4(2x + 1) + 2 = 5(x + 6)

Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:

a. The mean is of: 3.3

b. The standard deviation is of: 1.23.

c. They would have a mean of 3.3 and a standard deviation of 0.55.

For this problem, the mean is given by:

M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3

The standard deviation is:

\(S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23\)

It states that for distribution of sample means of size n:

Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.

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Answer:

12

Step-by-step explanation:

Im very sorry if it is wrong. I do not know any 3 step method.

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

Work Shown:

A = area of the triangle on top, aka ceiling

A = 0.5*base*height = 0.5*6*8 = 24

B = area of the triangle on the bottom, aka floor

B = A = 24

C = area of the front rectangular face

C = length*width = 10*7 = 70

D = area of the face in back on the left

D = length*width = 6*7 = 42

E = area of the face in back on the right

E = length*width = 8*7 = 56

Total surface area = A+B+C+D+E = 24+24+70+42+56 = 216 square meters

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

Alternative Method:

A = area of the triangle on top, aka ceiling

A = 0.5*base*height = 0.5*6*8 = 24

B = area of the triangle on the bottom, aka floor

B = A = 24

LA = lateral area = wall area

LA = (perimeter of the base)*(height)

LA = (6+8+10)*(7)

LA = 24*7

LA = 168

Total surface area = A+B+LA = 24+24+168 = 216 square meters

Answer:

11

Step-by-step explanation:

The required distance left to the walk will be 11 km.

The percentage is defined as a ratio expressed as a fraction of 100.

Let the total distance of the walk would be x km

As per the given information, the required solution would be as:

⇒ 45% of x = 9

45%  is expressed as 45/100 in fractional form

⇒ (45/100)x = 9

45/100  is expressed as 0.45 in decimal form

⇒ 0.45x = 9

⇒ x = 9/0.45

⇒ x = 20

So the total distance of the walk is 20 km

Since he has already walked 9 km.

So, he has left to the distance of the walk = 20 - 9 = 11 km

Therefore, the required distance left to the walk will be 11 km.

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Answer:

d)\( \frac{dy}{dx} = - \frac{6}{(2x - 5)^{4} } \)

Gradient of curve at y= ⅛ is \( - \frac{3}{8} \).

Step-by-step explanation:

Please see the attached pictures for the full solution.

The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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To solve the given initial-value problem using the Laplace transform, we follow these steps:

Apply the Laplace transform to both sides of the differential equation.

Use the properties of the Laplace transform to simplify the equation.

Solve the resulting algebraic equation for the transformed variable Y(s).

Apply the inverse Laplace transform to find the solution y(t) in the time domain.

Apply the Laplace transform to the given differential equation:

s^2Y(s) - sy(0) - y'(0) + 7sY(s) - y(0) = (1/s^2) - (1/s) - 1

Substitute the initial conditions y(0) = 0 and y'(0) = 1:

s^2Y(s) - s(0) - 1 + 7sY(s) - 0 = (1/s^2) - (1/s) - 1

Simplify the equation:

s^2Y(s) + 7sY(s) - 1 = (1/s^2) - (1/s) - 1

Combine like terms:

(s^2 + 7s)Y(s) = (1/s^2) - (1/s)

Solve for Y(s):

Y(s) = (1/s^3) - (1/s^2) / (s^2 + 7s)

Decompose the right side into partial fractions:

Y(s) = (1/s^3) - (1/s^2) = A/s + B/s^2 + C/s^3

Find the values of A, B, and C by equating the numerators:

1 = A(s^2 + 7s) + B(s^3 + 7s) + C(s^2)

Solve for A, B, and C:

A = -1/7

B = -1/7

C = 1/7

Substitute the values of A, B, and C back into the partial fractions expression:

Y(s) = (-1/7) * (1/s) + (-1/7) * (1/s^2) + (1/7) * (1/s^3)

Apply the inverse Laplace transform to obtain the solution y(t) in the time domain:

y(t) = (-1/7) * (1) + (-1/7) * (t) + (1/7) * (t^2) * u(t - 1)

where u(t - 1) is the unit step function that ensures the expression is zero for t < 1 and equal to t^2 for t ≥ 1.

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Suppose we're asked to solve the first order linear differnetial equation,

\(\longrightarrow\rm{\dfrac{dy}{dx}+y\cdot P(x)=Q(x)}\)

To solve this equation we have to find out a term called 'Integrating Factor' given by,

\(\rm{I_f=e^{\int P(x)\ dx}}\)

such that the solution of the equation is,

\(\displaystyle\longrightarrow\rm{y\cdot I_f=\int Q(x)\cdot I_f\ dx}\)

Here the given differential equation is,

\(\longrightarrow\rm{\dfrac{dy}{dx}-\dfrac{y}{x}=3x}\)

\(\longrightarrow\rm{\dfrac{dy}{dx}+y\left(-\dfrac{1}{x}\right)=(3x)}\)

Here,

\(\longrightarrow\rm{P(x)=-\dfrac{1}{x}}\)

Integrating wrt x,

\(\displaystyle\longrightarrow\rm{\int P(x)\ dx=-\int\dfrac{1}{x}\ dx}\)

\(\displaystyle\longrightarrow\rm{\int P(x)\ dx=-\ln|x|}\)

[We will consider constant of integration as zero.]

Then the integrating factor is,

\(\longrightarrow\rm{I_f=e^{\int P(x)\ dx}}\)

\(\longrightarrow\rm{I_f=e^{-\ln|x|}}\)

Since \(\rm{e^{b\,\ln(a)}=a^b,}\)

\(\longrightarrow\rm{I_f=x^{-1}}\)

\(\longrightarrow\rm{\underline{\underline{I_f=\dfrac{1}{x}}}}\)

Hence the integrating factor for the given differential equation is 1/x.

Answer:

From the given figure;

Reason: Alternate angle.

Solving for x;

Therefore, the value of x is;

Answer:

m=-2/5

Step-by-step explanation:

Slope is rise over run. In this graph the slope is negative because rise (change in the Y value) is decreasing.

Answer:

  (C)  2

Step-by-step explanation:

Given equations 2a + 7b+2c=16 and 2a + 3b +2c= 8, you want to know the value of b.

The coefficients of 'a' and 'c' are the same in the two equations, so we can eliminate those variables by subtracting one equation from the other. We can keep the resulting coefficient of 'b' positive if we subtract the second equation from the first.

  (2a +7b +2c) -(2a +3b +2c) = (16) -(8)

  4b = 8 . . . . . . . simplify

  b = 2 . . . . . . . divide by 4

The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given \($m =\frac{y_2 - y_1}{x_2 - x_1}\)  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is \(m*2=-1\)  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.\(m*-1=-1\) i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. \(3=-1/2*3+b\)  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

\(y=-x/2+9/2\)

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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Answer:

NEED OIL

Step-by-step explanation:

Answer:

2856

Step-by-step explanation:

This question is a little unclear. 6 times 17 times 28 is equal to 2856 if that is what you are trying to ask.

Matching design study , would conduct this study with a paired design with repeated measures . It helps to see that a chewing gum would help people memorize words or not.

Using a matching design, you will divide the subjects into 2 groups. Randomly selected 10 subjects from 20 subjects will be grouped in Each group .Then you will give all 10 participants one group a chewing gum. To conduct the study using an independent sample design, her one group of students was asked to remember words while chewing gum,and the other group of students was asked to remember words while chewing gum and other group will be asked to memorize words when not chewing the gum. This makes the study an independent samples design because in this way the samples are not paired with each other. Paired with repeated measures is more appropriate for this study because in the case of independent samples design the difference in memorization could not just be because of chewing gum but could be because of the memorization skill of the student. This variation is known as between subject variance.

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Answer:

The answer is x=4.

Step-by-step explanation:

Have a great day!

The algebraic expression for the scenario is 15 + x = 60

From the question, we have the following parameters that can be used in our computation:

Amount saved up = $15

Cost of item = $60

Amount gifted by your grandma = x

The above parameters means that the mathematical statement is an equation statement

So, we have the following representation

Amount saved up + Amount gifted by your grandma = Cost of item

Substitute the known values in the above equation, so, we have the following representation

15 + x = 60

Hence, the algebraic expression is 15 + x = 60

The question does not require that the equation be solved

However, when it is solved, we have:

15 + x = 60

Subtract 15 from both sides

x = 45

So, the amount is 45

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The expressions 2(3a - 2) and 2(5a - 2) are not equivalent. Since these two results are different, we can conclude that Suzanne's claim is incorrect.

To determine if two expressions are equivalent, we need to simplify them and see if they have the same result. Let's start by simplifying the first expression, 2(3a - 2):

2(3a - 2) = 2 * 3a - 2 * 2
          = 6a - 4

Now, let's simplify the second expression, 2(5a - 2):

2(5a - 2) = 2 * 5a - 2 * 2
          = 10a - 4

After simplifying both expressions, we can see that they are not the same. The first expression simplifies to 6a - 4, while the second expression simplifies to 10a - 4.

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What is Irrational Number?

An Irrational number is areal number that cannot be expressed as a ratio of integers; for example \(\sqrt{2}\) is an irrational number. We cannot express any irrational number in the form of ratio, such as p/q, where p and q are integers, q\(\neq\) 0. Again, the decimal expansion of an irrational number in neither terminating nor recurring.

Let us assume \(7\sqrt{56}\) is rational.

So, we can write this number as

\(7\sqrt{56}\) = a/b __(1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) divide by 7 both sides, we get

\(\sqrt{56}=\frac{a}{7b}\)

Here, a and b are integers, so a/7b is a rational number, so \(\sqrt{56}\) should be a rational number.

But \(\sqrt{56}\) is a irrational number, so it is Contradictory.

Therefore, \(7\sqrt{56}\) is irrational number.

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Answer:

The answer is A, D, and E. The first answer and then the last two.

Step-by-step explanation:

The first answer and then the last two.

Answer:

Profit = \(\frac{80p+170}{p}\) 

Step-by-step explanation:

Cost of the Yield =  \(\frac{100p+200}{p}\)  

Cost of the labour =  \(\frac{10p+50}{p}\)

Cost of the fertilisers = \( \frac{10p - 20}{p} \) 

Total expenses =\( \frac{10p + 50}{p}  +  \frac{10p - 20}{p}  =  \frac{20p + 30}{p}\)

Profit =  Cost of yield  - Total expenses

\(=>\frac{100p + 200}{p}  -  \frac{20p + 30}{p}\)  

\(=> \frac{80p + 170}{p} \)

Answer:

\( {(x - 4)}^{2} + 6\)

Step-by-step explanation:

\( {x}^{2} - 8x + 22 \\ \\ = {x}^{2} - 8x + 16 + 6 \\ \\ = {x}^{2} - 8x + {4}^{2} + 6 \\ \\ = {(x - 4)}^{2} + 6\)

The completed square form of  x² - 8x + 22 = 0 is (x - 4)² = - 6.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, a quadratic equation x² - 8x + 22 = 0.

We know (a - b)² = a² - 2ab + b².

∴ x² - 8x + 22 = 0 is

(x)² -2(x)(4) + 4² + 6 = 0.

(x - 4)² = - 6.

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Answer:

24

Step-by-step explanation:

GCF means greatest common factor.

Factors of 24:  1, 2, 3, 4, 6, 8, 12, 24

Factors of 48:  1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The greatest common factor between both sets is 24, so the GCF of 24 and 48 is 24.

The equation of line that passes through the point (6, -1) & is parallel to the line represented by 8x + 3y = 15, in standard form is: 8x + 3y = 45.

Equation of a line in standard form is:

Ax + By = C

where A, B & C are constants.

As the required line is parallel to the given line, that is 8x + 3y = 15, the slope of the required line will be same as that of the given line.

Slope intercept form of a line is:

y = mx + b

where, m is slope of the line, b is a constant.

Re-writing the equation of the given line in slope-intercept form:

⇒ 3y = -8x + 15

⇒ y = (-8/3)x + 5

⇒ slope = m = -8/3

Now as the required line is parallel to the given line, hence its slope-intercept form will be

y = (-8/3)x + b

As the line passes through the point (6, -1),

⇒ -1 = (-8/3)×6 + b

⇒ b = 15

Hence, the slope-intercept form of the required line is

y = (-8/3)x + 15

Re-writing it in standard form, the equation comes out to be

8x + 3y = 45

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Answer:

See below

Step-by-step explanation:

You can always plug in x's and solve for y.

The ratio of hieght of shadow to the height of individual is same for both individual. So height of shadow for Dr Evil's is,

The shadow of Dr Evil's is 6.857 ft.

Answer:

A. If angles XYZ and RST are congruent, then they are vertical angles.

Step-by-step explanation:

hope its right cuz on the test i got an 80%  cant see the answers sorry :/