 0} [/tex]

[tex]m = \frac{ - 10 - 10}{5} = \frac{ - 20}{5} = - 4[/tex]

Step-by-step explanation:

the average rate of change is

(f(high interval end) - f(low interval end))/(high interval end - low interval end)

in our case here

(f(5) - f(0)) / (5 - 0)

(-10 - 10) / 5 = -20/5 = -4

The dot product of the D⋅n is 32.

According to the statement

We have given the value of n vector and d matrix and we have to find the dot product of these.

So, For this purpose,

The given values:

n = {-2,-1} and D = [−4423].

The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers, and returns a single number.

So, The d matrix become

[tex]D = \left[\begin{array}{cc}-4&4&\\2&3&\\\end{array}\right][/tex]

Now solve it with the help of multiplication then the matrix become

D = (-12, -8)

and n = {-2,-1}

Now multiply both terms with the dot product.

So, the dot product of the both terms will become

D.n = 24 +8

Then

The output of the dot product of both terms is 32.

So, The dot product of the D⋅n is 32.

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Answer:

the answer is 46.47937775048613

Answer: False .

Step-by-step explanation: mark me brainliest

Answer:

false because l don't know

Answer:

$1317.14

Step-by-step explanation:

compounded continuously formula is A=Pe^rt

given that you want to have $1500 in 2 years while the rate is 6.5%, you have A, r, and t of the formula and you are just looking for the P.

plugging everything in...

1500=P (e)^2x0.065

P=1500/1.139

P=1317.14