explain the concepts of linear regression, including what you are evaluating, when it should be used, and the differences between a dependent variable and independent variable.

Answer:

[tex]y=-\frac{1}{4}x-6[/tex]

Or

y= -0.25x-6

Step-by-step explanation:

slope intercept form y=mx+b

m is slope and b is y intercept

We know y intercept is -6

To find slope we do y2-y1/x2-x1

(0,-6) and (4,-7) are the points we’ll use

-7-(-6)/4-(0)

-1/4

y= -1/4x-6

Hopes this helps please mark brainliest

Answer:

y= -1/4x + -6

Step-by-step explanation:

The number at the end (-6) is your Y intercept. You can find this by looking at the number that the blue line touches on the up and down graph line.

The middle number in your equation is the slope. You can find this by looking for two points where your blue line crosses the corner of the little boxes. Then you count how many boxes it takes to get from one point to another. Your slope is negative (because the left side is higher than the right) once you count between your points, put the rise number (up and down) over the run number (left to right). Here it would be -1/4

I added a picture to show u

:) pls lmk if u have any questions I'm not great at explaining

Answer: x=2 or x=7/11

explanation:

11x^2=7x+2x

11x^2-7x-2x=0

x(11x-7)-2(11x-7)=0

(x-2)(11x-7)=0

x=2 or x=7/11

They must invest $269.54 billion quarterly at 4% compound interest.

How can it determine how much it needs to invest now to reach $1,600 billion in twelve years?

We use the compound interest formula to figure out how much the International Monetary Fund needs to raise over the next 12 years in order to lend to developing nations at 4% interest compounded quarterly.

Interest that is calculated based on the initial principal as well as all of the interest that has accumulated over previous periods is referred to as compound interest. The power of compound interest is the process of producing "interest on interest. "Any frequency schedule, from continuous to daily to annual, can be used to compound interest.

What is the formula for compound interest?

Given that A = amount raised = $1600 billion, r = compound interest rate = 4% quarterly = 4%  1/4 year = 4%  4 = 16% = 0.16 per year, and n = number of years = 12, we have P = A/(1 + r)n. Substituting the values of the variables into the equation, we have P = $1600 billion/(1 + 0.16)12 P = $1600 billion/(1.16)12 P = $1600 billion/5.93

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Answer:

5

Step-by-step explanation:

To find the 10% of 50 we need to first divide 50 with 100 the multiply it by 10:

50 ÷ 100 × 10 = 5

This formula can be used for most of the percentage questions.

Answer:

5

Step-by-step explanation:

What is Function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

If each input value has one and only one output value, then a relation is by definition a function.

A function must have both an independent and at least one dependent variable. For instance, assuming a function:

"Y" stands for the dependent variable, and "x" stands for the independent variable.

The set of potential input values is known as the function's domain, while the set of potential output values is known as the range.

The slope of vertical lines is unknown. A vertical line is not an illustration of a functional connection because "x" is constant.

For horizontal lines, any x-value results in the same y-value. They are referred to as "Constant functions."

Accordingly, the following claims are accurate:

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The method to find the factors of 54 is shown below .

The Factor of a number is a number that given number without leaving any remainder .

For Example , 2 is a factor of 4 , because on dividing 4 by 2 , there is no remainder .

In the question ,

it is given that the number is 54 ,

first we divide the given by natural numbers ,

and the number that does not leave any remainder , will be the factors .

So , 54 ÷ 1 , it completely divides , So , 1 is a factor .

54 ÷ 2 = 27 , it completely divides , So , 2 is a factor .

54 ÷ 3 = 18 , it completely divides , So , 3 is a factor .

54 ÷ 6 = 9 , it completely divides , So , 6 is a factor .

54 ÷ 9 = 6 , it completely divides , So , 9 is a factor .

54 ÷ 18 = 3 , it completely divides , So , 18 is a factor .

54 ÷ 27 = 2 , it completely divides , So , 27 is a factor .

54 ÷ 54 = 1 , it completely divides , So , 1 is a factor .

So , the factors of 54 are 1 , 2 , 3 , 6 , 9 , 18 , 27 , 54 .

Therefore , the Factors of 54 are 1 , 2 , 3 , 6 , 9 , 18 , 27 , 54 .

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The absolute value depicted in the number line is

The number line shows a solid circle since it is not hollow circle or dot the inequality must either be

Solving the absolute value

= |x| ≥ 5

x ≥ ±5  

x ≥ 5

and

x ≤ 5

The number line shows greater that 5 and less than -5 which is shown in the equation

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Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we may still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to obtain the y-intercept. The key message is (0, y).

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The discounted price of the jeans on Valentines Day at the departmental store is $780.

Original price = $ 1300

Discount = 40%

Discount amount = 40% of 1300 = 520

Discounted sell price = 1300-520 = $780

The amount deducted from the list or marked price in order to provide a product for less is referred to as a "discount." Discounts can be expressed as percentages or as monetary amounts.

The discount formula accounts for the variation between the stated price, marked price, and selling price. Discounts are price reductions that a vendor makes on a product in an effort to boost sales of other products.

The discount formula helps determine how much money a buyer must hand over to the seller. The discount formula can also be calculated in percentages. Always factor in the selling price when calculating the reduction from the asking price.

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Answer:

It will take nine workers

Step-by-step explanation:

rate = [tex]\frac{widgets}{workersx time}[/tex]

[tex]\frac{3}{(3)(3)}[/tex] = [tex]\frac{1}{3}[/tex]

rate x time x workers = jobs

[tex]\frac{1}{3}[/tex] (6)(w) = 18

2w = 18  Divide both sides by 2

w = 9.

It will take 9 workers.

Answer:

No solution

Step-by-step explanation:

We can easily tell that there are no solutions by using the discriminant rule.

The discriminant rule comes directly from the discriminant of the quadratic equation and is b^2-4ac

It can tell us three things about the solution:

When the discriminant is less than 0, there is no solution.

When the discriminant equals 0, there is one distinct solution.

When the discriminant is greater than 0, there are two distinct solutions

In the problem a = 1, b = 6, c = 10.

Plugging in what we have gives us 6^2*4(1)(10) = -4.

-4<0 so there are no real solutions.

14 is the value of  y-intercept .

What in mathematics is a y-intercept?

The standard form of line intercept

               y = mx + c

 5x - 2y = -28

  - 2y = - 5x -28

    y = 5/2x + 14

lets compare with equation

 m = 5/2

 c = 14

Thus, the y-intercept is y= 14

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The complete question is -

What is the y-intercept of  5x - 2y = -28?

The equation of line is y = -3x - 9

To solve this problem we will use slope intercept form in straight lines.

The slope-intercept form is one of the ways to represent a straight line.

To form the slope-intercept form of a line we need the slope of the line and it,s y intercept.

y = Mx + c

Where,

M = Slope of the line

c = y-intercept of the line

(x,y) are the points that satisfy the line or we can say lie on a line.

now, moving to the problem  we have,

M = -3

x = -2

y = -3

Equation of line is y = -3x + c

There is one unknown term here which is c.

So to find it we will put (-2,-3) in the line.

-3 = (-3)(-2) + c

c = -9

Hence the equation of a line is y = -3x -9

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The given number 1,000,000 can be written in words as

Ten Lakhs only.

Given, a number 1,000,000

we have to write the given number in words.

now to write any number in words, we have to know the place value of the digits of the given number

As, the place value of the digit 1 is tenth lakh and remaining digits in the number are all zeros.

So, the number 1,000,000 can be written in words as

Ten Lakhs only.

Hence, the given number 1,000,000 can be written in words as

Ten Lakhs only.

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Tonya's homework assignment has four problems a, b, c, d. Her teacher instructed her to simplify each expression and then find out its value. The value of a is 3/28, the value of b is 1/2, the value of c is 15/56 and the value of d is 1/15.

Each problem has two fractions. They are given below and should be simplified.

a) 2/7 × 3/8 = 1/7 × 3/4 = 3/28

b) 2/3 × 3/4 = 1/1 × 1/2 = 1/2

c) 3/7 × 5/8 = 15/56

d) 3/10 × 2/9 = 1/5 × 1/3 = 1/15

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The length of BC is 10cm, in the given triangle.

What is are of the triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

BR = 3 cm, let's say AR = 4 cm, and AC = 11 cm.

Since tangents to an exterior point are always equal, we can conclude that BR = BP = 3 cm.

4 cm if AQ = AR

QC=AC-AQ=11 – 4 = 7 cm

Q = P = 7 cm

It follows that BC = BP+PC = 3 + 7 = 10 cm.

BC, therefore, has a length of 10 cm.

Therefore, BC is 10 cm long.

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Using the Probability Scale,

a) Letter D shows event is impossible.

b) Letter C show likely event

c) Probability that the selected bead is red or purple is 3/4.

Probability is an estimate or calculation of the likelihood or likelihood that something will happen. For example, the likelihood of an event occurring can be "certain," "impossible," or "probable."

In mathematics, probability is usually written as a fraction or decimal number between 0 and 1.

Probability Scale :

Impossible events have a probability of 0 and specific events have a probability of 1. This means that the probability cannot exceed 1. This can be expressed on a probability scale.

Now , we conclude from above discussion,

a) The letter D shows that the event that is impossible.

b) The letter C shows that the event is likely.

c) we have, total number of beads in bag = 12

blue beads in bag = 2

red beads in bag = 1

purple beads in a bag = 3

red Julia beads in a bag = 6

one randomly bead is selected from a bag .

Probability that the selected bead is purple (p)

= 3/12 = 1/4

Probability that the selected bead is red (p') = 1/12

Probability that the selected bead is red or purple (P) = p + p' = 1/4 + 1/12 = 3/4

Hence, the required probability is 3/4 and letter D , for probability of event is zero .

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Complete question:

Here is a probability scale It shows the probability of each of the events A, B, C and D.

a) Write down the letter of the event that is impossib/e.

b) Write down the letter of the event that is like/y.

A bag contains 12 beads

The rest of the beads are red Julia takes a bead from the bag at random

c) Show that the probability that this bead is purple or red is 3/4.

A scalene triangle exists with the side lengths 12,15 and 18 feet.

The three sides of the triangle are 12 feet , 15 feet and 18 feet.

Now we know from the properties of triangle that if the sum of the smaller sides is greater than the largest side , then it is a triangle.

Here we can see that the triangle is formed by the given sides.

Now, 12 +15 = 27 > 18 hence the triangle is possible.

Since all the sides are of different lengths the triangle is scalene.

Scalene refers to any triangle with three unequal sides. Because there are three different sides, there must also be three different sizes of angles. This triangle is one of the three varieties that can be distinguished by the traits of its sides.

A scalene triangle is a triangle with variable lengths for each of its three sides and three angles. The different measures have no impact on the total interior angle of the scalene triangle.

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The rhomboid EFGH is the consequence of four rigid transformations: reflecting across the x-axis, translating 4 units to the left, translating 2 units down and dilating with a scale factor of 0.5 and center at (0, 0). (Right choice: A)

In this problem we must determine the sequence of rigid transformations used to transform rhomboid ABCD into rhomboid EFGH. Rigid transformations are transformations that are applied on geometric loci such that its Euclidean distance is conserved. The most common rigid transformations are listed below:

After a quick inspection on the figure, we find a sequence formed by four rigid transformations:

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Simplifying 2(3x+4)-3(x-2) will give us 3x+14

Simplification simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

from the question,

Expanding the expression  2(3x+4)-3(x-2), will give us

=6x+8-3x+6

collecting like terms

=6x+2

Hence, 6x+2 is the result of simplifying and expanding  2(3x+4)-3(x-2)

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The Test of convergence of series, helps us to check the given series are absolutely convergent

divergent, conditionally convergent.

Using the convergence test we get,

a) The lim. 72 = 5 is divergent. The correct option is option( C).

b) lim 0:2 = 0.5 is absolutely convergent. The correct option is option ( A).

Firstly , we discuss how to check absolutely convergent , divergent or conditionally convergent.

Steps to Determine :

Step 1: Take the absolute value of the series. Then determine whether the series converges.

If it converges, then we say the series converges absolutely.

If it does not converge, then we say it does not converge absolutely and we follow to Step 2

Step 2: Use the Alternating Series Test to determine whether the original series converges or diverges.

If it converges, then we say the series converges conditionally.

If the Alternating Series Test fails, we attempt another test.

Absolute Convergence Test :

If ∑∞ |an| converges, then ∑∞ aₙ converges

n = 1 n =1

We say that ∑∞ aₙ converges absolutely

n=1

if this case is true. If a series does not converge absolutely but converges by another test, we say that the series converges conditionally.

The Alternating Series Test: An alternating series, ∑∞( −1)⁽ⁿ⁻¹⁾aₙ , converges if the following 3

n=1

conditions are satisfied:

n→∞

Geometric Series Test: a series of the form

∑∞ ar⁽ⁿ⁻¹⁾ , the series converges if |r|< 1 and

n=1

diverges if |r | ≥1 nᵗʰ Term Test/Divergence Test

∑∞ aₙ , diverges if lim aₙ

n=1 n→ ∞

does not exist or does not equal zero.

p-series Test : The series ∑∞ (1/nₚ) converges if

n=1

p>1 and diverges if p ≤1.

we have given that

a) ∑∞ |aₙ₊₁/aₙ| = 5 >1

n = 1

Ratio Test: If 0 < aₙ and limn→∞(aₙ₊₁/aₙ) < 1, then an converges.If the limit is greater than 1, then

the series diverges. And if the limit is equal to 1, then the test gives no information.

so, it is divergent

b) ∑∞ |aₙ₊₁ /aₙ| = 0.5 <1

n = 1

: If 0 < an and limn→∞(aₙ₊₁/aₙ) < 1, then series converges. So, it is absolutely convergent .

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For the given condition bad check submission and check verification system from a random sample of checks , the probability value is

0.0618 > 0.01 which proves that it does not provide sufficient evidence of the effective check verification system.

As given in the question,

Given 5% of all the submitted checks were bad.

Null hypothesis H₀ : p = 0.05

For effective check verification system

Hₐ : p < 0.05

Statistic test :

z = ( x - μ ) / (σ /√n)

Here , x = 45 / 1124

             = 0.04

Data collected from the random sample are:

μ = 0.05

σ = √ 0.05 × 0.95

n = 1124

Substitute all the values in the formula we get,

z = ( 0.04 - 0.05 ) / ( √ 0.05 × 0.95 / √1124 )

  = - 0.01 / 0.0065

  = - 1.54

Probability for z = - 1.54 is equal to 0.0618 ( from table )

Now 0.0618 > 0.01

Sufficient evidence does not exist for the check verification system.

Therefore,  the probability value is 0.0618 > 0.01  which proves that it does not provide sufficient evidence of the effective check verification system from a random sample of checks.

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Volume of beach ball or the amount of air will the beach ball hold is 2304π in³.

Formula

Volume of Sphere is 4/3πr³

The volume, V, of a sphere with radius r is  4/3πr³

By employing a technique that roughly represents the surface area of a sphere using square pyramids, it is possible to obtain the formula for the volume of a sphere using the formula for its surface area, which is 4πr^2.

Where r is the radius of the sphere .

As given

12 inches is the radius of a beach ball.

r = 12 in

Substitute the r in above volume equation,

V =4/3πr³

V=4/3π(12)³

V= 2304π in³

Therefore, the amount of air will the beach ball hold is 2304π in³.

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By applying the CI algorithm we can determine the machine cells (20%) as the machine M₁ is on 2nd , M₂ is on 5th, M₃ is on 3rd, M₄ is on 4th and M₅ is on 1st rank.  

First of all we have to assign the binary weight and to calculate decimal equivalent as follows:

Machines   1    2    3    4    5    6    7    8   Decimal Equivalent    Rank

                  2⁷  2⁶  2⁵  2⁴   2³   2²  2¹  2⁰

M₁               1    1           1     1                 1               217                        2    

M₂                    1     1     1            1                          116                        5  

M₃               1          1           1     1    1     1                175                       3    

M₄               1    1           1     1                 1                117                       4      

M₅               1    1     1           1    1     1     1               239                       1    

According to the rank wise we will rearrange the rows and we follow the same procedure as above for columns. In the above table we can observe that the rank is gets ordered. So that we can stopped the interaction.

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NOTE: The given question is incomplete on the portal. Here is the complete question.

QUESTION: The following matrix represents a manufacturing system with five machines and eight parts. Determine two machine cells with a suitable algorithm.

                                         Parts  

                       [tex]\begin{matrix} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \end{matrix} \\ \left[\begin{array}{ccccccccccc} 1 && & 1 & \,\,\,\, 1 \\ & 1 & & & & & 1\\ 1& & 1 && 1 \\ &1 && 1 & 1 & &1 \\ & & 1 & & &&1 \,\,\,\,\,\,\,\,\,\,\, \end{array}\right][/tex]

Apply the CI algorithm to determine the machine cells (20%).

190 cm² is the area of the trapezium tile

The area (A) of a trapezium  can be determined using the formula:

A = 1/2( a+b)h

Where

a and b  are the bases of trapezium, and,

h is the height (the perpendicular distance between a and b)

Given: a = 12 cm, b = 26 cm and h = 10 cm

A =  1/2 (a+b) h

A = 1/2(12+ 26)10

A = 1/2(38)10

A = 5 × 38 = 190 cm²

Therefore, the area of the tile is 190 cm²

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The joint probability mass function  of x,y is 0.1458  if x is number of tails in three flips of coins and y is the outcome of six-faced die.

We know very well that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.

Here, coin is tossed three times means that 2³=8 different possible outcomes possible.

The total combination of tail appearing in 3 times flipping are {TTT,TTH,THT,HTT,HTH,HHT,THH}

So, total 7 combinations are possible for a tail appearing on flipping coin three times.

So, probability of tail appearing in three flips=7/8

Therefore, value of x=7/8

Now, we know that a dice has six faces and for each face there is equal probability to come at the top face and that probability value is 1/6

So, joint probability of mass function of x,y = (probability of tail appearing in three flips × probability of outcomes of a six-sided dice)

=>P(x,y)=(7/8)×(1/6)

=>P(x,y) = 7/48

=>P(x,y)=0.1458

Hence, value of joint probability is 0.1458.

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"Past substance abuse pg. 1006" is the trait that has not been linked to non-compliance with antiretroviral treatment.

Human immunodeficiency virus (HIV) patients who are receiving antiretroviral therapy (ART) are being treated with anti-HIV medications.

Thus, "Past substance abuse pg. 1006" is the trait that has not been linked to non-compliance with antiretroviral treatment.

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Applying Pythagoras theorem, Δ ACB is defined giving the length of the third side BC is solved to be 10.9 m

Information given from the question is interpreted as

AB = opposite

AC = adjacent

BC = hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 9.4² + 5.5²

x² = 88.36 + 30.25

x² =  118.61

x = √118.61

x = 10.89082

x = 10.9 (to 3 SF)

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The integral as an equivalent integral are as follows.

a) ∫_{-6}^{6} ∫_{0}^{36} ∫_{x²}^{36} (-y) dy dz dx

b)  ∫_{0}^{36} ∫_{-6}^{6} ∫_{x²}^{36} (-y) dy dx dz

c)  ∫_{0}^{36} ∫_{x²}^{36} ∫_{-6}^{6} (-y) dx dy dz

e) ∫_{x²}^{36} ∫_{-6}^{6} ∫_{0}^{36} (-y) dz dx dy

What is an integral ?

Mathematicians define an integral as either a number equal to the area under the graph of a function for a certain interval or as a new function whose derivative is the original function (indefinite integral).

We write the equivalent integrals for given integral,

we get:

a) ∫_{-6}^{6} ∫_{0}^{36} ∫_{x²}^{36} (-y) dy dz dx

b)  ∫_{0}^{36} ∫_{-6}^{6} ∫_{x²}^{36} (-y) dy dx dz

c)  ∫_{0}^{36} ∫_{x²}^{36} ∫_{-6}^{6} (-y) dx dy dz

e) ∫_{x²}^{36} ∫_{-6}^{6} ∫_{0}^{36} (-y) dz dx dy

We changed places of integration, and changed boundaries for certain integrals.

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question:

Here is the region of integration of the integral Integral from negative 6 to 6 Integral from x squared to 36 Integral from 0 to 36 minus y dz dy dx. Rewrite the integral as an equivalent integral in the following orders. a. dy dz dx by. dy dx dz c. dx dy dz d. dx dz dy e. dz dx dy

For a single alveolus requires the surface area of 0.133 square meters for gas exchange.

In this question, we have been given each human lung contains about 300 million alveoli with a summed total surface area for gas exchange of 40 square meters.

we need to find  the approximate surface area of a single alveolus.

By unitary method the required surface area would be,

A = 40/300

A = 10/75

A = 0.133 square meters

Therefore, the approximate surface area of a single alveolus = 0.133 square meters

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