1) Matrices that have determinants are square matrices
2) Due to the inverse matrix's calculation utilizing a matrix's determinant, the determinant and the inverse matrix are connected.
3) The determinant affects whether a matrix has an inverse.
What is a matrix?A matrix is a collection of numbers that have been sorted into rows and columns to create a rectangular array. The elements, or entries, of the matrix are the integers.
If and only if the determinant of a square matrix A is nonzero, the matrix has an inverse. The matrix A is referred to as singular and devoid of an inverse if its determinant is zero.
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A population of insects in an entomology lab experiment grows according to the formula P = h(t) = 100/1+4e^-0.05t with t given in days.
(a) Find a formula for h¹(P). Show your work.
(b) Calculate h-¹(90) and interpret its meaning in the context of the problem. Show your work. Round to 1 decimal.
The formula for the inverse function h⁻¹(P) is:
The population of insects in the lab experiment is 90, then the number of days it takes for the population to reach that size is approximately 17.5 days.
To find the inverse function h⁻¹(P), we need to solve the equation P = h(t) for t in terms of P.
Starting with P = h(t) = [tex]100/1+4e^-^0^.^0^5^t[/tex]
we can first multiply both sides by [tex]1+4e^-^0^.^0^5^t[/tex] to get:
[tex]P(1+4e^-^0^.^0^5^t) = 100[/tex]
t = -20ln(4/(P-100)+1)
Therefore, the formula for the inverse function h⁻¹(P) is:
h⁻¹(P) = -20ln(4/(P-100)+1)
(b) To find h⁻¹(90)
we substitute P = 90 into the formula for h^-1(P):
h⁻¹(90) = -20ln(4/(90-100)+1)
= 17.5
This means that if the population of insects in the lab experiment is 90, then the number of days it takes for the population to reach that size is 17.5 days.
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Please help ASAP math question
The possible values of x, given the number of bets are $54,999, $14,999, and -$1.
The expected winnings would be -$0.97.
How to find the expected winning ?The possible values of the net winning would be the amount you win at net if you win first prize, second prize, or nothing.
The possible values would therefore be:
$54,999, $14,999, and -$1.
These show that if you win the first or second prize, you will deduct the $ 1 you bet. And if you win nothing, you would have lost $ 1.
The expected winnings would be:
= ∑ ( Probability of event x Potential net win / loss)
= ( 1 / 3, 000, 000 x 54, 999 ) + ( 2 / 3, 000, 000 x 14, 999 ) + ( 2,999, 997 / 3, 000, 000 x - 1 )
= - $ 0.97
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Una versión muy simplificada de una tabla de insumo-producto para la economía de Israel en 1958 divide dicha economía en tres sectores agricultura, manufactura y energía con los si-guientes resultados.
a) ¿Cuántas unidades de producción agrícola se requieren para obtener una unidad de produc-to agrícola?
b) ¿Cuántas unidades de producción agrícola se requieren para obtener 200 000 unidades de productos de esta naturaleza?
c) ¿Cuántas unidades de producción agrícola se requieren para obtener 50 000 unidades de energía?
d) ¿Cuántas unidades de energía se requieren para obtener 50 000 unidades de productos agrí-colas?
Note that:
a) 1 unit of agricultural production required to obtain 1 agricultural product.
b) 200,000 units of agricultural production are required to obtain 1 of agricultural product.
c) 22,727 units of agricultural production are required to obtain 50,000 units of energy.
d) we need 27,825 units of energy to produce 50,000 units of agricultural products.
How did we get the aabove answer?a) According to the table, the coefficient of production for agriculture is 0.293, that is
0.293 units of agricultural production = a unit of agricultural product.
b) To obtain 200,000 units of agricultural products we say
0.293 x 200,000,= 58,600 units of agricultural production.
c) the coefficient of production for energy with respect to agriculture is 0.044,
that is ,
0.044 units of agricultural production = a unit of energy.
So
50,000 units of energy,=
0.044 by 50,000,
= 2,200 units of agricultural production.
d) To obtain 50,000 units of agricultural products
use the Leontief inverse of the input-output table, which is simply the inverse of the coefficient matrix.
[ 3.4175 -0.2345 -0.5565 ]
[-0.1894 4.8264 -0.2114 ]
[-0.3074 0.1772 4.8324 ]
[ (3.4175 x0) + (-0.2345 x 0) + (-0.5565 x 50,000) ]
[ (-0.1894 x0) + (4.8264x 0) + (-0.2114 x50,000) ]
[ (-0.3074 x0) + (0.1772 x0) + (4.8324 x50,000) ]
[ -27,825 ]
[ -10,570 ]
[ 241,620 ]
Thus, we need 27,825 units of energy to produce 50,000 units of agricultural products.
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Write four math sentences that have an answer of 2.4. Use a different operation in each sentence.
The four math sentences that have an answer of 2.4 are 1.2 + 1.2, 1.2 * 2, 3.6 - 1.2 and 4.8/2
Writing four math sentences that have an answer of 2.4.From the question, we have the following parameters that can be used in our computation:
An answer of 2.4
Using a different operation in each sentence., we have the following math sentences
1.2 + 1.2
1.2 * 2
3.6 - 1.2
4.8/2
The solution to each of the above sentences is 2.4
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On average, 66% of the days in Seattle, Washington, are cloudy or rainy. Describe a model that you could use to simulate this situation.
Since on average, 66% of the days in Seattle, Washington, are cloudy or rainy, a model that could be used to simulate this situation is an experimental probability model of about 2/3.
How to describe a model that you could use to simulate this situation?In this scenario and exercise, you are to required to describe a model that you could be used to simulate a situation in which 66% of the days in Seattle, Washington, are cloudy or rainy on an average.
In this context, we can reasonably infer and logically deduce that the most accurate and feasible model to use would be an experimental probability model of about 2/3;
66% = 66/100 = 33/50 ≈ 2/3.
In conclusion, you should select two (2) red marbles that each represent cloudy or rainy days and one (1) blue marble that represent non-cloudy or non-rainy days, and then pick one marble randomly. Repeat several times in order to determine experimental probability that a day would either be cloudy or rainy.
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The sports shop has 63 part-time employees and 27 full-time employees. What percentage of
the employees at the sports shop work part-time?
Write your answer using a percent sign (%).
Answer:
70%
Step-by-step explanation:
63 / (63+27)
63 / 90 = 0.7
Turn 0.7 into a fraction, 70 under 100
Then rewrite the fraction 70 under 100 to 70%
The elevations of four locations are shown in the table. Which statement is true?
Location
New Orleans
Death Valley
Salton Trough
Rio Bravo
Elevation
(meters)
-2
-86
-69
95
New Orleans is closer to sea level than Salton
Trough.
Rio Bravo has a lower elevation than Salton
Trough.
New Orleans has a lower elevation than Death
Valley.
Rio Bravo is closer to sea level than Death
Valley.
The elevations of four locations.
Hence, the correct option is C.
Based on the elevation
New Orleans has an elevation of -2 meters, which means it is below sea level.Death Valley has an elevation of -86 meters, which means it is also below sea level, but at a lower elevation than New Orleans.Salton Trough has an elevation of -69 meters, which means it is also below sea level, but at a higher elevation than New Orleans.Rio Bravo has an elevation of 95 meters, which means it is above sea level, and thus cannot be closer to sea level than any of the other three locations.Therefore, New Orleans has a lower elevation than Death Valley.
Hence, the correct option is C.
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During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 10% per month.
State whether this increase was linear or exponential. If your food bill was $110 in one month during this period, what
was it three months later?
Step-by-step explanation:
Exponetial (compounding ) growth
New Price = original price ( 1 + .10)^n n is months .10 is 10% per month
= $ 110 ( 1.10)^3 = $ 146 . 41 three months later
A married couple would like to examine the potential of using their home equity to borrow funds in order to remodel their kitchen at a cost of $17,000. The couple purchased the home 3 years ago for its market value of $135,000. The interest rate on their 30-year fixed-rate mortgage is 4.25% and they were able to put down a 5% down payment towards the purchase. The market value of the home has grown at 2.5% per year and the current balance owed on the mortgage is $121,478. If the local Credit Union is offering to lend the couple up to 80% of their home equity in the form of a home equity loan to remodel their kitchen, will they be able to borrow the money necessary to complete the project this third year? Please explain how you calculated the answer.
Only afford a home with a market value of about $375,000, and she would require a down payment of $75,000 to do so.
First, we have to ascertain how much Kelly can comfortably afford to pay for her mortgage each month. Her income, expenses, and other financial commitments will determine this. Her monthly mortgage payment should not be more than 28% of her total monthly income, on average.
The loan is interest rate is the next thing we need to think about. Kelly will have a constant monthly payment for the duration of the loan thanks to a 30-year fixed rate loan at the current market rate of 4.25%.
With a 20% down payment and a loan with a 4.25% interest rate, we could be calculate the maximum purchase price to be roughly $375,000 using a mortgage calculator.
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Use the sine ratio the cones any ratio or the inverse sine to solve for s round each answer to the nearest tenth
The value of x is given as follows:
x = 13.1 ft.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.We have that the important parameters are given as follows:
Hypotenuse of x.Angle of 57º opposite to the side of length 11.Hence the value of x is obtained as follows:
sin(57º) = 11/x
x = 11/sine of 57 degrees
x = 13.1 ft.
Missing InformationThe triangle is given by the image presented at the end of the answer.
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Need help with this please. Be creative!!
The picture for reduction and enlargement is attached
What is scale factor?Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying. while that of decrease is reduction.
The drawing of the the reduction is a square of side 8 units. The scale factor given is 1/2 hence we have the dimensions are as follows
preimage: 8 units x 8 units
image: 4 units x 4 units
The drawing of the the enlargement is a circle of radius 2 units. The scale factor given is 2, hence we have the dimensions are as follows
preimage: radius = 2 units
image: radius = 4 units
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P
60°
30°
8 yd
Write your answer in simplest radical form.
yards
Using the sine ratio, the value of p in the right triangle, in simplest form is: p = 4.
How to Find the Missing Side in Simplest Radical Form?To find the value of p, we have to determine what formula to use. We would apply the sine ratio, which is:
sin ∅ = opposite side / hypotenuse.
From the right triangle in the diagram, we have:
sin 30 = p / 8
p = sin 30 * 8
Note: sin 30 = 1/2
Therefore, we have:
p = 1/2 * 8
p = 4
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Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?B)
B) 23 – 6x – 24 = x – 15
C) –1 – 6x = x – 15
D) –1 – 6x + 15 = x – 15 + 15
The step that indicates the addition property of equality while solving the equation -1 - 6x = x - 15 is : (b) -1 - 6x + 15 = x - 15 + 15.
The "addition-property" of equality states that if we add the same quantity to both sides of an equation, the equation remains true.
In the equation -1 - 6x = x - 15, we need to isolate the variable term 'x'.
To isolate variable "x", we are adding 15 to both sides of the equation, which is the addition property of equality. This step simplifies the equation and isolate the variable "x" on one side.
So, we get, -1 - 6x + 15 = x - 15 + 15,
Therefore, the correct step indicating the "addition-property" is (b).
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The given question is incomplete, the complete, the complete question is
Which of the following steps indicates the addition property of equality while solving the equation -1 - 6x = x - 15?
(a) x = 14/2
(b) -1 - 6x + 15 = x - 15 + 15
(c) -1 - 6x = x - 15
(d) 23 - 6x - 24 = x - 15
What happens to a consistent slope when the y value starts to decrease and the x value remains the same over time?
A. Y decreases and X decreases
B. Y decreases and X increases
C. Y increases and X increases
D. Y increases and X decreases
When the y-value starts to decrease and the x-value remains constant over time, Y decreases and X increases to a consistent slope.
A consistent slope represents a constant rate of change between two variables, typically represented by the ratio of the change in y to the change in x.
When the y-value starts to decrease and the x-value remains the same over time, the consistent slope represents a negative correlation between y and x.
This means that as the value of y decreases, the value of x remains the same or may increase, depending on the context of the problem.
Therefore, the answer is option B: Y decreases and X increases.
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Find the graphed inequality below
Please explain
Answer:
poor photo quality.
Step-by-step explanation:
Directions - Find the sector areas of both the grey and white areas:
*Use 3.14 in place of
285⁰
8 in
in²
in
(round to two decimal places)
(round to two decimal places)
E
The sector areas of the grey and white areas are 159.09 in² and 41.87 in²
Finding the sector areas of the grey and white areas:From the question, we have the following parameters that can be used in our computation:
Radius, r = 8 inchesCentral angle,= 45 degreesThe area of shaded sector is calculated as
Area = Central angle/360 * π * Radius^2
Substitute the known values in the above equation, so, we have the following representation
Gray = 285/360 * 3.14 * 8^2 = 159.09White = (360 -285)/360 * 3.14 * 8^2 = 41.87Hence, the area is 159.09
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In a circle with radius 2, an angle
intercepts an arc of length 7 π/2. Find the angle in radians in simplest form.
The angle in radians in simplest form is 7π/4 radians.
How to determine the angle in radians?In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.
Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):
Arc length = rθ
Where:
r represents the radius of a circle.θ represents the central angle.By substituting the given parameters into the arc length formula, we have the following;
7π/2 = 2 × θ
θ = 7π/4 radians.
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Fill in the missing values to make the equations true.
Answer:
a)
[tex] log_{7}(3) - log_{7}(5) = log_{7}( \frac{3}{5} ) [/tex]
b)
[tex] log_{3}(11) + log_{3}(2) = log_{3}(22) [/tex]
c)
[tex] - 4 log_{8}(3) = log_{8}( {3}^{ - 4} ) = log_{8}( \frac{1}{ {3}^{4} } ) [/tex]
Which of the following choices is a linear function?
Answer: f(x)=x-2
Step-by-step explanation:
Linear function means a straight line, so graph each one to find which is a straight line
the pH of a liquid is measure of how acidic or basic it is. the concentration of hydrogen ions in a liquid is labeled [H+]. use the formula pH=-log[H+] to find the pH level, to the nearest tenth, of a liquid with [H+] about 4.3 x 10^-14
13.4
14.6
-13.4
-14.6
any other answers from the Exponential and Logarithmic functions unit test part one? really struggling, offering 20 points and brainliest
Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter. Write four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon.
All the four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon are,
⇒ (1, 5) (2, 10) (3, 15) (4, 20)
Given that;
Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter.
Now,
Here are four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon:
⇒ (1, 5) (2, 10) (3, 15) (4, 20)
Hence, In each pair, the first number represents the side length of the pentagon, and the second number represents the perimeter of the pentagon.
And, If you add 1 to the side length in each pair, you'll see that the perimeter increases by 5, just as Fernando learned in math class.
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Simplify: (x^2-5x-36)/(x^3-17x^2+72x)
Group of answer choices
(x+3)/(x-6)
1/(-2x)
(x+4)/(x-8)
(x+4)/(x^2-8x)
Answer:
(x + 4)/x^2 - 8x)
Step-by-step explanation:
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The correct statements regarding the scatter plot are given as follows:
The line of best fit gives the best approximation between the SAT score and the GPA.The line of best fit can be used to predict the GPA based on the SAT score.A reasonable prediction of GPA for a SAT score of 2100 is a GPA of 3.5.What is the scatter plot?The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:
(SAT score, GPA).
There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.
For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.
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this figure represents a garden box.
How much soil will it take to fill the garden box?
The amount of soil to fill the garden box is V = 1,134 inches³
Given data ,
Let the volume of the first rectangular box be V₁
Let the volume of the second rectangular box be V₂
where Volume of Rectangle = Length x Width x Height
So , V₁ = 21 x 7 x 2
V₁ = 294 inches³
And , V₂ = 12 x 10 x ( 7 )
V₂ = 120 x 7
V₂ = 840 inches³
And , the total soil in the garden box = V₁ + V₂
Amount of soil in garden box = 1,134 inches³
Hence , the volume is V = 1,134 inches³
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What algebric equation can maxine use to calculate the total mass of pH powder that was sold? A,B,C,D and E.
A) Maxine calculated the total mass of pH powder sold on day 1 by evaluating the algebraic expressions for small and large container sales.
B) If the variable s represents the number of containers sold, the value of the algebraic expression 0.75s represents the total mass of pH powder sold each day.
C) The algebraic expression to represent the mass (in kilograms) of powder sold in large containers daily is 1.25l.
D) The algebraic expression to show how Maxine calculated the total mass of pH powder sold on day 1 is 0.75s + 1.25l, which is evaluated to be 49.25 kg.
E). Using the algebraic expression, the total mass of powder sold on Day 2 and 3 is as follows:
Day 2 = 66.75 kgDay 3 = 53.0 kg.What is an algebraic expression?An algebraic expression is a combination of of variables and constants, together with mathematical operands (addition, subtraction, division, and multiplication, etc.).
pH Plus Power Sales
Day # of small containers # of large containers Total Mass
(0.75 kg) (1.25 kg) (Kilograms)
Day 1 14 31 49.25 kg
Day 2 19 42 66.75 kg
Day 3 24 28 53.00 kg
Let the number of small containers sold = s
Let the number of large containers sold = l
The mass of a small container = 0.75 kg
The mass of a large container = 1.25 kg
Expressions:Total mass of small containers sold daily = 0.75s
Total mass of large containers sold daily = 1.25l
Total mass of small and large containers sold daily = 0.75s + 1.25l
Total Mass Sold:Day 1 = 0.75(14) + 1.25(31) = 49.25 kg
Day 2 = 0.75(19) + 1.25(42) = 66.75 kg
Day 3 = 0.75(24) + 1.25(28) = 53.00 kg
pH Plus Power Sales
Day # of small containers # of large containers Total Mass
(0.75 kg) (1.25 kg) (Kilograms)
Day 1 14 31 49.25 kg
Day 2 19 42
Day 3 24 28
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This data set represents the widths in yards of pieces of fabric used by a sewing group.
What is the mean of this data set?
{1 1/3, 1/4, 2/3, 1/2, 1 1/4}
Enter your answer as a fraction in simplest form in the box.
Answer:
[tex] \frac{4}{5} [/tex]
Multiply 6 × 3 then divide by 2 how do you simplify that expression
Answer:
6 × 3 = 18
18 ÷ 2 = 9
Therefore, the expression 6 × 3 ÷ 2 simplifies to 9
Step-by-step explanation:
To simplify the expression, we follow the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right.There
are no parentheses or exponents,so we multiply 6 by 3 to give us 18.
Then we divide 18 by 2 to give us 9.
There for the Expression simplifies to 9.
HOPE IT HELPS.
PLEASE MARK ❣️‼️ ME AS BRAINLIEST .
Alondra wrote the following incomplete statement. 4.3 < 4. _____ Which of the following strategies could Alondra use to help her complete the statement? Select all that apply.
A. Write any decimal value with a number greater than 3 in the tenths place
B. Write any decimal value with a number greater than 3 in the hundredths place
C. Write any decimal value greater than 30 hundredths
D. Write any decimal value with 2 digits
E. Write any decimal value with a 3 in the tenths place
The strategies that Alondra can use to complete the statement include:
A. Write any decimal value with a number greater than 3 in the tenths placeB. Write any decimal value with a number greater than 3 in the hundredths placeC. Write any decimal value greater than 30 hundredthsWhy are these strategies best ?When a decimal number is created by Alondra and possesses 4 or more in the tenths place, it will exceed 4.3, as stated to exemplify decimals including 4.31 or 4.32.
Similarly, if there are 3 units plus a greater number appended behind the second digit after the decimal point (hundredths place). Deriving an outcome extending further than 4.30 can occur for any value above that obtained from inputting the numbers 4 and 3 into their respective positions in a given sequence.
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20 Per Question, Algebra 2, Thanks :)
The fraction in factored form is determined as (x - 8)(x + 10) / (x - 10)(x + 8).
What is the quotient of the division?
The quotient of the division is calculated as follows;
( x² - 3x - 40 )/ (x² + 8x - 20) ÷ (x² + 13x + 40)/(x² + 12x + 20)
Factorize each of the expressions;
x² - 3x - 40
= x² + 5x - 8x - 40
= x(x + 5) - 8(x + 5)
= (x + 5)(x - 8)
x² + 8x - 20
= x² + 2x - 10x - 20
= x(x + 2) - 10(x + 2)
= (x + 2)(x - 10)
x² + 13x + 40
= x² + 5x + 8x + 40
= x(x + 5) + 8(x + 5)
= (x + 5)(x + 8)
x² + 12x + 20
= x² + 2x + 10x + 20
= x(x + 2) + 10(x + 2)
= (x + 2)(x + 10)
The fraction in factored form is written as;
(x + 5)(x - 8)/(x + 2)(x - 10) ÷ (x + 5)(x + 8)/(x + 2)(x + 10)
(x + 5)(x - 8)/(x + 2)(x - 10) x (x + 2)(x + 10)/(x + 5)(x + 8)
= (x - 8)(x + 10) / (x - 10)(x + 8)
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The scatter plot shows an increase in height of the children with their age.
Which type of association is seen between the age and height of the children?
A type of association that is seen between the age and height of the children include the following: C. positive linear association.
What is a positive correlation?In Mathematics and Statistics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.
This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Therefore, when one variable increases, the other variable generally increases, as well.
By critically observing the scatter plot shown in the image attached above, we can reasonably infer and logically deduce that there is a positive correlation between the x-values (age) and y-values (height) because they both increase simultaneously.
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