Which of the following are remote interior angles of Z5? Check all that apply.​

The solution to the algebraic equation, −0.4x − 3.1 = 5.9, is: x = -22.5

Given the algebraic equation, −0.4x−3.1 = 5.9, to solve for x, follow the steps below:

−0.4x − 3.1 = 5.9

−0.4x − 3.1 + 3.1 = 5.9 + 3.1

-0.4x = 9

-0.4x/-0.4 = 9/-0.4

x = -22.5

Therefore, the solution to the algebraic equation, −0.4x − 3.1 = 5.9, is: x = -22.5

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Answer:

This is a voluntary response sample and likely overestimates the frequency of exercise.

Step-by-step explanation:

I just took the unit test review.  The people taking the survey took it voluntarily and it overestimates exercise because it was offered to gym members.

The statement describes the bias that may arise from the results is "This is a voluntary response sample and likely overestimates the frequency of exercise".

Given that,

A nutritionist would like to estimate the number of times adults exercise each week.

To collect information, the nutritionist emails the members of the local fitness center.

We have to determine,

Which of the following describes the bias that may arise from the results?

According to the question,

A nutritionist would like to estimate the number of times adults exercise each week.

To collect information, the nutritionist emails the members of the local fitness center.

The people taking the survey took it voluntarily and it overestimates exercise because it was offered to gym members.

Hence, This is a voluntary response sample and likely overestimates the frequency of exercise.

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Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry

The lengths of the three pencils form a right-triangle, and the two-step problem is:

The lengths of the pencils are given as:

6cm, 8cm and 10cm

Using the Pythagoras theorem, we have:

6^2 + 8^2 = 10^2

Evaluate the exponents

100 = 100

Hence, the lengths of the three pencils form a right-triangle

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The number of square feet that are there for storing paint is 1/2

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

Area of the table = 3-square-foot

Number of sections = 6 sections

The number of square feet is there for storing paint is calculated as

The number of square feet = Area of the table/Number of sections

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

The number of square feet = 3-square-foot/6

Evaluate the quotient

The number of square feet = 1-square-foot/2

This gives

The number of square feet = 1/2 -square-foot

Hence, the square feet is 1/2

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Complete question

The table shows how a 3-square-foot shelf is split into 6 sections for storing art materials. How many square feet are there for storing paint?

Area (square feet)       Sections

             3                            6

             6                            12

             9                            18

Answer:

sum = n (n+1)

Step-by-step explanation:

Let S = sum

Gauss's approach

S = 2     + 4        + 6    + ...  + 2n -4  + 2n-2  +  2n

S = 2n + 2n-2 + 2n-4  +  ... +  6         + 4         + 2

add both equations term by term in order

2S = 2n+2  +  2n+2  + 2n+2 ..... (n times

therefore

S = n(n+1)

check:

n = 1,  S = 1(1+1) = 2   [= 2]

n = 2,  S = 2(2+1) = 6   [= 2+4]

...

checks

Gauss's approach was introduced by Carl Friedrich Gauss according to legend, while he was in primary school

The sum of 2 + 4 + 6 +...+ 2·n is n·(n + 1)

The reason the above expression is correct is as follows:

The required numbers to sum are;

Sum 2 to 2·n

The Gauss's approach involves the adding of the first and last and summing the result as follows:

2 × (2 + 4 + ... + 2·n) = (2·n + 2) + (2·n - 2 + 4) + (2·n - 4 + 6)+...+ (2 + 2·n)

Therefore, we have;

2 × (2 + 4 + ... + 2·n)  = n × (2·n + 2)

(2 + 4 + ... + 2·n)  = n × (2·n + 2)/2 = n·(n + 1)

The expression n × (2·n + 2)/2 = (n/2) × (2·n + 2) = (n/2) × (2 + 2·n)

(n/2) × (2 + 2·n) = (number of terms)/2 × (First + Last term)

Number of terms = n

First term = a₁

Last term = a₂

Sum of terms, Sₙ = (n/2) × (a₁ + aₙ) general form by Gauss's approach

Therefore;

The sum of 2 + 4 + 6 +...+ 2·n using the Gauss's approach is therefore;

(2 + 4 + ... + 2·n)  = n·(n + 1)

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Answer:

0.40

Step-by-step explanation:

The computation of the probability for the second student be sophomore and the first is a freshman is shown below:

Let us assume

Sophomore = S

Freshman = F

Based on this assumption, the probability is as follows

So,

\(= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}\)

= 0.40

Hence, the probability for the second student be sophomore and the first student be freshman is 0.40

The two linear equations have the same slope, -2/3, and different y-intercepts, thus, the lines are parallel.

A general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two linear equations are parallel if both lines have the same slope and different y-intercepts.

And two lines are perpendicular if the product between the slopes is equal to -1.

In this case, we have the two linear equations:

y= -(2/3)*x - 3

y= -(2/3)*x + 6

So you can see that both linear equations have the same slope -2/3 and different y-intercepts, thus, the lines are parallel.

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The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer:

y ≥ 14

Step-by-step explanation:

y - 27 ≥ -13

y ≥ -13 + 27

y ≥ 14

The equivalent expression for a*(b*c) is (a*b)*c.

when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.

The given expression is a*(b*c).

The associative property is holds for multiplication.

According to the definition of associative property when more than two numbers are multiplied the result remains the same, irrespective of how they are grouped.

The equivalent expression for a*(b*c) is (a*b)*c.

For example a=2,b=3 and c=1 then

a*(b*c) =2*(3*1)=6

(a*b)*c=(2*3)*1=6

a*(b*c)=(a*b)*c

Therefore (a*b)*c is equivalent expression for a*(b*c).

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''Start with a line and point K on that line'' is the next step in constructing a line perpendicular to a segment

Whenever two lines cross at a right angle, they are perpendicular or orthogonal. All four of the angles created by two perpendicular lines are 90 degrees.

If and only if the slope product of two non-vertical lines is negative one, those lines are perpendicular. In other words, two perpendicular lines' slopes are the negative reciprocals of one another. A vertical line is perpendicular to only horizontal lines and has an infinite slope (which have slope 0).

This provides a way to determine if two lines are parallel by using their equations. Additionally, this enables us to discover the equations of lines that are perpendicular to another line.

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The number which is not the part of the solution set to the inequality below is 27.

Given inequality is,

w - 10 ≤ 16

WE have to find the solution for the inequality.

Adding both side of the inequality with 10,

w - 10 + 10 ≤ 16 + 10

w ≤ 26

So the solution of the inequality consists of all the points which are less than or equal to 26.

So it contains 11, 15 and 26.

It does not contain 27.

Hence the solution does not contain 27.

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We have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - \(e^2\) ≠ 0) or a horizontal line (when v - \(e^2\) = 0), both of which are conic sections.

To show that the path of a moving point parallel to the axes of x and y with velocities u + ey and v + ex is a conic section, we can analyze the motion of the point using the principles of calculus and conic sections.

Let's denote the position of the point at any given time t as (x, y). We are given that the velocities along the x and y axes are u + ey and v + ex, respectively. This means that the derivatives of x and y with respect to time, dx/dt and dy/dt, can be expressed as:

dx/dt = u + ey

dy/dt = v + ex

Now, let's integrate these expressions to obtain x and y as functions of t. Integrating dx/dt with respect to t gives:

x = ut + eyt + C1

Similarly, integrating dy/dt with respect to t gives:

y = vt + ext + C2

Where C1 and C2 are constants of integration.

Now, we can eliminate the parameter t by expressing t in terms of x and y. From the equation y = vt + ext + C2, we can solve for t:

t = (y - ext - C2) / v

Substituting this value of t into the equation for x, we get:

x = u[(y - ext - C2) / v] + ey[(y - ext - C2) / v] + C1

Simplifying this equation, we obtain:

vx - u - evx + ue + vy - \(e^2\)x - eyC2 = C1v

Rearranging the terms, we get:

vx - vy + ue + evx - \(e^2\)x = C1v + eyC2 - u

Let's define new constants A = ue + ev and B = C1v + eyC2 - u. The equation then becomes:

(v - \(e^2\))x + (u + ev)y = A + B

This equation is in the standard form of a conic section, specifically a line. However, we can manipulate this equation further to reveal other possible conic sections.

Let's consider the case when v - \(e^2\) ≠ 0. In this case, we can divide both sides of the equation by v - \(e^2\), yielding:

x + [(u + ev)/(v - \(e^2\))]y = (A + B)/(v - \(e^2\))

Now, let's define another constant C = (u + ev)/(v -\(e^2\)) and rewrite the equation as:

x + Cy = D

Where D = (A + B)/(v - \(e^2\)).

This equation represents a line in the x-y plane.

On the other hand, if v - \(e^2\) = 0, the equation becomes:

0x + (u + ev)y = A + B

This simplifies to:

(u + ev)y = A + B

Which is a horizontal line parallel to the x-axis.

Therefore, we have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - \(e^2\) ≠ 0) or a horizontal line (when v - \(e^2\) = 0), both of which are conic sections.

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Answer:

\(B = 69\)

Step-by-step explanation:

Given

\(A = 2x +27\)

\(B = x +27\)

Required

Determine B

First, we need to solve for x

Since both angles are supplementary, then

\(A + B = 180\)

Substitute values for A and B

\(2x + 27 + x + 27 = 180\)

Collect Like Terms

\(2x + x = 180 - 27 - 27\)

\(3x= 126\)

Divide through by 3

\(x = 42\)

Recall that:

\(B = x +27\)

Substitute 42 for x

\(B = 42 + 27\)

\(B = 69\)

Answer:

The left graph

Step-by-step explanation:

Well the first big difference you see is that the right graph has 5 pieces of data between 10-19 and the left only has one. We actually only have one piece of data between 10-19 so our answer is the left graph.

Answer:

lesser x is -5x+1

Greater x is x-1

The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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Answer:

Step-by-step explanation:

8) a) In a parallelogram, opposite sides are equal and parallel.

               BC = AD

         12x - 1 = x  + 21

         12x      = x + 21  + 1

              12x = x + 22

         12x - x = 22

                11x = 22

                  x = 22 ÷ 11

                 x = 2

AD = x + 21

     = 2 + 21

AD = 23

In a parallelogram, adjacent angles are supplementary.

   ∠A + ∠D = 180°

\(\sf y - 9 + \dfrac{y}{2}=180\\\\ \dfrac{2y}{2}+\dfrac{y}{2}=180+9\\\\\)

        \(\dfrac{3y}{2}=189\\\\y =189*\dfrac{2}{3}\\\\y=63*2\\\\y = 126\)

∠D = 126 ÷2

     = 63

In parallelogram, opposite angles are congruent.

 ∠B = ∠D

   ∠B = 63°

Step-by-step explanation:

To find slope : y2- y1 / x2 - x1

we have ( -5 , 1 ) which is ( x1 , y1 )

and ( -2 , 7 ) is ( x2 , y2 )

so; 7 - 1 / -2 - (-5)

6/3

= 2

The conclusion of the hypothesis test is 0.342112

What is meant by hypothesis?

In statistics, hypothesis means an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

Here we have given that the factors that contribute to a person's wellbeing, That is Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status.

And we need to find the null and alternative hypothesis and the conclusion of the hypothesis test.

As per the given table of data we have to calculated the p value in order to find the null and alternative hypothesis,

For that we gathered the value of the following,

Number of samples = 9

Then the mean value of data = 83.63

And the standard deviation of the data = 80.475

Then the p - value is calculated as,

p-value ≈ 0.342112

This decision is made at significance level α = 0.05.

Therefore, the result is not statistically significant: there is not enough evidence to reject the null hypothesis.

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Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Three ways to label a base (b) and corresponding height (h) are:

1. Base as the bottom side, height as a perpendicular line segment.

2. Base as a side, height as a perpendicular line segment.

3. Base as the hypotenuse, height as a perpendicular line segment.

To label a base (b) and corresponding height (h), three possible ways can be demonstrated using the triangles below:

1. Triangle 1:

  - Base (b) is labeled as the bottom side of the triangle.

  - Height (h) is labeled as a vertical line segment perpendicular to the base, connecting the opposite vertex to the base.

2. Triangle 2:

  - Base (b) is labeled as the side of the triangle.

  - Height (h) is labeled as a vertical line segment perpendicular to the base, connecting the opposite vertex to the base.

3. Triangle 3:

  - Base (b) is labeled as the hypotenuse (the longest side) of the triangle.

  - Height (h) is labeled as a vertical line segment drawn from one of the vertices of the base, perpendicular to the base.

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Answer:

20 hope this is helpful and also enjoy your day

I am 5 when you multiply me by 6, then divide the product by 3, the quotient is 10.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Assuming I am 'n'.

∴ When you multiply me by 6, which is 6n, then divide the product by 3, which is 6n/3 the quotient is 10 which is 6n/3 = 10.

6n/3 = 10.

2n = 10.

n = 5.

So, I am an odd number 5.

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Answer:

4 hours

Step-by-step explanation:

Answer:

the answer is 4 HOURS

Step-by-step explanation:

i took the exam

The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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