Answer:
.
Step-by-step explanation:
sorry i hit my daily limit and i need more answers
which of the following graphs shows the solution set to the system of inequalities below? {y>12x 4y>5
Answer:
Step-by-step explanation:
the value of y varies exponentially with respect to x and the 1 -unit growth factor is 1.8 . which of the following is the best explanation for the meaning of this growth factor?
We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
Given that,
With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.
We have to find which of the following best describes the significance of this growth factor.
We know that,
The required expression for y with respect to x is
y=(1.8)ˣ------>equation(1)
1.8=1- unit growth factor.
Whenever x changes by 1.
x=x-1----->equation(2)
Putting equation (2) in (1)
y'=1.8ˣ⁺¹
y'=1.8ˣ×1.8----->equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ
y'=(1.8)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.
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y=(1.8)ˣ equation(1)
1.8=1- unit growth factor.
Whenever x changes by 1.
x=x-1 equation(2)
y'=1.8ˣ⁺¹
y'=1.8ˣ×1.8 equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ
y'=(1.8)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.
I really need help with these questions please help
The area, lengths and dimensions of the plot of land and the situation picture are as follows;
a. 282.2 ft
b. 2330 ft²
c. 42.8 ft
Exercise 364
The true statements are;
The perimeter of ΔPQU is greater than 13 units
The perimeter of ΔPQR is 12 units
The area of ΔPST is 7.5 square units
What is the perimeter of a shape or figure?The perimeter of a shape or figure is the length or distance of the edge boundary of the shape.
a. The perimeter of the plot of land, P, can be found as follows;
P = (70 - 0) + (60 - 0) + (80 - 0) + √((80 - 60)² + (0 - 70)²) ≈ 282.8
The perimeter of the fencing is approximately 282.8 feet
b. The shape of the plot of land is a trapezium
Area of the plot of land is therefore; A = 0.5 × (60 + 80) ×70 = 4900
The shape of the Parking Area is a trapezium, therefore;
Area of the Parking Area = 0.5 × ((49 - 8) + (60 - 8)) ×(70 - 50) = 930
The shape of the Warehouse is a square, therefore;
Area of the Warehouse = (49 - 8) × (50 - 10) = 1640
Area of the plot of land that does not include the warehouse and the parking area is therefore;
Required area = 4900 - (930 + 1640) = 2330
The area of the plot of land that does not include the warehouse and the parking area is 2330 ft²
c. The sum of the length of the legs of the parking area trapezoid, L, can be found as follows;
L = (70 - 50) + √((70 - 50)² + (60 - 49)²) ≈ 42.8
The total length of fence needed is about 42.8 ft
Exercise 364
The true statements are found as follows;
The perimeter of the ΔPQU = 4 + 4 + 4·√2 ≈ 13.66 > 13The perimeter of the ΔPQR = 3 + 4 + √(3² + 4²) = 12The perimeter of QRSTU = 3 + √(5² + 2²) + √(3² + 4²) + 4·√2 + √(5² + 2²) ≈ 24.43
The perimeter of QRSTU > 24
The area of ΔPRS = 0.5 × 3 × 5 = 7.5
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In a study, the residents of Edinburgh, Scotland, were classified as having either black hair, brown hair, blonde hair, or red hair. The probabilities of a randomly selected resident having black, brown, or blonde hair are 0.17, 0.47, and 0.20 respectively. Assuming each resident has one of these four hair colors,(a) what is the probability that a randomly selected resident has red hair?(b) what is the probability that a randomly selected resident has brown or black hair?(c) what is the probability that a randomly selected resident does not have blonde hair?
a) probability that a randomly selected resident has red hair is 0.16
b) probability that a randomly selected resident has brown or black hair is 0.67
c) probability that a randomly selected resident does not have blonde hair is 0.8.
P(black hair color) = 0.17
P (Brown hair) = 0.47
P (blonde hair) = 0.20
a) Probablity that a randomly chosen resident has red hair is:
P(red hair) = 1 - P(black hair) - P(brown hair) - P(blonde hair)
=> 1 - 0.17 - 0.47 - 0.20
=> 0.16
b) P(brown hair) + P(black hair) is the likelihood that a randomly chosen resident has brown or black hair (black hair)
= 0.47 + 0.20
= 0.67
c) The Probability that a randomly chosen resident does not have blonde hair is equal to 1 - P (blonde hair)
=> 1 - 0.20
=> 0.8
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The probability that a randomly selected resident has red hair and brown or black and black, brown, or blonde hair is 0.16, 0.80 and 0.20
The probabilities of a randomly selected resident having black, brown, or blonde hair are 0.17, 0.47, and 0.20 respectively.
P (black hair) = 0.17
P (brown hair) = 0.47
P (blonde hair) = 0.20
The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.
(a). Probability that a randomly selected resident has red hair is
P (red hair) = 1 -P(black hair)-P (brown hair)-P (blonde hair)
= 1 - 0.17 - 0.47 - 0.2
= 0.16
(b). Probability that a randomly selected resident has brown or black hair
= P (brown hair) + P (black hair)
= 0.47 + 0.20
= 0.67
(c). Probability that a randomly selected resident does not have blonde hair
= 1 - P (blonde hair)
= 1 - 0.20
= 0.80
Therefore, the probability is 0.16, 0.80 and 0.20.
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Which of the following functions is graphed below?
Answer:
D
Step-by-step explanation:
Looking at the graph, when x <= 1, the line is x + 6. Only one answer has this option.
In two or more complete sentences, describe the transformation(s) that take place on the parent function,
f(x) = log(x), to achieve the graph of g(x) = log(-3x - 9) - 1.
Answer:
The function g(x) = log(-3x - 9) - 1 is obtained from the parent function f(x) = log(x) through two transformations: a shift to the right and a shift downward. The shift to the right is achieved by multiplying x by -3 and subtracting 9, which results in a rightward shift in the function's graph. The shift downward is achieved by subtracting 1 from the final result, which results in a downward shift in the function's graph. These transformations result in a graph that is shifted to the right and downward compared to the graph of the parent function.
[tex]log( - 3x - 9) = log( 3( - x - 3)) \\ = log( 3) + log( - (x + 3))[/tex]
A vertical shift by 1 unit downwards
A vertical shift by log(3) units upwards
A horizontal shift by 3 units to the left
A reflection along the line x=-3
Determine a series of transformations that would map Figure T onto Figure U.
Press "try" to test a transformation or sequence of transformations.
The series of transformations that would map Figure T onto Figure U are:
Rotation TranslationWhat is rigid transformation?
Transformation is a process in which the dimensions of an object is resized, or its orientation is changed.
Rigid transformation is a topic that involves resizing an object, or changing its orientation. Some common methods used in transformation are: reflection, dilation, rotation and translation.
Reflection is the process in which a given object is turned about a reference point or line.Dilation involves changing the dimensions of a given object. Thus its size will be affected.
Rotation involves turning an object at a certain angle. Translation implies moving a whole object in a given direction and number of units.
In the given question, the required series of transformation are:
i. First rotating figure T at an angle of 90 degrees using its base as the reference line.
ii. Then translating the image some units.
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The graph of the function f(x) = −1 + 0.5x is shown on the coordinate plane. For what value of x does f(x) = 2?
A.
x = -6
B.
x = 5
C.
x = 5
D.
x = 6
x = 6 is the value of x does f(x) = 2.
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Here, we have
Given function: f(x) = −1 + 0.5x
We have to find the value of x does f(x) = 2.
For this, we put the different values of x and see what value satisfies the given function.
For x = -6
f(x) = −1 + 0.5(-6)
f(x) = -4
For x = 5
f(x) = −1 + 0.5(5)
f(x) = 1.5
For x = 6
f(x) = −1 + 0.5(6)
f(x) = 2
Hence, x = 6 is the value of x does f(x) = 2.
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A circular rug is cut from a square piece of carpet. Each side of the square piece of Carpet is 40 inches long. After cutting out the circular rug, approximately how much carpet will be left over?
Answer:
Below
Step-by-step explanation:
Area of square - area of circle = remnant area of circle = pi r^2
(40 x 40) - pi (20^2) = 343 . 4 in^2 left over
( this assumes the circle touches the edges of the square)
Based on the relative frequency histogram below , which of the following statements is supported by the plot? i. The IQR of the distribution is roughly 10
ii. There are no outliers in the distribution.
iii. It is not possible to estimate the median without knowing the sample size. iv. The distribution is multimodal v. The mean of the distribution is smaller than its median.
The statement supported by the plot is that the IQR of the distribution is roughly 10. It is possible to estimate the median from the plot, and the distribution appears to be unimodal, with the mean being smaller than the median. There are no outliers shown in the plot.
The relative frequency histogram provides a visual representation of the distribution of the data. From the plot, it is possible to estimate the median, which is the middle value of the distribution, as well as the interquartile range (IQR), which is the difference between the upper and lower quartiles. The IQR of the distribution is roughly 10, which can be seen by the distance between the upper and lower quartiles in the plot. Additionally, the distribution appears to be unimodal, which means that it has only one mode or peak. It is also apparent that the mean of the distribution is smaller than its median, as the peak is shifted to the left of the median. Finally, there are no outliers shown in the plot, as all of the values appear to be within the range of the distribution.
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Consider the following three polynomial functions.
f(x) =3x3 +5x-2
9 (x) =582-3x +2 m(x) =2x2 - 2x
Write an expression to represent f(x) + [g (x) - m(x)].
Use the carrot (^) for exponents and leave no spaces between terms.
The Solution for the given problem is 6x² +4x
What is Polynomial?
A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Solution:
We are given with the values of the following terms f(x), g(x), and m(x)
f(x) = 3x² + 5x - z
g(x) = 5x² - 3x + z
m(x) = 2x² - 2x
To find: f(x) + [g(x) - m(x)]
so, we need to put the respective values in the equation and simplify it
3x² + 5x - z + [5x² - 3x + z - 2x² + 2x]
3x² + 5x - z + [3x² - x + z]
6x² +4x
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tan^2x/sec^2x + cot^2x/csc^2x
The value of the trigonometric expression will be 1. Then the correct option is C.
What is trigonometry?Mathematical capabilities inspect the collaboration between the aspects and points of a three-sided structure.
The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.
The expression is given below.
⇒ tan²x / sec²x + cot²x / cosec²x
Simplify the expression, then the value of the expression is given as,
⇒ tan²x / sec²x + cot²x / cosec²x
⇒ (sin²x × cos²x) / cos²x + (cos²x × sin²x) / sin²x
⇒ sin²x + cos²x
⇒ 1
The worth of the mathematical articulation will be 1. Then, at that point, the right choice is C.
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Tim has 42 marbles. He divides them equally into 7 bags. How many marbles are in each bag?
Answer:
6 marbles per bag
Step-by-step explanation:
42 marbles * 1 bag / 7 bags =
42 * 1/7 =
42/7 = 6 marbles per bag
1 bag represents each bag of the 7 total bags.
Multiply 1 bag / 7 bags with 42 marbles(total amount of marbles) to get the marbles in EACH bag.
Answer:
let x = marbles in a bag
x = 42/7
x = 6
There are 6 marbles in each bag for 7 bags(6) + (6) + (6) + (6) + (6) + (6) + (6)
This is 7 bags, total of 42 marbles
this is my own explanation moderator, please dont delete just because its almost the same with previous answer. well its because its the only way to solve it hehe but i add another explanation, i really dont want to get warnings for this kind of questions you knoww..
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Using the year 2000 as the base year, compute
- nominal GDP [1 point]
- real GDP [1 point]
- GDP de
ator [1 point]
1) Nominal GDP = Current year price* Current year quantity
= 500*3000 + 400,000*20
= 1,500,000 + 8,000,000
= $9,500,000
2) Real GDP = Base year price* Current year quantity
= 500*2000 + 400,000*10
=1,000,000 + 4,000,000
= $5,000,000
3) GDP Deflator = Nominal GDP/Real GDP
=9,500,000/5,000,000
How many groups of \dfrac{7}{4}
4
7
start fraction, 7, divided by, 4, end fraction are in 111?
There are two groups of [tex]\dfrac{7}{4}[/tex], an integer which is equal to 1, and 0.75 which is decimal.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
The given fraction is,
[tex]\dfrac{7}{4}[/tex].
To find the groups of fraction,
Simplify the fraction,
[tex]\dfrac{7}{4} = 1 \dfrac{3}{4}\\\\ = 1.75[/tex]
There are two groups in the fraction of [tex]\dfrac{7}{4}[/tex] ,
Integer part which is 1.
And decimal part which is 0.75.
Hence, there are two groups of fraction [tex]\dfrac{7}{4}[/tex].
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The greatest common factor of 250 and 300 is?
Answer:
GCF: 50
Step-by-step explanation:
Let's test
50 ( 5 + 6)
= 250 + 300
So, my answer is correct!
I found it is 273 Megabytes is being download if the download is 17.7% completed how many megabytes have been downloaded Round your answer to the nearest 10th
The megabytes that have been downloaded will be 48 megabytes.
How to depict the percentage?Based on the information, percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since 273 megabytes is being download if the download is 17.7%, the megabytes that have been downloaded will be:
= 17.7% × 273
= 48 megabytes.
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Which of these expressions is equivalent to 5.8 ÷ 1.15 ?
0.58÷115 5.8÷115 58÷115 580÷115
The expression that is equivalent to 5.8 ÷ 1.15 is 580 ÷ 115
What are equivalent expressions?Equivalent expressions are expressions that have equal values when compared
How to determine the equations that are equivalent?From the question, we have the following parameters that can be used in our computation:
5.8 ÷ 1.15
Divide both sides of the equation by 1/10
So, we have the following representation
5.8 ÷ 1.15 = 5.8/(1/10) ÷ 1.15/(1/10)
Evaluate the quotients
So, we have the following representation
5.8 ÷ 1.15 = 58 ÷ 11.5
Multiply both sides of the equation by 10
So, we have the following representation
5.8 ÷ 1.15 = 580 ÷ 115
Hence, the equivalent equation is 580 ÷ 115
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How many positive integers have distinct prime digits?
Answer:
64
Step-by-step explanation:
There are 4 prime digits: 2, 3, 5, and 7.
If the number is one digit, there are 4 possible numbers.
If the number is two digits, there are 4(3)=12 possible numbers.
If the number is three digits, there are (4)(3)(2)=24 possible numbers.
If the number is four digits, there are (4)(3)(2)(1)=24 possible numbers.
Taking the sum, the answer is 64.
What is the equation for the line that passes through the points (3, 4) and (5,8)
The equation of a line is typically given in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). To find the equation of the line that passes through the points (3, 4) and (5, 8), we need to first calculate the slope of the line.
The slope of a line is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we have:
m = (8 - 4) / (5 - 3) = 4/2 = 2
Now that we know the slope of the line, we can use one of the given points to find the y-intercept. Let's use the point (3, 4). If we plug the values of x and y into the equation y = mx + b, we get:
4 = 2 * 3 + b
4 = 6 + b
-2 = b
Therefore, the equation of the line that passes through the points (3, 4) and (5, 8) is:
y = 2x - 2
the following sorting algorithm is stable and in runs in place. none of the others quicksort counting sort mergesort. true or false
A stable sorting algorithm is one that keeps the relative order of two equal elements. Quicksort is a sorting algorithm that has a high degree of instability, which means that it may alter the relative order of two equal components.
Which sorting algorithm is stable?The Merge Sort, Timsort, Counting Sort, Insertion Sort, and Bubble Sort are just a few examples of popular sorting algorithms that are by their very nature stable. Others, like Quicksort, Heapsort, and Selection Sort, are erratic. Stable sorting algorithms can be modified to be more efficient.
Because we swap elements according on the location of the pivot, QuickSort is an unstable algorithm (without considering their original positions). A sorting algorithm is said to sort in-place if it never stores more than a fixed number of input array members outside of the array. If the order of elements with the same value is not altered by a sorting technique, it is stable. Binary insertion sort is the only stable algorithm available from the options offered.
Therefore the correct answer is false.
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The height between two floors of a building is 10 feet. How many stairs would be required
if the rise of each stair is 8 inches?
Note: 1 foot = 12 inches
Answer:
15 stairs would be needed
Step-by-step explanation:
10x12= 120
15 x 8 = 120
Santa Santa can deliver presents to 15 children per hour. What is the maximum number of presents Santa can deliver to children’s in three hours?
Answer:
45
Step-by-step explanation:
15(3) = 45
find the measure of m< VTK
Measure of angle VTK is 90°.
Define angle.Angles come in many different varieties in geometry. Angle is among the most crucial and fundamental units. Two rays or lines are linked at their shared terminus when they create an angle. We use angles in many facets of our daily lives, starting with the construction of buildings, dams, and monuments, not only in mathematics. The study of angles is essential to civil engineering. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.
Given
∠VTK = 90°
∠VMK = 90°
∠VTK is given
∠VTK = 90°
Measure of angle VTK is 90°.
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Spencer sampled 50 students of a private school who were questioned about their scores in Mathematics. Spencer wants to test the hypothesis that the private school students score better than the general public which has an average of 62 marks with a population standard deviation of 7 marks.
z equals fraction numerator x with bar on top minus mu over denominator begin display style fraction numerator sigma over denominator square root of n end fraction end style end fraction
If the sample mean is 65 marks, what is the z-score? Answers are rounded to the hundredths place.
The answer is 3.03
What is a sample mean?A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set.
Given here μ=62 σ=7 sample mean x = 65 and n=50
now the formula given is z= x-μ / σ÷√n
= 65-62 / 7÷√50
= 3√50/7
= 3.03
Hence the final answer is 3.03
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Assume that a company uses a standard cost system and applies overhead to production based on direct labor-hours. It provided the following information for its most recent year:
Total budgeted fixed overhead cost for the year $ 300,000
Actual fixed overhead cost for the year $ 276,000
Budgeted direct labor-hours 60,000
Actual direct labor-hours 56,000
Standard direct labor-hours allowed for the actual output 58,000
What is the fixed overhead volume variance?
Multiple Choice
$20,000 U
$20,000 F
$10,000 U
$10,000 F
Group Ends
On solving the provided question, we can say that The $289,000 in fixed overhead that was used in production at that time
What are fixed overhead?In accounting and economics, expenses for a firm are referred to as "fixed costs," often known as "indirect costs" or "overhead costs" since they are independent of the volume of goods or services the organization produces. They often have a periodic nature, such monthly rent or interest payments. These expenses are frequently capital costs as well.
The fixed overhead rate equals the budgeted amount Budgeted hours / Fixed overhead costs
Fixed overhead rate (predetermined) = 300,000/60,000
The fixed overhead rate (predetermined) is $5 per hour.
Applied Standard hours permitted with a predetermined overhead rate equals fixed overhead (fixed)
Fixed overhead applied = 57,800 * $5 per hour
$289,000 for applied fixed overhead
Therefore, $289,000 in fixed overhead was allocated to production during that time.
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An experiment is carried out to determine the relationship between the average speed (rpm) and power (hp) of a mixer.
Construct a scatter plot for the data obtained in the experiment. Complete your work in the space provided or upload a
file that can display math symbols if your work requires it. Be sure to label the axes and include an appropriate scale for
the numerical labels.
Answer:
Step-by-step explanation:
So your first point has x=325.0 and y=1.10, your second point has x=348.9 and y=1.40, and so on.
The graph should look something like this:
The conclusion that you would draw from your plot is that the power seems to vary linearly with the speed. The data points are almost in a straight line. They are not perfectly aligned, of course. There is always some variability in real data, but you can see a trend.
round 87388 to the nearest thousand
Answer:
To round a number to the nearest thousand, we first need to identify the thousands digit in the number. In this case, the thousands digit is 8, because 87388 is between 80000 and 90000.
To determine whether to round up or down, we need to look at the hundreds digit, which is 7 in this case. If the hundreds digit is 5 or greater, we round up. If the hundreds digit is less than 5, we round down. In this case, the hundreds digit is 7, which is greater than or equal to 5, so we need to round up.
To round up, we add 1000 to 87388, which gives us 88388. So, 87388 rounded to the nearest thousand is 88000.
If the point starts at and rotates counterclockwise, which statement is TRUE? a. x=cosθ andy=sinθ and both functions have a period ofπ . b. x=sinθ andy=cosθ and both functions have a period of 2π . c. x=sinθ andy=cosθ and both functions have a period ofπ . d. x=sinθ andy=cosθ and both functions have a period of 2π .
The correct statement regarding the unit circle is given as follows:
x = cos(θ) and y = sin(θ), and both functions have a period of 2π.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
These points are contained according to the following identity:
[tex]\cos^2{\theta} + sin^2{\theta} = 1[/tex]
(standard identity of trigonometry).
From the x-coordinate and the y-coordinate of each point on the unit circle, the function definitions are given as follows:
x = cos(θ)y = sin(θ)The period of both functions is of 2π, as the entire unit circle forms an angle of 360º = 2π.
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NO LINKS!!
The approximate lengths and diameters (in inches) of bright common wire nails are shown in the table. Find a logarithmic equation that relates the diameter y of a bright common wire nail to its length x. (Use the first and last lengths and diameters to form the equation. Round your answers to three decimal places.)
ln(y)=
Length, x Diameter, y
2. 0.113
3. 0.151
4. 0.192
5. 0.222
6. 0.262
Answer:
[tex]\ln (y) = 0.210x-2.601[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Length & \sf Diameter \\x & y\\\cline{1-2} \vphantom{\dfrac12} 2 & 0.113\\\cline{1-2} \vphantom{\dfrac12} 3& 0.151\\\cline{1-2} \vphantom{\dfrac12} 4& 0.192\\\cline{1-2} \vphantom{\dfrac12} 5& 0.222\\\cline{1-2} \vphantom{\dfrac12} 6& 0.262\\\cline{1-2} \end{array}[/tex]
To convert y = abˣ to linear form, take natural logs of both sides and rearrange:
[tex]\begin{aligned}y=ab^x \implies \ln y &= \ln ab^x\\\implies \ln y &= \ln a + \ln b^x\\\implies \ln y &= \ln a + x \ln b\\\implies \ln y &=x \ln b+ \ln a\end{aligned}[/tex]
This is in the straight-line form y = mx + c.
Substitute the first and last values of x and y from the table into the natural log formula:
[tex]\ln 0.113 = 2 \ln b+\ln a[/tex][tex]\ln 0.262 = 6 \ln b+\ln a[/tex]Subtract the first equation from the second equation to eliminate ln(a);
[tex]\implies \ln 0.262 - \ln 0.113 = 6 \ln b - 2 \ln b[/tex]
[tex]\implies \ln 0.262 - \ln 0.113 = 4 \ln b[/tex]
Apply the quotient log law:
[tex]\implies \ln \dfrac{0.262}{0.113} = 4\ln b[/tex]
Rearrange and solve for ln(b):
[tex]\implies \ln b = \dfrac{1}{4}\ln \dfrac{0.262}{0.113}[/tex]
[tex]\implies \ln b = 0.210\; \sf (3\;d.p.)[/tex]
Substitute the found value of ln(b) into one of the equations and solve for ln(a):
[tex]\implies \ln 0.262 = 6 \cdot \dfrac{1}{4}\ln \dfrac{0.262}{0.113}+\ln a[/tex]
[tex]\implies \ln a=\ln 0.262 -\dfrac{6}{4}\ln \dfrac{0.262}{0.113}[/tex]
[tex]\implies \ln a = -2.601\; \sf (3\;d.p.)[/tex]
Substitute the found values of ln(a) and ln(b) into the formula to create an equation for ln(y):
[tex]\boxed{\ln (y) = 0.210x-2.601}[/tex]