The problem is saying there are two distinct zeros, and both are strictly lie between 0 and 1. The least positive integer value of "a" is 5 for which such a polynomial exists.
Let f(x) = ax² - bx + c , be our polynomial.
where a,b are integers coefficient and c constant. It has two distinct real roots lying between 0 and 1. f(x) can be written as, f(x) = a(x−α)(x−β)
where α and β are the roots of the equation.
we can be observed that f(0)f(1) > 0
As a,b and c are integers f(0)f(1) > 1
f(0) = aαβ , f(1)=a(1−α)(1−β)
=> a²(α)(1−α)(β)(1−β) > 0 -------(1)
Using A.M ≥ G.M, we get
(α+1−α+β+1−β)/4 > (αβ(1−α)(1−β))¹/⁴
Arithmetic Mean and Geometric Mean cannot be equal because the equation has distinct roots.
a²/16 > a²(αβ(1−α)(1−β)).
=> a²/16 > 1
=> a > 4
Therefore, the minimum value of 'a' is 5
The discriminant of the equation,
Δ = b²−4ac ≥ 0
=> b² >20c
consider the minimum value of c = 1,
we get b² >20
=> Minimum Value of b = 5.
Hence, the least positive integer of 'a' is 5.
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Given vectors u = (-8,-5) and
v = (-1, -2), find the sum u + v and write
the result in component form.
Answer:
u + v = < - 9, - 7 >
Step-by-step explanation:
to sum u and v add the corresponding x and y components of the 2 vectors
u + v
= < - 8, - 5 > + < - 1, - 2 >
= < - 8 - 1, - 5 - 2 >
= < - 9, - 7 >
Find the point, M, that is midway between P=(5,−8,−6) and Q=(-7,-2,-8).
The point, M, that is midway between P=(5,−8,−6) and Q=(-7,-2,-8) is
M = (-1, -5, -7)How to find the midwayIn geometry, the midpoint formula is an equation that determines the separation between two known coordinate locations at their halfway point.
The midway between the points P and Q is calculated using the method
Mid point = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)
Applying the method to the given points gives
P = (5, −8, −6) and Q = (-7, -2, -8)
M = ((5 + -7)/2, (-8 + -2)/2, (-6 + -8)/2)
M = (-1, -5, -7)
The coordinates of point M (-1, -5, -7) is the mid way between point P=(5,−8,−6) and Q=(-7,-2,-8).
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the velocity function (in meters per second) for a particle moving along a line is grven by u(t) : 2t-4, for 0 ( t < 6 (in seconds). what is the total distance traveied by the particle during this interval of tim
Hence, the total distance traveled by the particle is 16 meters
The velocity function for a particle moving along a line is given by u(t): 2t-4, for 0 < t < 6 (in seconds)
[tex]Distance(D) = \int\limits^a_b {u(t)} \, dt[/tex]
[tex]Distance(D) = \int\limits^6_0 {(2t-4)} \, dt[/tex]
In this time period velocity will be zero
So, u(t) = 0
2t-4=0
at t=2 seconds, velocity will be zero.
So,
[tex]Distance(D) = |\int\limits^2_0 {(2t-4)} \, dt| +| \int\limits^6_2 {(2t-4)} \, dt|[/tex]
[tex]Distance (D) = |[t^2-4t]\right\{{{2}\atop{0}}\right.|+|[t^2-4t]\right\{{{6}\atop{4}}\right.|[/tex]
[tex]Distance (D) = |[2^{2}-8-0+0]| + |[6^{2} -24-4^{2} +16]|[/tex]
[tex]Distance (D) = |4-8|+|36-24-16+16|[/tex]
[tex]Distance (D) = 4+12[/tex]
[tex]Distance (D) = 16 meters[/tex]
Hence, the total distance traveled by the particle is 16 meters
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What is specialized language?.
Specialized language is language that is distinctive and pertinent to a particular industry.
Define the term specialized language?Language that is relevant to and distinctive of an industry is referred to as specialised language.
A language that uses specialised terms and particular terminologies to distinguish itself from general language is referred to as specialised language.When used correctly for the audience, specialised terms can make literature easier to grasp.Any in-group or specialised language for use by small groups of people with similar interests is referred to as "jargon."According to Durham University researchers, the ability to express oneself uniquely through language necessitates the creation and flexible use of signals by people.They contend that it could only have occurred with the emergence of specific psychological skills, explaining why language is only found in humans.
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How do you find the roots and multiplicity of a polynomial?.
To find the roots and multiplicity of a polynomial, we first need to find its factors.
To do this, we use the factoring method of our choice (such as the quadratic formula, factoring by grouping, etc.), and then we determine how many times each factor occurs. The roots of the polynomial are the factors that have a multiplicity of 1, and the multiplicity of a root is the number of times that it occurs as a factor.
A polynomial is an equation that can be written in the form:
ax² + bx + c = 0
where a, b, and c are real numbers and x is a variable. The roots of a polynomial are the values of x that make the equation true. The multiplicity of a root is the number of times that the root appears as a solution to the equation.
To find the roots of a polynomial, you can use the Quadratic Formula:
x = (-b +/- sqrt(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the equation. The +/- sign indicates that there are two roots, one with a positive sign and one with a negative sign.
The multiplicity of a root can be found by counting how many times the root appears as a solution to the equation. For example, if the root x = 2 appears twice as a solution, then the multiplicity of the root is 2.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Applying the equation of the model, y = 123.1(1.069)^x:
a. 150.4 thousand students
b. 467.5 thousand students
How to Use an Equation for a Given Model?In the above problem given, we are told that the equation that models the the number of college students who studied abroad each year is: y = 123.1(1.069)^x, where:
The number of students from a country in thousands is represented as y
The number of years after 1998 is represented as x in the equation.
We can apply the equation for this model to solve the given problem as explained below:
a. 1998 to 2001 is 3 years. x = 3. Therefore, substitute x = 3 into y = 123.1(1.069)^x:
y = 123.1(1.069)^3
y = 150.4
Therefore, the number of students that are studying abroad in 2001 is about: 150.4 thousand.
b. 1998 to 2018 is 20 years. x = 20, therefore, substitute x = 20 into y = 123.1(1.069)^x:
y = 123.1(1.069)^20
y = 467.5
Number of students studying abroad in 2018 (y) is therefore about 467.5 thousand.
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When 1,250 superscript three-fourths is written in its simplest radical form, which value remains under the radical?10652.
The value under the radical is 8
what is power?How many times you should multiply a number depends on its power. Exponents and indices are other names for powers. For instance, 82 may also be referred to as "8 to the power 2," "8 to the second power," or just "8 squared."
What is exponent and power?Exponents and powers can be used to represent extremely large or extremely small numbers in a more straightforward way. To illustrate 3 x 3 x 3 x 3 in a straightforward manner, for instance, we could write it as 34, where 4 is the exponent and 3 is the base. It is said that the entire statement 34 has power.
Due to it,
1250^(3/4)
Having said that,
Since n is an integer number,
Greater than x is n.
actual number a
Therefore,
1250^(3/4)=5^(3) *((4)root(2)^3
1250^(3/4)=125 *((4)root(2)^3
Therefore, the value that is still below the radical is 8.
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For what values of r will the area of the shaded region be greater than or equal to 12 square units?
The values of r for which the shaded region will be greater than or equal to 12 square units is r ≥ 8
Given that,
We have to find the darkened region's area will be more than or equal to 12 square units for what values of r.
We can see a rectangle and a triangle in the given image.
The triangle is the part of the rectangle that is not coloured.
Thus;
Area of rectangle minus area of rectangle gives the area of the shaded area.
We know that formula for area of rectangle is;
Ar = length × width
Thus; Ar = 3 × r
Ar = 3r
Area of a triangle is;
At = ½ × base × height
At = ½ × r × 3
At = ½(3r)
Thus;
Area of shaded region = 3r - 1/2(3r)
Area of unshaded portion = 1.5r
We are informed that the unshaded area must have a minimum area of 12 and a maximum area of 12. Thus;
1.5r ≥ 12
r ≥ 12/1.5
r ≥ 8
Therefore, The values of r for which the shaded region will be greater than or equal to 12 square units is r ≥ 8
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What are the 5 examples of linear equation?.
The required five equation of linear equation are given below.
What is linear equation?A linear equation is a mathematical condition of the structure y=mx+b. including just a steady and a first-request (straight) term, where m is the incline and b is the y-catch. At times, the above is known as a "direct condition of two factors," where y and x are the factors.
According to question:Five examples of linear equation,
1) 2x – 3 = 0
2) 2y = 8
3) m + 1 = 0
4) x/2 = 3
5) x + y = 2
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when prove that all positive integers less than 4 are prime numbers by showing that 1, 2 and 3 are prime numbers, which of the following kinds of proof are we using?
Proof by contradiction
Trivial proof
Proof by induction
Exhaustive proof
To prove that all positive integers less than 4 are prime numbers, we will use the method of exhaustive proof.
Proof by contradiction is a method that establishes the the validity of a proposition, by assuming the proposition to be false leads to a contradiction.
Trivial Proof implies that if q is true then p → q is true regardless of the
truth value of p.
Proof by Induction is a method for proving that a statement P(n) is true for every natural number n
Finally, Proof by exhaustion, also known as proof by cases, is a method of proof in which the statement to be proved is split into a finite number of cases, and each type is then checked to see if the proposition in question holds.
Here, as we can see, by definition, exhaustive proof will be most appropriate as we can easily split the statement into 3 cases, taking the integers 1, 2 and 3 in each.
Thus, we will use Exhaustive Proof.
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A veterinarian uses weights in kilograms to figure out what dosages of medicines to prescribe for animals. For every 10 kilograms, there are 22 pounds. Calculate this animal’s weight in kilograms and explain your reasoning.
Fido the Labrador weighs 88 pounds.
The required weight of fido the labrador is 40 kilogram.
What is relation between kilogram and pound?
kilogram is the fundamental unit used to measure weight ans pound is used in UK to measure weight of any object.
As we have given in 10 kilogram, there are 22 pounds. So, one kilogram is equal to 2.2 pound.
According to given data in the question:We have to find the weight of fido the labrador in kilogram
here,weight in pound is 88
we know that one pound contain 1/2.2 kilogram
So, weight of 88 pound in kilogram = (88)1/2.2
weight in kilogram = 40 kilograms.
Hence, the required answer is 40 kilogram.
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What is the 3 phases of agile life cycle?.
The 3 phases of the agile life cycle:
The Continuous Delivery: Lean Life Cycle.
The Exploratory (Lean Startup) Life Cycle.
The Program Life Cycle for a Team of Teams.
What is the Agile cycle?
The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.
The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.
The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.
Hence,
The 3 phases of the agile life cycle:
The Continuous Delivery: Lean Life Cycle.
The Exploratory (Lean Startup) Life Cycle.
The Program Life Cycle for a Team of Teams.
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Stan and Talia each went to see a movie. Both movies started at 7:15.
Stan's movie ended at 9:40.
Talia's movie ended at 10:10.
Part A
Use the drop-down menus to complete the sentence about the length of Stan's movie.
Stan's movie lasted
Choose...
hours and
Choose...
minutes.
Part B
Use the drop-down menus to complete the sentence that compares the length of the two movies.
Talia's movie lasted
Choose...
hours and
Choose...
minutes longer than Stan's movie.
The length of Stan's movie is 2 hours 25 minutes
The length of Talia's movie is 2 hours 55 minutes.
What are the length of the movies?In order to determine the length of the movies, subtract the end time of the movie from the time the movie started.
Subtraction is the mathematical operation that is used to calculate the difference between two or more numbers. The sign that is used to represent subtraction is -.
Length of the movie = time the movie ended - time the movie started
Length of Stan's movie = 9:40 - 7:15 = 2 : 25 hours
Length of the Talia's movie = 10 : 10 - 7 : 15 = 2 : 55 hours
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The registration fee for a used car is 0.8% of the sale price of $5,100. How much is the fee?
If ADEF=AJAM, which statement will always be true?
The first statement is always true.
If m ∠m = 64° then m ∠F = 64°.
What is isomorphic triangles?
If there is an isomorphism connecting the vertices of P and Q, and that isomorphism has the property that three vertices of P form a triangle in Tp if and only if the mapping of the three vertices in Q, then the triangulations of two simple polygons, Tp and Tq, are said to be isomorphic (or occasionally compatible).
Given: ΔDEF ≅ ΔJAM
As the triangles are isomorphic that means that each angle of the triangle are same.
⇒ ∠D = ∠J
∠E = ∠A
∠F = ∠M
Hence, If m ∠m = 64° then m ∠F = 64° is true.
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I went into a store with a 70% off sign on the door. I found a pair of pants that were originally $49.99 for $30.00 I didn't think this was 70% off so I had to make sure. What were the real percentage off?
PLEASE HELP!!!!!!!!!
Answer:
The answer you are looking for would be 60% off.
Step-by-step explanation:
On a calculator, set up this equation:
0.60 x 49.99 = 29.994, rounded is $30.00
(Do this with all answer choices, just replace 0.60 with 0.70, 0.40 and so on).
But, 60% would be the answer.
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State your conclusion about Bill's exact binomial test in a complete sentence. That is, explain why you choose to reject the null or why you choose to fail to reject the null. Fail to reject the null hypothesis, because the p-value is not small (it's more than 10%). Fail to reject the null hypothesis, because the p-value is small (it's less than 2%). Reject the null hypothesis because the p-value is not small (it's more than 10%). Reject the null hypothesis because the p-value is small (it's less than 1%). Then confront Bill about his cheating, or play with someone else.
Reject the null hypothesis, because the P-value is small (it's less than 1%) then confront Bill about his cheating play with someone else.
Fail to reject the null hypotheses, because the P-value is not small (it's more them 10%).
One of the most generally utilized p-values is 0.05. If the determined p-values end up being under 0.05, the invalid speculation is viewed as bogus, or invalidated (subsequently the name invalid theory). What's more, on the off chance that the worth is more prominent than 0.05, the invalid speculation is viewed as obvious.
That p-value is the likelihood that we'll obtain similar outcomes as the invalid speculation, and in our model, the edge for that likelihood is 0.05. So if the determined p-value is under 0.05, it really intends that there's exceptionally less probability that we'll come by similar outcomes as the invalid speculation. Also, in the event that the p-value is more than 0.05, the likelihood of obtaining similar outcomes as invalid speculation is exceptionally high, so we can believe the invalid speculation to be valid.
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Penny works 43 hours at an hourly rate of $8.50. She was paid time
and a half for the overtime. What were her total wages?
Answer: $548.25
Step-by-step explanation: 43 x $8.50 = 365.5 x 1.5 = $548.25
Find -1 1/8 - 3/4.
First write the expression with a common denominator
-1 1/8 - 3/4 = -1 1/8 - ?/8
The value of the unknown is 6
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
the expression -1 1/8 - 3/4 = -1 1/8 - ?/8 shows that
-3/4=-?/8
the LCM of the denominator of two fractions is 8
multiply both sides by 8
-3/4×8=-?/8×8
therefore,. -? = -3×2
?= 6
Therefore the value if the unknown is 6
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The fraction is expressed with a common denominator as - 15/ 8
What is a fraction?A fraction is simply described as the part of a whole, element or number.
There are several types of fractions, which includes;
Simple fractionsComplex fractionsProper fractionsImproper fractionsMixed fractionsFrom the information given, we have the fractions;
-1 1/8 - 3/4.
Convert the mixed fraction to improper fraction
- 9/ 8 - 3/4
Find the Lowest common multiple
-9 - 6 /8
Subtract the numerators
-15/ 8
Hence, the value of the expression is -15/8
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What is the central angle called?.
The central angle states the property of the center of the circle, So It is called the central angle.
What is a Central Angle?
The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.
An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.
Hence,
The central angle states the property of the center of the circle, So It is called the central angle.
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7.3.3: basic class definition. define the missing method. licensenum is created as: (100000 * customid) licenseyear, where customid is a method parameter. sample output with inputs 2014 777:
Program in java ,
public int createLicenseNum(int customID){
licenseNum = (100000 * customID) + licenseYear;
return (licenseNum); }
createLicenseNum method takes customID as its parameter. The formula function :
licenseNum = (100000 * customID) + licenseYear;
100000 is multiplied to the customID and the result is added to the licenseYear and is assignedlicenseNum.
When the CreateLicenseNum function is invoked it computes and returns the value of licenseNum as:
licenseNum = (100000 * customID) + licenseYear;
= (100000 * 777) + 2014
= 77700000 + 2014
licenseNum = 77702014
Output is:
Dog license: 77702014
Function call JAVA:
public class CallDogLicense {
public static void main(String[] args) {
DogLicense dog1 = new DogLicense();
dog1.setYear(2014);
dog1.createLicenseNum(777);
System.out.println("Dog license: " + dog1.getLicenseNum()); //calls getLicenseNum to get the computed licenceNum value
return; } }
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What is the monthly finance charge if the average daily balance is $30, the daily periodic rate is 0.07%, and the number of days in the cycle is 30? a. 21¢ b. 63¢ c. 90¢
The monthly finance charge is 63 cents.
Here we have to find the monthly finance charge.
The given data:
Average daily balance = $30
The daily periodic rate = 0.07%
The number of days in a cycle is 30.
The formula to find the finance charge:
Finance charge = APR balance × number of days in billing cycle / 365
As it is given a daily periodic rate this means that:
APR / 365 = 0.07%
= 0.0007
Hence, putting the value in the formula we have:
Finance charge = 0.0007 × 30 × 30
= 0.63
As we know that $1 = 100 cents
So finance charge = 0.63 × 100
= 63 cents
Therefore the finance charge is 63 cents.
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Julie has a block of wood that has a height of 9 cm, a width 2 cm, and a length of 3 cm. What formula would Julie use to find the volume of this wooden block?
Answer:
V=HWL
54cm³
Step-by-step explanation:
V=HWL
∴V=9*2*3
V=54cm³
Enter the correct answer in the box. What is the standard form polynomial representing the volume of this shipping container? rectangular prism-shaped shipping container with length labeled 4 times x squared plus 3x, width labeled x squared minus 8, and height labeled 6x plus 15.
The standard form polynomial representing the volume of this shipping container is expressed as V = 24x⁵+78x⁴-147x³-624x²-360x
Volume of the shipping container = Lengt * Breadth * Height
Given
Length = 4x² + 3x
Breadth = x² – 8
Height = 6x +15
Volume of the container = ( 4x² + 3x)( x² - 8)(6x+15)
( 4x² + 3x)( x² - 8) = 4x⁴-32x²+3x³-24x
( 4x² + 3x)( x² - 8) = 4x⁴+3x³-32x²-24x
(4x⁴+3x³-32x²-24x)(6x+15) = 24x⁵+60x⁴+18x⁴+45x³-192x³-480x²-144x²-360x
Collect like terms
( 4x² + 3x)( x² - 8)(6x+15) = 24x⁵+78x⁴-147x³-624x²-360x
Hence the standard form polynomial representing the volume of this shipping container is expressed as V = 24x⁵+78x⁴-147x³-624x²-360x
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The table given shows the length, in feet, of dolphins at an aquarium.
3 15 30 19 11 18 17 12
Are there any outliers in the data?
There is an outlier at 3 feet.
There is an outlier at 30 feet.
There are outliers at 3 and 30 feet.
There are no outliers.
Answer:
......................................................d
There are two outliers in the given data and they are 3 and 30. Hence, option C is correct.
What is the arithmetic sequence?Two definitions are given for an arithmetic sequence. A "series where the variances in between every two succeeding terms are the same" is what it is. Each term in an algebraic expression is created by multiplying its previous term by a specified integer (either positive, negative, or zero).
As per the given information in the question,
The length of dolphins is given as:
3, 15, 30, 19, 11, 18, 17, 12
As we can see in this data every length is somewhere close to 20 but lengths 3 and 30 are not similar to others.
So, these two are outliers.
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Find the coordinates of point $p$ along the directed line segment $ab$ , from $a\left(-2,-4\right)$ to $b\left(6,\ 1\right)$ , so that the ratio of $ap$ to $pb$ is $3$ to $2$.
The coordinates of point $p$ along the directed line segment $ab$ is at the point (2.8, -1).
Step 1
To find the coordinates of P so that AP to PB is the given ratio, first look for the slope in rise over run form.
Then, determine the ratio by thinking of it as dividing into segments.
After, add the ratio (in fraction or in decimal) of the run to the x-coordinate and add the ratio (in fraction or in decimal) of the rise to the y-coordinate of the first point in the line segment.
Step 2
First, let us find the slope of the line through rise over run and do not simplify the slope:
[tex]m = \frac{rise}{run}\\ \\m = \frac{1-(-4)}{6-(-2)} \\\\= \frac{5}{8}[/tex]
Since the ratio is 3:2, we want to partition the entire segment into 5 parts with P located at 3\5 of the segment from point A. Therefore, we add 0.6 of the run to the x−coordinate and of the rise to the
y−coordinate:
rise=5⋅0.6=3 y=−4+3=−1
run=8⋅0.6=4.8 x=−2+4.8=2.8
Therefore, the point is at (2.8,−1).
Hence the answer is the coordinates of point $p$ along the directed line segment $ab$ is at the point (2.8, -1).
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Callan knows that the area of a square piece of artwork he owns is 289 square inches. Which shows the correct step he should take if he wants to find out the side lengths of the piece of artwork?.
Answer:
One side length is 17. Because you square root 289 to figure out the side length.
Step-by-step explanation:
The area of a square is a side length * a side length
or l^2 = 289
sqrt or 289 = 17
Can you use a right triangle to represent the distance between any two points on the coordinate plane?.
Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.
We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:
( 3, 4 ) and ( − 2, 1 )
We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.
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The table shows the sales of a health and beauty supply company, in millions of dollars, for several years. Let x be the number of years since 2010.
Year 2011 2012 2013 2014 2015
Sales 12.2 19.1 29.4 37.3 45.7
a. Write the equation for the best-fit line for the data. Round to the nearest hundredth, if necessary.
y =
x +
Part B
Select the correct choices to complete the sentence.
b. Find and interpret the correlation coefficient.
r ≈ , 1 of 4.
Select Choice
The equation , 2 of 4.
Select Choice
the data very well. Its , 3 of 4.
Select Choice
value means that as the years since 2010 increase, sales, in millions of dollars, , 4 of 4.
Select Choice
.
a. The equation for the line of best-fit is:
y = 8.52x + 11.7.
b. The correlation coefficient is of: 0.9987, hence there is a strong positive correlation between the variables.
How to find the equation of the line of best fit and the correlation coefficient?To obtain the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
The points in this problem are given on the table as follows:
(0, 12.2), (1, 19.1), (2, 29.4), (3, 37.3), (4, 45.7).
As we consider the input x as the number of years since 2011.
Then, using the calculator, the equation is given as follows:
y = 8.52x + 11.7.
Using a correlation coefficient calculator, the numeric value of the coefficient is of:
r = 0.9987.
Hence the correlation between the variables is classified as follows:
Positive, as the correlation coefficient is positive.Strong, as the correlation coefficient is greater than 0.6.More can be learned about regression equations at https://brainly.com/question/26755306
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Paul and Brian win some money and share it in the ratio 3:4. Paul gets £30. How much did Brian get?
Answer:
£10
Step-by-step explanation:
3:4 is equal to 3/4 (three-quarters)
Paul gets 75%, and Brian gets 25%.
Paul gets £30. 30 is 3/4 of what number?
75/100 × x = 30
Multiply both sides by 100 and divide both sides by 75
x = 30 × 100/75
x = 30 x 1.33333333333
x= 40
£30 is 75% of £40
30/40 x 100 = 75%
10/40 x 100 = 25%
Brian gets £10
