a. The decision rule for a significance level of 0.10 is to reject the null hypothesis if the test statistic is greater than the critical value or if the p-value is less than 0.10.
b. To compute the value of the test statistic, we can use the formula:
Test statistic = (sample proportion - hypothesized proportion) / standard error
Given that the sample proportion is p = 0.87, the hypothesized proportion is p₀ = 0.83, and the sample size is n = 100, the standard error can be calculated as:
Standard error = sqrt((p₀ * (1 - p₀)) / n)
Plugging in the values, we get:
Standard error = sqrt((0.83 * (1 - 0.83)) / 100) ≈ 0.0367
Now, we can calculate the test statistic:
Test statistic = (0.87 - 0.83) / 0.0367 ≈ 1.092
c. To make a decision regarding the null hypothesis, we compare the test statistic to the critical value or compare the p-value to the significance level (0.10 in this case). If the test statistic is greater than the critical value or the p-value is less than 0.10, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Since the value of the test statistic is approximately 1.092, we compare it to the critical value or calculate the p-value to determine the decision.
Learn more about null hypothesis here:
https://brainly.com/question/31816995
#SPJ11
The Cougars scored t more touchdowns this year than last year. Last year, they only scored 7 touchdowns. Choose the expression that shows how many touchdowns they scored this year.
The expression that shows how many touchdowns the Cougars scored this year would be 7 + t, where "t" represents the additional touchdowns scored compared to last year.
To calculate the total number of touchdowns the Cougars scored this year, we need to consider the number of touchdowns they scored last year (which is given as 7) and add the additional touchdowns they scored this year.
Since the statement mentions that they scored "t" more touchdowns this year than last year, we can represent the additional touchdowns as "t". By adding this value to the number of touchdowns scored last year (7), we get the expression:
7 + t
This expression represents the total number of touchdowns the Cougars scored this year. The variable "t" accounts for the additional touchdowns beyond the 7 they scored last year.
Read more on expression here: https://brainly.com/question/1859113
#SPJ11
Water runs into a concel tank at the rate of 12(m^(3))/(m). How fast is the water lerel rising when the water is 10m deep. Given the base radius of The fank is 26m and the height of the fank is 8m
If water runs into a conical tank at the rate of 12 (m³)/min, the base radius of the tank is 26m and the height of the tank is 8m, then the rate at which the water level is rising when the water is 10m deep is 0.0117 m/min.
To find the rate at which water is rising when the depth is 10m, follow these steps:
The formula to find the volume of a cone is V= (1/3)πr²h, where r is the radius of the base of the cone and h is the height of the cone.We can say that r/h= 26/8 ⇒r= 13/4·h. So, the volume V= (1/3)π(13/4·h)²h ⇒V= 13/12·π·h³Differentiating both sides with respect to the time t, we get (13/4)πh²(dh/dt) = dV/dt. Since, dV/dt = 12 (m³)/min and h = 10m, substituting these values in the formula, we get 12= (13/4)π(10)²(dh/dt) ⇒dh/dt= (48/13)·(7/22)·(1/100) = 0.0117 m/min.Learn more about volume:
brainly.com/question/24259805
#SPJ11
Argue the solution to the recurrence T(n)=T(n−1)+log(n) is O(log(n!)) Use the substitution method to verify your answer.
Expand log(m!) + log(m+1) using logarithmic properties:
T(m+1) ≤ c * log((m!) * (m+1)) + d
T(m+1) ≤ c * log((m+1)!) + d
We can see that this satisfies the hypothesis with m+1 in place of m.
To argue the solution to the recurrence relation T(n) = T(n-1) + log(n) is O(log(n!)), we will use the substitution method to verify the answer.
Step 1: Assume T(n) = O(log(n!))
We assume that there exists a constant c > 0 and an integer k ≥ 1 such that T(n) ≤ c * log(n!) for all n ≥ k.
Step 2: Verify the base case
Let's verify the base case when n = k. For n = k, we have:
T(k) = T(k-1) + log(k)
Since T(k-1) ≤ c * log((k-1)!) based on our assumption, we can rewrite the above equation as:
T(k) ≤ c * log((k-1)!) + log(k)
Step 3: Assume the hypothesis
Assume that for some value m ≥ k, the hypothesis holds true, i.e., T(m) ≤ c * log(m!) + d, where d is some constant.
Step 4: Prove the hypothesis for n = m + 1
Now, we need to prove that if the hypothesis holds for n = m, it also holds for n = m + 1.
T(m+1) = T(m) + log(m+1)
Using the assumption T(m) ≤ c * log(m!) + d, we can rewrite the above equation as:
T(m+1) ≤ c * log(m!) + d + log(m+1)
Now, let's expand log(m!) + log(m+1) using logarithmic properties:
T(m+1) ≤ c * log((m!) * (m+1)) + d
T(m+1) ≤ c * log((m+1)!) + d
We can see that this satisfies the hypothesis with m+1 in place of m.
To know more about logarithmic, visit:
https://brainly.com/question/30226560
#SPJ11
From problem 3.23 in Dobrow: Consider the Markov chain with k states 1,2,…,k and with P 1j
= k
1
for j=1,2,…,k;P i,i−1
=1 for i=2,3,…,k and P ij
=0 otherwise. (a) Show that this is an ergodic chain, hence stationary and limiting distributions are the same. (b) Using R codes for powers of this matrix when k=5,6 from the previous homework, guess at and prove a formula for the stationary distribution for any value of k. Prove that it is correct by showing that it a left eigenvector with eigenvalue 1 . It is convenient to scale to avoid fractions; that is, you can show that any multiple is a left eigenvector with eigenvalue 1 then the answer is a version normalized to be a probability vector. 3.23 Consider a k-state Markov chain with transition matrix P= 1
2
3
k−2
k−1
k
0
1
1/k
1
0
⋮
0
0
0
2
1/k
0
1
⋮
0
0
0
3
1/k
0
0
⋮
0
0
⋯
⋯
⋯
⋯
⋯
⋮
⋯
⋯
0
k−2
1/k
0
0
⋮
0
1
1
k−1
1/k
0
0
⋮
0
0
0
k
1/k
0
0
⋮
0
0
⎠
⎞
. Show that the chain is ergodic and find the limiting distribution.
(a) The Markov chain is ergodic because it is irreducible and aperiodic. (b) the stationary distribution of the Markov chain is a vector of all 1/k's.
(a) The Markov chain is ergodic because it is irreducible and aperiodic. It is irreducible because there is a path from any state to any other state. It is aperiodic because there is no positive integer n such that P^(n) = I for some non-identity matrix I.
(b) The stationary distribution for the Markov chain can be found by solving the equation P * x = x for x. This gives us the following equation:
x = ⎝⎛
⎜⎝
1
1/k
1/k
⋯
1/k
1/k
⎟⎠
⎞
⎠ * x
This equation can be simplified to the following equation:
x = (k - 1) * x / k
Solving for x, we get x = 1/k. This means that the stationary distribution is a vector of all 1/k's.
To prove that this is correct, we can show that it is a left eigenvector of P with eigenvalue 1. The left eigenvector equation is:
x * P = x
Substituting in the stationary distribution, we get:
(1/k) * P = (1/k)
This equation is satisfied because P is a diagonal matrix with all the diagonal entries equal to 1/k.
Therefore, the stationary distribution of the Markov chain is a vector of all 1/k's.
To learn more about Markov chain here:
https://brainly.com/question/30465344
#SPJ4
Correct Question :
Consider the Markov chain with k states 1,2,…,k and with [tex]P_{1j[/tex]= 1/k for j=1,2,…,k; [tex]P_{i,i-1[/tex] =1 for i=2,3,…,k and [tex]P_{ij[/tex]=0 otherwise.
(a) Show that this is an ergodic chain, hence stationary and limiting distributions are the same.
(b) Using R codes for powers of this matrix when k=5,6 from the previous homework, guess at and prove a formula for the stationary distribution for any value of k. Prove that it is correct by showing that it a left eigenvector with eigenvalue 1 . It is convenient to scale to avoid fractions; that is, you can show that any multiple is a left eigenvector with eigenvalue 1 then the answer is a version normalized to be a probability vector.
An object is moving at constant velocity. It then starts to accelerate at a rate of 1.4m^(2) for 2 seconds. At the end, it is now traveling at a speed of 22.8mis. What was the initial velacity (speed ) of the object in mis? Correcc?
The initial velocity of the object was 20.0 m/s. It was initially moving at this constant velocity before experiencing acceleration for 2 seconds, which resulted in a final velocity of 22.8 m/s.
To find the initial velocity of the object, we can use the equations of motion. Since the object was initially moving at a constant velocity, its acceleration during that time is zero.
We can use the following equation to relate the final velocity (v), initial velocity (u), acceleration (a), and time (t):
v = u + at
Given:
Acceleration (a) = 1.4 m/s^2
Time (t) = 2 seconds
Final velocity (v) = 22.8 m/s
Plugging in these values into the equation, we have:
22.8 = u + (1.4 × 2)
Simplifying the equation, we get:
22.8 = u + 2.8
To isolate u, we subtract 2.8 from both sides:
22.8 - 2.8 = u
20 = u
Therefore, the initial velocity (speed) of the object was 20.0 m/s.
To know more about Velocity, visit
https://brainly.com/question/25749514
#SPJ11
Find the arc length of the graph of the function over the indicated interval. (Round your answer to three decimal places.) y=ln(sin(x)), [ π/4, 3π/4]
The arc length of the graph of y = ln(sin(x)) over the interval [π/4, 3π/4] is ln|1 - √2| - ln|1 + √2| (rounded to three decimal places). Ee can use the arc length formula. The formula states that the arc length (L) is given by the integral of √(1 + (dy/dx)²) dx over the interval of interest.
First, let's find the derivative of y = ln(sin(x)). Taking the derivative, we have dy/dx = cos(x) / sin(x).
Now, we can substitute the values into the arc length formula and integrate over the given interval.
The arc length (L) can be calculated as L = ∫[π/4, 3π/4] √(1 + (cos(x) / sin(x))²) dx.
Simplifying the expression, we have L = ∫[π/4, 3π/4] √(1 + cot²(x)) dx.
Using the trigonometric identity cot²(x) = csc²(x) - 1, we can rewrite the integral as L = ∫[π/4, 3π/4] √(csc²(x)) dx.
Taking the square root of csc²(x), we have L = ∫[π/4, 3π/4] csc(x) dx.
Integrating, we get L = ln|csc(x) + cot(x)| from π/4 to 3π/4.
Evaluating the integral, L = ln|csc(3π/4) + cot(3π/4)| - ln|csc(π/4) + cot(π/4)|.
Using the values of csc(3π/4) = -√2 and cot(3π/4) = -1, as well as csc(π/4) = √2 and cot(π/4) = 1, we can simplify further.
Finally, L = ln|-√2 - (-1)| - ln|√2 + 1|.
Simplifying the logarithms, L = ln|1 - √2| - ln|1 + √2|.
Learn more about arc length here : brainly.com/question/15750671
#SPJ11
Given A=⎣⎡104−2⎦⎤ and B=[6−7−18], find AB and BA. AB=BA= Hint: Matrices need to be entered as [(elements of row 1 separated by commas), (elements of row 2 separated by commas), (elements of each row separated by commas)]. Example: C=[142536] would be entered as [(1,2, 3),(4,5,6)] Question Help: □ Message instructor
If the matrices [tex]A= \left[\begin{array}{ccc}1\\0\\4\\ -2\end{array}\right][/tex] and [tex]B=\left[\begin{array}{cccc}6&-7&-1& 8 \end{array}\right][/tex], then products AB= [tex]\left[\begin{array}{cccc}6&-7&-1&8\\0&0&0&0\\24&-28&-4&32\\-12&14&2&-16\end{array}\right][/tex] and BA= [tex]\left[\begin{array}{c}-14\end{array}\right][/tex]
To find the products AB and BA, follow these steps:
If the number of columns in the first matrix is equal to the number of rows in the second matrix, then we can multiply them. The dimensions of A is 4×1 and the dimensions of B is 1×4. So the product of matrices A and B, AB can be calculated as shown below.On further simplification, we get [tex]AB= \left[\begin{array}{ccc}1\\0\\4\\ -2\end{array}\right]\left[\begin{array}{cccc}6&-7&-1& 8 \end{array}\right]\\ = \left[\begin{array}{cccc}6&-7&-1&8\\0&0&0&0\\24&-28&-4&32\\-12&14&2&-16\end{array}\right][/tex]Similarly, the product of BA can be calculated as shown below:[tex]BA= \left[\begin{array}{cccc}6&-7&-1& 8 \end{array}\right] \left[\begin{array}{ccc}1\\0\\4\\ -2\end{array}\right]\\ = \left[\begin{array}{c}6+0-4-16\end{array}\right] = \left[\begin{array}{c}-14\end{array}\right][/tex]Therefore, the products AB and BA of matrices A and B can be calculated.
Learn more about matrix:
brainly.com/question/11989522
#SPJ11
\section*{Problem 2}
\subsection*{Part 1}
Which of the following arguments are valid? Explain your reasoning.\\
\begin{enumerate}[label=(\alph*)]
\item I have a student in my class who is getting an $A$. Therefore, John, a student in my class, is getting an $A$. \\\\
%Enter your answer below this comment line.
\\\\
\item Every Girl Scout who sells at least 30 boxes of cookies will get a prize. Suzy, a Girl Scout, got a prize. Therefore, Suzy sold at least 30 boxes of cookies.\\\\
%Enter your answer below this comment line.
\\\\
\end{enumerate}
\subsection*{Part 2}
Determine whether each argument is valid. If the argument is valid, give a proof using the laws of logic. If the argument is invalid, give values for the predicates $P$ and $Q$ over the domain ${a,\; b}$ that demonstrate the argument is invalid.\\
\begin{enumerate}[label=(\alph*)]
\item \[
\begin{array}{||c||}
\hline \hline
\exists x\, (P(x)\; \land \;Q(x) )\\
\\
\therefore \exists x\, Q(x)\; \land\; \exists x \,P(x) \\
\hline \hline
\end{array}
\]\\\\
%Enter your answer here.
\\\\
\item \[
\begin{array}{||c||}
\hline \hline
\forall x\, (P(x)\; \lor \;Q(x) )\\
\\
\therefore \forall x\, Q(x)\; \lor \; \forall x\, P(x) \\
\hline \hline
\end{array}
\]\\\\
%Enter your answer here.
\\\\
\end{enumerate}
\newpage
%--------------------------------------------------------------------------------------------------
The argument is invalid because just one student getting an A does not necessarily imply that every student gets an A in the class. There might be more students in the class who aren't getting an A.
Therefore, the argument is invalid. The argument is valid. Since Suzy received a prize and according to the statement in the argument, every girl scout who sells at least 30 boxes of cookies will get a prize, Suzy must have sold at least 30 boxes of cookies. Therefore, the argument is valid.
a. The argument is invalid. Let's consider the domain to be
[tex]${a,\; b}$[/tex]
Let [tex]$P(a)$[/tex] be true,[tex]$Q(a)$[/tex] be false and [tex]$Q(b)$[/tex] be true.
Then, [tex]$\exists x\, (P(x)\; \land \;Q(x))$[/tex] is true because [tex]$P(a) \land Q(a)$[/tex] is true.
However, [tex]$\exists x\, Q(x)\; \land\; \exists x \,P(x)$[/tex] is false because [tex]$\exists x\, Q(x)$[/tex] is true and [tex]$\exists x \,P(x)$[/tex] is false.
Therefore, the argument is invalid.
b. The argument is invalid.
Let's consider the domain to be
[tex]${a,\; b}$[/tex]
Let [tex]$P(a)$[/tex] be true and [tex]$Q(b)$[/tex]be true.
Then, [tex]$\forall x\, (P(x)\; \lor \;Q(x) )$[/tex] is true because [tex]$P(a) \lor Q(a)$[/tex] and [tex]$P(b) \lor Q(b)$[/tex] are true.
However, [tex]$\forall x\, Q(x)\; \lor \; \forall x\, P(x)$[/tex] is false because [tex]$\forall x\, Q(x)$[/tex] is false and [tex]$\forall x\, P(x)$[/tex] is false.
Therefore, the argument is invalid.
To know more about argument visit:
https://brainly.com/question/2645376
#SPJ11
Find the maximum and minimum points of each of the following curves 1. y=5x−x^2 / 2 + 3/ √x
The maximum point of the curve is approximately (2.069, 15.848), and there is no minimum point.
To find the maximum and minimum points of the curve y = 5x - x^2/2 + 3/√x, we need to take the derivative of the function and set it equal to zero.
y = 5x - x^2/2 + 3/√x
y' = 5 - x/2 - 3/2x^(3/2)
Setting y' equal to zero:
0 = 5 - x/2 - 3/2x^(3/2)
Multiplying both sides by 2x^(3/2):
0 = 10x^(3/2) - x√x - 3
This is a cubic equation, which can be solved using the cubic formula. However, it is a very long and complicated formula, so we will use a graphing calculator to find the roots of the equation.
Using a graphing calculator, we find that the roots of the equation are approximately x = 0.019, x = 2.069, and x = -2.088. The negative root is extraneous, so we discard it.
Next, we need to find the second derivative of the function to determine if the critical point is a maximum or minimum.
y'' = -1/2 - (3/4)x^(-5/2)
Plugging in the critical point x = 2.069, we get:
y''(2.069) = -0.137
Since y''(2.069) is negative, we know that the critical point is a maximum.
Therefore, the maximum point of the curve is approximately (2.069, 15.848).
To find the minimum point of the curve, we need to check the endpoints of the domain. The domain of the function is x > 0, so the endpoints are 0 and infinity.
Checking x = 0, we get:
y(0) = 0 + 3/0
This is undefined, so there is no minimum at x = 0.
Checking as x approaches infinity, we get:
y(infinity) = -infinity
This means that there is no minimum as x approaches infinity.
To learn more about derivative click here
brainly.com/question/25324584
#SPJ11
Sets V and W are defined below.
V = {all positive odd numbers}
W {factors of 40}
=
Write down all of the numbers that are in
VOW.
The numbers that are in the intersection of V and W (VOW) are 1 and 5.
How to determine all the numbers that are in VOW.To find the numbers that are in the intersection of sets V and W (V ∩ W), we need to identify the elements that are common to both sets.
Set V consists of all positive odd numbers, while set W consists of the factors of 40.
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40.
The positive odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, and so on.
To find the numbers that are in the intersection of V and W, we look for the elements that are present in both sets:
V ∩ W = {1, 5}
Therefore, the numbers that are in the intersection of V and W (VOW) are 1 and 5.
Learn more about intersection at https://brainly.com/question/29185601
#SPJ1
If three diagnosed her drawn inside a hexagram with each one passing through the center point of the hexagram how many triangles are formed
if three diagonals are drawn inside a hexagram, each passing through the center point of the hexagram, a total of 18 triangles are formed.
If three diagonals are drawn inside a hexagram, each passing through the center point of the hexagram, we can determine the number of triangles formed.
Let's break it down step by step:
1. Start with the hexagram, which has six points connected by six lines.
2. Each of the six lines represents a side of a triangle.
3. The diagonals that pass through the center point of the hexagram split each side in half, creating two smaller triangles.
4. Since there are six lines in total, and each line is split into two smaller triangles, we have a total of 6 x 2 = 12 smaller triangles.
5. Additionally, the six lines themselves can also be considered as triangles, as they have three sides.
6. So, we have 12 smaller triangles formed by the diagonals and 6 larger triangles formed by the lines.
7. The total number of triangles is 12 + 6 = 18.
In conclusion, if three diagonals are drawn inside a hexagram, each passing through the center point of the hexagram, a total of 18 triangles are formed.
To know more about probability, visit:
https://brainly.com/question/31828911
#SPJ11
The weight of Royal Gala apples has a mean of 170g and a standard deviation of 18g. A random sample of 36 Royal Gala apples was selected.
Show step and equation.
e) What are the mean and standard deviation of the sampling distribution of sample mean?
f) What is the probability that the average weight is less than 170?
g) What is the probability that the average weight is at least 180g?
h) In repeated samples (n=36), over what weight are the heaviest 33% of the average weights?
i) State the name of the theorem used to find the probabilities above.
The probability that the average weight is less than 170 g is 0.5. In repeated samples (n=36), the heaviest 33% of the average weights are over 163.92 g.
Sampling distribution refers to the probability distribution of a statistic gathered from random samples of a specific size taken from a given population. It is computed for all sample sizes from the population.
It is essential to estimate and assess the properties of population parameters by analyzing these distributions.
To find the mean and standard deviation of the sampling distribution of the sample mean, the formulas used are:
The mean of the sampling distribution of the sample mean = μ = mean of the population = 170 g
The standard deviation of the sampling distribution of the sample mean is σx = (σ/√n) = (18/√36) = 3 g
The central limit theorem (CLT) is a theorem used to find the probabilities above. It states that, under certain conditions, the mean of a sufficiently large number of independent random variables with finite means and variances will be approximately distributed as a normal random variable.
To find the probability that the average weight is less than 170 g, we need to use the standard normal distribution table or z-score formula. The z-score formula is:
z = (x - μ) / (σ/√n),
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the given values, we get
z = (170 - 170) / (18/√36) = 0,
which corresponds to a probability of 0.5.
Therefore, the probability that the average weight is less than 170 g is 0.5.
To find the probability that the average weight is at least 180 g, we need to calculate the z-score and use the standard normal distribution table. The z-score is
z = (180 - 170) / (18/√36) = 2,
which corresponds to a probability of 0.9772.
Therefore, the probability that the average weight is at least 180 g is 0.9772.
To find the weight over which the heaviest 33% of the average weights lie, we need to use the inverse standard normal distribution table or the z-score formula. Using the inverse standard normal distribution table, we find that the z-score corresponding to a probability of 0.33 is -0.44. Using the z-score formula, we get
-0.44 = (x - 170) / (18/√36), which gives
x = 163.92 g.
Therefore, in repeated samples (n=36), the heaviest 33% of the average weights are over 163.92 g.
Sampling distribution is a probability distribution that helps estimate and analyze the properties of population parameters. The mean and standard deviation of the sampling distribution of the sample mean can be calculated using the formulas μ = mean of the population and σx = (σ/√n), respectively. The central limit theorem (CLT) is used to find probabilities involving the sample mean. The z-score formula and standard normal distribution table can be used to find these probabilities. In repeated samples (n=36), the heaviest 33% of the average weights are over 163.92 g.
To know more about z-score visit:
brainly.com/question/31871890
#SPJ11
if you are given a box with sides of 7 inches, 9 inches, and 13 inches, what would its volume be?
To calculate the volume of a rectangular box, you multiply the lengths of its sides.
In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:
Volume = Length × Width × Height
Volume = 7 inches × 9 inches × 13 inches
Volume = 819 cubic inches
So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.
In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.
Learn more about Cubic Formula here :
https://brainly.com/question/27377982
#SPJ11
A foundation invests $70,000 at simple interest, a part at 7%, twice that amount at 3%, and the rest at 6.5%. What is the most that the foundation can invest at 3% and be guaranteed $4095 in interest
The maximum amount that the foundation can invest at 3% and be guaranteed $4095 in interest is $56,000. Therefore, the option (B) is correct.
Foundation invested $70,000 at simple interest, a part at 7%, twice that amount at 3%, and the rest at 6.5%.The foundation wants to invest at 3% and be guaranteed $4095 in interest. To Find: The maximum amount that the foundation can invest at 3%Simple interest is the interest calculated on the original principal only. It is calculated by multiplying the principal amount, the interest rate, and the time period, then dividing the whole by 100.The interest (I) can be calculated by using the following formula; I = P * R * T, Where, P = Principal amount, R = Rate of interest, T = Time period. In this problem, we will calculate the interest on the amount invested at 3% and then divide the guaranteed interest by the calculated interest to get the amount invested at 3%.1) Let's calculate the interest for 3% rate;I = P * R * T4095 = P * 3% * 1Therefore, P = 4095/0.03P = $136,5002) Now, we will find out the amount invested at 7%.Let X be the amount invested at 7%,Then,2X = Twice that amount invested at 3% since the amount invested at 3% is half of the investment at 7% amount invested at 6.5% = Rest amount invested. Now, we can find the value of X,X + 2X + Rest = Total Amount X + 2X + (70,000 - 3X) = 70,000X = 28,000The amount invested at 7% is $28,000.3) The amount invested at 3% is twice that of 7%.2X = 2 * 28,000 = $56,0004) The amount invested at 6.5% is, Rest = 70,000 - (28,000 + 56,000) = $6,000.
Let's learn more about interest:
https://brainly.com/question/25720319
#SPJ11
Work Rate. As a typist resumes work on a research paper, (1)/(6) of the paper has already been keyboarded. Six hours later, the paper is (3)/(4) done. Calculate the worker's typing rate.
If a typist resumes work on a research paper, (1)/(6) of the paper has already been keyboarded and six hours later, the paper is (3)/(4) done, then the worker's typing rate is 5/72.
To find the typing rate, follow these steps:
To find the typist's rate of typing, we can use the work formula, Work = rate × time. The typist has completed 1/6 of the research paper after a certain amount of time. Let this time be t. Therefore, the work done by the typist in time t is: W1 = 1/6We can also calculate the work done by the typist after 6 hours. At this time, the typist has completed 3/4 of the research paper. Therefore, the work done by the typist after 6 hours is: W2 = 3/4 - 1/6. We can simplify the expression by finding the lowest common multiple of the denominators (4 and 6), which is 12. W2 = (9/12) - (2/12) ⇒W2 = 7/12. We know that the time taken to complete W2 - W1 work is 6 hours. Therefore, we can find the typist's rate of typing (r) as:r = (W2 - W1)/t ⇒Rate of typing, r = (7/12 - 1/6)/6 ⇒r = (7/12 - 2/12)/6 ⇒r = 5/12 × 1/6r = 5/72.The worker's typing rate is 5/72.
Learn more about rate:
https://brainly.com/question/119866
#SPJ11
find the equation for the circle with a diameter whose endpoints are (1,14) and (7,-12) write in standard form
To write the equation for a circle with a diameter whose endpoints are (1, 14) and (7, -12) in standard form, we'll need to follow the following steps:Step 1: Find the center of the circle by finding the midpoint of the diameter.
= [(x1 + x2)/2, (y1 + y2)/2]Midpoint
= [(1 + 7)/2, (14 + (-12))/2]Midpoint
= (4, 1)So, the center of the circle is (4, 1).Step 2: Find the radius of the circle. The radius of the circle is half the length of the diameter, which is the distance between the two endpoints. The distance formula can be used to find this distance. Diameter
= √((x2 - x1)² + (y2 - y1)²)Diameter
= √((7 - 1)² + (-12 - 14)²)Diameter
= √(6² + (-26)²)Diameter
= √(676)Diameter
= 26So, the radius of the circle is half the diameter or 26/2 = 13.Step 3: Write the equation of the circle in standard form, which is (x - h)² + (y - k)²
= r². Replacing the center (h, k) and radius r, we get:(x - 4)² + (y - 1)² = 13²Simplifying this equation, we get:x² - 8x + 16 + y² - 2y + 1 = 169x² + y² - 8x - 2y - 152
= 0
To know more about endpoints visit:
https://brainly.com/question/29164764?referrer=searchResults
#SPJ11
The president of Doerman Distributors, Inc., believes that 30% of the firm's orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers. Assume that the president is correct and p=0.30. What is the sampling error of p
ˉ
for this study? If required, round your answer to four decimal places.
Sampling error is a statistical error caused by choosing a sample rather than the entire population. In this study, Doerman Distributors Inc. believes 30% of its orders come from first-time customers, with p = 0.3. The sampling error for p ˉ is 0.0021, rounded to four decimal places.
Sampling error: A sampling error is a statistical error that arises from the sample being chosen rather than the entire population.What is the proportion of first-time customers that Doerman Distributors Inc. believes constitutes 30% of its orders? For a sample of 100 orders,
what is the sampling error for p ˉ in this study? We are provided with the data that The president of Doerman Distributors, Inc. believes that 30% of the firm's orders come from first-time customers. Therefore, p = 0.3 (the proportion of first-time customers). The sample size is n = 100 orders.
Now, the sampling error formula for a sample of a population proportion is given by;Sampling error = p(1 - p) / nOn substituting the values in the formula, we get;Sampling error = 0.3(1 - 0.3) / 100Sampling error = 0.21 / 100Sampling error = 0.0021
Therefore, the sampling error for p ˉ in this study is 0.0021 (rounded to four decimal places).
To know more about Sampling error Visit:
https://brainly.com/question/29974523
#SPJ11
Solve the differential equation (27xy + 45y²) + (9x² + 45xy)y' = 0 using the integrating factor u(x, y) = (xy(2x+5y))-1.
NOTE: Do not enter an arbitrary constant.
The general solution is given implicitly by
The given differential equation is `(27xy + 45y²) + (9x² + 45xy)y' = 0`.We have to solve this differential equation by using integrating factor `u(x, y) = (xy(2x+5y))-1`.The integrating factor `u(x,y)` is given by `u(x,y) = e^∫p(x)dx`, where `p(x)` is the coefficient of y' term.
Let us find `p(x)` for the given differential equation.`p(x) = (9x² + 45xy)/ (27xy + 45y²)`We can simplify this expression by dividing both numerator and denominator by `9xy`.We get `p(x) = (x + 5y)/(3y)`The integrating factor `u(x,y)` is given by `u(x,y) = (xy(2x+5y))-1`.Substitute `p(x)` and `u(x,y)` in the following formula:`y = (1/u(x,y))* ∫[u(x,y)* q(x)] dx + C/u(x,y)`Where `q(x)` is the coefficient of y term, and `C` is the arbitrary constant.To solve the differential equation, we will use the above formula, as follows:`y = [(3y)/(x+5y)]* ∫ [(xy(2x+5y))/y]*dx + C/[(xy(2x+5y))]`We will simplify and solve the above expression, as follows:`y = (3x^2 + 5xy)/ (2xy + 5y^2) + C/(xy(2x+5y))`Simplify the above expression by multiplying `2xy + 5y^2` both numerator and denominator, we get:`y(2xy + 5y^2) = 3x^2 + 5xy + C`This is the general solution of the differential equation.
To know more about differential equation, visit:
https://brainly.com/question/32645495
#SPJ11
1. Using f(x) = x² + 3x + 5 and several test values, consider the following questions:
(a) Is f(x+3) equal to f(x) + f(3)? (b) Is f(-x) equal to -f(x)? 2. Give an example of a quantity occurring in everyday life that can be computed by a function of three or more inputs. Identify the inputs and the output and draw the function diagram.
1a) No, f(x + 3) ≠ f(x) + f(3) as they both have different values.
1b) No, f(-x) ≠ -f(x) as they both have different values. 2) A real-life example of a function with three or more inputs is calculating the total cost of a trip, with inputs being distance, fuel efficiency, fuel price, and any additional expenses.
1a) Substituting x + 3 into the function yields
f(x + 3) = (x + 3)² + 3(x + 3) + 5 = x² + 9x + 23;
while f(x) + f(3) = x² + 3x + 5 + (3² + 3(3) + 5) = x² + 9x + 23.
As both expressions have the same value, the statement is true.
1b) Substituting -x into the function yields f(-x) = (-x)² + 3(-x) + 5 = x² - 3x + 5; while -f(x) = -(x² + 3x + 5) = -x² - 3x - 5. As both expressions have different values, the statement is false.
2) A real-life example of a function with three or more inputs is calculating the total cost of a trip. The inputs are distance, fuel efficiency, fuel price, and any additional expenses such as lodging and food.
The function diagram would show the inputs on the left, the function in the middle, and the output on the right. The output would be the total cost of the trip, which is calculated by multiplying the distance by the fuel efficiency and the fuel price, and then adding any additional expenses.
To learn more about efficiency
https://brainly.com/question/27432004
#SPJ11
Cheryl was taking her puppy to get groomed. One groomer. Fluffy Puppy, charges a once a year membership fee of $120 plus $10. 50 per
standard visit. Another groomer, Pristine Paws, charges a $5 per month membership fee plus $13 per standard visit. Let f(2) represent the
cost of Fluffy Puppy per year and p(s) represent the cost of Pristine Paws per year. What does f(x) = p(x) represent?
f(x) = p(x) when x = 24, which means that both groomers will cost the same amount per year if Cheryl takes her puppy for grooming services 24 times in one year.
The functions f(x) and p(x) represent the annual cost of using Fluffy Puppy and Pristine Paws for grooming services, respectively.
In particular, f(2) represents the cost of using Fluffy Puppy for 2 standard visits in one year. This is equal to the annual membership fee of $120 plus the cost of 2 standard visits at $10.50 per visit, or:
f(2) = $120 + (2 x $10.50)
f(2) = $120 + $21
f(2) = $141
Similarly, p(x) represents the cost of using Pristine Paws for x standard visits in one year. The cost consists of a monthly membership fee of $5 multiplied by 12 months in a year, plus the cost of x standard visits at $13 per visit, or:
p(x) = ($5 x 12) + ($13 x x)
p(x) = $60 + $13x
Therefore, the equation f(x) = p(x) represents the situation where the annual cost of using Fluffy Puppy and Pristine Paws for grooming services is the same, or when the number of standard visits x satisfies the equation:
$120 + ($10.50 x) = $60 + ($13 x)
Solving this equation gives:
$10.50 x - $13 x = $60 - $120
-$2.50 x = -$60
x = 24
So, f(x) = p(x) when x = 24, which means that both groomers will cost the same amount per year if Cheryl takes her puppy for grooming services 24 times in one year.
Learn more about cost from
https://brainly.com/question/25109150
#SPJ11
Find the mean, variance, and standard deviation of the following situation: The probabilicy of drawing a red marble from a bag is 0.4. You draw six red marbles with replacement. Give your answer as a
The mean (anticipated value) in this case is 2.4, the variance is roughly 2.8, and the standard deviation is roughly 1.67.
To find the mean, variance, and standard deviation in this situation, we can use the following formulas:
Mean (Expected Value):
The mean is calculated by multiplying each possible outcome by its corresponding probability and summing them up.
Variance:
The variance is calculated by finding the average of the squared differences between each outcome and the mean.
Standard Deviation:
The standard deviation is the square root of the variance and measures the dispersion or spread of the data.
In this case, the probability of drawing a red marble from the bag is 0.4, and you draw six red marbles with replacement.
Mean (Expected Value):
The mean can be calculated by multiplying the probability of drawing a red marble (0.4) by the number of marbles drawn (6):
Mean = 0.4 * 6 = 2.4
Variance:
To calculate the variance, we need to find the average of the squared differences between each outcome (number of red marbles drawn) and the mean (2.4).
Variance = [ (0 - 2.4)² + (1 - 2.4)² + (2 - 2.4)² + (3 - 2.4)² + (4 - 2.4)² + (5 - 2.4)² + (6 - 2.4)² ] / 7
Variance = [ (-2.4)² + (-1.4)² + (-0.4)² + (0.6)² + (1.6)² + (2.6)² + (3.6)² ] / 7
Variance ≈ 2.8
Standard Deviation:
The standard deviation is the square root of the variance:
Standard Deviation ≈ √2.8 ≈ 1.67
Therefore, in this situation, the mean (expected value) is 2.4, the variance is approximately 2.8, and the standard deviation is approximately 1.67.
Learn more about Mean on:
https://brainly.com/question/1136789
#SPJ11
Write an equation for the line passing through the given pair of points. Give the final answer in (a) slope-intercept form and (b) standard form. Use the smallest possible positive integer coefficient for x when giving the equation in standard form. (−4,0) and (0,9) (a) The equation of the line in slope-intercept form is (Use integers or fractions for any numbers in the equation.) (b) The equation of the line in standard form is
The equation of the line for the given points in slope-intercept form is y = (9/4)x + 9 and the equation of the line for the given points in standard form is 9x - 4y = -36
(a) The equation of the line passing through the points (-4,0) and (0,9) can be written in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we use the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) = (-4,0) and (x₂, y₂) = (0,9).
m = (9 - 0) / (0 - (-4)) = 9 / 4.
Next, we can substitute one of the given points into the equation and solve for b.
Using the point (-4,0):
0 = (9/4)(-4) + b
0 = -9 + b
b = 9.
Therefore, the equation of the line in slope-intercept form is y = (9/4)x + 9.
(b) To write the equation of the line in standard form, Ax + By = C, where A, B, and C are integers, we can rearrange the slope-intercept form.
Multiplying both sides of the slope-intercept form by 4 to eliminate fractions:
4y = 9x + 36.
Rearranging the terms:
-9x + 4y = 36.
Since we want the smallest possible positive integer coefficient for x, we can multiply the equation by -1 to make the coefficient positive:
9x - 4y = -36.
Therefore, the equation of the line in standard form is 9x - 4y = -36.
Learn more about slope-intercept form here : brainly.com/question/30381959
#SPJ11
Let φ ≡ x = y*z ∧ y = 4*z ∧ z = b[0] + b[2] ∧ 2 < b[1] < b[2] < 5. Complete the definition of σ = {x = , y = , z = 5, b = } so that σ ⊨ φ. If some value is unconstrained, give it a greek letter name (δ, ζ, η, your choice).
To complete the definition of σ = {x = , y = , z = 5, b = } so that σ ⊨ φ, we need to assign appropriate values to the variables x, y, and b based on the given constraints in φ.
Given:
φ ≡ x = y*z ∧ y = 4*z ∧ z = b[0] + b[2] ∧ 2 < b[1] < b[2] < 5
We can start by assigning the value of z as z = 5, as given in the definition of σ.
Now, let's assign values to x, y, and b based on the constraints:
From the first constraint, x = y * z, we can substitute the known values:
x = y * 5
Next, from the second constraint, y = 4 * z, we can substitute the known value of z:
y = 4 * 5
y = 20
Now, let's consider the third constraint, z = b[0] + b[2]. Since the values of b[0] and b[2] are not given, we can assign them arbitrary values using Greek letter names.
Let's assign b[0] as δ and b[2] as ζ.
Therefore, z = δ + ζ.
Now, we need to satisfy the constraint 2 < b[1] < b[2] < 5. Since b[1] is not assigned a specific value, we can assign it as η.
Therefore, the final definition of σ = {x = y * z, y = 20, z = 5, b = [δ, η, ζ]} satisfies the given constraints and makes σ a model of φ (i.e., σ ⊨ φ).
Note: The specific values assigned to δ, η, and ζ are arbitrary as long as they satisfy the constraints given in the problem.
To know more about constraints visit:
https://brainly.com/question/32387329
#SPJ11
On thursday 240 adults and children attended a show the ratio of adults to children was 5 to 1 how many children attended the show
40 children attended the show.
To find the number of children who attended the show, we need to determine the proportion of children in the total attendance.
Given that the ratio of adults to children is 5 to 1, we can represent this as:
Adults : Children = 5 : 1
Let's assume the number of children is represented by 'x'. Since the ratio of adults to children is 5 to 1, the number of adults can be calculated as 5 times the number of children:
Number of adults = 5x
The total attendance is the sum of adults and children, which is given as 240:
Number of adults + Number of children = 240
Substituting the value of the number of adults (5x) into the equation:
5x + x = 240
Combining like terms:
6x = 240
Solving for 'x' by dividing both sides of the equation by 6:
x = 240 / 6
x = 40
Therefore, 40 children attended the show.
Learn more about the show. from
https://brainly.com/question/27710307
#SPJ11
Propositional logic. Suppose P(\mathbf{x}) and Q(\mathbf{x}) are two primitive n -ary predicates i.e. the characteristic functions \chi_{P} and \chi_{Q} are primitive recu
In propositional logic, a predicate is a function that takes one or more arguments and returns a truth value (either true or false) based on the values of its arguments. A primitive recursive predicate is one that can be defined using primitive recursive functions and logical connectives (such as negation, conjunction, and disjunction).
Suppose P(\mathbf{x}) and Q(\mathbf{x}) are two primitive n-ary predicates. The characteristic functions \chi_{P} and \chi_{Q} are functions that return 1 if the predicate is true for a given set of arguments, and 0 otherwise. These characteristic functions can be defined using primitive recursive functions and logical connectives.
For example, the characteristic function of the conjunction of two predicates P and Q, denoted by P \land Q, is given by:
\chi_{P \land Q}(\mathbf{x}) = \begin{cases} 1 & \text{if } \chi_{P}(\mathbf{x}) = 1 \text{ and } \chi_{Q}(\mathbf{x}) = 1 \ 0 & \text{otherwise} \end{cases}
Similarly, the characteristic function of the disjunction of two predicates P and Q, denoted by P \lor Q, is given by:
\chi_{P \lor Q}(\mathbf{x}) = \begin{cases} 1 & \text{if } \chi_{P}(\mathbf{x}) = 1 \text{ or } \chi_{Q}(\mathbf{x}) = 1 \ 0 & \text{otherwise} \end{cases}
Using these logical connectives and the primitive recursive functions, we can define more complex predicates that depend on one or more primitive predicates. These predicates can then be used to form propositional formulas and logical proofs in propositional logic.
Learn more about "propositional logic" : https://brainly.com/question/27928997
#SPJ11
Given f(x)=x^2+3, find and simplify. (a) f(t−2) (b) f(y+h)−f(y) (c) f(y)−f(y−h) (a) f(t−2)= (Simplify your answer. Do not factor.)
The simplifed value of the function f(x) = x^2 +3 is f(t-2) = t^2 -4t +7. The simplified value of the function f(x) = x^2+3 is f(y+h) - f(y) = 2yh +h^2.
Given f(x)=x²+3, we have to find and simplify:
(a) f(t-2).The given function is f(x)=x²+3.
Substitute (t-2) for x:
f(t-2)=(t-2)²+3
Simplifying the equation:
(t-2)²+3 = t² - 4t + 7
Hence, (a) f(t-2) = t² - 4t + 7.
(b) f(y+h)−f(y).
The given function is f(x)=x²+3.
Substitute (y+h) for x and y for x:
f(y+h) - f(y) = (y+h)²+3 - (y²+3)
Simplifying the equation:
(y+h)²+3 - (y²+3) = y² + 2yh + h² - y²= 2yh + h²
Hence, (b) f(y+h)−f(y) = 2yh + h².
(c) f(y)−f(y−h).
The given function is f(x)=x²+3.
Substitute y for x and (y-h) for x:
f(y) - f(y-h) = y²+3 - (y-h)²-3
Simplifying the equation:
y² + 3 - (y² - 2yh + h²) - 3= 2yh - h²
Hence, (c) f(y)−f(y−h) = 2yh - h².
Let us know more about function : https://brainly.com/question/31062578.
#SPJ11
Let f(z)=ez/z, where z ranges over the annulus 21≤∣z∣≤1. Find the points where the maximum and minimum values of ∣f(z)∣ occur and determine these values.
The maximum value of |f(z)| occurs at z = i/2, with a value of 2|e^(i/2)|. The minimum value of |f(z)| occurs at z = -i/2, with a value of 2|e^(-i/2)|.
To find the points where the maximum and minimum values of |f(z)| occur for the function f(z) = e^z/z in the annulus 1/2 ≤ |z| ≤ 1, we can analyze the behavior of the function in that region.
First, let's rewrite the function as:
f(z) = e^z / z = e^z * (1/z).
We observe that the function f(z) has a singularity at z = 0. Since the annulus 1/2 ≤ |z| ≤ 1 does not include the singularity at z = 0, we can focus on the behavior of the function on the boundary of the annulus, which is the circle |z| = 1/2.
Now, let's consider the modulus of f(z):
|f(z)| = |e^z / z| = |e^z| / |z|.
For z on the boundary of the annulus, |z| = 1/2. Therefore, we have:
|f(z)| = |e^z| / (1/2) = 2|e^z|.
To find the maximum and minimum values of |f(z)|, we need to find the maximum and minimum values of |e^z| on the circle |z| = 1/2.
The modulus |e^z| is maximized when the argument z is purely imaginary, i.e., when z = iy for some real number y. On the circle |z| = 1/2, we have |iy| = |y| = 1/2. Therefore, the maximum value of |e^z| occurs at z = i(1/2).
Similarly, the modulus |e^z| is minimized when the argument z is purely imaginary and negative, i.e., when z = -iy for some real number y. On the circle |z| = 1/2, we have |-iy| = |y| = 1/2. Therefore, the minimum value of |e^z| occurs at z = -i(1/2).
Substituting these values of z into |f(z)| = 2|e^z|, we get:
|f(i/2)| = 2|e^(i/2)|,
|f(-i/2)| = 2|e^(-i/2)|.
The values of |e^(i/2)| and |e^(-i/2)| can be calculated as |cos(1/2) + i sin(1/2)| and |cos(-1/2) + i sin(-1/2)|, respectively.
Therefore, the maximum value of |f(z)| occurs at z = i/2, and the minimum value of |f(z)| occurs at z = -i/2. The corresponding maximum and minimum values of |f(z)| are 2|e^(i/2)| and 2|e^(-i/2)|, respectively.
To learn more about functions visit : https://brainly.com/question/11624077
#SPJ11
Use the first derivative test to determine all local minimum and maximum points of the function y=(1)/(4)x^(3)-3x.
Therefore, the local minimum is at (2, -5) and the local maximum is at (-2, 1).
To determine the local minimum and maximum points of the function y = (1/4)x³ - 3x using the first derivative test, follow these steps:
Step 1: Find the first derivative of the function.
Taking the derivative of y = (1/4)x³ - 3x, we get:
y' = (3/4)x - 3
Step 2: Set the first derivative equal to zero and solve for x.
To find the critical points, we set y' = 0 and solve for x:
(3/4)x² - 3 = 0
(3/4)x² = 3
x² = (4/3) * 3
x² = 4
x = ±√4
x = ±2
Step 3: Determine the intervals where the first derivative is positive or negative.
To determine the intervals, we can use test values or create a sign chart. Let's use test values:
For x < -2, we can plug in x = -3 into y' to get:
y' = (3/4)(-3)² - 3
y' = (3/4)(9) - 3
y' = 27/4 - 12/4
y' = 15/4 > 0
For -2 < x < 2, we can plug in x = 0 into y' to get:
y' = (3/4)(0)² - 3
y' = -3 < 0
For x > 2, we can plug in x = 3 into y' to get:
y' = (3/4)(3)² - 3
y' = (3/4)(9) - 3
y' = 27/4 - 12/4
y' = 15/4 > 0
Step 4: Determine the nature of the critical points.
Since the first derivative changes from positive to negative at x = -2 and from negative to positive at x = 2, we have a local maximum at x = -2 and a local minimum at x = 2.
Therefore, the local minimum is at (2, -5) and the local maximum is at (-2, 1).
TO know more about derivative visit:
https://brainly.com/question/29144258
#SPJ11
the probability that i wear boots given that it's raining is 60%. the probability that it's raining is 20%. the probability that i wear boots is 9% what is the probability that it rains and i wear boots? state your answer as a decimal value.
The probability that it rains and I wear boots is 0.12.
To solve this problem, we will use the concept of conditional probability, which deals with the probability of an event occurring given that another event has already occurred.
First, let's assign some variables:
P(Boots) represents the probability of wearing boots.
P(Rain) represents the probability of rain.
According to the information provided, we have the following probabilities:
P(Boots | Rain) = 0.60 (the probability of wearing boots given that it's raining)
P(Rain) = 0.20 (the probability of rain)
P(Boots) = 0.09 (the probability of wearing boots)
To find the probability of both raining and wearing boots, we can use the formula for conditional probability:
P(Boots and Rain) = P(Boots | Rain) * P(Rain)
Substituting the given values, we get:
P(Boots and Rain) = 0.60 * 0.20 = 0.12
Therefore, the probability of both raining and wearing boots is 0.12 or 12%.
To know more about probability here
https://brainly.com/question/11234923
#SPJ4
Given the function f(x)=2(x-3)2+6, for x > 3, find f(x). f^-1x)= |
The given function equation is f⁻¹(x) = √[(x - 6)/2] + 3, for x > 6.
The function is given by: f(x) = 2(x - 3)² + 6, for x > 3We are to find f(x) and f⁻¹(x). Finding f(x)
We are given that the function is:f(x) = 2(x - 3)² + 6, for x > 3
We can input any value of x greater than 3 into the equation to find f(x).For x = 4, f(x) = 2(4 - 3)² + 6= 2(1)² + 6= 2 + 6= 8
Therefore, f(4) = 8.Finding f⁻¹(x)To find the inverse of a function, we swap the positions of x and y, then solve for y.
Therefore:f(x) = 2(x - 3)² + 6, for x > 3 We have:x = 2(y - 3)² + 6
To solve for y, we isolate it by subtracting 6 from both sides and dividing by
2:x - 6 = 2(y - 3)²2(y - 3)² = (x - 6)/2y - 3 = ±√[(x - 6)/2] + 3y = ±√[(x - 6)/2] + 3y = √[(x - 6)/2] + 3, since y cannot be negative (otherwise it won't be a function).
Therefore, f⁻¹(x) = √[(x - 6)/2] + 3, for x > 6.
To know more about function visit:
brainly.com/question/29103939
#SPJ11