Given the point ( 2, 1) on a tangent line to the curve f(x) = x2 – 2x + 5 find the point(s) where the tangent touches f(x). [5 Marks) Section 4: Application 13. Find the equation of the tangent to the function f(x) = 1 2 3 + x2 X if x = 1. [6 Marks]
Answers
This quadratic equation has no real solutions, which means that the tangent line does not touch the curve f(x) at any real points.
To find the point(s) where the tangent line touches the curve f(x), we first need to find the slope of the tangent line at the given point (2,1).
The slope of the tangent line at (2,1) is equal to the derivative of the function f(x) evaluated at x = 2.
f(x) = x^2 – 2x + 5
f'(x) = 2x - 2
Therefore, f'(2) = 2(2) - 2 = 2
So the slope of the tangent line at (2,1) is 2.
Now we can use the point-slope form of the equation of a line to find the equation of the tangent line.
y - 1 = 2(x - 2)
Simplifying this equation, we get:
y = 2x - 3
To find the point(s) where the tangent touches f(x), we need to solve the system of equations formed by setting f(x) equal to y and substituting the equation for y from the tangent line:
x^2 – 2x + 5 = 2x - 3
Simplifying and solving for x, we get:
x^2 - 4x + 8 = 0
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Complete question is:
Given the point ( 2, 1) on a tangent line to the curve f(x) = x^2 – 2x + 5 find the point(s) where the tangent touches f(x).
Related Questions
A waterwheel of radius 3m is submerged such that its bottom is 2m underwater. At t=0, a boot (submerged to a depth of 2m) gets stuck in a spoke. Five seconds late the boot is at a high point. a)Find all possible times when the boot will be 2m above the water. b) Determine the length of time the boot is a bove water level.
Answers
We know that the waterwheel has a radius of 3 meters, this means that it has a diameter of 6 meters. Now since it is spinning we can describe its motion (and then the motion of the boot) with a cosine or sine function.
We know that in general a sinusoidal model is describe as:
\(y=A\sin (B(t+C))+D\)where A is the amplitude, the period is 2pi/B, C is the phase shift and D is the vertical shift.
In this case the amplitude will be 3 (since it is the radius of the wheel).
We also need that the period to be 10, this comes from the fact that it takes the boot five second to at the top, which means it will take 10 seconds to return to the bottom. From this we have:
\(\begin{gathered} \frac{2\pi}{B}=10 \\ B=\frac{2\pi}{10} \\ B=\frac{\pi}{5} \end{gathered}\)Now since we need that the motion starts at the bottom of the whell this means we need the minimum of the function to be at t=0, hence we need that the product BC to be -pi/2, then:
\(\begin{gathered} BC=-\frac{\pi}{2} \\ C=\frac{\frac{\pi}{2}}{\frac{\pi}{5}} \\ C=\frac{5}{2} \end{gathered}\)Finally we know that the wheel is two meters underwater, this means that the vertical shift to be +1.
Hence the function that describes the motion is:
\(y=3\sin (\frac{\pi}{5}(t-\frac{5}{2}))+1\)Once we have the motion describe we can answer the questions.
a)
To determine all possible times when the boot is 2 m above water we equate the expression for the height of the boot to two and solve for t:
\(\begin{gathered} 3\sin (\frac{\pi}{5}(t-\frac{5}{2}))+1=2 \\ 3\sin (\frac{\pi}{5}(t-\frac{5}{2}))=1 \\ \sin (\frac{\pi}{5}(t-\frac{5}{2}))=\frac{1}{3} \\ \frac{\pi}{5}(t-\frac{5}{2})=\sin ^{-1}(\frac{1}{3}) \\ \frac{\pi}{5}t-\frac{\pi}{2}=\sin ^{-1}(\frac{1}{3}) \\ \frac{\pi}{5}t=\frac{\pi}{2}+\sin ^{-1}(\frac{1}{3}) \\ t=\frac{5}{2}+\frac{5}{\pi}\sin ^{-1}(\frac{1}{3}) \end{gathered}\)Adding the period we have:
\(t=\frac{5}{2}+\frac{5}{\pi}\sin ^{-1}(\frac{1}{3})+10n\)This gives the values while ascending. To find the times while it descends we use the fact that:
\(\begin{gathered} 3\sin (\frac{\pi}{5}(t-\frac{5}{2}))+1=2 \\ 3\lbrack\sin (\frac{\pi t}{5})\cos (\frac{\pi}{2})-\sin (\frac{\pi}{2})\cos (\frac{\pi t}{5})\rbrack+1=2 \\ -3\cos (\frac{\pi t}{5})=1 \\ \cos (\frac{\pi t}{5})=-\frac{1}{3} \\ \frac{\pi t}{5}=\cos ^{-1}(-\frac{1}{3}) \\ t=\frac{5}{\pi}\cos ^{-1}(-\frac{1}{3}) \end{gathered}\)Substracting this to the period we have:
\(t=10n-\frac{5}{\pi}\cos ^{-1}(-\frac{1}{3})\)Therefore the times for which the boot will be two meters above are:
\(\begin{gathered} t=\frac{5}{2}+\frac{5}{\pi}\sin ^{-1}(\frac{1}{3})+10n \\ t=10n-\frac{5}{\pi}\cos ^{-1}(-\frac{1}{3}) \end{gathered}\)This is approximately to the times:
\(t=3.03,\text{ 6.95, 13.03, 16.95,}\ldots..\)b)
The boot is above water from the time when y=0, then:
\(\begin{gathered} 3\sin (\frac{\pi}{5}(t-\frac{5}{2}))+1=0 \\ \sin (\frac{\pi}{5}(t-\frac{5}{2}))=-\frac{1}{3} \\ \frac{\pi}{5}(t-\frac{5}{2})=\sin ^{-1}(-\frac{1}{3}) \\ t-\frac{5}{2}=\frac{5}{\pi}\sin ^{-1}(-\frac{1}{3}) \\ t=\frac{5}{2}+\frac{5}{\pi}\sin ^{-1}(-\frac{1}{3}) \\ t=1.959 \end{gathered}\)to the time when y is once again zero,
\(\begin{gathered} -3\cos (\frac{\pi t}{5})=-1 \\ \cos (\frac{\pi t}{5})=\frac{1}{3} \\ \frac{\pi}{5}t=\cos ^{-1}(\frac{1}{3}) \\ t=\frac{5}{\pi}\cos ^{-1}(\frac{1}{3}) \end{gathered}\)Substracting this to the period we have:
\(t=10-\frac{5}{\pi}\cos ^{-1}(\frac{1}{3})=8.04\)Therefore the boot is above water appoximately 6.081 seconds.
is 2y-3>11 a expression equation or inequality
Answers
Answer:
Inequality
Step-by-step explanation:
An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. An equation is a mathematical sentence that says two expressions are equal.
Bobby is buying ribs for his 4th of July cookout. The ribs are on sale for $3. 50 per pound. If Bobby buys 5. 5 pounds of ribs, how much does he spend?
Answers
Using simple mathematical operations, we know that Bobby buys 5.5 pounds of ribs for $19.25.
What are mathematical operations?Indicates a mathematical operation, akin to the superposition principle, where the action on the sum of two functions is equal to the sum of the actions of the operation on each function (e.g., differentiation, multiplication by a constant).
So, we know that:
The ribs are for sale at $3.50 per pound.
Bobby buys 5.5 pounds of ribs.
Then, the amount bobby spends on ribs will be:
5.5 * 3.50
$19.25
Therefore, using simple mathematical operations, we know that Bobby buys 5.5 pounds of ribs for $19.25.
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Which of the following functions best describes this graph
Answers
Answer: y=x^2+8x+12
Step-by-step explanation:
In an experiment you pick at random a bit string of length 5. Consider
the following events: E1: the bit string chosen begins with 1, E2: the
bit string chosen ends with 1, E3: the bit string chosen has exactly
three 1s.
(a) Find p(E1jE3).
(b) Find p(E3jE2).
(c) Find p(E2jE3).
(d) Find p(E3jE1 \ E2).
(e) Determine whether E1 and E2 are independent.
(f) Determine whether E2 and E3 are independent
Answers
The given set of probabilities are: (a) p(E1|E3) = 3/10, (b) p(E3|E2) = 1/2, (c) p(E2|E3) = 3/10, (d) p(E3|E1 ∩ E2) = 1/3, (e) E1 and E2 are not independent, (f) E2 and E3 are not independent.
(a) To find p(E1|E3), we need to find the probability that the bit string begins with 1 given that it has exactly three 1s. Let A be the event that the bit string begins with 1 and B be the event that the bit string has exactly three 1s. Then,
p(E1|E3) = p(A ∩ B) / p(B)
To find p(A ∩ B), we need to count the number of bit strings that begin with 1 and have exactly three 1s. There is only one such string, which is 10011. To find p(B), we need to count the number of bit strings that have exactly three 1s. There are 10 such strings, which can be found using the binomial coefficient:
p(B) = C(5,3) / 2^5 = 10/32 = 5/16
Therefore, p(E1|E3) = p(A ∩ B) / p(B) = 1/10.
(b) To find p(E3|E2), we need to find the probability that the bit string has exactly three 1s given that it ends with 1. Let A be the event that the bit string has exactly three 1s and B be the event that the bit string ends with 1. Then,
p(E3|E2) = p(A ∩ B) / p(B)
To find p(A ∩ B), we need to count the number of bit strings that have exactly three 1s and end with 1. There are two such strings, which are 01111 and 11111. To find p(B), we need to count the number of bit strings that end with 1. There are two such strings, which are 00001 and 00011.
Therefore, p(E3|E2) = p(A ∩ B) / p(B) = 2/2 = 1.
(c) To find p(E2|E3), we need to find the probability that the bit string ends with 1 given that it has exactly three 1s. Let A be the event that the bit string ends with 1 and B be the event that the bit string has exactly three 1s. Then,
p(E2|E3) = p(A ∩ B) / p(B)
To find p(A ∩ B), we need to count the number of bit strings that have exactly three 1s and end with 1. There are two such strings, which are 01111 and 11111. To find p(B), we already found it in part (a), which is 5/16.
Therefore, p(E2|E3) = p(A ∩ B) / p(B) = 2/5.
(d) To find p(E3|E1 \ E2), we need to find the probability that the bit string has exactly three 1s given that it begins with 1 but does not end with 1. Let A be the event that the bit string has exactly three 1s, B be the event that the bit string begins with 1, and C be the event that the bit string does not end with 1. Then,
p(E3|E1 \ E2) = p(A ∩ B ∩ C) / p(B ∩ C)
To find p(A ∩ B ∩ C), we need to count the number of bit strings that have exactly three 1s, begin with 1, and do not end with 1.
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Find the solution of the differential equation dydx=y2 4 that satisfies the initial condition y(7)=0
Answers
The particular solution to the differential equation with the initial condition y(7) = 0 is:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.
To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:
Step 1: Write the given differential equation in the form dy/dx = f(x, y).
In this case, dy/dx = y² - 4.
Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:
dy / (y² - 4) = dx.
Step 3: Integrate both sides of the equation:
∫ dy / (y² - 4) = ∫ dx.
Let's solve each integral separately:
For the left-hand side integral:
Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).
Using partial fractions, we can decompose the left-hand side integral:
1 / (y² - 4) = A / (y - 2) + B / (y + 2).
Multiply both sides by (y - 2)(y + 2):
1 = A(y + 2) + B(y - 2).
Expanding the equation:
1 = (A + B)y + 2A - 2B.
By equating the coefficients of the like terms on both sides:
A + B = 0, and
2A - 2B = 1.
Solving these equations simultaneously:
From the first equation, A = -B.
Substituting A = -B in the second equation:
2(-B) - 2B = 1,
-4B = 1,
B = -1/4.
Substituting the value of B in the first equation:
A + (-1/4) = 0,
A = 1/4.
Therefore, the decomposition of the left-hand side integral becomes:
1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).
Integrating both sides:
∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.
Integrating the right-hand side:
∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy
= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,
where C₁ is the constant of integration.
For the right-hand side integral:
∫ dx = x + C₂,
where C₂ is the constant of integration.
Combining the results:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.
Simplifying the equation:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).
Combining the constants of integration:
C = C₂ - C₁, where C is a new constant.
Finally, we have the solution to the differential equation that satisfies the initial condition:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.
To find the value of the constant C, we use the initial condition y(7) = 0:
(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.
Simplifying the equation:
(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,
(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,
0 = 7 + C,
C = -7.
Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:
(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.
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You are given two functions, f: RR, f (x) = 3x and g:R+R, 9(r) = x+1 a. Find and record the function created by the composition of f and g, denoted gof. b. Prove that your recorded function of step (a.) is both one-to-one and onto. That is prove, gof:R R; (gof)(x) = g(f (r)). is well-defined where indicates go f is a bijection. For full credit you must explicitly prove that go f is both one-to-one and onto, using the definitions of one-to-one and onto in your proof. Do not appeal to theorems. You must give your proof line-by-line, with each line a statement with its justification. You must show explicit, formal start and termination statements as shown in lecture examples. You can use the Canvas math editor or write your math statements in English. For example, the statement to be proved was written in the Canvas math editor. In English it would be: Prove that the composition of functions fand g is both one-to-one and onto.
Answers
a) The function gof is gof(x) = 3x + 3.
b) The function gof: RR is well-defined.
a. The value of function gof(x) = 3x + 3.
To find the composition gof, we substitute the expression for g into f:
gof(x) = f(g(x))
= f(x + 1)
= 3(x + 1)
= 3x + 3
b. To prove that gof is both one-to-one and onto, we need to show the following:
(i) One-to-one: For any two different inputs x1 and x2, if gof(x1) = gof(x2), then x1 = x2.
(ii) Onto: For every y in the range of gof, there exists an x such that gof(x) = y.
Proof of one-to-one:
Let x1 and x2 be two different inputs. Assume that gof(x1) = gof(x2).
Then, 3x1 + 3 = 3x2 + 3.
Subtracting 3 from both sides, we have 3x1 = 3x2.
Dividing both sides by 3, we obtain x1 = x2.
Therefore, gof is one-to-one.
Proof of onto:
Let y be any real number in the range of gof, which is the set of all real numbers.
We need to find an x such that gof(x) = y.
Consider the equation 3x + 3 = y.
Subtracting 3 from both sides, we have 3x = y - 3.
Dividing both sides by 3, we obtain x = (y - 3)/3.
Thus, for any y in the range of gof, we can find an x such that gof(x) = y.
Therefore, gof is onto.
Since gof is both one-to-one and onto, it is a bijection.
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9/10 x 60 / 5 as a fraction
Answers
Answer:
10 4/5
Step-by-step explanation:
Answer:
10 and 4/5
Step-by-step explanation:
9/10 * 60/5 = 540/50
multiply numerator by denominator,
n : 9*60 = 540
d : 10*5 = 50
540/50
54/5 simplify
10 and 4/5
Sophie checks her bike for repairs every 9 days and Susan checks hers every 12 days. If they both check their bikes today, after how many days do the both check their bike again?
Answers
Answer:
Sophie in 9 days and Susan in 12 days
Step-by-step explanation:
This question is very vague and the answer in clearly in front of your eyes.
.Here is the sales and profit data for a sporting goods company with 12 stores. Use the data to answer the regression problem #4.
Sales in $ millions
Profits in $ millions
7
.15
2
.10
6
.13 4
.15
14
.25
15
.27
16
.24
12
.20 What is the r value?
Do you consider the correlation strong?
What is the expected profit when sales are $10 million?
Answers
The r-value for the given sales and profit data is 0.951. Yes, the correlation is considered strong. we can use the regression line equation derived from the given data.
The r-value, also known as the correlation coefficient, measures the strength and direction of the linear relationship between two variables. In this case, the r-value of 0.951 indicates a strong positive correlation between sales and profits.
A correlation coefficient ranges from -1 to +1. A value of +1 indicates a perfect positive correlation, meaning that as one variable increases, the other variable increases proportionally. In our case, as sales increase, profits also tend to increase, but not necessarily at a perfect rate.
The strength of the correlation can be interpreted based on the magnitude of the r-value. Generally, an r-value above 0.8 is considered a strong correlation. In our case, the r-value of 0.951 indicates a strong positive correlation between sales and profits.
To estimate the expected profit when sales are $10 million, we can use the regression line equation derived from the given data. However, since the data points provided are limited,
we cannot calculate the regression line or the expected profit accurately. To make a more precise estimation, a larger dataset with a wider range of sales values would be required.
In summary, the r-value of 0.951 suggests a strong positive correlation between sales and profits. However, without a complete dataset or a regression line equation, we cannot accurately determine the expected profit when sales are $10 million.
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A bread is cut into 10 equal parts. How many children can share all parts of the bread if each child takes 0.2 parts
Answers
5 children can share all parts of the bread if each child takes 0.2 parts.
What are Fractions?Fraction are numbers of the form \(\frac{a}{b}\) where a and b are real numbers. It is represented as a portion or part of a whole.
The number on the top is called numerator and the number on the bottom is called denominator.
There are 10 equal parts of bread and each child takes 0.2 part.
Total parts of the bread = 10
Part each child takes = 0.2 = \(\frac{2}{10}\)
2 parts out of 10 are taken by each child.
Remaining are \(\frac{8}{10}\) parts.
\(\frac{2}{10}\) × 4 = \(\frac{8}{10}\)
Remaining parts can be shared by 4 children.
Hence number of children who can share the bread if each takes 0.2 parts = 5
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Soda Tak claims that Diet Tak has 40mg of sodium per can. You work for a consumer organization that tests such claims. You take a random sample of 60 cans and find that the mean amount of sodium in the sample is 41.9mg. The population standard deviation in all cans is 5.2mg. You suspect that there is more than 40mg of sodium per can. Find the z-score.
Answers
Answer:
Z - score = 2.83
Step-by-step explanation:
Given the following :
Number of samples (N) = 60
Sample mean (x) = 41.9mg
Population mean (μ) = 40mg
Population standard deviation (sd) = 5.2
Using the relation :
Z = (x - μ) / (sd / √N)
Z = (41.9 - 40) / (5.2 / √60)
Z = 1.9 / (5.2 / 7.7459666)
Z = 1.9 / 0.6713171
Z = 2.8302570
Therefore, the z-score = 2.83
The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 32 liters, and standard deviation of 10.4 liters. A) What is the probability that daily production is less than 31.5 liters? Answer= (Round your answer to 4 decimal places.) B) What is the probability that daily production is more than 32.3 liters? Answer= (Round your answer to 4 decimal places.)
Answers
A) The probability that daily production is less than 31.5 liters = 0.4802 (Approx.)
B) The probability that daily production is more than 32.3 liters = 0.4886 (Approx.)
Given: Mean daily production of a herd of cows is normally distributed
Mean = 32, Standard Deviation = 10.4
A) Probability Density Function of Normal Distribution is given by: \($$P(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{ -\frac{(x - \mu)^2}{2 \sigma^2} }$$where,$\mu$ = Mean$ ~\sigma$ = Standard Deviation\)
x = Value of random variable
The probability that daily production is less than 31.5 liters = P(x < 31.5)
Lets calculate z-score.
\($$z = \frac{x-\mu}{\sigma}$$$$z = \frac{31.5-32}{10.4}$$$$z = -0.0481$$\)
Now, from z-table or using calculator P(z < -0.0481) = 0.4802 (Approx.)
Hence, the probability that daily production is less than 31.5 liters = 0.4802 (Approx.)
B) The probability that daily production is more than 32.3 liters = P(x > 32.3)
Lets calculate z-score.\($$z = \frac{x-\mu}{\sigma}$$$$z = \frac{32.3-32}{10.4}$$$$z = 0.0288$$\)
Now, from z-table or using calculator P(z > 0.0288) = 0.4886 (Approx.)
Hence, the probability that daily production is more than 32.3 liters = 0.4886 (Approx.)
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Find the critical numbers of the function f below, and describe the behavior of f at these numbers.List your answers in increasing order, with the smallest one first. Enter your answers as whole numbers or fractions.f(x) = x8(x - 4)7At ___ the function has a local maxmum .At ___ the function has a local minimum.At ___ the function has not a max and min.
Answers
The critical numbers in increasing order, we have:
x = 0, 4/9, 4
At x = 0, the function has a local minimum.
At x = 4/9, the function has a local maximum.
At x = 4, the function has neither a local maximum nor minimum.
To find the critical numbers of the function f(x) = \(x^8(x - 4)^7\):
We need to take the derivative of the function and set it equal to zero.
f'(x) = \(8x^7(x - 4)^7 + 7x^8(x - 4)^6(-1)\)
Setting f'(x) = 0 and solving for x, we get:
x = 0 or x = 4/9
To describe the behavior of f at these critical numbers:
At x = 0, the function has a local minimum.
This is because the derivative changes sign from negative to positive at this point, indicating a change from decreasing to increasing behavior.
At x = 4/9, the function has a local maximum.
This is because the derivative changes sign from positive to negative at this point, indicating a change from increasing to decreasing behavior.
At x = 4, the function has neither a local maximum nor minimum.
This is because the derivative is zero at this point, but does not change sign. Instead, the behavior of the function changes from decreasing to increasing to decreasing again as we move from left to right around x = 4.
Listing the critical numbers in increasing order, we have:
x = 0, 4/9, 4
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Two systems of equations are shown: System A System B 6x + y = 2 2x − 3y = −10 −x − y = −3 −x − y = −3 Which of the following statements is correct about the two systems of equations? The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A. They will have the same solution because the first equations of both the systems have the same graph. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical.
Answers
Answer:
well i dont know this sorry
Step-by-step explanation:
HELP ASAP
please graph the equation, i know its b please graph it!!
Answers
Why is it important to control all variables except one when studying cause-and-effect relationships.
Answers
By controlling variables, we can isolate the impact of a specific variable on the outcome, allowing us to draw accurate conclusions.
The reason it is important to control all variables except one when studying cause-and-effect relationships is to establish a clear understanding of the relationship between the cause and the effect. By controlling variables, we can isolate the impact of a specific variable on the outcome, allowing us to draw accurate conclusions.
Here is a step-by-step explanation of why controlling variables is important:
1. Identifying the cause: When studying cause-and-effect relationships, we are interested in understanding the effect that a particular variable has on the outcome. By controlling all other variables, we can determine the true cause of the effect.
2. Eliminating confounding factors: Confounding factors are variables that can influence the outcome but are not the actual cause. By controlling these variables, we can eliminate their impact and prevent them from clouding the true cause-and-effect relationship.
3. Establishing a clear connection: By controlling all variables except one, we can clearly attribute any changes in the outcome to the specific variable being studied. This allows us to establish a direct cause-and-effect relationship and avoid drawing incorrect conclusions.
4. Replicability and reliability: Controlling variables ensures that the study can be replicated by other researchers. This enhances the reliability of the findings and allows for further investigation and validation of the cause-and-effect relationship.
Example: Let's say we want to study the effect of a new fertilizer on plant growth. If we don't control variables such as sunlight, water, temperature, and soil quality, these factors could potentially impact plant growth and confound the results. By controlling these variables and only changing the fertilizer, we can accurately determine the impact of the fertilizer on plant growth.
In summary, controlling variables except one when studying cause-and-effect relationships is important because it allows us to identify the true cause, eliminate confounding factors, establish a clear connection, and ensure replicability and reliability of the findings.
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Trinity has 48.75 inches of ribbon. She cut the ribbon into 15 equal-sized pieces. What is the length of each piece of ribbon?
Answers
The length of each piece be 3.25 inches.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have Trinity who has 48.75 inches of ribbon. She cut the ribbon into 15 equal-sized pieces.
Assume that the length of each piece be [x]. Then, we can write -
15x = 48.75
x = 48.75/15
x = 3.25 inches
Therefore, the length of each piece be 3.25 inches.
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I’m not sure which one is the right answer
Answers
The past observation of the annual sale of a company shows trend but not seasonality. The estimated values by the relevant smoothing method are as follows:
Last estimated smoothed value = 3.4 in 2022.
Last estimated trend value = 0.4 in 2022
estimated alpha = 0.8 in 2022
estimated beta = 0.5 in 2022
what is the forecast of sale for 2023
Answers
The forecasted sales for 2023 using the given estimated values and smoothing method is 3.8.
To forecast the sales for 2023 using the given estimated values and smoothing method, we can apply the exponential smoothing formula:
Forecast for 2023 = Last estimated smoothed value + Last estimated trend value
Given:
Last estimated smoothed value = 3.4
Last estimated trend value = 0.4
Forecast for 2023 = 3.4 + 0.4
= 3.8
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A soccer couch bought eight soccer balls.This line plot shows the weight of each ball the couch bought?
Answers
The weight of the soccer balls bought by the coach is 40.18 pounds. therefore, option a.40.18 is correct.
To determine the weight of the soccer balls the coach bought, we need
to analyze the given line plot. The line plot shows the weight of each of
the 11 soccer balls bought by the coach.
The first step is to find the scale of the line plot. In this case, the scale is
in pounds, and the plot ranges from 0 to 8 pounds. Each "x" on the plot
represents one soccer ball, and the height of the "x" shows the weight of
that ball in pounds.
To find the total weight of the soccer balls bought by the coach, we
simply need to add up the weights of all the balls. Looking at the line
plot, we can see that there are:
2 balls that weigh 1 pound each
1 ball that weighs 3 pounds
1 ball that weighs 2 pounds
1 ball that weighs 5 pounds
1 ball that weighs 3.7 pounds
1 ball that weighs 8 pounds
2 balls that weigh 4 pounds each
1 ball that weighs 8.48 pounds
Adding all these weights together, we get:
1 + 1 + 3 + 2 + 5 + 3.7 + 8 + 4 + 4 + 8.48 = 40.18 pounds
Therefore, the weight of the soccer balls bought by the coach is 40.18 pounds.
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Question
A soccer couch bought eight soccer balls. This line plot shows the weight of each ball the couch bought?
what is the total weight, in pounds, of all the soccer balls the coach bought?
a. 40.18 b. 60 c. 30 d. 20
Solve for n. 9 = 12n Simplify your answer as much as possible. plzzzzzz help me
Answers
Answer:
3=4
Step-by-step explanation:
12n = 9
12n/12 = 9/12
n = 9/12
Lastly, reduce 9/12 to lowest terms. Divide 9/12 by 3/3:
n = ¾
Let vector a = 3i + j - k.
Find the vector b in the direction of vector a such that |b| = 5
Answers
Answer:
5i +(5/3)j - (5/3)k
Step-by-step explanation:
Vector b is in the same direction as vector a, so it is a scalar multiple of a.
b = ca for some positive real number c.
b = c(3i + j - k) = 3ci + cj - ck
|b| = sqrt[(3c)^2 + c^2 - c^2] = sqrt(9c^2) = 3c
If |b| = 5, then 3c = 5 and c = 5/3
That makes b = (5/3)(3i + j - k) = 5i +(5/3)j - (5/3)k
44. Which number line represents
the solutions for the inequality
45 + 4x> 125?
А
18 19 20
21
22 23 24 25 26
B
18 19 2022 23 24 25 26
21
с
22 23 24 25 26
18 19 20 21
D
18 19 20 21 22
23 24 25 26
Answers
Step-by-step explanation:
=> 45 + 4x > 125
=> 4x > 125 - 45
=> 4x > 30
=> x > 30/4
=> x > 7.5
what is the answer to 5+3x(5-2) ^2
Answers
Answer:
576
Step-by-step explanation:
5 + 3 = 8
5 - 2 = 3
8 x 3 = 24
24 to the second power is 576
Answer:
27x+5
Step-by-step explanation:
5+3x(5-2)^2
5+3x(3)^2
5+3x*9
5+27x
27x+5
Can someone help me pleasee!! question 10 help a girl out :)
Answers
Answer:
52
Step-by-step explanation:
just finished taking it
Answer:
no
Step-by-step explanation:
A piece of paper is used to make a cylinder (without a top and bottom) that is 8 inches long and has a radius of 1.5 inches. Assuming no part of the paper overlap’s, what is the area of the piece of paper? Show work
Answers
Answer:
75.36
Step-by-step explanation:
Formula for circumference of circle is: πd
radius is half of the diameter so we have to multiply that by 2.
1.5*2=3
π in decimal form = 3.14
3*3.14=9.42
That is one side of the rectangle. The height of the rectangle is 8. Multiply the two sides.
9.42*8=75.36
The area of the rectangle is 75.36.
Hope this helps!
If not, I am sorry.
The diagram shows two right-angled triangles that share a common side. 6 10. Show that x is between 11 and 12.
Answers
We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:
Triangle 1:
Side adjacent to the right angle: 6 (let's call it 'a')
Side opposite to the right angle: x (let's call it 'b')
Triangle 2:
Side adjacent to the right angle: x (let's call it 'c')
Side opposite to the right angle: 10 (let's call it 'd')
Using the Pythagorean theorem, we can write the following equations for each triangle:
Triangle 1:\(a^2 + b^2 = 6^2\)
Triangle 2: \(c^2 + d^2 = 10^2\)
Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:
\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)
Substituting b = c, we get:
\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)
Now, let's add these two equations together:
\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)
Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12
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Marissa is selling paintings for $15 each and bracelets for $7 each. Her goal is to sell at least $800 in products, and she must sell at least 60 bracelets. Which of the
following combinations will satisfy these constraints?
O20 paintings and 65 bracelets
O25 paintings and 60 bracelets
O26 paintings and 61 bracelets
014 paintings and 45 bracelets
Answers
Answer:
the answer is: 026 paintings and 61 bracelets
Step-by-step explanation:
20•15=300+65•7=755
25•15=375+60•7=795
26•15= 390+61•7=817
14•15= 210+41•7=497
Answer: 26 paintings and 61 bracelets
Step-by-step explanation:
-145.035 ÷ 75 I’ll give you brainliest :p
Answers
Answer:
\(-1.9338\)
Step-by-step explanation: