HOW TO SOLVE LINEAR REGRESSIONS

Answer:

translation

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a. The equation whose solutions are the points of intersection of the graphs is y = -0.14x + 0.80.

b. The points of intersection are (-0.827, 0.918) and (0.951, 0.675).

The solution has been obtained using the slope - intercept form.

What is the slope - intercept form?

When you are aware of the slope of the line being investigated and the given point is also the y intercept, use the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is represented by the symbol b in the equation.

a. From the graph, we have two points of intersection.

Using this, we get the slope as;

m = -0.14

Now, using the slope intercept form, we get the intercept as

b = 0.80

So, the equation comes out to be

y = -0.14x + 0.80

b. The graph of the equations have been attached below.

From the graph, we get the points of intersection as (-0.827, 0.918) and (0.951, 0.675). Both the points have their x-coordinate within the interval [0, 2).

Hence, the required solutions have been obtained.

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Answer:

The discriminant is:

(-3)^2 - 4(1)(18) = 9 - 72 = -63

Since this discriminant is negative, f(x) does not have any real number solutions.

Applying the intersecting secants and chords theorem, the indicated measures in the circle is: HW = 35 units;   MN = 49.5 units.

To find the measures indicated, we will apply the intersecting secants and chords theorem to form an equation, then solve.

a. HZ * HW = HX * HY [based on the intersecting secants theorem]

Plug in the values:

16.8 * HW = 14 * 42

HW = 588/16.8

HW = 35 units

b. VK * VJ = VM * VN [based on the intersecting chords theorem]

Plug in the values:

27 * 18 = 36 * VN

VN = 486/36

VN = 13.5 units

MN = VM + VN = 36 + 13.5

MN = 49.5 units

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Answer:

15

Step-by-step explanation:

Let's call the number we try to find "[tex]x[/tex]"

In the problem, we know that "26 is less than twice a number" is the same as "4". So we can write this as an equation:

[tex]2x - 26 = 4[/tex]

Now we can solve for x by isolating it on one side of the equation.

First, we isolate "2x" by flipping "-26" to the other side, which will now be "26".

[tex]2x = 4 + 26[/tex]

Then we add

[tex]2x = 30[/tex]

finally, we isolate the x by dividing each side with 2

2x ÷ 2 = 30 ÷ 2
x = 15

The function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

The function f(x,y) = x² + y² represents the sum of the squares of the variables x and y. To find the extreme values of this function, we need to take the partial derivatives with respect to x and y and set them equal to zero.

∂f/∂x = 2x = 0

∂f/∂y = 2y = 0

From these equations, we can see that the critical point occurs at (x,y) = (0,0).

To determine whether this is the maximum or minimum, we can use the second partial derivative test. The second partial derivatives are:

∂²f/∂x² = 2

∂²f/∂y² = 2

∂²f/∂x∂y = 0

At (0,0), ∂²f/∂x² > 0 and ∂²f/∂y² > 0, so the critical point is a minimum.

Therefore, the function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.

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The exponential growth model is represented by the function y = 10 · 3ˣ. (Correct choice: D)

In this problem we must determine what function does represent an exponential growth model. With this purpose, we must define and understand the following functions:

Exponential growth model

y = a · rˣ, for r > 1.

Exponential decay model

y = a · rˣ, for 0 < r < 1.

Polynomic model

y = ∑ cₙ · xⁿ

The function y = 10 · 3ˣ represents an exponential growth model.

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Simplifying further, you can move any negative exponents to the denominator by changing their sign:

t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)

what is denominator  ?

In a fraction, the denominator is the bottom number that represents the total number of equal parts into which the whole is divided. For example, in the fraction 3/4, the denominator is 4, which indicates that the whole has been divided into four equal parts.

In the given question,

When multiplying two terms with the same base, you can add their exponents, so:

t⁻¹ u v⁴* t⁻¹ u⁻⁷ v⁰ = t⁻² u⁻⁶ v⁴

Simplifying further, you can move any negative exponents to the denominator by changing their sign:

t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)

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The specified scalar or vector 5u(3v - 4w) is equal to -420i + 250j.

We can begin by distributing the scalar 5 to the vector 3v - 4w:

5u(3v - 4w) = 5u(3v) - 5u(4w)

Next, we can find the scalar multiples:

5u(3v) = 5(-4i + 2j)(3(3i - j)) = 5(-36i + 10j)

5u(4w) = 5(-4i + 2j)(4(-6j)) = 5(48i - 40j)

Now we can substitute these values back into the original expression:

5u(3v - 4w) = 5(-36i + 10j) - 5(48i - 40j)

Simplifying:

5u(3v - 4w) = -420i + 250j

Therefore, 5u(3v - 4w) = -420i + 250j.

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Answer:

123 feet/41 yards

Step-by-step explanation:

When solving problems like this, we need to understand and note down what we already know to make our lives easier.

- He walks 13 different dogs

- the park is a perfect square

- he takes each dog for one full lap

- That day, he walked 6396ft

- He takes each dog the same distance

Now, let's find the unit value (how much ft does he walk if he takes JUST ONE dog around Greenpoint Park?)

Just divide: 6396 / 13 = 492 ft

Meaning, that when Harrold takes JUST ONE dog around the park, which is a perfect square, he walks 492 feet.

One full lap around the square shaped park is just 4 sides of the square.

So, he walks 492 ft every 4 sides.

However, the question specifically asked for one side.

Just divide again to get your answer:

492 / 4 = 123 ft

Therfore, the length of one side of the park is 123 feet, which is 41 yards.

Answer:

2 and 4

Step-by-step explanation:

1)

14x+6=2(5x+3)

14x+6=10x+6

No Solutions

2)

3(x-5)+6=x-(9-2x)

3x-9=3x-9

Infinitely Many

3)

2+5x-9=3x+2(x-7)

5x-7=5x-14

No Solutions

4)

3(4x-6)+2=-4(4-3x)

12x-16=12x-16

Infinitely Many

The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below

A curve displaying an exponential function is known as an exponential graph. A curve with a horizontal asymptote and a rising or decreasing slope characterizes the graph of an exponential function. i.e., it begins as a horizontal line, grows or drops gradually, and then the growth or decay accelerates.

The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2

The vertical shift = 2

vertical shrink = 1/2

Kindly find the attached graph below

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The length of the apothem is 10. 99cm

To determine the apothem of a polygon, we have to use the formula;

a = s/2 tan (180/n)

Such that the parameters are;

Now, substitute the values, we have;

a = 8/2tan(180/9)

divide the values

a = 8/2tan 20

Find the values

a = 8/0. 7279

Divide the values

a = 10. 99cm

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______________________________

______________________________

The statement that best describes the relationship between the two variables is "There is an association because the relative frequencies by column are different, and the relative frequencies by row are also different." (option a).

To understand the relationship between these two variables, we need to analyze the frequencies by row and by column. The rows represent one variable (in this case, gender), and the columns represent the other variable (participation in school sports).

If we look at the relative frequencies by row, we see that the percentage of girls participating in school sports is higher in the fall (63%) than in the spring (43%), while for boys, the opposite is true. This indicates an association between gender and participation in school sports, as the relative frequencies vary by row.

Alternatively, if we look at the relative frequencies by column, we see that the percentage of boys participating in school sports is higher in the spring (57%) than in the fall (37%), while for girls, the opposite is true. This also indicates an association between gender and participation in school sports, as the relative frequencies vary by column.

Therefore, we can conclude that the best statement to describe the relationship between the two variables is option A: "There is an association because the relative frequencies by column are different, and the relative frequencies by row are also different."

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Complete Question:

Siloni computed in a two-way table the relative frequencies of boys’ and girls’ participation in school sports at her school.

School Sports Participation by Gender Fall Spring

Boys 37% 57%

Girls 63% 43%

Which statement best describes the relationship between the two variables?

a) There is an association because the relative frequencies by column are different.

b) There is an association because the relative frequencies by row are different.

c) There is no association because the relative frequencies by column are different.

d) There is no association because the relative frequencies by row are different.

Part A) The vertex of the graph of the function, (t, h(t)) is (2, 68).

Part B) The t-coordinate of the vertex represent is the time it takes for the ball to reach its maximum height (option b)

Part C) The h(t)-coordinate of the vertex represent is the ball's maximum height (option a).

Part A asks for the vertex of the graph of the function, which is the point where the function reaches its maximum or minimum value. To find the vertex of a quadratic function like

=> h(t) = 4 + 64t – 16t²,

we can use the formula

=>  t = -b/2a,

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c and t is the input variable (in this case, the time).

The t-coordinate of the vertex is simply the value we get when we plug this formula into our equation.

So, for

=> h(t) = 4 + 64t – 16t²,

we have a = -16, b = 64, and c = 4.

Plugging these values into the formula

=> t = -b/2a,

we get

=> t = -64/(2*(-16)) = 2.

The t-coordinate of the vertex is therefore 2.

To find the h(t)-coordinate of the vertex, we can simply plug t = 2 into the function h(t) = 4 + 64t – 16t² and evaluate it.

This gives us

=> h(2) = 4 + 64(2) – 16(2²) = 68.

Therefore, the vertex of the graph of h(t) is (2, 68).

Part B asks what the t-coordinate of the vertex represents. We know that the t-coordinate is the time at which the ball reaches its maximum height.

Therefore, the correct answer is B: the time it takes for the ball to reach its maximum height.

Part C asks what the h(t)-coordinate of the vertex represents. We just found that the h(t)-coordinate of the vertex is the maximum height of the ball.

Therefore, the correct answer is A: the ball's maximum height.

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The given slope of the graph is explaining about the swimmer's lap completion throughout the time of 10 minutes.

In the given graph on the x-axis, we can find the time (in minutes) of 10 minutes.

On the y-axis, the graph represents the number of laps the swimmer is completing.

When we observe closely, the slope is giving very important information. At initial time=0, the no. of laps remaining for swimmer is 30. We can show this data clearly as below:

Number of laps remaining----------Time (in minutes)

30 --- 0

27 --- 1

24 --- 2

21 --- 3

18 --- 4

15 --- 5

12 --- 6

9 --- 7

6 --- 8

3 --- 9

0 --- 10

From the above slope data, we can conclude that for every 1 minute of time elapsing, the swimmer is completing 3 laps.  

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Where the above conditions exist, the probability is that about 41.19% of tires woudl be eligible for free replacement.

Using a standard normal distribution table or   calculator, we can find the z   scores corresponding to 35,000 miles and 40,000 miles...

z 1 = ( 35,000 - 40,000) / 3,700 = -1.35

z 2 = (40,000 -   40,000) / 3,700 = 0

Then, we can find the area between these z  scores, which represents the proportion of tires that would fail before 40,000 miles and qualify for a free replacement:

P( -1.35  < Z < 0) = 0.4119 or 41.19%

What it means is that , about 41.19% of the tires would qualify for a free replacement.

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I'm taking linear algebra right now so this one hits home :)

Elementary Row Operations (EROs) are very important and not too difficult, so let's dive into the problem!

You're given the matrix below and asked to perform a single ERO to produce a matrix with a 1 at the position (1,1):

[tex]\begin{bmatrix}3 & 10 & 5\\2 & -1 & 1\end{bmatrix}[/tex]

Think of the two rows as separate entities in the matrix. Ultimately we want to have the index (1,1) currently holding the number 3 to become the number 1. To do this, logically you just need to subtract 2. Now, looking at the rows we have, a simple row operation is quite apparent.

Simply subtract row 2 from row 1, shown below:

[tex]\begin{bmatrix}3-2 & 10-(-1) & 5-1\\2 & -1 & 1\end{bmatrix}[/tex]

Now, simplify and you will have the answer:

[tex]\begin{bmatrix}1 & 11 & 4\\2 & -1 & 1\end{bmatrix}[/tex]

Notice that our matrix now has the required number 1 in row 1 and column 1, therefore, the matrix above is our answer! Let me know if you have any questions!

The side that corresponds to uv is LK

The scale factor is 3 : 1

To solve for the scale factor between two geometric figures, follow these steps:

Identify corresponding sides or corresponding lengths between the two figures.

Choose one pair of corresponding sides and write a proportion using the lengths of those sides.

Solve for the scale factor by simplifying the proportion.

The shape in UV occupies the space of 6 boxes

The space in LK is made of 2 boxes

Hence we have 6 : 2

= 3 : 1

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Answer:

C

Step-by-step explanation:

If it is perpendicular to the line y = ¾x+7 then the gradient if the line must be the negative reciprocal of 3/4. The gradient must be - 4/3. So A, B and D are rejected. Left is C

Let's replace now.

For C,

Let's take y=-4/3x-10 into consideration at the point (-12,6)

Y should be equal to 6 when we replace x by -12

Let's try

Y = -4/3(-12) - 10 = 16 - 10 = 6

Yup. C is your answer.

Answer:90% probability

Step-by-step explanation:

To calculate the experimental probability of the cup landing on its side, we can use the formula:

experimental probability = number of times the cup landed on its side / total number of trials

For the first set of trials, the experimental probability is:

experimental probability = 19/20 = 0.95

For the second set of trials, the experimental probability is:

experimental probability = 81/90 = 0.9

So the experimental probability of the cup landing on its side for the first set of trials is higher than for the second set of trials. However, since the number of trials is relatively small, it is possible that this difference is due to chance and does not reflect a real difference in the probability of the cup landing on its side. To determine this with more confidence, we would need to conduct more trials and perform statistical tests to determine whether the difference is statistically significant.

Answer: The odds against selecting a diamond are 3:1 (or 3/4)

Step-by-step explanation: Which means that there are 3 ways to not select a diamond and only 1 way to select a diamond. The odds in favor of selecting a diamond are 1:3 (or 1/4), which means that there is only 1 way to select a diamond and 3 ways to not select a diamond.

Answer:

O (x + 1)2 + (y + 2)² = 9

Step-by-step explanation:

This is because the distance between points A and B is 3 units, and the distance between points B and C is 4 units, making the triangle a 3-4-5 right triangle. Point B is located at (-1, 1), which is 3 units away from point A (-1, -2) and 4 units away from point C (-5, 1). Therefore, the circle with center (-1, -2) and radius 3 would pass through point B, and its equation would be:

(x + 1)2 + (y + 2)² = 3²

(x + 1)2 + (y + 2)² = 9

Answer: The volume of the prism is 4200 cubic units.

Explanation:

The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height. For a hexagonal base with a side length of 10, we can divide it into six equilateral triangles with side lengths of 10. Each equilateral triangle has an area of (1/2)bh, where b is the base and h is the height. Since the base of each equilateral triangle is also 10, we have:

Area of one equilateral triangle = (1/2)(10)(10√3/2) = 50√3

Area of the hexagonal base = 6 times the area of one equilateral triangle = 6(50√3) = 300√3

Now we can use the formula for the volume of a prism:

V = Bh = (300√3)(14) = 4200 cubic units.

Therefore, the volume of the prism is 4200 cubic units.

The journal entry to record the transaction is given:

Account Debit Credit

Cash $464,000

Common Stock, $3 par value $87,000

Paid-in capital in excess of par  $377,000

A journal entry is used to record a business transaction in the accounting records of a business.

A journal entry is usually recorded in the general ledger. Alternatively, it may be recorded in a subsidiary ledger that is then summarized and rolled forward into the general ledger

Assuming the shares have a $3 par value and sell for $16 cash per share:

Cash reeived from issuance of 29,000 common shares = 29,000 x $16 = $464,000

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Answer:

Step-by-step explanation:

The standard form equation for an ellipse with center at the origin is:

x^2/a^2 + y^2/b^2 = 1

where 'a' is the distance from the center to the vertices along the x-axis and 'b' is the distance from the center to the vertices along the y-axis.

In this case, the center is at the origin, and a vertex is at (3, 0). So, we know that 'a' = 3.

We also know that the distance from the center to the focus is 'c', and that:

c^2 = a^2 - b^2

Since the center is at the origin, 'c' is the distance from the focus (1, 0) to the origin, which is 1. So, we can solve for 'b' as:

c^2 = a^2 - b^2

1^2 = 3^2 - b^2

b^2 = 3^2 - 1^2

b^2 = 8

b = sqrt(8) = 2sqrt(2)

Substituting these values into the standard form equation, we get:

x^2/3^2 + y^2/(2sqrt(2))^2 = 1

Simplifying:

x^2/9 + y^2/8 = 1

So, the equation in standard form for the given ellipse is:

9x^2 + 8y^2 = 72

Answer:

  a) 10:30 a.m.

  b) 75 km/h

Step-by-step explanation:

You want to know the leaving time and speed of a car from Woodlands to Muar if it left half an hour later and arrived half an hour earlier than a coach that traveled the 150 km distance at a speed of 50 km/h and arrived at 1 p.m..

The travel time of the coach is found from the relation ...

  time = distance/speed

  time = (150 km)/(50 km/h) = (150/50) h = 3 h

Then the coach left Woodlands at ...

  1 pm -3 h = 10 am

The car left half an hour later than the coach, so left at 10:30 a.m..

The car arrived at Muar at 12:30 p.m. so had a travel time of ...

  12:30 -10:30 = 2 h

The speed over the 150 km distance is given by ...

  speed = distance/time

  speed = (150 km)/(2 h) = (150/2) km/h = 75 km/h

The average speed of the car was 75 km/h.

__

Additional comment

The car passed the coach at 11:30 a.m., when both had covered half the distance.

The scenario that can be represented by the inequalities 1.25 < x < 1.5 is: A. A container of milk costs at least $1.25 but less than $1.50

The inequality 1.25 < x < 1.5 represents a range of values between 1.25 and 1.5, where x falls within that range.

Option A, which states that a container of milk costs at least $1.25 but less than $1.50, fits this range.

Option B, which states that a student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework, does not fit this range, as it represents a range of time values and not a range of numerical values.

Option C, which states that a tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%, does not fit this range either, as it represents two separate ranges of values.

Option D, which states that the point value of a test item is more than 1.25 points and less than 1.5 points, fits this range as well.

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