The area of the entire rectangle is 20x^2 - 10x - 30
How to determine the area of the entire rectangleFrom the question, we have the following parameters that can be used in our computation:
Height = 5
Width = 4x^2 - 2x - 6
Using the above as a guide, we have the following:
The area of a rectangle is the product of its dimension
So, we have
Area = Height * Width
Substitute the known values in the above equation, so, we have the following representation
Area = 5 * (4x^2 - 2x - 6)
Evaluate
Area = 20x^2 - 10x - 30
Hence, the area is 20x^2 - 10x - 30
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Question 6, please help
6/10
Corsica adds 3/32 = 0.09375 ounces of water to the bucket per second.
To find how many ounces of water are added to the bucket per second, we need to rearrange the given equation to solve for the rate of change of the water, which is the change in the amount of water per unit of time.
Starting with:
3W = 32S
We can divide both sides by S:
3W/S = 32
Now we can see that the left-hand side represents the amount of water (in ounces) added per second, since W/S is the rate of change of the water with respect to time.
Therefore, we can conclude that Corsica adds 3/32 = 0.09375 ounces of water to the bucket per second.
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I’m so confused pls help me <3
Answer:16.7%
Step-by-step explanation: He has a 33% chance of losing in chess and 50% of losing in pool. So when you convert the two percentages to decimals and multiply them the result is 0.167. Convert the number back into a percentage, it's 16.7%.
The cuboid below is made of silver and has a mass of 416 g. Calculate its density, in g/cm³. If your answer is a decimal, give it to 1 d.p. Picture attached!
The density of the cuboid is 10.4 g/cm3 ( 1 d.p)
What is density?Density is the ratio of mass of a substance to its volume. It is measured in kg/m³ or g/cm³. It is a scalar quantity.
The density of a substance bis expressed as;
d = mass/volume
The mass = 416g
and the volume = l× w × h
length of the cuboid = 4cm
width of the cuboid = 2cm
and height = 5cm
Therefore the volume is calculated as :
V = 4× 2 × 5
V = 40cm³
the volume of the cuboid is 40cm³
The density can now be calculated as :
density = mass/volume
density = 416/40
= 10.4g/cm³
therefore the density of the cuboid is 10.4 g/cm³
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This question has two parts. First, answer Part A. Then, answer
Part A
Find the Error A student was finding the value of x.
Which of the following explains the student's error?
The student's error is adding two non-adjacent angles and then solving for x.
What are the opposite angles?
Opposite angles are the angles directly opposite each other where two lines cross. The intersection point is called the vertex, which is where the lines connect to form the angle. Opposite angles are also called vertical angles.
The student's error is that they incorrectly added the two given angles together.
The angles 2x+6 and 60 are not adjacent angles and therefore cannot be added together to find the sum of the two angles.
In the figure, if the angle formed by the intersection of the lines is labeled as angle A, then we know that angle A is equal to 2x+6 and angle B is equal to 60.
These two angles are opposite angles and not adjacent angles, so they do not add up to 180 degrees.
Therefore, the student's error is adding two non-adjacent angles and then solving for x.
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Find the surface area of the sphere. Round your answer to the nearest hundredth.
Rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.
What is surface area ?Surface area is the measure οf the tοtal area that the surface οf an οbject οccupies. It is a twο-dimensiοnal measurement, typically expressed in square units, such as square meters (m²) οr square feet (ft²).
Tο find the surface area (A) οf a sphere with a given circumference (C), we first need tο find the diameter (d) οf the sphere.
The fοrmula fοr the circumference (C) οf a sphere is:
C = 2πr
where r is the radius οf the sphere.
Given that the circumference is 4π ft, we have:
4π = 2πr
Sοlving fοr r, we get:
r = 2 ft
Nοw we can use the fοrmula fοr the surface area οf a sphere with diameter d:
A = 4π(d/2)²
Substituting d = 4 ft (since diameter = 2r), we get:
A = 4π(4/2)²
A = 4π(2)²
A = 4π(4)
A = 16π
A ≈ 50.27
Therefοre, rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.
A ≈ 50.27
Therefοre, rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.
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Is the perimeter of the composite figure equal to the sum of the perimeters of the individual figures? Explain by selecting all the statements that apply
It depends on the specific composite figure. In general, the perimeter of a composite figure is not always equal to the sum of the perimeters of the individual figures that make it up.
However, in some cases, it is possible to calculate the perimeter of a composite figure by adding the perimeters of the individual figures and subtracting the lengths of any shared sides.
For example, if a composite figure is made up of two rectangles that share a side, then the perimeter of the composite figure is equal to the sum of the perimeters of the two rectangles minus the length of the shared side.
In other cases, such as when a composite figure has curved sides or irregular shapes, the perimeter cannot be calculated simply by adding the perimeters of the individual figures.
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Write a quadratic equation with the given roots. Write the equation in the form ax2 + bx + c = 0 where a, b, and c are integers. 4/3 and -1
[tex]\begin{cases} x = \frac{4}{3} &\implies 3x=4\implies 3x -4=0\\ x = -1 &\implies x +1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( 3x -4 )( x +1 ) = 0} \hspace{5em}\stackrel{\textit{now assuming that}}{a=1}\hspace{3em}1( 3x -4 )( x +1 ) = 0 \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x^2-x-4=0 \end{array}}~\hfill[/tex]
Mira looks at her fitness monitor and sees that she has run 2 miles so far. If this distance is 40% of the total distance she plans to run, how many total miles does Mira plan to run?
Answer: 30
Step-by-step explanation:
I think 0.o
Let's represent the total distance that Mira plans to run with "x".
According to the problem, 2 miles is 40% of the total distance, so we can write:
2 = 0.4x
To find the value of "x", we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.4:
2 ÷ 0.4 = x
Simplifying the left side gives us:
5 = x
Therefore, Mira plans to run a total of 5 miles.
Challenging y’all a little
Answer:
identify a relationship among Tn,Sn and Sn-1 where n>1
A game show has a contestant pick one of five doors to reveal the prize the contestant wins. A photo of a new boat is behind one of the doors, and joke prizes are behind the others. Which BEST describes the probability of winning the new boat?
*
impossible
likely
unlikely
certain
Answer:
Step-by-step explanation:
The probability of winning the new boat is unlikely, since there is only one boat behind one of the five doors, while the other four doors have joke prizes. Assuming that each door has an equal chance of being selected by the contestant, the probability of choosing the door with the boat is 1/5 or 20%. However, the probability of not winning the boat is 4/5 or 80%. Therefore, it is unlikely that the contestant will win the boat.
17. Which graphic organizer correctly groups the following numbers? (1 point) 4.1,-9,3,-2.2
A graphic organizer that correctly groups the following numbers 4.1, -9, 3, -2.2 is; B. graphic organizer B.
What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 6, 4.1, -2.2 12, 1/2, 0.5, √16, -29, etc.
What is an integer?In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).
Based on the given data set 4.1, -9, 3, -2.2, the numbers should be correctly grouped as follows;
Rational number = 4.1 and -2.2.
Integer = -9.
Whole number = 3.
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Type your answer in to the boxes. The three points marked on the graph are the vertices (corners) of a parallelogram Y 10 q 8 5 B 3 2 2 3 5 6 7 8 9 10 X What are the coordinates of the fourth vertex?
The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).
What is cοοrdinate?A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.
First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:
Distance Yq = [tex]\sqrt{[(10-8)^2 + (5-10)^2] }[/tex]
Distance Yq = [tex]\sqrt{8 + 25 }[/tex]
Distance Yq =[tex]\sqrt{ 33}[/tex]
Distance 5B = [tex]\sqrt{[(3-2)^2 + (2-3)^2] }[/tex]
Distance 5B = [tex]\sqrt{2}[/tex]
Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:
x = (33/2)
Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,
Slοpe Yq = (10-5)/(8-10) = -5/2Slοpe B-missing vertex = -5/2
write the equatiοn οf the line passing thrοugh B and the missing vertex:
y - 2 = (-5/2)(x - 3)
Simplifying, we get:
y = (-5/2)x + (19/2)
Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.
Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).
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Majka company was started on january 1, year 1. During year 1, the company experienced the following accounting events: (1) issued 50,000 worth of common stock (2) earned cash revenues of $33,700, (3) paid cash expenses of $14,900, and (4) paid a $3,200 cash dividend to its stockholders. These were the only events that affected the company during year 1
(1) In General Ledger, Cash Account is $ 13900 , In revenue account The balance is $ $28600, in expense account the balance is $ $13200 and Trial balance is $28600.
(2) The income statement is $ 15400.
(3) Statement of Changes in Stockholders' Equity is $13900.
(4) Balance sheet is $ 13900.
Record the effects of each accounting event under the appropriate general ledger account headings.
Using the accounting equation, we have:
Asset = Shareholder's equity + Liabilities
Cash = Retained earning + Common stock
Cash = $28,600 - $13,200 - $1,500 = $13,900 = Assets
Retained earning = $28,600 - $13,200 - $1,500 = $13,900
Common stock = 0
Retained earning + Common stock = $13,900 + 0 = Shareholder's equity
Liabilities = 0
Therefore, we have:
(1) Majka Company
Accounting Equation for Year 1
Asset ($) = Shareholder's equity + Liabilities
13,900 = 13,900 + 0
(2) Prepare an income statement
Details Amount ($)
Revenue 28,600
Expenses (13,200)
Net Profit 15,400
Dividend (1,500)
Retained earning 13,900
(3) Statement of changes in stockholders’ equity
Details Amount ($)
Common stock 0
Beginning retained earning 0
Retained earning for the year 13,900
Stockholders’ equity 13,900
(4) Mijka Company, Balance sheet as at December 31, Year 1,
Details Amount ($)
Assets:
Cash 13,900
Liabilities:
Current and Long terms 0
Net total assets 13,900
Stockholders’ equity:
Common stock 0
Retained earning 13,900
Stockholders’ equity 13,900
Complete Question:
Majka Company was started on January 1, Year 1. During Year 1, the company experienced the following three accounting events: (1) earned cash revenues of $28,600, (2) paid cash expenses of $13,200, and (3) paid a $1,500 cash dividend to its stockholders. These were the only events that affected the company during Year 1. Required Record the effects of each accounting event under the appropriate general ledger account headings. Prepare an income statement, statement of changes in stockholders’ equity, and a balance sheet dated December 31, Year 1, for Mijka Company.
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jar contains 30 red balls and 20 white balls. twenty-five balls are randomly selected from the jar with replacement. what is the probability that a red ball was selected more than 20 times?
The probability that a red ball was selected more than 20 times when 25 balls are randomly selected from the jar with replacement is 0.037.
Given that a jar contains 30 red balls and 20 white balls. Also, 25 balls are randomly selected from the jar with replacements. We need to find the probability that a red ball was selected more than 20 times.
The binomial probability distribution function can be represented as follows:
[tex]P(X = k) = \ ^nC_k . p^k . q^{(n-k)}[/tex]
where n is the number of trials, k is the number of successes,
p is the probability of success,
q = 1 - p is the probability of failure.
Here, the probability of selecting a red ball is 30/50 = 3/5.
So, the probability of selecting a white ball is 2/5.
Here, we have n = 25 trials, p = 3/5, q = 2/5.
Let X be the number of times a red ball is selected. Then we need to find P(X > 20).
So, P(X > 20) = 1 - P(X ≤ 20)
= 1 - Σ P(X = k), k = 0 to 20
[tex]= 1 - \sum \ ^nC_k . p^k . q^{(n-k)}[/tex], k = 0 to 20
[tex]P(X = k) = \ ^nC_k . p^k . q^{(n-k)}[/tex]
[tex]P(X > 20) = 1 - \sum \ ^nC_k . p^k . q^{(n-k)}[/tex], k = 0 to 20
= [tex]1 - { \ ^nC_0 . p^0 . q^{(n-0)} + \ ^nC_1 . p^1 . q^{(n-1)} + \ ^nC_2 . p^2 . q^{(n-2)} + ... + \ ^nC_{20} . p^{20} . q^{(n-20)}}[/tex]
= 1 - {1 . (3/5)^0 . (2/5)^25 + 25 . (3/5)^1 . (2/5)^24 + 300 . (3/5)^2 . (2/5)^23 + ... + 1.623 x 10^10 . (3/5)^20 . (2/5)^5}
= 1 - 0.963
= 0.037
Therefore, the probability that a red ball was selected more than 20 times when 25 balls are randomly selected from the jar with replacement is 0.037.
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a CD usually sells for $11.00. if the CD is 10% off and the sales tax is 7% what is the total price of the CD, including tax
0.90 x $11.00 = $9.90
This is the price of the CD before taxes are applied. To find the total price, including tax, we need to add the 7% sales tax to the discounted price:
Total price = discounted price + (sales tax x discounted price)
Total price = $9.90 + (0.07 x $9.90)
Total price = $9.90 + $0.69
Total price = $10.59
Therefore, the total price of the CD, including tax, is $10.59.
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The sun orbits the Milky Way galaxy at about 135 miles per second. Write your answers to the following in scientific notation.
A. How far does the sun travel in an hour?
B. How far does the sun travel in a week?
Expressing this in scientific notation, we get: Distance traveled in a week = 3.77 x [tex]10^7[/tex] miles/week
What is speed?Speed is a measure of how fast an object is moving, usually expressed in units of distance per unit time. It is defined as the distance traveled by an object divided by the time it takes to travel that distance.
According to question:The speed of the sun orbiting the Milky Way galaxy is 135 miles per second.
A. To find how far the sun travels in an hour, we need to multiply its speed by the number of seconds in an hour:
Distance traveled in an hour = 135 miles/second x 60 seconds/minute x 60 minutes/hour
Distance traveled in an hour = 486,000 miles/hour
Expressing this in scientific notation, we get:
Distance traveled in an hour = 4.86 x [tex]10^5[/tex] miles/hour
B. To find how far the sun travels in a week, we need to multiply its speed by the number of seconds in a week:
Distance traveled in a week = 135 miles/second x 60 seconds/minute x 60 minutes/hour x 24 hours/day x 7 days/week
Distance traveled in a week = 37,656,000 miles/week
Expressing this in scientific notation, we get:
Distance traveled in a week = 3.77 x [tex]10^7[/tex] miles/week
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rewrite the following into the stnadard from of a quadratic equation
[tex]2x^{2} -1[/tex]
Answer:
[tex]2x^{2} +0x+-1=0[/tex]
Step-by-step explanation:
The standard form of a quadratic equation is:
[tex]ax^{2} +bx+c=0[/tex]The expression provided ([tex]2x^{2} -1[/tex]), can be rewritten in standard form by setting it to equal zero:
[tex]2x^{2} -1 = 0[/tex]In this case, a would be equal to 2, b equal to 0, and c equal to -1.
write 3/4 5/7 19/25 11/5 smallest to largest
Answer:[tex]\frac{5}{7} \\\\ \\\\\frac{3}{4} \\\\\frac{19}{25} \\\\\frac{11}{5}[/tex]
Step-by-step explanation:
The manager of a store orders mystery games that cost $7.30 and sells them for $15.33. What is the mark-up as a percentage?
In order to find the price increase in percentage terms, we divide the price difference by the cost price.
The difference:
[tex]15.33-7.30=8.03[/tex]Rate:
[tex]\frac{8.03}{7.30}=\frac{x}{100}[/tex]
If we solve for [tex]x[/tex] in this equation, it will give us the price increase as a percentage.
The price increase should be [tex]110[/tex]%.
Suppose the demand and supply of tea are modeled by the two following functions: Q = 34P + 53 Q = -25P + 177 What is the equilibrium price of tea? Round your answer to two places after the decimal point (0.01).
According to the question the equilibrium price of tea is 2.10.
What is equilibrium?Equilibrium is a state of balance in which all forces acting on an object are equal and opposite, so no net force is acting on the object. This state of balance is also known as a "steady state". Equilibrium is an important concept in many areas of science, such as physics and chemistry, because it allows us to analyze how objects interact in a stable environment. Equilibrium can also be used to describe a state of financial balance, where all parties involved in a transaction are satisfied with the outcome.
The equilibrium price can be found by setting the two equations equal to one another and solving for P.
34P + 53 = -25P + 177
59P = 124
P = 124/59
P = 2.10
Therefore, the equilibrium price of tea is 2.10.
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Write down the domain and range of: y = 2*
The domain is (-∝, ∝) and the range is y > 0
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
y = 2^x
The domain of the function is the set of all real numbers
This is so because there is no restriction on the input values
The range of the function is the set of positive real numbers
Since any positive number can be obtained by raising 2 to a power, and the function is never negative or zero.
We can write the range as y > 0.
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The perimeter of a rectangle is 72, and the width is 4 less
han 3 times the length. What is the length?
12
O 10
O 16
O 14
Answer:
Answer: 10
Step-by-step explanation:
Let L be the length of the rectangle, and W be the width.
From the problem, we know that:
The perimeter of the rectangle is 72, which means that:
2(L + W) = 72
L + W = 36
The width is 4 less than 3 times the length:
W = 3L - 4
Substituting W = 3L - 4 into the first equation, we get:
L + 3L - 4 = 36
4L = 40
L = 10
Therefore, the length of the rectangle is 10. Answer: 10
Does the following set of ordered pairs represent a function?
(2,3) (3,4) (2,5) (5,8)
Answer:
No
Step-by-step explanation:
In order for a set of ordered pair to be a function all the x values need to be different. In this case we have two of the same x values so this set won't be a function.
On Wednesday, Sally's turtle walked from the starting line all the way to point T and then back to point M. How far did her turtle walk altogether on Wednesday?
Sally's turtle walked a total of 30 feet altogether on Wednesday.
To determine the total distance the turtle went, we need to know the distances between the beginning line and points T and M.
According to the diagram, there are 12 feet between the beginning line and point T and 8 feet between the starting line and point M.
The turtle travels a distance of: when it moves from the starting line to point T and then returns to point M.
Distance between the beginning line and point T plus the distances between point T and point M and point M from the starting line equals 12 + 10 + 8 = 30 feet.
So, on Wednesday, Sally's turtle travelled a total of 30 feet.
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the amount of time tim spends answering work e-mails in a given day has a mean of one hour and a standard deviation of ten minutes. what would best describe the total amount of time, measured in hours, tim would spend answering e-mails over the course of 100 days
The best estimate for the total amount of time Tim would spend answering e-mails over the course of 100 days is 100 hours with a standard deviation of 0.53 hours.
To find the total amount of time Tim would spend answering emails over the course of 100 days, we need to use the concept of the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approaches a normal distribution regardless of the underlying distribution.
To calculate the standard deviation of the total amount of time Tim spends answering emails over 100 days, we can use the formula:
standard deviation = square root of (n * variance)
where n is the number of days and variance is the variance of the amount of time Tim spends in a day answering emails.
Substituting the values, we get:
standard deviation = square root of (100 * 0.0028) = 0.53 hours
Therefore, Tim would spend an average of 100 hours over the span of 100 days responding to emails, with a standard deviation of 0.53 hours, according to the best estimate.
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Jaquira wants to set a ladder against the house to change a light above the garage. The ladder is 18 feet long. If the ladder needs to reach the light, which is 15 feet above the ground, how far away should Jaquira place the base of the ladder from the house? Round to the nearest tenth.
Answer:
≈ 9.9 feet
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem. Let x be the distance from the house to the base of the ladder. Then:
x^2 + 15^2 = 18^2
Simplifying and solving for x, we get:
x = sqrt(18^2 - 15^2) = 9.9 feet (rounded to the nearest tenth)
Therefore, Jaquira should place the base of the ladder approximately 9.9 feet away from the house.
THE TEMPERATURE IN AUSTRIA ONE MORNING WAS -5 DEGREE CELCIOS AT 8 OCLOCK AND INCREASED BY 2 DEGREE CELCIOS EVERY HOUR UNTIL 12 OCLOCK ,WHAT WILL BE THE TEMPERATURE BE AT HLF PAST 11
Answer: 2° Celsius.
Step-by-step explanation:
Write a multiplication equation shat shows how the denominators of 3/4 and 1/2 are related. Explain how this equation helps you write 1/2 as an equivalent fraction with a denominator of 4
To find the multiplication equation that shows how the denominators of 3/4 and 1/2 are related, we can simply multiply the two denominators together:
3/4 x 1/2 = 3/8
Therefore, the denominators are related by the equation 4 x 2 = 8.
To write 1/2 as an equivalent fraction with a denominator of 4, we need to multiply both the numerator and denominator by the same factor that will transform the denominator of 2 to a denominator of 4.
Using the multiplication equation we found earlier, we can see that we need to multiply both the numerator and denominator of 1/2 by 2 (since 2 x 2 = 4). This gives us:
1/2 x 2/2 = 2/4
Therefore, 1/2 can be written as an equivalent fraction with a denominator of 4 as 2/4.
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The equation 3600b² = hw represents the relationship among the body surface area b (in square meters), height h (in
centimeters), and weight w (in kilograms) of a person. To the nearest tenth, approximate the body surface area of a person who
is 168 centimeters tall and weighs 60 kilograms.
The body surface area is about (blank)
square meters.
Answer: 0.2 square meters.
Step-by-step explanation:
We are given the equation:
3600b² = hw
We need to find the value of b, given that h = 168 cm and w = 60 kg.
First, we need to convert the height from centimeters to meters:
h = 168 cm = 1.68 m
Substituting the given values:
3600b² = (1.68)(60)
3600b² = 100.8
b² = 100.8/3600
b² = 0.028
Taking the square root of both sides:
b = √0.028
b ≈ 0.167
Rounding to the nearest tenth:
b ≈ 0.2
Therefore, the body surface area of a person who is 168 centimeters tall and weighs 60 kilograms is about 0.2 square meters.
The correlation be reasonable to conclude that the data come from a r X Table of critical values Sample Size, n Critical Value Sample Size, n Critical Value 5 0.880 16 0.941 6 0.888 17 0.944 7 0.898 18 0.946 8 0.906 19 0.949 9 0.912 20 0.951 10 0.918 21 0.952 11 0.923 22 0.954 12 0.928 23 0.956 13 0.932 24 0.957 14 0.935 25 0.959 15 0.939 30 0.960
a) there is a strong positive correlation between the variables based on the given correlation coefficient and critical value
To interpret correlation values, the Table of Critical Values must be used. In this case, the correlation be reasonable to conclude that the data come from a r X. Table of critical values Sample Size, n Critical Value Sample Size, n Critical Value 5 0.880 16 0.941 6 0.888 17 0.944 7 0.898 18 0.946 8 0.906 19 0.949 9 0.912 20 0.951 10 0.918 21 0.952 11 0.923 22 0.954 12 0.928 23 0.956 13 0.932 24 0.957 14 0.935 25 0.959 15 0.939 30 0.960. The correlation coefficient is found between -1 and 1. Correlation values near 1 indicate a strong positive correlation, while those near -1 indicate a strong negative correlation. Correlation values near zero, on the other hand, indicate no correlation between the variables. In this case, we can interpret that the correlation is significant because it falls outside of the range of -0.880 and 0.880. We can see that the correlation value of 0.918 is higher than the critical value of 0.880 for the sample size of 10 from the given table of critical values. As a result, it can be concluded that there is a strong positive correlation between the variables based on the given correlation coefficient and critical value.
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