Answer:
Step-by-step explanation:
A. To find the formula for f'(x) using the limit definition of the derivative, we need to evaluate the following limit:
f'(x) = lim(h->0) [f(x + h) - f(x)] / h
Substituting f(x) = 3x^2 - 5, we get:
f'(x) = lim(h->0) [3(x + h)^2 - 5 - (3x^2 - 5)] / h
Expanding the square, simplifying, and canceling out the constant terms, we get:
f'(x) = lim(h->0) [6xh + 3h^2] / h
Canceling out the h's, we get:
f'(x) = lim(h->0) (6x + 3h)
Taking the limit as h approaches 0, we get:
f'(x) = 6x
Therefore, the formula for f'(x) is:
f'(x) = 6x
B. To evaluate f'(-1), we simply substitute x = -1 into the formula we found in part A:
f'(-1) = 6(-1) = -6
Therefore, f'(-1) = -6.
What is 14 1/3- 6 5/8
Answer: To subtract mixed numbers with different denominators, we need to convert them into like fractions first.
14 1/3 can be converted to an improper fraction as follows:
14 1/3 = (14 x 3 + 1) / 3 = 43/3
6 5/8 can be converted to an improper fraction as follows:
6 5/8 = (6 x 8 + 5) / 8 = 53/8
Now we can subtract the fractions:
43/3 - 53/8
To get a common denominator, we can multiply the denominators together: 3 x 8 = 24
43/3 x 8/8 = 344/24
53/8 x 3/3 = 159/24
Now we can subtract the numerators:
344/24 - 159/24 = 185/24
Therefore, 14 1/3 - 6 5/8 = 185/24 or 7 13/24 as a mixed number in simplest form.
Step-by-step explanation:
The simplified value of 14 1/3- 6 5/8 is 7 17/24.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
To subtract 6 5/8 from 14 1/3, we need to have the same denominator.
Converting the mixed numbers to improper fractions, we get:
14 1/3 = 43/3
6 5/8 = 53/8
Now, we need to find a common denominator, which is 24.
Multiplying the numerator and denominator of 43/3 by 8 and 53/8 by 3, we get:
43/3 * 8/8 = 344/24
53/8 * 3/3 = 159/24
Now, we can subtract:
43/3 - 53/8 = (344/24) - (159/24) = 185/24
Therefore, 14 1/3 - 6 5/8 = 185/24 or 7 17/24 as a mixed number.
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Antonio is wrapping a birthday gift for his brother. He starts with 2 meters of ribbon. Then, he cuts off 27 centimeters to decorate the gift. How many centimeters of ribbon does he have left now?
Answer: 173 centimeters of ribbon left
Step-by-step explanation:
Antonio starts with 2 meters of ribbon, which is equal to 200 centimeters (since 1 meter = 100 centimeters). He cuts off 27 centimeters to decorate the gift, so he is left with:
200 - 27 = 173 centimeters
Therefore, Antonio has 173 centimeters of ribbon left.
Write a verbal description of the set {a, e, i, o, u}
Quadralateral ABCD is a rectangle. BE = 2x+1 and AC 6x -12. What is BE
Answer:
BE=15
Step-by-step explanation:
Since E is the center, BE=2x+1
And AC is 6x-12 with E being a midpoint.
Since AC is 2 segments and BE is only 1 then you multiply 2x+1 by 2 so that
you can find x. You multiply 2x+12 by 2 because E is the midpoint so that means ED is the same value as BE
6x-12=4x+2
BD=AC
6x-4x-12=2
2x=2+12
2x=14
x=7
BE= 2x+1
2(7)=14+1=15
This scatter plot shows Marie's best 200 meter times each week after she began training. The equation represents the linear model for this data. y=−0.4x+29.8 According to the model, what will Marie's lowest time be after 14 weeks? Enter your exact answer in the box.
Answer:
So the answer is 24.2
Step-by-step explanation:
Good luck to you!
according to the model, Marie's lowest time after 14 weeks of training will be 24.2 seconds.
What is a linear equation?
Based on the given linear model, we know that Marie's best 200 meter time (y) is a function of the number of weeks of training (x), and can be calculated using the equation:
y = -0.4x + 29.8
To find Marie's lowest time after 14 weeks, we simply need to substitute x = 14 into the equation and solve for y:
y = -0.4(14) + 29.8
y = -5.6 + 29.8
y = 24.2
Therefore, according to the model, Marie's lowest time after 14 weeks of training will be 24.2 seconds.
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this side lengths of a tringal are 6,8.10. is this a right triangle
Answer:
yes
Step-by-step explanation:
It is a Pythagorean triangle 3-4-5
Hope this helps.
Make a tree diagram to show all the possible sequences of answers for four multiple-choice questions, each with five possible responses. Assuming that you are guessing the answers so that all outcomes listed in the tree are equally likely, what is the probability that you will guess the one sequence that contains all four correct answers?
Answer: Here's a tree diagram that shows all the possible sequences of answers for four multiple-choice questions, each with five possible responses:
/-- A -- A -- A -- A
/
/ /-- A -- A -- A -- B
/ /-- A -- A -- B -- A
/ /-- A -- B -- A -- A
/ /-- B -- A -- A -- A
/ /
/ / /-- A -- A -- B -- B
/ / /-- A -- B -- A -- B
/ / /-- A -- B -- B -- A
/ / /-- B -- A -- A -- B
/ / /-- B -- A -- B -- A
/ / /-- B -- B -- A -- A
/
/ /-- A -- B -- B -- B
/ /-- B -- A -- B -- B
/ /-- B -- B -- A -- B
/ /-- B -- B -- B -- A
/
/ /-- A -- B -- B -- B
/ /-- B -- A -- B -- B
/-- B -- B -- A -- B
/-- B -- B -- B -- A
Each branch in the tree represents the guess for one of the questions, and the letters A and B represent the possible answers. There are 5 branches coming out of each node in the tree because there are 5 possible answers for each question.
To find the probability of guessing the one sequence that contains all four correct answers, we multiply the probabilities of following the path A-A-A-A:
P(A-A-A-A) = (1/5) * (1/5) * (1/5) * (1/5) = 1/625
Therefore, the probability of guessing the one sequence that contains all four correct answers is 1/625 or about 0.16%.
Step-by-step explanation:
Adrian and Bryan both worked a total of 88 hours in a week. Bryan worked 8 hours more than Adrian. Find the number of hours each man had worked. Enter the correct answers in the boxes. Adrian: h Bryan: h
Answer:
Let's assume Adrian worked for x hours. Then, Bryan worked for (x + 8) hours.
According to the problem, the total hours worked by both is 88, so we can set up the equation:
x + (x + 8) = 88
Simplifying the equation:
2x + 8 = 88
Subtracting 8 from both sides:
2x = 80
Dividing both sides by 2:
x = 40
So Adrian worked for 40 hours and Bryan worked for 48 hours (since Bryan worked 8 hours more than Adrian).
Answer:
Adrian: 40 hours
Bryan: 48 hours
Step-by-step explanation:
What is eight less than the product of two and a number equals four translated into an equation
Answer:
Let's break down the given sentence into an equation.
Let's assume the number is represented by 'x'.
The product of two and a number: 2x
Eight less than the product of two and a number: 2x - 8
Equals four: 2x - 8 = 4
Therefore, the equation is 2x - 8 = 4.
calculate the following using the column method to 3045 - 2572
The subtraction of 3045 and 2572 by the column method has the result given as follows:
473.
How to obtain the subtraction using the column method?When we subtract two amounts by the column method, we subtract digit by digit separately, hence:
3045
-2572
5 > 2, hence:
5 - 2 = 3.
4 is less than 7, and 0 is also less than 5, hence we must borrow from the last column, where 2 - 2 will be of zero, hence:
14 - 7 = 7.9 - 5 = 4. -> one was borrowed to the 4 - 7 subtraction.Hence the result of the subtraction is given as follows:
3045 - 2572 = 473.
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For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 33 beats per minute, the mean of the listed pulse rates is 77.0 beats per minute, and their standard deviation is s= 27.6 beats per minute.
For the functions f(x)=2x−2 and g(x)=6x2−3, find (g∘f)(x).
Answer: To find (g∘f)(x), we need to first find the composite function g(f(x)):
g(f(x)) = g(2x - 2)
We can now substitute the expression for f(x) into g(x):
g(f(x)) = g(2x - 2) = 6(2x - 2)^2 - 3
Expanding the squared term, we get:
g(f(x)) = 6(4x^2 - 8x + 4) - 3
Simplifying and combining like terms, we get:
g(f(x)) = 24x^2 - 48x + 21
Therefore, (g∘f)(x) = 24x^2 - 48x + 21.
Step-by-step explanation:
8y³+10y²-63y÷2y+7
give me ans quickly
Step-by-step explanation:
you can simply solve this question by simple division
Can you please give me the answers of the following questions on the attached files
a) The 8 in the number 24.387 is in the hundredths place, its value is 8/100 or 2/25.
b) One and three quarter million can be written in figures as 1,750,000.
c) 2/10 or 1/5.
d) 0.26 < 0.62 < 2.06 < 6.2
e) 13.4 > 13.390.33 = 1/38 = 2³
What is the inequality equation?An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
a) The 8 in the number 24.387 is in the hundredths place.
Therefore, its value is 8/100 or 2/25.
b) One and three quarter million can be written in figures as 1,750,000.
c) The 2 in the number 48.52 is in the tenths place.
Therefore, its value is 2/10 or 1/5.
d) Ordering the numbers from smallest to largest:
0.26 < 0.62 < 2.06 < 6.2
e) Completing the statements using the symbols <, > or = :
13.4 > 13.390.33 = 1/38 = 2³
Hence, The answers to each question are:
a) 8/100 or 2/25.
b) 1,750,000.
c) 2/10 or 1/5.
d) 0.26 < 0.62 < 2.06 < 6.2
e) 13.4 > 13.390.33 = 1/38 = 2³
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What is correct regarding a
normal distribution?
The normal distribution has a bell-shaped curve, with the highest point at the mean and a gradual decrease in frequency on either side.
What is Normal Distribution ?
A normal distribution is a continuous probability distribution that is often used in statistics to model a wide variety of phenomena, such as measurements of height, weight, or IQ.
The normal distribution is symmetric. This means that the distribution is mirror-image symmetric around its mean, so that the same proportion of values lie on either side of the mean.
The normal distribution is characterized by two parameters: its mean (μ) and standard deviation (σ). The mean is the center of the distribution, while the standard deviation measures the spread of the distribution.
The total area under the normal distribution curve is equal to 1. This means that the probability of any event occurring is between 0 and 1.
The empirical rule, also known as the 68-95-99.7 rule, applies to normal distributions. This rule states that approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data will fall within three standard deviations of the mean.
Therefore, The normal distribution has a bell-shaped curve, with the highest point at the mean and a gradual decrease in frequency on either side.
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Solve for the value of q
Answer:
-3
Step-by-step explanation:
i hope thisis the right aswrr
I really don’t understand please help me
The probability that this person also sailed is 1.
What is probability?
In mathematics, probability is a measure of the likelihood or chance that an event will occur. It is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Out of 50 people, 40 took part in walking and 18 took part in sailing. However, 3 people did neither activity, which means that 40 + 18 - 3 = 55 people took part in at least one of the activities.
Let's represent the set of people who walked as A, and the set of people who sailed as B. We want to find the probability that a randomly chosen person from A is also in B, which can be represented as P(B|A).
Using the formula for conditional probability, we have:
P(B|A) = P(A and B) / P(A)
We know that P(A and B), the probability that a person took part in both walking and sailing, is 50 - 3 = 47 (since 3 people did neither activity). We also know that P(A), the probability that a person took part in walking, is 40.
Therefore,
P(B|A) = 47 / 40
which simplifies to
P(B|A) = 1.175
probabilities cannot be greater than 1, so the actual probability is 1, meaning that it is certain that a person who walked also sailed.
Hence, The probability that this person also sailed is 1.
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need help with these two when somebody can do so, thanks.
Answer:
1. 92 m²
2. 184 cm²
Step-by-step explanation:
1.
Look at the left triangle.
Imagine that the 8 m segment continues to the bottom, and you have a horizontal leg there.
The hypotenuse measures 15 m.
The vertical leg is 8 m + 4 m = 12 m.
a² + b² = c²
12² + b² = 225
b = 9
The horizontal leg is 12 m.
A = 2 × 12 m × 9 m / 2 - 4 m × 4 m
A = 92 m²
2.
Bottom rectangle: length = 20 cm; width = 7 cm
Upper trapezoid: bottom base = 20 cm - 13 cm = 7 cm; height = 15 cm - 7 cm = 8 cm; upper base = 4 cm
A = 20 cm × 7 cm + (1/2)(7 cm + 4 cm)(8 cm)
A = 184 cm²
Jason and Piera decide to start a college savings account for their newborn son, Joseph. They want to have $40,000 available for him when he is 18, and they expect the account to have an average return of 7%. How much do they need to deposit each month to reach this goal?
Round answer to 2 decimal places.
Answer:
Step-by-step explanation:
pls help i am having a panic attack
The value of cos(2x+y) is -12/65.
Describe cosine ?Cosine, commonly denoted as cos, is a mathematical function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. In other words, it is the ratio of the length of the adjacent side of an angle to the hypotenuse of the right triangle containing that angle. Cosine is one of the basic trigonometric functions, along with sine and tangent, and is widely used in mathematics, physics, and engineering to model various phenomena.
Cosine is periodic with a period of 2π, and its values range from -1 to 1. When the angle is 0°, the cosine is equal to 1, indicating that the adjacent side of the triangle is equal to the hypotenuse.
We can use the trigonometric identities for cosine to find cos(2x+y), using the values of x and y given:
cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)
To find cos(2x), we can use the double angle identity for cosine:
cos(2x) = cos²(x) - sin²(x)
To find cos(x) and sin(x), we can use the fact that x = sin⁻¹(4/5) and the Pythagorean theorem:
sin(x) = 4/5
cos(x) = √(1 - sin²(x)) = √(1 - 16/25) = 3/5
Substituting these values into the double angle identity, we get:
cos(2x) = cos²(x) - sin²(x) = (3/5)² - (4/5)² = -7/25
To find sin(2x), we can use the double angle identity for sine:
sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5) = 24/25
To find cos(y) and sin(y), we can use the fact that y = tan⁻¹(12/5) and the Pythagorean theorem:
sin(y) = 12/13
cos(y) = 5/13
Substituting these values into the expression for cos(2x+y), we get:
cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)
= (-7/25)(5/13) - (24/25)(12/13)
= -60/325
= -12/65
Therefore, cos(2x+y) = -12/65.
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The equation of a line is given by 3x +4y =12. Solve for y.
Answer:
[tex]y = -\frac{3x}{4} + 3[/tex]
Step-by-step explanation:
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Remember to do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 3x from both sides of the equation:
[tex]3x + 4y = 12\\4y + 3x (-3x) = 12 (-3x)\\4y = -3x + 12[/tex]
Next, divide 4 from both sides of the equation:
[tex]4y = -3x + 12\\\frac{(4y)}{4} = \frac{(-3x + 12)}{4} \\y = \frac{-3x + 12}{4}\\ y = -\frac{3x}{4} + 3[/tex]
[tex]y = -\frac{3x}{4} + 3[/tex] is your answer.
~
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The state transportation commission counted cars traveling east and west across a toll bridge. The commission counted 7,000 cars, 6,020 of which were traveling east. What percentage of the cars counted were traveling east? Write your answer using a percent sign (%).
To find the percentage of cars that were traveling east, we can use the following formula:
percentage = (part / whole) x 100%
where "part" is the number of cars traveling east, and "whole" is the total number of cars counted.
In this case, we know that 6,020 cars were traveling east, out of a total of 7,000 cars counted. So we can plug these values into the formula:
percentage = (6,020 / 7,000) x 100%
percentage = 0.86 x 100%
percentage = 86%
Therefore, 86% of the cars counted were traveling east across the toll bridge.
Can someone help me understand this question.... Thank you
Claude is buying boxes of cinnamon rolls from a bakery. Each box is $6. Which of the following statements are true? (Choose 2 statements.)
A. The independent variable is the number of boxes of cinnamon rolls Claude buys.
B. The dependent variable is the amount of money you spend on the cinnamon rolls.
C. The dependent variable is the number of boxes of cinnamon rolls Claude buys.
D. The independent variable is the amount of money you spend on the cinnamon rolls.
E. None of the above statements are true.
2.Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a similar sampling probability than others.
correct answer is False
3. Ruben randomly called 100 phone numbers in his town in order to survey them about their shopping habits. 55 people decided to participate in the survey.
This is an unbiased sample.
False
The correct statements are:
A. The independent variable is the number of boxes of cinnamon rolls Claude buys.
B. The dependent variable is the amount of money Claude spends on the cinnamon rolls.
What is independent variable?
The independent variable is the variable that is manipulated or controlled by the experimenter, and in this case, Claude is choosing how many boxes of cinnamon rolls to buy.
1. The dependent variable is the variable that is affected by the independent variable, and in this case, the amount of money Claude spends depends on the number of boxes he buys.
Therefore, statement A and B are correct, while C, D, and E are not true in this context.
2. Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a similar sampling probability than others. (FALSE)
3. Ruben randomly called 100 phone numbers in his town in order to survey them about their shopping habits. 55 people decided to participate in the survey.
This is an unbiased sample. (FALSE)
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help please geometry
Applying similar triangles the length of EB is 14.6
How to find length EBSimilar triangles is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
DE and DF, EB and FC
The solution is worked out using sides BC and FE, then AC and DF
DE / EB = DF / FC
17.5 / EB = 13.1 / 10.9
cross multiplying
17.5 * 10.9 = 13.1 * EB
EB = 14.6
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A certain distance is covered in 3 hours at an average speed of 120km/h how long will it take to cover the same distance at an average speed of 90km/h
Therefore , the solution of the given problem of speed comes out to be it will take 4 hours to travel the same distance at an average speed of 90 km/h.
What is speed?We can determine something's speed by keeping a watch on it from a distance. The amount of distance an object can move in a specific amount of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most popular pace measurements are miles per hour (mile), kilometres per hour (kilometres), and metres for each second (m/s) (mph).
Here,
Applying the algorithm
Distance is determined by multiplying time and motion.
We can make the two equations equal because we know that the distance travelled in both scenarios is the same:
Distance = time + speed1
1 = time2 + speed2
where time1 is the first time (3 hours), speed1 is the first average speed (120 km/h), speed2 is the second average speed (90 km/h), and we're trying to determine time2.
Inputting the numbers provided yields:
Distance: 360 km at 120 km/h for three hours.
We can now determine the time2:
360 kilometres are equal to 90 kilometres per hour multiplied by two.
time2 = 360 km x 90 km/hr = 4 hours
Therefore, it will take 4 hours to travel the same distance at an average speed of 90 km/h.
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There are 24 people running in a race. 1/4 are wearing green shorts. 1/6 are wearing red shorts. The rest are wearing blue shorts. How many people are wearing blue shorts?
Use a tape diagram to help you answer the question.
Solve. Show or explain your work.
Answer:
First, let's find the fraction of people wearing green or red shorts:
1/4 + 1/6 = 3/12 + 2/12 = 5/12
This means that 5/12 of the people are wearing either green or red shorts. To find the fraction of people wearing blue shorts, we need to subtract this from 1 (since the three options are exhaustive):
1 - 5/12 = 7/12
So, 7/12 of the people are wearing blue shorts. To find out how many people this represents, we can multiply this fraction by the total number of people in the race:
7/12 x 24 = 14
Therefore, 14 people are wearing blue shorts.
Step-by-step explanation:
Answer:
To use a tape diagram, we can start by drawing a rectangle to represent the total number of people in the race. Then, we can divide it into four equal parts to represent the people wearing green shorts and into six equal parts to represent the people wearing red shorts.
Let's use the letter "B" to represent the number of people wearing blue shorts. We know that the total number of people is 24, so we can write:
4 parts + 6 parts + B parts = 24
Simplifying this equation, we get:
10 + B = 24
Subtracting 10 from both sides, we get:
B = 14
Therefore, 14 people are wearing blue shorts.
To double-check our answer, we can add up the number of people in each category:
4 parts out of 24 = 6 people wearing green shorts
6 parts out of 24 = 4 people wearing red shorts
B parts out of 24 = 14 people wearing blue shorts
6 + 4 + 14 = 24, which matches the total number of people in the race.
Please help. ASAP!!!!!
Answer:
½(a+b)h
½(24+32)×18
504ft²
I might be wrong
the distance between (3, -6) and (3, -10)
Answer:
4 units
Step-by-step explanation:
Since the x-value is the same in both ordered pairs, you can just figure out the y-step ([tex]y_{2} -y_{1}[/tex]) and get your distance. -10 - (-6) = -4, so a distance of 4 units (negative sign does not matter in this case).
If both the x-values and y-values were different, another way to solve is to figure out the y- and x-steps and plug them into the Pythagoras theorem [tex]A^2+B^2 = C^2[/tex], with A being the horizontal distance (x-step) and B being the vertical distance (y-step).
You can also find the distance between 2 points by using the distance formula, which is [tex]d = \sqrt{(x_{2}-x_{1})^{2} - (y_{2}-y_{1})^{2}[/tex]. After inserting the x- and y-coordinates of your ordered pair you get [tex]d = \sqrt{(3-3)^{2} - (-10-(-6))^{2}[/tex]
Simplifying:
[tex]d = \sqrt{- (-10-(-6))^{2}}[/tex]. [tex](3-3)^{2}[/tex] was eliminated.
Then we distribute the negative signs: [tex]d = \sqrt{- (-10+6)^{2}}[/tex] --> [tex]d = \sqrt{(10-6)^{2}}[/tex].
[tex]d = \sqrt{(4)^{2}}[/tex] --> [tex]d = \sqrt{16}[/tex] --> [tex]d = 4[/tex]
So, the distance between the points is 4 units.
Side note: The distance formula works in the same way as the Pythagoras theorem.
An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
Number of TV commercials, x 4
4
6
12
17
Car sales, y (in hundreds)
2
5
8
9
The linear regression equation for the data given in the table is presented as follows:
y = 0.51x + 1.07.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.
The points for the data-set in this problem are given as follows:
(4,2), (6, 5), (12, 8), (17,9).
Inserting these four points into a linear regression calculator, the linear regression equation for the data given in the table is presented as follows:
y = 0.51x + 1.07.
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144 is 90% what is the other 10 percent
Answer:
To find out what is the other 10%, you can use the following formula:
(100% - 90%) = 10%
So, if 144 is 90% of a value, we can divide 144 by 0.9 to find the total value:
144 / 0.9 = 160
Therefore, the other 10% of 160 is:
0.1 x 160 = 16
Step-by-step explanation: