Mar18/Q9 - V2
2^p=1\8^4
Find the value of p.

The value of M is:

M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.

In this question we have a product of two nonzero real numbers equal to 5, whose mathematical form is:

p · q = 5, where p = 2 · x + √(4 · x² + 5) = k and q = 2 · y + √(4 · y² + 5) = 5 / k

Then, we proceed to find the solutions for x and y in terms of k:

2 · x + √(4 · x² + 5) = k

2 · x = k - √(4 · x² + 5)

4 · x² = k² - 2 · k · √(4 · x² + 5) + 4 · x² + 5

2 · k · √(4 · x² + 5) = k² + 5

4 · k² · (4 · x² + 5) = (k² + 5)²

4 · x² + 5 = (k² + 5)² /(4 · k²)

4 · x² = (k² + 5)² /(4 · k²) - 5

x = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5], for k ≠ 0.

2 · y = 5 / k - √(4 · y² + 5)

4 · y² = 25 / k² - (10 / k) · √(4 · y² + 5) + 4 · y² + 5

(10 / k) · √(4 · y² + 5) = 25 / k² + 5

(100 / k²) · (4 · y² + 5) = (25 / k² + 5)²

4 · y² + 5 = (k² / 100) · (25 / k² + 5)²

4 · y² = (k² / 100) · (25 / k² + 5)² - 5

y = ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5], for k ≠ 0.

Therefore, the value of M is:

M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.

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Answer:

2/5 or 0.4

Step-by-step explanation:

First we have to make equation into the gradient slope form :

y=mx+c    m is gradient and c is y-intercept

15y-6x=8

First we add 6x to both sides :

15y = 6x+8

Now we divide both sides by 15 :

y = 6x+8 / 15

Split the fraction on the right :

y = 6x/15 + 8/15

6x/15 = 6/15x

Our gradient will be 6/15 = 2/5 or 0.4

Hope this helped and have a good day

The reflection of the word DAD across the y-axis is not the same

The statement is given as:

MOM, when reflected over the y-axis = MOM

The above is true because the letters M and O have reflectional symmetry across the y-axis

However, the letter D do not have a reflectional symmetry across the y-axis

So, the letters would not remain the same when reflected

Hence, the reflection of the word DAD across the y-axis is not the same

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Answer:

1: Linear

2: Linear

Step-by-step explanation:

Scenario 1:

Equation: y=8x  (where x represents # of hours worked)

The graph would be linear.

Scenario2:

Equation: y=5x (where x is the # of boxes of donuts purchased)

The graph would be linear. ( I assumed that each box is $5 since 5/1=10/2 )

A similar situation could be: In an art shop, crayons are sold. It costs $7 for 1 box of crayons.

- The graph would be linear, and it would be constant as long as the price for each box of crayons is not changed. Equation is: y=7x

I'm not sure if this is exactly what the last question asked, pretty sure this would be an okay example.

Answer:

70°

Step-by-step explanation:

This is a question on angle properties.

Angle K + 35 + 75 = 180 (Sum of angles in a triangle)

Angle K + 110 = 180

Angle K = 180 - 110 = 70°

Answer:

angle k = [tex]\boxed {70}^\circ[/tex]

Step-by-step explanation:

The angles in a triangle add up to 180°.

∴ ∠k + 75° + 35° = 180°

⇒ ∠k + 110° = 180°

⇒ ∠k = 180° - 110°

⇒ ∠k = 70°

The equation for the plane through the points p(0, 1, 1), q(1, 0, 1) and r(1, 1, 0) is x + y + z = 2

Given,

Three points :- p(0, 1, 1), q(1, 0, 1), r(1, 1, 0)

We can take this as ([tex](x_{1} ,y _{1}, z_{1} ), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})[/tex] respectively.

Thus,

The equation for the plane through the points

Here,

The formula of equation of the plane passing through three non collinear points

[tex]x-x_{1} y-y_{1} z-z_{1} \\x_{2} -x_{1} y_{2} -y_{1} z_{2} -z_{1} = 0\\x_{3} -x_{2} y_{3} -y_{2} z_{3} -z_{2}[/tex]

by substituting the values in the formula of equation of the plane

x-0  y-1  z-1

1-0  0-1  1-1    = 0

1-0  1-1  0-1

x  y  z

1  -1  0   =  0

1  0  -1

x(1) - (y-1)(-1) - (z-1)(-1) = 0

x + y - 1 + z - 1 = 0

x + y + z + 2 = 0

x + y + z = 2

The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

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The equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

For given question,

We have been given three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0)

We need to find an equation for the plane through the given three points.

We know that the equation of the plane through the points [tex](x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)[/tex] is,

[tex]\begin{vmatrix}x-x_1 & y-y_1 & z-z_1\\x_2-x_1 & y_2-y_1 & z_2-z_1\\x_3-x_1 & y_3-y_1 & z_3-z_1\end{vmatrix}=0[/tex]

Assume that for given points,

[tex](x_1,y_1,z_1)=(0, 1, 1)\\\\(x_1,y_1,z_1)=(1, 0, 1)\\\\(x_1,y_1,z_1)=(1, 1, 0)[/tex]

So, the equation of the plane passing though given points would be,

[tex]\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1-0 & 0-1 & 1-1\\1-0 & 1-1 & 0-1\end{vmatrix}=0\\\\\\\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1 & -1 & 0\\1 & 0 & -1\end{vmatrix}=0\\\\\\\Rightarrow x(1-0)-(y-1)(-1-0)+(z-1)(1-0)=0\\\\\Rightarrow x+y-1+z-1=0\\\\\Rightarrow x+y+z=2[/tex]

Therefore, the equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

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Answer:

0

Step-by-step explanation:

In cartesian graphs, the slope or a gradient of a fully horizontal line will always be 0.

The equations intersect at the point (3 ,3 ).

An equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

4y –x = 9 (1)

y = 2x − 3 (2)

You should replace the variable y of equation 1 to equation 2. Then, you will have:

4*(2x-3)-x=9

8x-12-x=9

8x-x=9+12

7x=21

x=3

If x=3, from equation 2 you can find the value of y. Thus, y=2*3-3=6-3=3

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The number of ways people can get off the elevator is 604800 ways.

In this question,

Number of people, n = 7

Number of floors, r = 10

The first person can leave elevator in one of 10 ways. Then second person has to choose from one of remaining 9 floors. Then third person in 8, fourth in 7 ways and so on.

Number of ways people can get off the elevator can be calculated as

⇒ [tex]nP_r=\frac{n!}{(n-r)!}[/tex]

⇒ [tex]10P_{7}=\frac{10!}{(10-7)!}[/tex]

⇒ [tex]10P_{7}=\frac{10!}{(3)!}[/tex]

⇒ [tex]10P_{7}=\frac{(10)(9)(8)(7)(6)(5)(4)3!}{(3)!}[/tex]

⇒ [tex]10P_{7}=(10)(9)(8)(7)(6)(5)(4)[/tex]

⇒ 604800 ways.

Hence we can conclude that the number of ways people can get off the elevator is 604800 ways.

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The concept exhibited by the thirteen year old who was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" is an example of; Intuitive thought.

It follows from the task content that the thirteen year old was unsure of one of her responses. she decided to go with the answer that felt the ""most right."".

Such concept may be attributed to Intuitive thought.

This follows from the fact that the internal impulse which prompts individuals to make decisions is termed; Intuition.

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The correct student's t- distribution requires knowing the degrees of freedom. The degrees of freedom are there for a sample of size n is B) n-1.

Distribution is described as the technique of having items to consumers. An instance of distribution is rice being shipped from Asia to the USA. The frequency of occurrence or quantity of lifestyles.

Distribution manner to spread the product for the duration of the market such that a big quantity of humans should purchase it. Distribution involves doing the following matters. An amazing delivery machine to take the goods into one-of-a-kind geographical regions.

Distribution is one of the four elements of the advertising and marketing mix. Distribution is the method of creating a service or product available for the consumer or enterprise user who needs it. this may be executed without delay through the manufacturer or service company or the usage of indirect channels with vendors or intermediaries.

Disclaimer: The question is incomplete. Please read below to find the missing content.

Question: To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?

A) n

B) n-1

C) n+1

D) [X - μ / (s / n)]

The degrees of freedom depends on the number of parameters you are estimating.

8=

i-1

In student t distribution we estimate the population mean through sample mean and population standard deviation through sample standard deviation

So here both parameters depend on the sample mean i.e. we just calculate from a sample of size n so

Degrees of freedom for students t distribution is B) n-1

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The length of the radius of a circle exists 41 units.

Given: The center exists at -7+2i and a point in the circle at 33+11i.

The radius of the circle exists given by the following formula;

The radius of the circle [tex]$=\sqrt{x^{2}+y^{2}}$[/tex]

The center exists at -7 + 2i and a point in the circle at 33 + 11i.

[tex]$&x(33-(-7)), y(2 \mathrm{i}-11 \mathrm{i}) \\[/tex]

simplifying the equation, we get

[tex]$&\mathrm{x}(33+7), \mathrm{y}(-9 \mathrm{i}) \\[/tex]

[tex]$&\mathrm{x}(40), \mathrm{y}(-9(-1)) \\[/tex]

[tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex]

The center of the circle exists at [tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex].

The length of the radius of a circle exists,

Radius [tex]$}=\sqrt{x^{2}+y^{2}} \\[/tex]

substituting the values of x and y, we get

Radius[tex]$}=\sqrt{40^{2}+9^{2}} \\[/tex]

Radius [tex]$}=\sqrt{1600+81} \\[/tex]

Radius [tex]$=\sqrt{1681} \\[/tex]

Radius = 41 unit

Therefore, the length of the radius of a circle exists 41 unit.

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The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

According to the statement

We have given that the sin(x) = 5/13 , x in quadrant iii

And we have to Find the value of cos x using the following:

So, For this purpose, we know that the trigonometry terms are:

sin2(x) + cos2(x) = 1;  

or cos2(x) = 1-sin2(x)

And

cos2(x) = 1-(-5/13)2 =

cos2(x) = 144/169;  

We know that the

In quadrant III both the sin and cos are negative so

cos(x) = -12/13 (after taking square roots).

And

Then tan(x) = sin(x)/cos(x) = (-5/13)/(-12/13) = 5/12.

Now you can use the angle addition formulas to find sin(2x), cos(2x), and tan(2x).

Now

sin(x + x) = sinx * cosx + cosx * sinx

              = (-5/13)*(-12/13) + (-12/13)(-5/13) = 120/169

And

cos(x + x) = cosX * cos(x) - sinx*sinx

               = (-12/13)(-12/13) - (-5/13)(-5/13)

               =  119/169

So,

You could use the tan double angle formula, but it is easiest to use  

tan(2x) = sin(2x)/cos(2x)  = (120/169) / (119/169)

          = 120/119.

So, The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

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Answer:

Step-by-step explanation:

I gotcha my dude.......

x-5 and 2x+3

Using the normal distribution, the z-score that separates the bottom​ 70% from the top​ 30% is z = 0.525.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score that separates the bottom​ 70% from the top​ 30% is z with a p-value of 0.7, hence z = 0.525.

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The size of the largest angle of the pentagon will be 150°.

A pentagon is the polygon that has five sides. It should be noted that the interior angle of a regular pentagon is 540°.

The given ratio is 2:3:4:4:5. Therefore, the size of the largest angle of the pentagon will be:

= 5/(2+3+4+4+5) × 540

= 5/18 × 540

= 150°

In this case, the size of the largest angle of the pentagon will be 150°.

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Answer:

  (c)  f(g(3)) > g(f(3))

Step-by-step explanation:

The relationship between the function values can be found by evaluating the functions.

The order of operations tells us we must first evaluate g(3).

  g(x) = -3x +15

  g(3) = -3(3) +15 = 6

Then we can evaluate f(x) for x=6:

  f(x) = 7x

  f(6) = 7(6) = 42

So, the composition is ...

  f(g(3)) = 42

As above, we must first evaluate f(3):

  f(3) = 7(3) = 21

Then we can evaluate g(x) for x=21:

  g(21) = -3(21) +15 = -63 +15 = -48

That means the composition is ...

  g(f(3)) = -48

The first is greater than the second.

  42 > -48

  f(g(3)) > g(f(3))

ADG is an equilateral triangle, then, line AD is equivalent to line AG.

From the information given, we have to prove that;

AD=AG

It is important to note that the triangle ADG is an equilateral triangle.

The properties of an equilateral triangle are;

Since ADG is an equilateral triangle, then, line AD is equivalent to line AG

Thus, since ADG is an equilateral triangle, then, line AD is equivalent to line AG.

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Answer: Refer to the histogram diagram below

The frequency table is in another attachment, and may be optional.

======================================================

Explanation:

The first task is to sort the values from smallest to largest. Luckily the data set is already sorted for us.

The smallest number is 22. This is the min. Since we're doing intervals of 10 percent, this means the first bin spans from 20% to 29%, assuming we're only involving whole number percentages. Then the next bin is from 30% to 39%, and so on, until reaching the last bin of 90% to 99%

The bin labels are shown along the bottom of the histogram.

-----------

The height of each bar represents how many students are in that specific bin. The first bar is 1 unit tall because there's only one student in the 20% to 29% range (that 22% mentioned earlier).

The next bar is 2 units tall because of the scores of 30% and 37%. They are in the range from 30% to 39%

The next bar is 4 units tall because of the scores 45,46,46,49.

This process is done with the other values to get the histogram you see below.

The frequency table is shown in a separate attachment, but your teacher may only want the histogram part. I would ask him/her for clarification.

The third column of the frequency table is optional to show where all the scores fit (and to help confirm the frequencies). This will help confirm the answer. Most histograms commonly only show the first two columns.

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

While it's a good thing to know how to do this by hand, it's recommend to use software to generate the histograms when it comes to real world applications. Eg: making a presentation to the boss.

The program I used was LibreOffice which is free and effectively identical to excel. There are other options you could pick from.

Side note: There are no gaps between the bars when it comes to histograms. In contrast, a bar chart will have gaps.

Answer:

D is correct

Step-by-step explanation:

Since you have 2 parallel lines cut by a transversal, <BAC and <BDE are corresponding angels.  Corresponding angles are congruent.  You are able to prove that 2 pairs of angles are congruent so the triangles are similar.  All of the answers show that the 2 triangles share angle B as the first part of the answer.

Answer:

A) f(x) = x^2 +8(x+2)

Step-by-step explanation:

We will start by putting y=0

0 = x^2+8(x+2) -Apply distributive property

0 = x^2+8x+16

0=(x+4)(x+4)

0=x+4, 0=x+4

x=-4

There is only one zero, and that is x=-4

Brainiest would be appreciated.

First one

Because

If we solve for x

Option A

Using the combination formula, it is found that Julia can take 15 combinations.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

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

For this problem, 4 students are taken from a set of 6, hence the number of combinations is given as follows:

[tex]C_{6,4} = \frac{6!}{4!2!} = 15[/tex]

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Please see the picture below

13.1 = 13.10

---> 13.1 > 13.01

---> 13.01 < 13.1

The correct answer is <

Answer: a = 24 units²

Step-by-step explanation:

      Let us graph the figure given. This shape appears to be a trapezoid. Now, we can solve for the area. This shape also has a height of 4, which I forgot to show in the picture.

       In the formula, h is the height, a is a base, and b is the other base.

            [tex]\displaystyle a=\frac{a+b}{2} h[/tex]

            [tex]\displaystyle a=\frac{4+8}{2} 4[/tex]

            [tex]\displaystyle a=\frac{12}{2} 4[/tex]

            [tex]\displaystyle a=(6)4[/tex]

            [tex]\displaystyle a=24\; \text{units}^{2}[/tex]

Answer: 1.71, 1 3/4, 16/9, pie

Step-by-step explanation: We convert all the numbers to improper fractions. 1.71 = 171/100. 1 3/4 = 175/100 because 3/4 is 0.75. pi is 3.14... which is larger than all of the other numbers. So, pi is the largest. For 16/9, we can just divide to find the solution. Once you divide, you will notice that the answer is 1.77777777... This means that it is larger than 1.71 and 1.75 so 16/9 is the second largest. 1.71 is smaller than 1.75 so the order is 1.71, 1 3/4, pie, 16/9

If you know the slope of the lines, you can also use these methods:

- see if the slopes multiplied by each other are -1 (should be if they're perpendicular)

- test if the slopes are opposite reciprocals (if they are, they are perpendicular)

Answer:

[tex]\displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x=2(e-1)[/tex]

Step-by-step explanation:

Given definite integral:

[tex]\displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x[/tex]

Integration by substitution:

Substitute u for one of the functions to give a function that's easier to integrate.

[tex]\textsf{Let }u=\sqrt{x}[/tex]

Find the derivative of u and rewrite it so that dx is on its own:

[tex]\implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{2\sqrt{x}}[/tex]

[tex]\implies \text{d}x=2 \sqrt{x}\:\text{d}u}[/tex]

[tex]\implies \text{d}x=2u\:\text{d}u[/tex]

Use the substitution to change the limits of the definite integral from x-values to u-values:

[tex]\textsf{When }x=0 \implies u=\sqrt{0}=0[/tex]

[tex]\textsf{When }x=1 \implies u=\sqrt{1}=1[/tex]

Therefore, the limits are unchanged.

[tex]\boxed{\begin{minipage}{3 cm}\underline{Integrating $e^x$}\\\\$\displaystyle \int e^x\:\text{d}x=e^x+\text{C}$\end{minipage}}[/tex]

Substitute everything into the original integral and solve:

[tex]\begin{aligned}\implies \displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x & =\displaystyle \int^1_0 \dfrac{e^u}{u} \cdot 2u\:\:\text{d}u \\\\ & = \displaystyle \int^1_0 2e^u\:\:\text{d}u \\\\ & = 2 \int^1_0 e^u\:\:\text{d}u\\\\ & = 2 \left[ e^u\right]^1_0\\\\ & = 2 \left[e^1-e^0\right]\\\\& = 2(e-1)\end{aligned}[/tex]

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Answer:

A: (4,7)

B: (2,1)

C: (6,1)

Step-by-step explanation:

To plot the points, go along the x-axis (the horizontal line with the x on the end) and stop where the dot is. Whatever number the dot is above is the   x-coordinate. Then, however many numbers you go up by to reach the dot is your y-coordinate.

hope this helps :)