Find the real solutions of the following equation. (4x - 1)2 - 6(4x – 1) +9=0"

Answer:

5 2 thats them so 5 2 that them

the answer is 3

.............. .......

Given,\(P(M) = 0.6, P(N|M) = 0.5 and P(N|M') = 0.6\)

We need to find P(M'|N).Using Bayes' theorem, we know that: \(P(M|N) = (P(N|M) * P(M)) / P(N\)

)Let's calculate each term: \(P(N) = P(N|M) * P(M) + P(N|M') * P(M')P(M') can be calculated as:P(M') = 1 - P(M) = 1 - 0.6 = 0.4Using the above formula, we get:P(N) = (0.5 * 0.6) + (0.6 * 0.4) = 0.42 + 0.24 = 0.66\)

Now we can calculate \(P(M|N):P(M|N) = (0.5 * 0.6) / 0.66 = 0.4545\)

To find\(P(M'|N)\), we can use the fact that:\(P(M'|N) = 1 - P(M|N)\)Substituting the value of P(M|N), we get:\(P(M'|N) = 1 - 0.4545 = 0.5455\)Therefore, the required probability is 0.5455.

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The question is an illustration of systems of equations, where 2 or more equations model a particular subject.

The system of equations is:

\(\mathbf{j + p = 75}\)

\(\mathbf{660j + 450p = 675}\)

Let:

j represents jogging

p represents power yoga

She wants to spend 75 minutes.

This is represented as:

\(\mathbf{j + p = 75}\)

The total calories to burn out is 675.

This is represented as:

\(\mathbf{660j + 450p = 675}\)

Hence, the system of equations is:

\(\mathbf{j + p = 75}\)

\(\mathbf{660j + 450p = 675}\)

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Answer:

x=9

Step-by-step explanation:

plug in the number 9

-2(9)= -18

-18+3= -15

The required length of the curve with the specified limits is calculated to be  23,423 units.

The curve r(t) is given as (5 t, 2 sin t, 2 cos t) where −4 ≤ t ≤ 5.

The expression to find the arc length of a parametric vector curve, we use,

Arc length = ∫√[ (dx/dt)² + (dy/dt)² + (dz/dt)²]

The above expression is derived from the Pythagoras theorem.

Applying the formula on the above curve, we have,

dx/dt = d/dt (5t) = 5

dy/dt = d/dt (2 sin t) = 2 cos t

dz/dt = d/dt (2 cos t) = -2 sin t

Arc length = ∫√[ 5² + (2 cos t)² + (-2 sin t)²]

Arc length = ∫ √[ 25 + 4 cos² t + 4 sin² t]

⇒ 2/3 [25 + 4 cos² t + 4 sin² t]^(3/2) × (25t + sin2t/4 + t/2 + t/2 - sin 2t/4)

⇒ 2/3  [25 + 4 cos² t + 4 sin² t]^(3/2) × (25t)

⇒ 50t/3  [25 + 4 cos² t + 4 sin² t]^(3/2)

⇒ 50t/3  [25 + 4(1)]^(3/2) = 50t/3 (29)^(3/2) = 156.16 × 50t/3

⇒ 156.16 × 50t/3 (the limits are from -4 to 5)

⇒ 13,013 - (-10,410)

⇒ 23,423 units.

Thus, the length of the given curve is 23,423 units.

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The correct expression to access the last element would be a(1, 4), which is equal to 9.

If a = [3 5 7 9], the expression a(4, end) refers to the element in the fourth row and last column of matrix a.

In this case, matrix a has only one row, so a(4, end) is not a valid expression since there are no rows beyond the first row. Therefore, it doesn't correspond to any specific value in the matrix.

The correct way to access elements in matrix a would be a(1, 4), which represents the value in the first row and fourth column, resulting in the value 9.

To summarize, a(4, end) is not a valid expression for the given matrix a=[3 5 7 9].

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The integral ∫ln(\(x^{31\))/\(x^2\) dx converges if and only if the corresponding improper integral converges. But since the improper integral evaluates to ∞, the original integral diverges.

We can use the integral test to determine if the integral ∫\(ln(x^{31})/x^2\) dx converges or diverges. Specifically, we'll compare this integral to the corresponding improper integral:

∫\(ln(t^{31})/t^2\) dt, from 1 to infinity

Let u = \(ln(t^{31}), du = (1/t) \times 31t^{30\) dt, and dv =\(1/t^2\)dt, v = -1/t. Then we have:

∫\(ln(t^{31)}/t^2\) dt = -ln\((t^{31})\)/t |_1^∞ + ∫31/\(t^2\) \(\times\)1/t dt

The first term evaluates to:

(-ln(∞^31)/∞) - (-ln(\(1^{31})\)/1) = -∞ + 0 = ∞

The second term evaluates to:

31 ∫dt/\(t^3\) = -31/t^2 |_1^∞ = -31/∞ + 31/1 = 31

So the integral ∫ln\((x^{31)}/x^2\) dx converges if and only if the corresponding improper integral converges. But since the improper integral evaluates to ∞, the original integral diverges.

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Answer: 3.6

Step-by-step explanation: What i did was determined how many minutes are in a hour which are 60 minutes. so due to the fact that you're looking for the travel in (15) "minutes" I had to divide 54 by 15. Which gives you 3.6

Answer: 113.5

Step by Step Explanation:

The constant of proportionality of the linear function is 1.

According to the question,

       Appling division method,

         1/8 ÷ 1/8 = 1

          8 ÷ 8 =1

          12 ÷ 12 = 1

          18 ÷ 18 =1

The result of each division is the same i.e 1.

So,

the constant of proportionality of the linear function is  1.

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Answer:

y = 3/4x +7/2

Step-by-step explanation:

slope of line = difference of 2nd x value - 1st x value/ 2nd y value - 1st y value

x difference /y difference = 3/4 = slope

y = 3/4x

to find y-intercept, add a variable

y = 3/4x + B

then add the first x and y value point numbers into equation

0 = 3/4(4) + B

-3 = B

put back B into equation.

y = 3/4x - 3 which is the linear path the biker is going

now you can use another variable to find the new bike path

y = 3/4x + A

plug in the x value 2 and y value 5 from (2,5)

5 = 3/2 + A

A = 7/2

there-fore the new line which is parallel to the old line is:

y = 3/4x +7/2

Answer:

The answer is,

A. 1/2

Step-by-step explanation:

2/3 - 1/6,

We make the denominators equal,

multiplying and dividing 2/3 by 2, we get,

(2/2)(2/3) = 4/6,

then,

(NOTE: 2/2 = 1, and multiplying with 1 makes no difference)

2/3 - 1/6

= (2/2)(2/3) - 1/6

= 4/6 - 1/6

= (4-1)/6

=3/6

=1/2

Answer: 25w+54

Step-by-step explanation:

Distribute:

=7w+(6)(3w)+(6)(9)

=7w+18w+54

Combine Like Terms:

=7w+18w+54

=(7w+18w)+(54)

=25w+54

Answer:

=25w+54

Answer:

25w + 54

Step-by-step explanation:

7w + 6(3w + 9)

7w + 18w + 54

25w + 54

The complex number and it's conjugate are given as follows:

A complex number is a number that is composed by a real part and an imaginary part, as follows:

z = a + bi.

In which:

The number z has a real part of 4 and an imaginary part of -4, hence it is given as follows:

z = 4 - 4i.

For the conjugate, we keep the real part, changing the sign of the imaginary part, hence:

\(\bar{z} = 4 + 4i\)

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The major axis lies along the z-axis, while the minor axis lies along the x-axis.

Given quadric surface is ( 3x)² − y + (2z)² = 0.

The equation of a quadric surface can be given by Ax² + By² + Cz² + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0, where A, B, C, D, E, F, G, H, I, J ∈ ℝ and (x, y, z) ∈ ℝ³.

(a) Type of quadric surface defined by the above equation is an elliptic paraboloid.

(b) The trace obtained by intersecting the surface with the xy-plane can be obtained by replacing z with 0. So, the equation is 9x² - y = 0, which can be written as y = 9x².

The trace is a parabola which opens upwards and intersects the y-axis at the origin.

(c) The trace obtained by intersecting the surface with the plane y = 1 can be obtained by replacing y with 1.

So, the equation is 9x² + 4z² = 1.The trace is an ellipse in the xz-plane, centered at the origin.

The major axis lies along the z-axis, while the minor axis lies along the x-axis.

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FIRST ONE b SECOND d

Step-by-step explanation:

Answer:

first one is b and the second is d

Step-by-step explanation:hope this helped have a great day (;

Answer:

Approx 3 hours.

Step-by-step explanation:

750 + 255c = 1605

255 c = 855

c = approximately 3 hours.

Answer:

The crew worked 6 hours.

Step-by-step explanation:

$255 x 6 = $1530

Add the "Per Day Fee" of $75

$1530 + $75 = $1605 Dollars

Answer:

2

Step-by-step explanation:

because line a d divided the triangle ABC is into equal parts therefore line BD is equal to line DC which is equal to 2

Using the concept of even and odd functions, it is found that, considering the function has a local max at (-1,3):

For a function increasing on [2,5], we have that:

Hence, considering the function has a local max at (-1,3):

For a function increasing on [2,5], we have that:

For even functions it will decrease because we have that f(4) > f(3), for example, hence f(-4) > f(-3).

For the odd function it will increase because if f(4) > f(3), then f(-3) > f(-4) due to the negative signal.

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The surface area of the tissue box with 8 inch length, 4 inch width and 3 inch height is 136 square inches

The shape of the tissue box is rectangular box

The length of the box = 8 inches

The width of the box = 4 inches

The height of the box = 3 inches

The surface area of the box = 2(lw + lh + wh)

Where l is the length of the box

w is the width of the box

h is the height of the box

Substitute the values in the equation

Surface area = 2(8×4 + 8×3 + 4×3)

= 2(32 + 24 + 12)

= 2(68)

= 136 square inches

Hence, the surface area of the tissue box is 136 square inches

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Answer:

216g of margarine

Step-by-step explanation:

From the above question:

12 small cakes required 108g of margarine

If he would be making 24 of the small cakes, hence, that would be calculated as:

12 small cakes = 108g of margarine

24 small cakes = x

Cross Multiply

12 × x = 24 × 108g

x = 24 × 108g/12

x = 216g of margarine

Therefore, he would need 216g of margarine to make 24 of small cakes

Answer: 1

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

2x^2+10x+12

Divide through by 2

x^2 +5x+6=0

x^2 +3x+2x+6

x(x+3)+2(x+3)=0

(x+2)(x+3)=o

x=-2 or x=-3

Answer:

A

Step-by-step explanation:

I believe its A cause i just did the same question

Answer:

4 1/4.

Step-by-step explanation:

First convert to improper fractions:

1 3/4 = (4*1 + 3)/4 = 7/4

2 1/2 = (2*2 + 1)/2 = 5/2

So it becomes:

7/4 + 5/2

The LCM of 2 and 4  is 4 so we write:

7/4 + 10/4

= 17/4

Now convert this to a mixed number:

17 / 4 = 4 remainder 1

So the answer is 4 1/4.

Answer:

4¼ is the answer

Step-by-step explanation:

\( \\ 1 \frac{3}{4} + 2\frac{1}{2} \)

\( \\ \rightarrow \frac{7}{4} + \frac{5}{2} \)

\( \\ \rightarrow\frac{7 + 10}{4} \)

\( \\ \rightarrow \frac{17}{4} \)

\( \\ \rightarrow 4\frac{1}{4} \)

As we can see 17/4 is not divisible by 4 so if we divide it we will get decimal number or mixed number and we need the answer in mixed number so the number 4¼ is in the simplest form and is the answer.

Hope it's helpful!

Using our trig functions, we know that tan x = opposite side of a right triangle divided by the adjacent side of the right triangle.

So, tan x = p/r.

Answer: tan x°

The trigonometric function gives the ratio of different sides of a right-angle triangle. The ratio of p and r can be written as tan(x°) and sec(y°).

The trigonometric function gives the ratio of different sides of a right-angle triangle.

\(\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\)

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

As per the given figure, the ratio of the p\r can be written as shown below,

In terms of angle x,

tan(x°) = p units / r units

tan(x°) = p/r

In terms of angle y,

tan(y°) = r / p

1 / tan(y°) = r/p

sec(y°) = r/p

Hence, the ratio of p and r can be written as tan(x°) and sec(y°).

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In the given scenario, where there is one infinitely long track and overtaking is impossible, the initial situation consists of three equally spaced trains, each moving at a different speed. The trains have the capability to link up when one catches up to the other, resulting in a single train moving at the speed of the slower train.

As the trains move, they will eventually reach a configuration where the fastest train catches up to the middle train. At this point, the fastest train will link up with the middle train, forming a single train moving at the speed of the middle train. The remaining train, which was initially the slowest, continues to move independently at its original speed. Over time, the process continues as the new single train formed by the fastest and middle trains catches up to the remaining train. Once again, they link up, forming a single train moving at the speed of the remaining train. This process repeats until all the trains eventually merge into a single train moving at the speed of the initially slowest train. In summary, on this strange railway line, where trains can only link up and cannot overtake, the initial configuration of three equally spaced trains results in a sequence of mergers where the trains progressively combine to form a single train moving at the speed of the initially slowest train.

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Applying the definition of the midpoint of a segment, the length of segment AB is: 4.5 cm.

The midpoint of a line segment is the point where the line segment is bisected to form two equal parts.

Given:

AC = 3 cm [given]

Therefore,

1/2(AC) = AD = DC

1/2(3) = AD = DC = 1.5 cm

Therefore:

AD = 1.5 cm

DC = 1.5 cm

CB = DC

Substitute  

CB = 1.5 cm

AB = AD + DC + CB [segment addition postulate]

Substitute

AB = 1.5 + 1.5 + 1.5

AB = 4.5 cm

In conclusion, applying the definition of the midpoint of a segment, the length of segment AB is: 4.5 cm.

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The general expression for the parabola is

Where h and k represent the coordinates of its vertex.

h is the x-coordinate

k is the y-coordinate

If the vertex is (0,-14), then h=0 and k=-14, so the formula for the paravola will be:

Now using the coordinates of the point (5,6) to replace in the formula, you can clear the value of "a"

y= 6

x= 5

a=0.80

The formula for the parabola is

56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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