Since c must be between 1 and 3, we can eliminate the negative solution and calculate that c = 2.089. Therefore, the answer is 0. The correct option is (A).The Mean Value Theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the slope of the tangent line.
Applying this theorem to the function f(x) = 2x³ - 4x² + 1 on the interval [1,3], we know that there exists a value c in (1,3) such that the slope of the tangent line at c is equal to the slope of the secant line between f(1) and f(3).
To find the value of c, we can start by calculating the slope of the secant line:
slope = (f(3) - f(1)) / (3 - 1)
= (2(3)³ - 4(3)² + 1 - 2(1)³ + 4(1)²⁻¹) / 2
= 26
Next, we need to find the derivative of f(x):
f'(x) = 6x² - 8x
Now we can set the slope of the tangent line equal to the slope of the secant line and solve for c:
6c² - 8c = 26
3c² - 4c - 13 = 0
Using the quadratic formula, we get:
c = (4 ± sqrt(4² - 4(3)(-13))) / (2(3))
c = (4 ± sqrt(160)) / 6
c = 2.089 or c = -1.422
Therefore, the answer is 0.
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You’re in a math class of 16 students (including yourself). Your teacher has a bag of 16 chocolate bars, and says “This morning, I had exactly one golden ticket. There’s an 80% chance I put it in one of these bars, and a 20% chance I threw it away.”
She then passes the bag around, and everyone takes a bar at random. You keep your bar closed while each of the other students in the class opens theirs and discovers no golden ticket inside.
What are the chances your bar has the golden ticket in it?
Please enter your answer as a percent from 0 to 100 without the % symbol, and round to the nearest integer. E.g. if your answer is 55.37%, please enter it as 55.
The chances of your bar having the golden ticket are still 80%.
The chances of your bar having the golden ticket in it are still 80%.
Even though the other students have opened their bars and found no golden ticket, the probability of the golden ticket being in the remaining bar has not changed.
The fact that the other students opened their bars and found nothing does not affect the probability of your bar containing the golden ticket.
Therefore, the chances of your bar having the golden ticket are still 80%.
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FILL IN THE BLANK. If n(E1 and E2​)=3
and
​n(E1​)=12​,
then
​P(E2​|E1​)=​_______.
If n(E1 and E2) = 3 and n(E1) = 12, then P(E2|E1) = 1/4. To find the probability P(E2|E1), given that n(E1 and E2) = 3 and n(E1) = 12, we'll use the conditional probability formula. The formula is P(E2|E1) = P(E1 and E2) / P(E1).
Step 1: Find the probabilities of the events.
P(E1) = n(E1) / total outcomes = 12 / total outcomes
P(E1 and E2) = n(E1 and E2) / total outcomes = 3 / total outcomes
Step 2: Plug the probabilities into the conditional probability formula.
P(E2|E1) = P(E1 and E2) / P(E1)
Step 3: Substitute the values from Step 1 into the formula.
P(E2|E1) = (3 / total outcomes) / (12 / total outcomes)
Step 4: Simplify the expression.
P(E2|E1) = 3/12
Step 5: Reduce the fraction to the simplest form.
P(E2|E1) = 1/4
So, the probability of event E2 occurring given that event E1 has occurred is 1/4 or 0.25.
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A probability that can be deducted through logical reasoning before an experiment is performed is what type of probability?"
A probability that can be deducted through logical reasoning before an experiment is performed is Theoretical probability.
What is Theoretical probability?Theoretical probability is based on what is expected to happen, or a theory, using reasoning. It is based on knowledge and mathematics. An experiment is not conducted to find theoretical probability.
How to calculate Theoretical probability?The formula to calculate the theoretical probability of event A happening is:
P(A) = number of desired outcomes / total number of possible outcomes
For example, the theoretical probability that a dice lands on “2” after one roll can be calculated as:
P(land on 2) = (only one way the dice can land on 2) / (six possible sides the dice can land on) = 1/6
Thus, A probability that can be deducted through logical reasoning before an experiment is performed is Theoretical probability.
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approximately how many times larger is 4.2 x 10-¹ than 1.4 x 10-5?
C) 3 x 104
B) 3.3 x 103
A) 3 x 10-4
D) 3.3 × 10-3
4.2 x 10-¹ is approximately 3 x 10^4 times larger than 1.4 x 10-5.
A patient needs to receive 35 mg of amoxicillin orally. The drug is available in a strength of 100 mets How many teaspoons of the drug must the patient swallow to receive the correct dose?
The patient needs to swallow 0.35 teaspoons of the drug to receive the correct dose.
To determine the number of teaspoons of the drug the patient needs to swallow, we can set up a proportion based on the drug's strength.
Let x represent the number of teaspoons the patient needs to swallow.
We can set up the proportion as follows:
100 mg / 1 teaspoon = 35 mg / x teaspoons
To solve for x, we can cross-multiply and then divide:
100 mg * x teaspoons = 35 mg * 1 teaspoon
100x = 35
x = 35 / 100
x = 0.35
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need help by today forgot to do it oh and could you show your work how you got your answers
The street dance group performed a total of 4.5 hours for 8 days during the summer.
From the given image, on the first two days which are Day-1 and Day-2 they performed for 1/4 hour which is 0.25 hours on each day. The next 3 days which are day-3, day-4, and day-5 they performed for 2/4 hour which is 0.5 hour on each day. For the next 2 days which is day-6 and day-7, they performed for 3/4 hours which is 0.75 hours for each day. On the final day which is day-8, they performed for 1 hour.
To find mathematically, the total hours they performed in 8 days is
Total hours = (2 x 0.25) + (3 x 0.5) + (2 x 0.75) + 1 (1)
= 0.5 + 1.5 + 1.5 + 1
= 4.5 hours
From the above analysis, we can conclude that the dance group performed for a total of 4.5 hours for 8 days.
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A ball is thrown downward from the top of a 180 foot building with an initial velocity of 16 ft per second. The height of the ball h in feet after t seconds is given by the equation h=-16t^2-16t+180 how long after the ball is thrown will it strike the ground
Answer:
-16t^2 - 16t + 180 = 0
4t^2 + 4t - 45 = 0
t = (-4 + √(4^2 - 4(4)(-45))/(2×4)
= (-4 + √736)/8 = (-4 + 4√46)/8
= (-1 + √46)/2 = 2.89 seconds
How do I solve this ????
The solution to the inequality is 2x + y < 7 and the graph is plotted
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
2x + y < 7
On simplifying the equation , we get
Let the point be P ( 2 , 3 )
2 ( 2 ) + 3 < 7
4 + 3 < 7
7 is not less than 7
So , it is not a solution to the inequality
Hence , the equation is 2x + y < 7
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10 increased by the product of a number and 7 is greater than -24. Use the variable b for the unknown number.
The solution for the inequality is b > -34/7.
Inequality refers to the phenomenon of unequal and/or unjust distribution of resources and opportunities among members of a given society.
The inequality can be expressed as:
10 + 7b > -24
To solve for b, we need to isolate the variable b. We can do this by subtracting 10 from both sides of the inequality:
10 + 7b - 10 > -24 - 10
This simplifies to:
7b > -34
Finally, we divide both sides of the inequality by 7 to solve for b:
(7b) / 7 > (-34) / 7
b > -34/7
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The coefficient of determination Group of answer choices cannot be negative is the square root of the coefficient of correlation is the same as the coefficient of correlation can be negative or positive
Answer:
Postive, The coefficient of determination is a measure of how well the regression line fits the data points. It represents the proportion of variation in the dependent variable that can be explained by the independent variable. The coefficient of determination ranges from 0 to 1, with higher values indicating a stronger relationship between the variables. Importantly, it cannot be negative.
The coefficient of determination is equal to the square of the coefficient of correlation, which measures the strength and direction of the linear relationship between two variables. However, unlike the coefficient of determination, the coefficient of correlation can be negative or positive. A negative value indicates an inverse relationship between the variables, while a positive value indicates a direct relationship.
The coefficient of determination, also known as R-squared, is a measure of how well the regression line fits the data. It represents the proportion of variation in the dependent variable that can be explained by the independent variable(s). R-squared ranges from 0 to 1, with higher values indicating a better fit. It cannot be negative, as it is a squared value. The square root of the coefficient of correlation is equal to the coefficient of determination. The coefficient of correlation can be negative or positive, indicating the direction of the relationship between the variables.
From the central limit theorem, we know that is we draw a SRS from any population then the sampling distribution of the sample mean will be EXACTLY Normal.
The central limit theorem states that if we draw a simple random sample (SRS) from any population, regardless of the shape of the population distribution.
The sampling distribution of the sample mean will be approximately normal if the sample size is large enough. This means that the mean of the sampling distribution will be the same as the mean of the population, and the standard deviation of the sampling distribution will be the standard error of the mean, which is equal to the standard deviation of the population divided by the square root of the sample size. Therefore, the central limit theorem allows us to make inferences about the population mean based on the sample mean, as long as we have a large enough sample size.
According to the Central Limit Theorem, if we draw a Simple Random Sample (SRS) from any population, the sampling distribution of the sample mean will APPROXIMATELY be normal, not exactly normal. This approximation improves as the sample size increases, especially when the sample size is large (usually n ≥ 30). The Central Limit Theorem allows us to make inferences about the population based on the sampling distribution.
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The sum of the circumferences of circles H, J, and K shown at the right is 56pi units. Find KJ.
The length of line segment KJ is equal to 24 units.
How to determine a missing side of a triangle
In this problem we find the representation of a geometric system consisting in three circles and a right triangle. A circumference is described by the following equation:
s = 2π · r
Where:
s - Circumferencer - RadiusThe sum of the three circumferences is introduced below:
56π = 2π · (7 · x)
56π = 14π · x
x = 4
And the length of line segment KJ is now computed:
KJ = 6 · x
KJ = 6 · 4
KJ = 24
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138. Copy List with Random Pointer
A linked list is given such that each node contains an additional random pointer which could point to any node in the list or null.
Return a deep copy of the list.
After creating all the new nodes, we can traverse the original list again and set the random pointers of each new node based on the mapping stored in the hash map. Finally, we can return the head of the new list.
This problem requires creating a deep copy of a linked list that contains an additional random pointer for each node.
The random pointer can point to any node in the list or be null.
To solve this problem, we need to traverse the original linked list and create a new node for each node in the original list. The new node should have the same value as the original node and a null random pointer. We can store a mapping between the original node and the new node in a hash map.
After creating all the new nodes, we can traverse the original list again and set the random pointers of each new node based on the mapping stored in the hash map. Finally, we can return the head of the new list.
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Consider the following experiment:
Rolling a die.
What is the sample space of the experiment? What is the probability of getting a 1 or a 2?
a.
3
b.
C.
d.
12 possible outcomes; P(1 or 2) =
12
12 possible outcomes; P(1 or 2) = 3
6 possible outcomes; P(1 or 2) = 4
6 possible outcomes; P(1 or 2) = 3
Answer: the total number of possible outcomes.
Step-by-step explanation:
A pitcher contains 5 quarts of water. Josy says the pitcher con trains 10 cups of water. Then find the correct number of cups the pitcher contains
The pitcher contains 20 cups of water, not 10 cups as Josy mistakenly claimed.
A quart contains 4 cups of water. Therefore, a pitcher containing 5 quarts of water will have 5 x 4 = 20 cups of water.
Josy's statement that the pitcher contains 10 cups of water is incorrect. The pitcher contains 20 cups of water, as we just determined.
To verify this, we can use the conversion factor between quarts and cups. 1 quart equals 4 cups. Thus, to find the number of cups in 5 quarts of water, we multiply 5 by 4, which gives us 20 cups. Therefore, the correct number of cups the pitcher contains is 20 cups, not 10 cups as Josy had stated.
It is important to understand the relationship between different units of measurement when working with quantities such as volume or weight. In this case, knowing that 1 quart is equivalent to 4 cups allowed us to make the conversion easily and determine the correct number of cups in the pitcher.
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Test Yourself
To show that a real number is rational, we must show that we can write it as ___________________________________.
Answer: a/b
Step-by-step explanation:
There isn't really an explanation for this but
a ration number has to be able to be written as a fraction
for example, the number 6 is rational
we can prove this because 6 can be written as 6/1.
Suppose that you wish to test H0: μ ≥ 0 and you find that the z statistic associated with xx is z = -2.88. Which alternative hypothesis would this z value support?
The z-value of -2.88 would support the alternative hypothesis that the population mean is less than 0 (μ < 0).
Suppose that you wish to test H0: μ ≥ 0 find z statistic associated with xx is z = -2.88. Which alternative hypothesis would this z value support? The rejection region for a two-tailed hypothesis test at 5% level of significance is +/- 1.96. Since -2.88 is outside this range, we can reject the null hypothesis at 5% level of significance. The alternative hypothesis depends on the direction of the z-value. Since the z-value is negative, it indicates that the sample mean is more than 2.88 standard errors below the hypothesized population mean. This supports the alternative hypothesis that the population mean is less than 0 (μ < 0).Learn more about "null hypothesis"
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In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the:
A) t-statistic separately for β2 = 0, β2 = 0.
B) F-statistic for the joint hypothesis that β0 = 0, β1 = 0.
C) t-statistic separately for β3 = 0.
D) F-statistic for the joint hypothesis that β2 = 0, β3= 0.
To test that the two regressions are identical, we need to test the null hypothesis that the coefficients β2 and β3 are equal to zero.
The correct answer is D) F-statistic for the joint hypothesis that β2 = 0, β3= 0.
We can do this by using the F-statistic for the joint hypothesis that β2 = 0 and β3 = 0.
The F-statistic is calculated as follows:
F = [(RSSR - RSSUR) / 2] / [RSSUR / (n - 4)],
where RSSR is the residual sum of squares from the restricted model (with both β2 and β3 set to zero), RSSUR is the residual sum of squares from the unrestricted model (with all coefficients estimated), and n is the sample size.
If the F-statistic is larger than the critical value from the F-distribution with 2 degrees of freedom in the numerator and n-4 degrees of freedom in the denominator at the desired level of significance, we reject the null hypothesis and conclude that the two regressions are not identical.
Option A) is incorrect because testing β2 and β3 separately does not provide a joint test of whether the two regressions are identical.
Option B) is incorrect because it tests a different hypothesis about the intercept and slope coefficients.
Option C) is incorrect because it only tests whether the interaction effect is significant, but it does not test whether the two regressions are identical.
D) F-statistic for the joint hypothesis that β2 = 0, β3= 0.
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E is the center of the circle. The diagram is not drawn to scale.
A rectangular prism has 312 cubes each cubes has an edge legnth of 1/5 cm what is the legnth of the rectangle
The length of the rectangular prism is 7800 times the edge length of a cube, which is 7800 × (1/5) cm = 1560 cm.
To find the length of the rectangular prism, we need to consider the relationship between the number of cubes, the volume of the prism, and the dimensions of the prism.
The volume of a rectangular prism is given by the formula V = l × w × h, where l represents the length, w represents the width, and h represents the height.
In this case, we are given that the prism consists of 312 cubes, and each cube has an edge length of 1/5 cm. Since each cube has the same edge length, we can say that the width, height, and length of the prism are all multiples of 1/5 cm.
Let's assume the length of the rectangular prism is x times the edge length of a cube (1/5 cm). Therefore, the length of the prism is (1/5) × x cm.
The number of cubes (312) is equal to the volume of the prism. The volume of the prism can be calculated by multiplying the dimensions:
312 = (1/5) × x × (1/5) × (1/5)
Simplifying the expression:
312 = (1/25) × x
To solve for x, we multiply both sides of the equation by 25:
312 × 25 = x
x = 7800
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How many times larger is 9 x 105 than 5 x 103?
1.8
18
180
1,800
The number of times by which 9 × 10⁵ is larger than 5 × 10³ as required to be determined is; 180.
How larger is 9 × 10⁵ compared to 5 × 10³?It follows from the task content that the number 9 × 10⁵ is to be compared to 5 × 10³ and determine how larger it is.
On this note, to determine how large 9 × 10⁵ is compared to 5 × 10³; we have that;
(9 × 10⁵) / (5 × 10³)
= (9/5) × (10⁵/10³)
= 1.8 × 100
= 180.
Consequently, the correct answer as required is 180.
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Answer: 180
Step-by-step explanation:
try it and find out........ because it is right -.-
The weights of Gala apples are normally distributed with a mean of 208 grams and a standard deviation of 30 grams.
The proportion of Gala apples weighing less than 162 grams is approximately 0.0628 or 6.28% (rounded to four decimal places).
To solve this problem, we need to use the standard normal distribution formula and z-score. The z-score is a measure of how many standard deviations a value is away from the mean. In this case, we want to find the z-score for a Gala apple weighing 162 grams:
z = (162 - 208) / 30 = -1.5333
We can look up the probability of a z-score being less than -1.5333 in a standard normal distribution table, which gives us a value of 0.0628.
In other words, if we were to randomly select a large number of Gala apples from the population with the given mean and standard deviation, we would expect about 6.28% of them to weigh less than 162 grams.
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Complete question is:
The weights of Gala apples are normally distributed with a mean of 208 grams and a standard deviation of 30 grams. Determine the proportion of Gala apples weighing less than 162 grams. Round your answer to 4 decimal places.
Giving Brainliest Answer to whoever answers first! (I need it answered ASAP!!!)
Write a real-life story that models the following equation;
y=1/2x + 4 y= -2x +14
(Solve by Graphing)
I already know the answer to that problem, it's (4,6) if that helps, but I just need a story.
Thank You!
The real-life story that models the system of equations is shown below
Writing a real-life story for the equationsFrom the question, we have the following system of equations that can be used in our computation:
y = 1/2x + 4
y = -2x + 14
There are several real life stories we can use
One of them is as follows
Ridwan has $4 in his savings account and saves 50 cents every week. Lanre has $14 in his savings accounts and withdraws $2 every week.
Calculate the number of weeks where both would have the same amount in their accounts
The graph of the scenario is attached and the solution is (4, 6)
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what is the answer to number 2 at the top?
The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1
Writing an exponential function for the graph of g(x)From the question, we have the following parameters that can be used in our computation:
Parent function: y = 2^x
The graph of the transformed exponential function g(x) passes through the points (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)
So, we have the following transformation steps:
1st Transformation:
Reflect y = 2^x across the y-axis
So, we have
y = 2^-x
2nd Transformation:
Translate y = 2^-x down by 1 unit
So, we have
y = 2^-x - 1
This means that
g(x) = 2^-x - 1
Hence, the equation of the function g(x) is g(x) = 2^-x - 1
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Use the multiplication rule to simplify:
67.6²
I'm guessing that you want to simplify [tex]67.6^2[/tex]
The two above the 67.2 is a square or a power.
Usually when you take something to a power, you mutiply the number of time by the power:
Examples: [tex]78^2[/tex] would be 78*78
[tex]23^5[/tex] would be 23*23*23*23*23
Questions?
67.6² would simply be 67.6*67.6.
So therefore it is 4569.76
Help please (Image attached)
The value of the infinite series as n tends to 0 is: 0
How to estimate infinite series?Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.
From the infinite series, we want to find the value of the series as n tends to 0.
We are given the series as:
x/2ˣ
At x = 0, we have:
0/2⁰ = 0/1 = 0
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The diameter of a circle is 12 cm. Find its circumference in pi
Answer:
12π
Step-by-step explanation:
We Know
Circumference of a circle = d x π
d = 12 cm
Find its circumference in pi.
Let's solve
12 x π = 12π
So, the circumference of the circle is 12π
Answer:
C=12π
C≈37.69911 cm
Step-by-step explanation:
d=2r, with d being diameter and r being the radius.
C=2πr, with C being the circumference and r being the radius.
Therefore, C=πd.
C=πd
C=π(12)
C=12π
C≈37.69911 cm
Hope this helps and good luck on your homework!
Question content area top
Part 1
An airliner carries 350 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69. 0 in and a standard deviation of 2. 8 in. Complete parts (a) through (d)
The probability that he can fit without bending is 0.9938.
We have,
Mean = 69
standard Deviation = 2.8
So, The probability that he can fit without bending is
z= (x - [tex]\mu[/tex]) / [tex]\sigma[/tex]
z = (76 - 69)/2.8
z = 2.5
z = 2.5
and, P- value for 2.5 = 0.9938.
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What is 3x3 – 11x2 – 26x 30 divided by x – 5? 3x2 – 4x 6 3x2 4x – 6 3x2 26x 8 3x2 – 26x 8
The correct option will be B 3x²+4x-6.
The given polynomial is 3x³-11x²-26x+30.
We need to divide it from x-5,
So,
Factoring the polynomial,
3x³-11x²-26x+30 = 3x²(x-5)+4x(x-5)+6(x-5)
= 3x²+4x-6(x-5)
Now dividing,
3x²+4x-6(x-5) / (x-5) = 3x²+4x-6
Hence, the correct option will be B 3x²+4x-6.
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A straight line of the form ŷ=a+bx is fitted to the 5 data points (1,0), (0,3), (3,1), (2,-3), and (4,2) by the method of least squares. What is the value of b?
The value of b is -0.45.
Calculate the mean of x and y values.
The mean of x values is: [tex]x=\frac{(1 + 0 + 3 + 2 + 4)}{5} =2[/tex]
The mean of y values is: [tex]y =\frac{ (0 + 3 + 1 - 3 + 2)}{5} =0.6[/tex]
Calculate the sample covariance between x and y values.
The sample covariance between x and y is: [tex]s_{xy} =[/tex] Σ [tex]\frac{[(xi - x)(yi - y)]}{(n-1)}[/tex]
where Σ denotes the sum of, xi and yi are the i-th values of x and y, respectively, and n is the sample size.
[tex]s_{xy} = \frac{ [(1 - 2)(0 - 0.6) + (0 - 2)(3 - 0.6) + (3 - 2)(1 - 0.6) + (2 - 2)(-3 - 0.6) + (4 - 2)(2 - 0.6)]}{(5 - 1)}[/tex]
[tex]s_{xy} = -1.8[/tex]
Calculate the sample variance of x values.
The sample variance of x is:
[tex]s_{x^{2} } =[/tex] Σ [tex]\frac{(xi - x)^2}{(n-1)}[/tex]
[tex]s_{x^{2} } =\frac{[(1 - 2)^2 + (0 - 2)^2 + (3 - 2)^2 + (2 - 2)^2 + (4 - 2)^2] }{(5 - 1)}[/tex]
[tex]s_{x^{2} } = 4[/tex]
Calculate the value of b.
The value of b is given by:
[tex]b = \frac{s_{xy} }{s_{x^{2} } }[/tex]
[tex]b = \frac{-1.8}{4}[/tex]
[tex]b = - 0.45[/tex]
Therefore, the value of b in the equation of a straight line that is fitted to the 5 data points by the method of least squares is -0.45.
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