The dimensions of a right circular cylinder of maximum volume are
[tex]5\sqrt{6}[/tex] and [tex]10\sqrt{3}[/tex].
Given the radius of sphere is 15 cm.
Let's assume radius of right circular cylinder = r
height of right circular cylinder = h.
Since the cylinder is inscribed in the sphere, their centers will coincide. As a result, the height is divided into two equal portions from the sphere's center. Therefore, we can apply Pythagoras' Theorem to get the cylinder's half-height in terms of radius.
[tex]R^2 = r^2 + (h/2)^2[/tex].
[tex]r^2=R^2-h^2/4[/tex]
Volume of cylinder = [tex]\pi r^2h[/tex]
Now we can substitute value of [tex]r^2[/tex] in volume of cylinder.
V = π*([tex]R^2[/tex] - [tex]h^2[/tex]/4)*h
taking R = 15 .
V = π*(225 - [tex]h^2[/tex]/4)*h
V = π*225*h - π*[tex]h^3[/tex]/4
For maximum volume we have to do derivative of volume = 0
derivative with respect to h.
V' = π*225 - 3*π[tex]h^2[/tex]/4
V' = 0
π*225 - 3*π[tex]h^2[/tex]/4 = 0
3*[tex]h^2[/tex]/4 = 225
[tex]h^2[/tex] = 75*4
h = [tex]10\sqrt{3}[/tex]
put the value of h in [tex]r^2=R^2-h^2/4[/tex]
[tex]r^2[/tex] = 225 - (300/4)
[tex]r^2[/tex] = 150
r = [tex]5\sqrt{6}[/tex]
Given Question is incomplete, Complete Question here
find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. what is the maximum volume?
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A lake fishing map is laid out on a coordinate plane with each unit equal to 1 mile. The boat is launched from the point (-5, 0) and goes to point (-5, 5) to fish. From
there, the boat travels to (0, 0) to fish and then goes back to the launch point
Determine the total number of miles traveled. Round to the nearest whole number.
05 miles
07 miles
O17 miles
O50 miles
The total number of miles traveled is given by the following option:
17 miles.
How to obtain the total distance?The total distance is divided into three parts, obtained as follows:
First part: From point (-5,0) to point (-5,5).Second part: From point (-5,5) to point (0,0).Third part: From point (0,0) back to the launch point of (-5,0).The generic notation of two points is given as follows:
[tex](x_1,y_1), (x_2,y_2)[/tex]
The distance between two points is then given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence each distance in this problem is given as follows:
First part: 5 miles.Second part: 7 miles.Third part: 5 miles.The total distance is the sum of each distance, hence it is given as follows:
5 miles + 7 miles + 5 miles = 17 miles.
Hence the third option is correct.
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Circle A has center of (−2, −1) and a radius of 2, and circle B has a center of (1, 2) and a radius of 4. What steps will help show that circle A is similar to circle B? Group of answer choices Translate circle A using the rule (x − 3, y − 3) Rotate circle A 180° about the origin Reflect circle A over the line y = x Dilate circle A by a scale factor of 2
Circle A will be enlarged by a scale factor of 2 to assist demonstrate how circle A and circle B are comparable.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
The equation of a circle with the center and radius r
( x − a )² + ( y − b )² = r²
The equation of circle A,
(x-(-2))²+(y-(-1))²=2²
x²+4+4x
The equation of circle B,
(x-1)²+(y-2)²=4²
Thus, circle A will be enlarged by a scale factor of 2 to assist demonstrate how circle A and circle B are comparable.
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write a formula for f, the specific antiderivative of f. (remember to use absolute values where appropriate.) f(u)
The antiderivative of a function f will be the integral of differentiated value of the function i.e. the function itself.
What is Antiderivative of a function?
A function is said to be antiderivative if its derivative equals the original function. The antiderivative function is the same as an indefinite integral. The limit of a sum of terms f (x) x in the limit that approaches zero, where is the integrand function, is known as a definite integral.
Considering a function f(x) = Sin x
dy/dx = Cos x
Now, the integral of Cos x would be known as Anti derivative.
here, ∫ Cos x = Sin x
thus, Anti derivative of Cos x is equal to the function itself.
hence, proved.
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The length of a rectangular poster is 2 more inches than three times its width. The area of the poster is 161 square inches. Solve for the dimensions (length and width) of the poster.
The length and width of the rectangular poster are 23 inches and 7 inches respectively.
Here we have to find the dimensions of the length and width of the rectangular.
Data given:
length of the rectangular poster is 2 more than three times its width.
Let us assume that the width of the rectangular is x.
The area of the poster = is 161 inches²
So by this, we get the length 3x + 2.
width = x
length = 3x + 2
The formula of the area of the rectangular:
Area = length × width
161 = (3x+ 2) × x
161 = 3x² + 2x
3x² + 2x - 161 = 0
3x² + 23x - 21x - 161 = 0
x(3x + 23) - 7( 3x + 23) = 0
(3x + 23) ( x -7)= 0
x = -23/3, 7
As the length cannot be negative so we get the value of x as 7
width = 7 inches
length = 3x + 2
= 3×7 + 2
= 21 + 2
= 23inches
Therefore the length and width are 23 inches and 7 inches respectively.
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what is the relative humidity of the parcel at sea level on the leeward side? (fill in only the letter: a, b, c, or d, all caps) a) 25%, b) 33%, c) 100%, or d) 58%
The relative humidity of the parcel at sea level on the leeward side is 58% that is option D
The amount of water vapour in an air-water mixture relative to the maximum amount is known as relative humidity (RH). RH is a comparison between the humidity of a specific water-air mixture and the saturation humidity ratio at a particular temperature (dry-bulb)
By deducting the temperature on the wet-bulb thermometer from the temperature on the dry-bulb thermometer and utilizing a relative humidity chart, one may determine the relative humidity.
The relative humidity of the parcel at sea level on the leeward side is 58%
Option d is the correct answer
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For the following problems, write the equation that is relevant to solve the problem, the values of the variables that you will use in that equation, and a complete sentence stating what your answer to the question is. Your answer must include appropriate units 1. Five and a half years ago, Elena invested $20,000 in a retirement fund that grew at a rate of 2.96% compounded continuously. What is the investment worth today? What was the interest earned for that investment so far? 2. How long will it take for an investment with an annual rate of 2.85% compounded quarterly to double in value? (Doubling time). How long will it take for the same investment to quadruple in value?
Investment worth today is $23520 and interest earned = $3520 on compound interest.
What is compounding interest?
Compound interest is interest calculated on the initial principal, that conjointly includes all of the accumulated interest from previous periods.
Generating "interest on interest" is thought because the power of interest.
Main body:
1)
time = 5.5 years
rate = 2.96%
Principle amount = $20000
Compounding interest = P(1+r/n)^tn
where
n = number of times interest applied per time period
t=number of time periods elapsed
here n = 365
Amount = 20000(1+0.0296/365)^5.5*365
= 20000*1.176
= $23520
hence ,interest earned = $23520 - $20000 = $3520
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a sample of difference scores has a mean of 5 with a variance of 100. if effect size is measured using cohen’s d, what is the value of d?
The value of d is 0.05.
What is cohen?
A standardized effect size called Cohen's d is used to compare the means of two groups. It's frequently applied when contrasting a treatment with a control group. It may be an acceptable effect size to include with the findings of the t-test and the ANOVA. Cohens d is often used in psychology.
Here, we have
Given
Mean = 5
Standard deviation = 100
We have to find the value of d
So, we apply here formula for d
Cohen d = mean / standard deviation ........................1
Now, we put the value of mean and standard deviation and we get
Cohen d = 5 / 100
Cohen d = 0.05
Hence, the value of d is 0.05
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There are two sets of rainfall data for two different time periods in the same location. Period 1: 2. 3, 2. 1, 2. 2, 2. 2, 2. 2, 2. 1, 2. 4, 2. 5, 2. 2, 2. 0, 1. 9, 1. 9, 2. 1, 2. 2, 2. 3 period 2: 2. 3, 2. 1, 3. 3, 1. 5, 3. 6, 1. 6, 3. 0, 1. 1, 4. 7, 2. 1, 2. 4, 1. 9, 2. 8, 0. 5, 2. 3 what can you say about the agreement in the data sets?.
A scatter plot or scatter gram chart can highlight the distribution patterns or demonstrate and compare the two data sets.
What is scatter plot ?
Dots are used to indicate values for two separate numeric variables in a scatter plot . The values for each data point are shown by the position of each dot on the horizontal and vertical axes.
Scatter plot shows the relationships between variables are visualized using scatter plots.
The given data can highlight the distribution patterns or demonstrate two sets of rainfall data for two different time periods in the same location.
From the given data, it is observed that the given data is observed in the scatter plot.
Hence, a scatter plot or scatter gram chart can highlight the distribution patterns or demonstrate and compare the two data sets.
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Each bag of cereal should contain 350 grams. a box was selected at ramdon and weighed 342 grams. what is the percent error?
The percentage error in selecting the random box is 2.285 %
Let the total amount of bag of cereal be = 350 grams
The box selected at random had a weight of = 342 grams
We know the formula of percentage error.
The percentage error is calculated by the formula
Percentage Error =
( ( Original Value - Observed Value ) / Original Value ) x 100
Plug the values in above formula:
Percentage Error = ( ( 350 - 342 ) / 350 ) x 100
= ( 8 / 350 ) x 100
= 0.02285 x 100
= 2.285 %
Hence , The percentage error in selecting the random box is 2.285 %
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The deli ell 3 time a many tuna andwiche in one month a roat beef. How many more tuna andwiche were old than roat beef I’m 5 month? Explain
More than twice as many roast beef sandwiches as the deli sold over the course of five months.
Explain the term thrice of the number?Three times, such as a series; three times or in three different ways. in a threefold amount or level.Let the tuna sandwich sold by deli be 'x'
Then, tuna sandwich for 5 months-
1st month - x1
2nd month - x2
3rd month - x3
4th month - x4
5th month - x5
Then,
Selling of roast beef sandwich is 3 times more than tuna sandwich.
Then, roast beef sandwich for 5 months-
1st month -3x1
2nd month - 3x2
3rd month -3x3
4th month - 3x4
5th month - 3x5
Thus, the difference is-
Difference = (3x5 + 3x4 + 3x3 + 3x2 + 3x1) - (x1 + x2 + x3 + x4 + x5)
Difference = 2x1 + 2x2 + 2x3 + 2x4 + 2x5
Thus, more than twice as many roast beef sandwiches as the deli sold over the course of five months.
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Answer:
Step-by-step explanation:
A new health drink has 170% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 50 mg. How many milligrams of the vitamin are in the drink?
Brandon enters bike races. He bikes 6 1/2 miles every 1/2 hour. Complete the table to find how far Brandon bikes for each time interval.
Answer:
Step-by-step explanation:
HELPPP MREEEEEEEEEEEED SLAY
Answer:
l. and ll and lll only
Step-by-step explanation:
Horizontal lines are parallel so as suggested in:
1. Vertical angles are congruent, so 5a = 115.
2. Alternate interior angles are congruent, so b - 12 = 65.
3. Corresponding angles are congruent and linear angle pairs sum up to 180, so (b-12) + 65 = 180.
However, alternate interior angles are congruent,
as stated in 2nd suggestion too, so the sum is not 180 but 130.
Therefore 4th suggestion is not correct.
algebra 1
solve the system of equations without graphing. show reasoning.
please explain bc i have no clue what im doing
Answer:
(2,-1)
Step-by-step explanation:
Determine the ratio of the geometric sequence: 1/16, -1/4, 1,...
Answer:
The common ratio of the given sequence is - 4-------------------------------
Given sequence:
1/16, - 1/4, 1, ...Find the common ratio, the ratio of two consecutive terms:
r = 1 ÷ (- 1/4) = 1 × (- 4) = - 4or
r = - 1/4 ÷ 1/16 = - 1/4 × 16 = - 4Let x and y be some integers. Consider the following statement: If xis odd and y is odd, then xy is odd. Proof. Assume that x is odd and y is odd. Then there exists some k integers such that x=2k+1 and m=2k+1. Then xy=(2k+1)(2k+1)=4k2+4k+1=2(2k2+2k)+1. Since 2k2+2k is an integer because k is an integer then xy is odd. The proof is correct but the statement is incorrect The statement is correct, but the proof is incorrect. The statement and proof are incorrect. The statement and the proof are correct.
hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.
Odd number integers = 2k + 1, where k is integer
Even number integer = 2k
Odd integer + even integer
= 2k + 1 + 2k
= 4k + 1
= 2(2k) + 1
Let 2k = t, where t is integer
= 2t + 1
= Odd integer by definition
If number is 2t + 1 where t belongs to integer, then it is odd integer.
Hence proved.
The question is incomplete. The complete question is :
Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd
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for a study with 4 groups, how many independent research questions can be asked? this is the same as the maximum number of planned research questions recommended in your book.
In a book, a study of analysis with four groups is recommended to include a maximum of four prepared research topics.
These projects give you and your students the chance to research watershed-related subjects outside of the regular chemical water testing every three weeks. They give your pupils the chance to hone their research and scientific method skills, examine issues related to waterways that interest them, and analyze data and solve problems. For a study with four groups, a book can only prescribe a maximum of four planned research topics.
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help me out with probability
The probability of selecting D twice in the random selection is D. 4 / 9.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
It should be noted that the probability of selecting D will be:
= 2 / 3.
Therefore, the probability of selecting D twice will be the multiplication of the probability that's gotten twice. This will be illustrated thus:
= 2 / 3 × 2 / 3
= 4 / 9
Therefore, the probability is 4 / 9.
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the numbers 1447, 1005, and 1231 have something in common: each is a 4-digit number beginning with 1 that has exactly two identical digits. how many such numbers are there?
There can be 432 Types of Combinations for a 4-digit number beginning with 1 that has exactly two identical digits
What is permutation and combination?
The process of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics involve permutations in some form or another. They frequently appear when various orderings on particular finite sets are taken into account.The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.[tex]$11xy,\qquad 1x1y,\qquad1xy1$[/tex]
Because the number must have exactly two identical number digits,[tex]$x\neq y$[/tex], [tex]$x\neq1$, and $y\neq1$[/tex]. Hence, there are [tex]$3\cdot9\cdot8=216$[/tex] number of this form.
Now suppose that the two identical digits are not 1. Reasoning similarly to before, we have the following possible combination:
[tex]$1xxy,\qquad1xyx,\qquad1yxx.$[/tex]
Again,,[tex]$x\neq y$[/tex], [tex]$x\neq1$, and $y\neq1$[/tex]. There are [tex]$3\cdot9\cdot8=216$[/tex] numbers of this form.
Thus the answer is 216+216=432
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I need part a and how the answer was made ‼️
Answer:
Step-by-step explanation:
a mouse weighs around 18–35 gram. [ 1] , while an average elephant around 5,443 kilogram. [ 2] Which means an elephant is about 200,000 times heavier then a mouse. (of course, a baby elephant of 100 kilogram compared to a heavy mouse (33 1 3 gram) only weighs 3000 times heavier) Footnotes. [ 1] Species Specific Information: Mouse.
Brandon went to the store to buy some walnuts. The price per pound of the walnuts is $6.50 per pound and he has a coupon for $3.75 off the final amount. With the coupon, how much would Brandon have to pay to buy 5 pounds of walnuts? Also, write an expression for the cost to buy
p
p pounds of walnuts, assuming at least one pound is purchased.
Yes. Yes I know. It’s stuff from years ago. My teacher is making me do this review thing and I don’t remember anything past a week ago.
Your friend simplifies the following problem. Describe what error was made. No credit for just the correct final answer, we are looking for you to tell us what is wrong with how this was solved.
The error was made when he added the number in the radical expression in the computation, despite the fact that the numbers do not have the same base.
What are the radical expressions?Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.
The expression is given in the question following:
4√5 + 7√3
11√8
The error was made in that he add the number in the radical expression in the calculation while the terms are not the same base.
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A local deli makes turkey sandwiches and salami sandwiches at a weekly ratio of 2 salami sandwiches for every 5 turkey sandwiches. If the deli makes 60 turkey sandwiches this week, how many salami sandwiches did they make?
5 salami sandwiches
16 salami sandwiches
30 salami sandwiches
24 salami sandwiches
A local deli makes turkey sandwiches and salami sandwiches at a weekly ratio of 2 salami sandwiches for every 5 turkey sandwiches. If the deli makes 60 turkey sandwiches this week, how many salami sandwiches did they make?
5 salami sandwiches
16 salami sandwiches
30 salami sandwiches
24 salami sandwiches
2 to 5 = x to 60
60/5 = 12
2 * 12 = 24
14 on a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. what was the number of men on the sight-seeing tour?
The number of men on the sight - seeing tour was 22 .
In the question ,
it is given that,
the ratio of women to children on the tour is = 5 : 2
let the number of men in the sight seeing tour = m
let the number of women in the sight seeing tour = w
let the number of children in the sight seeing tour = c
So , w/c = 5x/2x
also the ratio of children to men is 5/11 ,
c = 5y and m = 11y
the number of women on the sight seeing tour is less than 30 ,
which is 5x < 30 ,
x < 6
but we have c = 2x and 5y ,
and since c is a multiple of 5 , 2x also has to be a multiple of 5 ,
earlier we got , x < 6 ,
Now using x =5 , we get c = 2*5 = 10
and so , 10 = 5y
y = 2 ,
So , the number of men = 11y = 11*2 = 22 men
Therefore , the number of men are 22 .
The given question is incomplete , the complete question is
On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.
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When Angel left his house in the morning, his cell phone battery was partially charged. Let B represent the charge remaining in Angel's battery, as a percentage, t hours since Angel left his house. A graph of B is shown below. Write an equation for B then state the x-intercept of the graph and determine its interpretation in the context of the problem.
The equation of the function is: B = -5x + 30
X-intercept is 6, which means after 6 hours, the battery is totally drained.
What is the X-intercept of a Function?The x-intercept of a function is the point on the x-axis that the line intercepts, which is the value of x when y = 0.
Find the slope of the function (m):
Slope (m) = change in B / change in t = (20 - 10) / (2 - 4)
Slope (m) = 10/-2
Slope (m) = -5
The y-intercept (b) = 30.
Write the equation of the function by substituting m = -5 and b = 30 into B = mt + b:
B = -5x + 30
The x-intercept of the function is 6, which represents the hours it took for the whole battery to drain.
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you are analyzing a pcr run and see that one of your samples is a high positive but the internal control failed. what should you do?
Try reducing your annealing temperature by a few degrees and repeat the PCR.
What is the principle of PCR machine ?
The PCR technique is based on the enzymatic replication of DNA. In PCR, a short segment of DNA is amplified using primer mediated enzymes. DNA Polymerase synthesis new strands of DNA complementary to the template DNA.
You should try reducing your annealing temperature by a few degrees and repeat the PCR. If the problem is due to a high annealing temperature, then you should start to see something. Or, even better, if your PCR machine has a gradient functionality then perform a gradient PCR to test a variety of annealing temperatures at once.To learn more about PCR check the given link
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Choose the expression that is equivalent to the quantity 9 raised to the negative second power times 9 raised to the seventh power end quantity all raised to the negative third power −99 negative 1 divided by 9 raised to the sixth power 1 divided by 9 raised to the fifteenth power 927
The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power
How to use the Law of Indices?
We want to find the expression that is equivalent to the quantity nine raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power. Indices display the results of multiples of a number, such as squared or cubed, or they display the roots of numbers, such as the square root. The laws of indices can be used to condense some indexed terms.This is written as;
(9⁻² * 3⁵)⁻²
According to laws of indices, we know that;
(a²)³ = a²*³ = a⁶
Thus;
(9⁻² * 3⁵)⁻²= (9⁻²)⁻² * (3⁵)⁻²
⇒ 9⁴ * 1/3¹⁰
⇒ 9⁴/3¹⁰
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Answer:The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power
The floor of a rectangular living room is 12 meters by 5 meters. What is the distance between opposite corners of the living room?
Answer: I dunno
Step-by-step explanation:
Answer: 13
Step-by-step explanation: Solve this problem by. using the Pythagorean Theorem
[tex]12^{2} + 5^{2} = \sqrt[2]{C}[/tex]
144 + 25 = 169
[tex]\sqrt[2]{169}[/tex] = 13
THe Hypotenuse or distance between the triangle diagonals is 13.
suppose that a full 3-ary tree has 100 internal vertices. how many leaves does it have? suppose that a full 4-ary tree has 100 leaves. how many internal vertices does it have?
Answer:
i = (L – 1)/(m – 1) = 99/3 = 33. i = 33.
Step-by-step explanation:
Which table could be a partial set of values for a linear function?
Responses
x y table 1
0 0
1 1
2 4
3 9
x y 0 0 1 1 2 4 3 9 , , ,
x y table 2
0 0
1 1
2 8
3 27
x y 0 0 1 1 2 8 3 27 , , ,
x y table 3
0 0.0
1 0.5
2 1.0
3 1.5
x y 0 0.0 1 0.5 2 1.0 3 1.5 , , ,
x y table 4
0 0.0
1 0.5
2 2.0
3 4.5
Answer:
table 3
Step-by-step explanation:
As we know that
A Linear function is the one whose graph represents a line OR value of its dependent and independent variable change at a rate which remains constant throughout.
Now in the fourth table the values of x and y are given as show below: