What is the equation of the straight line which passes through the point 1 2?

The Equation for parallel line is: y= 4x - 13

The Equation for perpendicular line is: y= 1/4 x + 2

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

The passing point is (4, 3).

Now, the slope of given line

= Rise / Run

= 4 / 1

= 4

So, the slope for parallel line is 4 and for perpendicular line is -1/4.

Now, the line passes through (4, 3)

For parallel line

y= 4x+ b

3 = 4(4)+ b

3- 16 = b

b= -13

So, Equation for parallel line is: y= 4x - 13

For Perpendicular line

y= 1/4 x+ b

3 = 1/4(4)+ b

3- 1 = b

b= 2

So, Equation for Perpendicular line is: y= 1/4 x + 2

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Answer:

Yes, 11/81 is an irrational number.

Step-by-step explanation:

Because it is a fraction with a non-terminating, non-repeating decimal expansion.

The standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

Given, the chance that a certain type of thumbtack lands point up when you toss it in the air is 80%.

we have to find the standard deviation of the proportion of the given data that it lands point up out of 100 tosses.

Number of trials be, 100

probability of success be, 80/100 = 0.8

On using the formula of Standard deviation, we get

standard deviation = n×p×(1 - p)

standard deviation = 100×0.8×(1 - 0.8)

standard deviation = 100×0.8×0.2

standard deviation = 16

So, the standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

Hence, the standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

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The 350 percent is less than the cube root of 50.

Here given two numbers,

∛50 and 350%

To compare the numbers we have to make to to simplest fraction,

∛50

The radical form of the cube root of 50 is ∛50, and the exponent form is (50)⅓ . The prime factorization of 50 is 2 x 5 x 5,

so the cube root of 50 in its simplest radical form is ∛50 .

50 cube root : 3.684031499

350%

The number 350% can be expressed as ,

350 / 100

350/100 = 3.5

So by comparing 3.684031499 and 3.5, 3.684031499 is larger

So ∛50 is larger than 350%

Therefore 350% is < ∛50.

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Answer:

350 percent is less than the cube root of 50

Step-by-step explanation:

A strong negative linear association between two variables is scatter plot 4.

What is standard normal random?
We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.

Very dispersed and lacking in association is scatter plot 1.

Positive correlation may be seen in scatter plots 2 and 3.

Scatter figure #4 clearly illustrates a strong inverse relationship between the variables.

Hence the Correct answer is scatter plot 4.

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The point that the line also pass would be; C. (8,4)

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Given that line has a slope of - 1/4 and passes through the point (4,2).

Now Write the equation as;

y - 2 = -1/4(x - 4)

y = -1/4x + 6

Hence, The answer is; C. (8,4)

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The linear function in this problem is defined as follows:

y = -328.275x + 3142.5.

The number of CD's sold by year decreases by about 328 million per year. About 3143 million of CD's were sold in 2010.

The estimate for the year of 2019 is of: 188 million CD's.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients of the function are defined as follows:

Two points of the linear function in this problem are given as follows:

(2, 2485.6), (6, 1172.5)

The slope is given by the change in y divided by the change in x, hence:

m = (1172.5 - 2485.6)/4 = -328.275.

Then:

y = -328.275x + b.

When x = 2, y = 2485.6, hence the intercept b is obtained as follows:

2485.6 = -328.275(2) + b.

b = 2485.6 + 328.275(2)

b = 3142.5.

Hence the function is:

y = -328.275x + 3142.5.

2019 is nine years after 2010, hence the estimate is obtained as follows:

y = -328.275(9) + 3142.5 = 188 million CD's.

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The Volume of the Cylindrical Silo is 88000 cubic feet

What is Volume?

Volume is a measurement of three-dimensional space that is occupied. It is frequently mathematically quantified using SI-derived units or different imperial or US customary units. The concept of length is linked to the definition of volume.

Solution:

Given:

Height of the Container = 70 feet

Circumference of the Base = 125.7 feet

To Find: Volume of the Container

Volume = πr²h

Circumference = 2πr

125.7 = 2 * 3.14 * r

r = 20.01

Volume = 3.14 * 20.01 * 20.01 * 70

Volume = 88007.94 cubic feet

Volume = 88000 cubic feet (approx)

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Mrs. Gilmore and Brianna are 17 feet apart.

Pythagoras theorem is one of the mathematical principles that can be applied to determine the value of the unknown side of a right angled triangle. Where a right angled triangle is one with one of its angles to equal [tex]90^{o}[/tex].

In the given question, sketching the distance apart of each person, it would form a right angled triangle.

Let the distance in feet between Mrs. Gilmore and Brianna be represented by d.

Then;

[tex]/Hyp/^{2}[/tex] = [tex]Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]d^{2}[/tex] = [tex]15^{2}[/tex] + [tex]8^{2}[/tex]

   = 225 + 64

   = 289

d = 17

Therefore, Mrs. Gilmore and Brianna are 17 feet apart.

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As per the daily mean, the peak power load when max is possible to calculate with a computer or calculator.

The highest outdoor temperature and the mean daily peak power load for a sample of 6 days are provided in the table. However, it is impossible to estimate the peak power load when the highest temperature is 84 without more details. The presented data only reflects a sample of 6 days, which may not be typical of the full population, and the connection between peak power load and maximum temperature may not be linear. Furthermore, using the provided data to conduct any calculations is impossible without access to a computer or calculator.

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The range of the given piecewise function is [-1, 27].

A function with many parts of curves in its graph is said to be a piecewise function. It is a function with various definitions at various intervals of x.

The given function is a piecewise function,

[tex]f(x)=\begin{cases}{{x^2+2\;&\text{if}\;-5\le x < 3 \\{x-4\;&\text{if}\;3\le x < 7}}\end{cases}[/tex]

From the given function,

The set of values for all the output values can be referred to as a function's range. To find a range,

Then, the range can be written as [-1, 27]. Therefore, the first option is correct.

The complete question is -

Find the range of the following piecewise function.

[tex]f(x)=\begin{cases}{{x^2+2\;&\text{if}\;-5\le x < 3 \\{x-4\;&\text{if}\;3\le x < 7}}\end{cases}[/tex]

a)  [-1,27] b) [18,-2] c) [1,27] d) [-4,0].

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The area of the shaded sector is 9π unts²

The term "turn" also refers to a 360° rotation. Angles between 0° and 360° are calculated. We require a circle's circumference, which is equal to 2 r r, where r is the circle's radius.

In any circle of radius r, the ratio of the arc length ℓ to the circumference equals the ratio of the angle θ subtended by the arc at the center and the angle in one revolution. Thus, measuring the angles in radians, ℓ2πr=θ2π⟹ ℓ=rθ.

Find the diagram attached

Given the following

Radius = 6

Theta = pi/2 = 90°

Area of the sector = theta/360×πr²

Area if the sector = 90/360 × π(6)²

Area of the Sector = 1/4 × 36π

Area of the sector = 9π unts²

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The solution for the given inequality is 1 < m ≤ 4. The graph for the obtained solution set is shown below.

Two expressions are related by comparative operations like 'less than or 'greater than or 'less than or equal or 'greater than or equal. Then that equation is said to be an "inequality equation".

For example, a < k ≥ b, etc.

The given inequality equation is

-2 < 3m - 5 ≤ 7

On adding 5 to the inequality, we get

-2 + 5 < 3m - 5 + 5 ≤ 7 + 5

⇒ 3 < 3m ≤ 12

On dividing by 3, we get

⇒ 3/3 < 3m/3 ≤ 12/3

⇒ 1 < m ≤ 4

Therefore, the solution set for the given inequality is (1, 4].

The obtained solution set is shown on the number line here.

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The price paid by Jason for the gallons of gas he used for the trip is $2.15per gallon of gas.

As given in the question,

Reading of odometer in the starting of trip = 42,876.1

Reading of odometer in the end of trip = 43,156.1

Total distance covered by Jason on his trip = 43,156.1 - 42,876.1

                                                                         = 280 miles

Average miles per gallon of Jason's car = 35 miles per gallon

Gallons of gas used by Jason on his trip = 280 / 35

                                                                   = 8 gallons

Amount of money used to fill gas = $17.20

Price of the gas per gallon = 17.20 / 8

                                            = $2.15 per gallon of gas.

Therefore, the price paid by Jason for the per gallon of gas is equal to $2.15 per gallon of gas.

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Sampling bias, also known as sample selection bias, refers to flaws in research studies that arise when researchers do not appropriately select their subjects.

When a sample is collected in such a way that some members of the intended population have a significantly lower or higher sampling risk than others, sampling bias is reduced.

It yields a skewed sample of a population (or non-human variables) in which not all individuals, but rather cases, were picked in the same way. If this is not considered, the outcomes may be incorrectly attributed to the study problem rather than the sample method.

Sampling bias is often classified as a subset of selection bias, also known as sample selection bias, but some believe it to be a separate type of bias.

The difference between sampling bias and selection bias, though not frequently recognized, is that sampling bias reduces a test's external validity, whereas selection bias only addresses the internal validity of differences or similarities detected in the sample at hand.

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With the help of time -distance formula we can calculate travel time in km for any given problem or situation.

We know the formula we relate to distance and  time that which  is called time -distance formula is :

t= d/s, where d is the distance and s is the speed of the object.To calculate travel time in km, first, we need to divide the total distance in km by the average speed of travel in terms of km/hour, later multiplying the result by 60 to get the travel time in minutes.

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Answer:

Step-by-step explanation:

So hi this is saveon and this is how you do the question so first you divide 44.52 by 21 you will get 2.12 feet and that is your answer

It is 2.12 feet wide.

What is rectangle ?

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

An equiangular quadrilateral is another name for a rectangle. The reason for this is that a rectangle is a quadrilateral form (4-sided shape) with parallel sides that are equal to one another and four corners with 90o angles. A rectangle can also be referred to as an equiangular quadrilateral because all of the angles are 90 degrees.

Rectangle area = width * height

44.52 / 21

= 2.12 feet

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The degree of the product of the two polynomial is 6.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² − 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Given that there are two polynomial.

The sum of two polynomials has degree 4.

Thus the degree of a polynomial is 4.

The degree of the another polynomial is less than or equal to 4.

Also the difference of their degree is 2.

Thus the degree of the another polynomial is (4 - 2) =2.

The degree of the polynomials whose degree are a and b is a+b.

The degree of the product of the given polynomial is (4 + 2) = 6.

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The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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The factors of the polynomial  t¹² – r³s¹⁵ is (t⁴ + rs⁵)(t⁸ - rs⁵t⁴+ r²s¹⁰). The correct answer is B.

The definition of a factor is a number that completely divides another number. If adding two whole numbers results in an item, the numbers we are adding are variables of the item since the item can be used to separate them.

By using formula

(a³ - b³) = ( a+ b)( a² -ab + b²)

Then,

t¹² – r³s¹⁵ = (r⁴)³ - (rs⁵)³

=(r⁴ + rs⁵)((t⁴)² - rs⁵t⁴ + (r⁵)²)

=(r⁴ + rs⁵)(t⁸ - (rs⁵t⁴) + r²s¹⁰)

Thus, required answer is (r⁴ + rs⁵)(t⁸ - (rs⁵t⁴) + r²s¹⁰), So option (B) is correct.

Your question is incomplete but most probably your full question was

Factor t¹² – r³s¹⁵ is

a.(t⁸ – rs⁵t⁴ – r²s¹⁰)

b. (t⁴ – rs⁵)(t⁸- rs⁵t⁴+ r²s¹⁰)

c. (t⁹ – rs¹²)(t¹⁸+rs¹²t⁹ +r²s²⁴) (t⁴ rs⁵)

d. (t⁸ – rs⁵t⁴)( r²s¹⁰)

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The value of the correlation coefficient between exam 1 score and exam 2 score is -1.

Given:

suppose that every student in this class earns exactly twice as many points on exam 2 as on the exam 1.

what would be the value of the correlation coefficient between exam 1 score and exam 2 score = ?

1. the coefficient will be exactly one since it measures linear dependence and these are perfectly linear dependent.

2. the coefficient will be exactly one since it measures linear dependence and these are perfectly linear dependent.

3. the coefficient will be exactly one, it doesn't matter which score is higher.

4. the expected value will be 0 since there won't be any correlation between random values.

5. the coefficient will be -1 every high score is matched by a low score on the other test.

Hence we get the required answer.

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If the heights of five dogs are 400 mm, 370 mm, 470 mm, 330 mm and 500 mm. Then the standard deviation of the heights of the dogs is:

c) 70 mm

Given:

five friends were comparing the height of their dogs.

the heights at the shoulders were 400mm, 370mm, 470mm, 330mm and 500mm.

we are asked to find out the standard deviation of the heights of these dogs = ?

First find mean :

(400+ 370+470 + 330 + 500)/5

Mean = 2070/5

Mean = 414

standard deviation = √∑(xi - mean)²/N-1

= √(400-414)²+(370-414)²+(470-414)²+(330-414)²+(500-414)²/4

= √(14)²+(-44)²+(56)²+(-84)²+(86)²/4

= √196+1936+3136+7056+7396/4

= √19720/4

= √4930

= 70.21

rounding it to the nearest integer.

= 70 mm

Hence we get the required standard deviation as 70 mm.

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Solution of the inequality representing charges of company A is less than the company B for the mileage of 75miles or more.

As given in the question,

Let 'x' miles be the number of miles driven by company A.

For the given conditions:

Equation of company A is:

110 + 0m

Equation of company B is

65 + 0.60x

Inequality between company A and company B is:

110 + 0m < 65 + 0.60x

⇒0.60x > 110 - 65

⇒x > 45 / 0.60

⇒ x > 75 miles or more

Therefore, from the inequality 75 miles or more company A charges less than the company B.

The complete question is:

Laura is going to rent a truck for one day. there are two companies she can choose from, and they have the following prices. company A charges $110 and allows unlimited mileage. company B has an initial fee of $65 and charges an additional $0.60 for every mile driven. For what mileages will company A charge less than company B? use for the number of miles driven, and solve your inequality for .

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Answer:

20:3 ratio

Step-by-step explanation:

Answer:20 horses to 3 cows or 20:3

Step-by-step explanation:

The answer would be 20:3. If you notice that Both 40 and 6 can be divided by 2 so you would divide 40 by 2 and get 20 as your answer. And for the next you would divide 6 by 2 getting 3. So your ratio would be 20 horses to 3 cows or 20:3. I hope you were able to understand and I hope this helps you! I'm so sorry I didn't see your question earlier!

Answer:

Step-by-step explanation:

To put in slope intercept form, isolate y.

4y = -2x +4

Further divide by 4 to isolate y.  What you do on one side of an equation, you also do on the other side.

4y/4 = -2x/4 +4/4

y = -1/2x +1

Answer:

The cost for the video game system is $96.90.

Step-by-step explanation:

Answer:

it is equal to 8.07

Step-by-step explanation: