The general solution of the differential equation y' + xy = y² will be
[tex]y =\frac{2e^{x^2/2}}{C_1 - \sqrt{2\pi}erfi(x/\sqrt{2}) }[/tex]
Here we see that the given equation is
y' + xy = y²
This clearly is a Bernoulli equation.
Hence we will divide the entire equation by y² to get
y'/y² + x/y = 1
Let z = 1/y
hence,
dz/dx = -y'/y²
Hence we get
-z' + xz = 1
Hence we get the Integrating factor as
[tex]e^{\int{xdx}}= e^{x^2/2}[/tex]
Multiplying this on both sides we get
(xz - z')[tex]e^{x^2/2}[/tex] = [tex]e^{x^2/2}[/tex]
Cearly LHS is equal to
[tex]\frac{d}{dx}(ze^{x^2/2})[/tex]
Hence we get
[tex]\frac{d}{dx}(ze^{x^2/2}) =e^{x^2/2}[/tex]
Integrating both sides with respect to dx will give us
[tex]ze^{x^2/2} + C_1= \frac{\sqrt{\pi}}{2} erfi(x) + C_2[/tex]
Hence simplifying the equation and putting th value of z in terms of y gives us the general solution
[tex]y =\frac{2e^{x^2/2}}{C_1 - \sqrt{2\pi}erfi(x/\sqrt{2}) }[/tex]
To learn more about Differential Equation visit
https://brainly.com/question/31684625
#SPJ4
Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean μ=41 and standard deviation σ=6. Use the TI-84 Plus calculator to answer the following. (a) What is the probability that a randomly chosen tire has a lifetime greater than 47 thousand miles? (b) What proportion of tires have lifetimes between 36 and 45 thousand miles? (c) What proportion of tires have lifetimes less than 44 thousand miles? Round the answers to at least four decimal places.
(a) To calculate the probability that a randomly chosen tire has a lifetime greater than 47 thousand miles, we can use the normal distribution on the TI-84 Plus calculator.
1. Press the "2nd" button, followed by "Vars" (DISTR).
2. Select "2: normalcdf(" for the cumulative distribution function.
3. Enter the lower bound, which is 47, the upper bound as a large number (e.g., 10^99), the mean (μ) as 41, and the standard deviation (σ) as 6.
4. Press "Enter" to calculate the probability.
The result will be the probability that a randomly chosen tire has a lifetime greater than 47 thousand miles.
(b) To find the proportion of tires that have lifetimes between 36 and 45 thousand miles, we use the normal distribution again.
1. Press the "2nd" button, followed by "Vars" (DISTR).
2. Select "2: normalcdf(" for the cumulative distribution function.
3. Enter the lower bound as 36, the upper bound as 45, the mean (μ) as 41, and the standard deviation (σ) as 6.
4. Press "Enter" to calculate the proportion.
The result will be the proportion of tires that have lifetimes between 36 and 45 thousand miles.
(c) To determine the proportion of tires that have lifetimes less than 44 thousand miles, we can use the normal distribution on the calculator.
1. Press the "2nd" button, followed by "Vars" (DISTR).
2. Select "2: normalcdf(" for the cumulative distribution function.
3. Enter the lower bound as -10^99, the upper bound as 44, the mean (μ) as 41, and the standard deviation (σ) as 6.
4. Press "Enter" to calculate the proportion.
The result will be the proportion of tires that have lifetimes less than 44 thousand miles.
Remember to round the answers to at least four decimal places.
Learn more about standard deviation here:
https://brainly.com/question/13498201
#SPJ11
The width of the smaller rectangular fish tank is 7.35 inches. The width of a similar larger rectangular fish tank is 9.25 inches. Estimate the length of the larger rectangular fish tank.
A. about 20 in.
B. about 23 in.
C. about 24 in.
D. about 25 in.
Answer:
D
Step-by-step explanation:
[tex]\frac{7.35}{9.25}[/tex] = [tex]\frac{20}{x}[/tex] cross multiply and solve for x
7.5x = (20)(9.25)
7.35x = 185 divide both sides by 7.25
[tex]\frac{7.35x}{7.35}[/tex] = [tex]\frac{185}{7.35}[/tex]
x ≈ 25.1700680272
Rounded to the nearest whole number is 25.
Helping in the name of Jesus.
(a) With domain of discourse as the real numbers, prove that the following statement is true: ∀x((x>1)→(x 2
+4>x+4)) (b) With domain of discourse as the real numbers, determine if the following statement is true or false and justify your answer: ∀x(x>0∧−x 2
<0) (c) With domain of discourse as the real numbers, prove that the following statement is false: ∀x∃y(y 2
−2) (d) State whether or not P≡Q, when P is the proposition (p→q)→(q∧r) and Q is the proposition p∨r. Prove the result.
Consider an arbitrary value, let's say x = 2. For x = 2, the statement (x > 1) → (x^2 + 4 > x + 4) becomes (2 > 1) → (2^2 + 4 > 2 + 4), which simplifies to (true) → (8 > 6). Since both the antecedent and consequent are true, the implication holds true. This demonstrates that the statement holds for x = 2, further supporting the initial claim that for every value of x greater than 1, the inequality x^2 + 4 > x + 4 holds true.
(a) To prove the statement ∀x((x>1)→(x^2+4>x+4)), we need to show that for every value of x greater than 1, the inequality x^2 + 4 > x + 4 holds true.
Let's consider an arbitrary value of x greater than 1. We can rewrite the inequality as x^2 - x > 0. Factoring out x, we have x(x - 1) > 0.
Now we consider two cases:
Case 1: x > 0 and x - 1 > 0
In this case, both x and (x - 1) are positive, and the product of two positive numbers is positive. Therefore, x(x - 1) > 0 holds.
Case 2: x < 0 and x - 1 < 0
In this case, both x and (x - 1) are negative. Multiplying two negative numbers also gives a positive result. Therefore, x(x - 1) > 0 holds.
Since the inequality x(x - 1) > 0 holds in both cases, we have shown that for every x > 1, the statement (x > 1) → (x^2 + 4 > x + 4) is true.
(b) The statement ∀x(x > 0 ∧ -x^2 < 0) is false. To justify this, we can find a counterexample. Let's consider x = -1.
For x = -1, the statement becomes (-1 > 0 ∧ -(-1)^2 < 0), which simplifies to (false ∧ -1 < 0). Since false ∧ anything is always false, the statement is false for x = -1. Therefore, the universal statement is false.
(c) To prove that the statement ∀x∃y(y^2 - 2) is false, we need to show that there exists an x for which the statement is false.
Let's consider x = 0. For x = 0, the statement becomes ∃y(y^2 - 2). However, there is no real number y such that y^2 - 2 = 0. Therefore, the statement is false for x = 0, which proves that the universal statement is false.
(d) P ≡ Q is false. To prove this, we can show that P and Q have different truth values for at least one assignment of truth values to the propositional variables p, q, and r.
Let's consider the assignment where p is true, q is true, and r is false. For this assignment, P evaluates to (true → true ∧ false), which simplifies to (true ∧ false), resulting in false.
On the other hand, Q evaluates to true ∨ false, which is true.
Since P and Q have different truth values for this assignment, we can conclude that P ≡ Q is false.
Learn more about arbitrary value here:
https://brainly.com/question/29093928
#SPJ11
a) perform a linear search by hand for the array [20,−20,10,0,15], loching for 0 , and showing each iteration one line at a time b) perform a binary search by hand fo the array [20,0,10,15,20], looking for 0 , and showing each iteration one line at a time c) perform a bubble surt by hand for the array [20,−20,10,0,15], shouing each iteration one line at a time d) perform a selection sort by hand for the array [20,−20,10,0,15], showing eah iteration one line at a time
In the linear search, the array [20, -20, 10, 0, 15] is iterated sequentially until the element 0 is found, The binary search for the array [20, 0, 10, 15, 20] finds the element 0 by dividing the search space in half at each iteration, The bubble sort iteratively swaps adjacent elements until the array [20, -20, 10, 0, 15] is sorted in ascending order and The selection sort swaps the smallest unsorted element with the first unsorted element, resulting in the sorted array [20, -20, 10, 0, 15].
The array is now sorted: [-20, 0, 10, 15, 20]
a) Linear Search for 0 in the array [20, -20, 10, 0, 15]:
Iteration 1: Compare 20 with 0. Not a match.
Iteration 2: Compare -20 with 0. Not a match.
Iteration 3: Compare 10 with 0. Not a match.
Iteration 4: Compare 0 with 0. Match found! Exit the search.
b) Binary Search for 0 in the sorted array [0, 10, 15, 20, 20]:
Iteration 1: Compare middle element 15 with 0. 0 is smaller, so search the left half.
Iteration 2: Compare middle element 10 with 0. 0 is smaller, so search the left half.
Iteration 3: Compare middle element 0 with 0. Match found! Exit the search.
c) Bubble Sort for the array [20, -20, 10, 0, 15]:
Iteration 1: Compare 20 and -20. Swap them: [-20, 20, 10, 0, 15]
Iteration 2: Compare 20 and 10. No swap needed: [-20, 10, 20, 0, 15]
Iteration 3: Compare 20 and 0. Swap them: [-20, 10, 0, 20, 15]
Iteration 4: Compare 20 and 15. No swap needed: [-20, 10, 0, 15, 20]
The array is now sorted: [-20, 10, 0, 15, 20]
d) Selection Sort for the array [20, -20, 10, 0, 15]:
Iteration 1: Find the minimum element, -20, and swap it with the first element: [-20, 20, 10, 0, 15]
Iteration 2: Find the minimum element, 0, and swap it with the second element: [-20, 0, 10, 20, 15]
Iteration 3: Find the minimum element, 10, and swap it with the third element: [-20, 0, 10, 20, 15]
Iteration 4: Find the minimum element, 15, and swap it with the fourth element: [-20, 0, 10, 15, 20]
To know more about Iteration refer to-
https://brainly.com/question/31197563
#SPJ11
A spherical balloon is inflated so that its volume is increasing at the rate of 2.4 cubic feet per minute. How rapidly is the diameter of the balloon increasing when the diameter is 1.2 feet? ____ft/min A 16 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2ft/s, how fast will the foot of the ladder be moving away from the wall when the top is 12 feet above the ground?____ ft/s
A) when the diameter of the balloon is 1.2 feet, the diameter is increasing at a rate of approximately 0.853 feet per minute .
B) when the top of the ladder is 12 feet above the ground, the foot of the ladder is moving away from the wall at a rate of approximately 0.8817 ft/s.
To find the rate at which the diameter of the balloon is increasing, we can use the relationship between the volume and the diameter of a sphere. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter is twice the radius, we have d = 2r.
Given that the volume is increasing at a rate of 2.4 cubic feet per minute, we can differentiate the volume equation with respect to time t to find the rate of change of volume with respect to time:
dV/dt = (4/3)π(3r²)(dr/dt)
Since we are interested in finding the rate at which the diameter (d) is increasing, we substitute dr/dt with dd/dt:
dV/dt = (4/3)π(3r²)(dd/dt)
We also know that r = d/2, so we substitute it into the equation:
dV/dt = (4/3)π(3(d/2)²)(dd/dt)
= (4/3)π(3/4)d²(dd/dt)
= πd²(dd/dt)
Now we can substitute the given values: d = 1.2 ft and dV/dt = 2.4 ft³/min:
2.4 = π(1.2)²(dd/dt)
Solving for dd/dt, we have:
dd/dt = 2.4 / (π(1.2)²)
dd/dt ≈ 0.853 ft/min
Therefore, when the diameter of the balloon is 1.2 feet, the diameter is increasing at a rate of approximately 0.853 feet per minute.
For the second question, we can use similar reasoning. Let h represent the height of the ladder, x represent the distance from the foot of the ladder to the wall, and θ represent the angle between the ladder and the ground.
We have the equation:
x² + h² = 16²
Differentiating both sides with respect to time t, we get:
2x(dx/dt) + 2h(dh/dt) = 0
We are given that dx/dt = 2 ft/s and want to find dh/dt when h = 12 ft.
Using the Pythagorean theorem, we can find x when h = 12:
x² + 12² = 16²
x² + 144 = 256
x² = 256 - 144
x² = 112
x = √112 ≈ 10.58 ft
Substituting the values into the differentiation equation:
2(10.58)(2) + 2(12)(dh/dt) = 0
21.16 + 24(dh/dt) = 0
24(dh/dt) = -21.16
dh/dt = -21.16 / 24
dh/dt ≈ -0.8817 ft/s
Therefore, when the top of the ladder is 12 feet above the ground, the foot of the ladder is moving away from the wall at a rate of approximately 0.8817 ft/s.
To know more about diameter click here :
https://brainly.com/question/29844000
#SPJ4
Suppose we have a spinner with the numbers 1 through 10 on it. The experiment is to spin the spinner and record the number spun. Then C = {1,2,...,10}. Define the events A, B, and C by A = {1,2}, B = {2,3,4}, and C = {3, 4, 5, 6}, respectively.
Ac = {3,4,...,10}; A∪B = {1,2,3,4}; A∩B = {2}
A∩C=φ; B∩C={3,4}; B∩C⊂B; B∩C⊂C
A ∪ (B ∩ C) = {1, 2} ∪ {3, 4} = {1, 2, 3, 4} (1.2.1) (A∪B)∩(A∪C)={1,2,3,4}∩{1,2,3,4,5,6}={1,2,3,4} (1.2.2)
the solution is
a) {0,1,2,3,4}, {2}; (b) (0,3), {x : 1 ≤ x < 2};
(c) {(x, y) : 1 < x < 2, 1 < y < 2}
please explain how to get the answer using stats
The set of events for the experiment of spinning the spinner and recording the number spun is {0,1,2,3,4}, {2}; (0,3), {x : 1 ≤ x < 2}; {(x, y) : 1 < x < 2, 1 < y < 2}.
Given the experiment of spinning the spinner and recording the number spun.
We know that C = {1,2,3,4,5,6,7,8,9,10}.
And the events A, B, and C are defined by A = {1,2}, B = {2,3,4}, and C = {3, 4, 5, 6}, respectively.
From this we get, Ac = {7,8,9,10}
A ∪ B = {1, 2, 3, 4}
A ∩ B = {2}
A ∩ C = Ø
B ∩ C = {3, 4}
B ∩ C ⊂ B and B ∩ C ⊂ C
So, the given equations are,
A ∪ (B ∩ C) = {1, 2} ∪ {3, 4} = {1, 2, 3, 4} ...(1.2.1)
(A ∪ B) ∩ (A ∪ C) = {1, 2, 3, 4} ∩ {1, 2, 3, 4, 5, 6} = {1, 2, 3, 4} ...(1.2.2)
Now let's solve the answer using statistics:
The set of events is {0,1,2,3,4}, {2}
The set of events is (0,3), {x : 1 ≤ x < 2}
The set of events is {(x, y) : 1 < x < 2, 1 < y < 2}
Therefore, we can conclude that the set of events for the experiment of spinning the spinner and recording the number spun is {0,1,2,3,4}, {2}; (0,3), {x : 1 ≤ x < 2}; {(x, y) : 1 < x < 2, 1 < y < 2}.
To know more about statistics visit:
brainly.com/question/32237714
#SPJ11
Estimate how many hours it would take to run (at 10k(m)/(h) ) across the Philippines from Batanes to Jolo. Assuming that inter -island bridges are in place and Jolo is about 3,000km away from Batanes.
It would take approximately 300 hours to run at 10 km/h across the Philippines from Batanes to Jolo.
Given that we need to estimate how many hours it would take to run (at 10k(m)/(h)) across the Philippines from Batanes to Jolo. Let's assume that inter-island bridges are in place and Jolo is about 3,000 km away from Batanes. Thus, the solution is as follows: Distance to be covered = 3,000 km Speed = 10 km/h Hence, the time taken to travel the entire distance = Distance ÷ speed= 3,000 km ÷ 10 km/h= 300 hours. Therefore, it would take approximately 300 hours to run at 10 km/h across the Philippines from Batanes to Jolo.
To know more about estimating time: https://brainly.com/question/26046491
#SPJ11
Find (h∘h)(x) for the function h(x)=sqrt(x+17) and simplify.
The expression (h∘h)(x) for the function h(x) = √(x + 17) simplifies to [(x + 17)^(1/2) + 17]^(1/2).
To find (h∘h)(x) for the function h(x) = √(x + 17), we need to apply the function h(x) to itself.
First, let's substitute h(x) into the expression:
(h∘h)(x) = h(h(x))
Substituting h(x) = √(x + 17), we have:
(h∘h)(x) = √(√(x + 17) + 17)
Now, let's simplify the expression.
Substitute x into h(x):
h(x) = √(x + 17)
Substitute h(x) into the expression (h∘h)(x):
(h∘h)(x) = √(√(x + 17) + 17)
To simplify this expression, we need to apply the square root operation twice.
Apply the first square root:
√(x + 17) = (x + 17)^(1/2)
Apply the second square root:
√((x + 17)^(1/2) + 17) = [(x + 17)^(1/2) + 17]^(1/2)
Therefore, (h∘h)(x) simplifies to:
(h∘h)(x) = [(x + 17)^(1/2) + 17]^(1/2)
This is the simplified form of (h∘h)(x) for the function h(x) = √(x + 17).
To learn more about functions visit : https://brainly.com/question/11624077
#SPJ11
Hi, if anyone could help with this question I'd really appreciate it. (There are two screenshots, one with the actual question and the other with the diagram.) Thanks :)
a) the solution to the simultaneous equations is x = 2 and y = 7.
b i) The value of y in each equation is 7.
ii) The value of y, which is 7, is the same for both equations. This means that the solution (x = 2, y = 7) satisfies both equations and is consistent across both equations.
a) To solve the simultaneous equations y = 2x + 3 and y = -x + 9, we can set them equal to each other:
2x + 3 = -x + 9
Adding x to both sides:
3x + 3 = 9
Subtracting 3 from both sides:
3x = 6
Dividing by 3:
x = 2
Now that we have the value of x, we can substitute it back into either equation to find the corresponding value of y. Let's use the first equation:
y = 2(2) + 3
y = 4 + 3
y = 7
Therefore, the solution to the simultaneous equations is x = 2 and y = 7.
b) Substituting the value of x = 2 into each equation:
For the equation y = 2x + 3:
y = 2(2) + 3
y = 4 + 3
y = 7
For the equation y = -x + 9:
y = -(2) + 9
y = -2 + 9
y = 7
i) The value of y in each equation is 7.
ii) The value of y, which is 7, is the same for both equations. This means that the solution (x = 2, y = 7) satisfies both equations and is consistent across both equations.
In summary, when solving the simultaneous equations, we find that x = 2 and y = 7. When substituting this solution back into the original equations, we notice that the value of y is the same (7) in each equation. This confirms the consistency of the solution.
For more such questions on equations visit:
https://brainly.com/question/17145398
#SPJ8
A is 40% smaller than B, and C is 20% bigger than A. Which of the following statement If B decreases by 20%, it will be the same value as C. C is 20% smaller than B If C increases by 20%, it will be the same value as B. B is 20% bigger than C. All the above statements are true. None of the above statements is true. No answer
The right response is that B is 20% larger than C.
Let's analyze the given information and the statements:
Given:
A is 40% smaller than B.
C is 20% bigger than A.
Statement 1: If B decreases by 20%, it will be the same value as C.
This statement cannot be determined based on the given information. We don't have the exact values of B and C, so we cannot make a conclusive comparison.
Statement 2: C is 20% smaller than B.
This statement cannot be true because it contradicts the given information that C is 20% bigger than A. If C were 20% smaller than B, it would mean C is smaller than A.
Statement 3: If C increases by 20%, it will be the same value as B.
This statement cannot be determined based on the given information. We don't have the exact values of B and C, so we cannot make a conclusive comparison.
Statement 4: B is 20% bigger than C.
This statement is consistent with the given information that A is 40% smaller than B, and C is 20% bigger than A. If A is smaller than B, and C is bigger than A, then it follows that B is bigger than C.
Based on the analysis, the only statement that is true is Statement 4: B is 20% bigger than C.
Therefore, the correct answer is: B is 20% bigger than C.
Learn more about conclusive comparison on:
https://brainly.com/question/28243444
#SPJ11
Consider the following data:
-4, 11, -9,-4, 13, 12, 5
Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place.
Rounding to one decimal place, the sample variance is approximately 84.0.
To calculate the sample variance, we need to follow these steps:
Calculate the mean of the data.
Subtract the mean from each data point, square the result, and sum them up.
Divide the sum by n-1, where n is the sample size.
Step 1: Calculate the mean
The mean is the sum of all data points divided by the sample size:
(mean) = (-4 + 11 - 9 - 4 + 13 + 12 + 5) / 7 = 2
Step 2: Subtract the mean, square the result, and sum them up.
Now we subtract the mean from each data point, square the result, and sum them up:
(-4 - 2)^2 = 36
(11 - 2)^2 = 81
(-9 - 2)^2 = 121
(-4 - 2)^2 = 36
(13 - 2)^2 = 121
(12 - 2)^2 = 100
(5 - 2)^2 = 9
Sum = 504
Step 3: Divide the sum by n-1.
The sample size is n=7, so we divide the sum by 6 (n-1):
(sample variance) = 504 / 6 = 84
Rounding to one decimal place, the sample variance is approximately 84.0.
Learn more about decimal from
https://brainly.com/question/1827193
#SPJ11
For the plecewise function, find the values h( -7),h(-5), h(2), and h(6) h(x)={(-2x-14, for x<-6),(2, for -65x<2),(x+3, for x>=2):}
The values h(-7), h(-5), h(2), and h(6) are to be calculated for the following piecewise function;
h(x)={(-2x-14, for x<-6),(2, for -6<=x<2),(x+3, for x>=2):}
For h(-7)
where x = -7 we see that x is less than -6. Thus h(x) = (-2x - 14).
Hence h(-7) = (-2(-7) - 14) = 0
For h(-5)
where x = -5 we see that -6 ≤ x < 2. Thus h(x) = 2.
Hence h(-5) = 2
For h(2)
where x = 2 we see that x ≥ 2. Thus h(x) = x + 3
Hence h(2) = 2 + 3 = 5
For h(6)
where x = 6 we see that x ≥ 2. Thus h(x) = x + 3
Hence h(6) = 6 + 3 = 9.
Given that the piecewise function is of the form;
h(x) = {(-2x-14, for x<-6),(2, for -6<=x<2),(x+3, for x>=2):}
If we take the values less than -6, the function equals -2x - 14. Hence if we substitute x = -7;h(x) = (-2x-14)
h(-7) = (-2(-7) - 14) = 0
Thus h(-7) = 0If we take the values between -6 and 2, the function equals 2. Hence if we substitute x = -5;
h(x) = 2
h(-5) = 2
Thus h(-5) = 2
If we take the values greater than or equal to 2, the function equals x + 3. Hence if we substitute x = 2;h(x) = x+3h(2) = 2+3
Thus h(2) = 5
If we substitute x = 6;
h(x) = x+3h(6) = 6+3
Thus h(6) = 9
Learn more about piecewise function: https://brainly.com/question/28225662
#SPJ11
Find dy/dx for the given function. y= csc(x)/x
dy/dx=
Therefore, the required derivative is dy/dx = (-csc(x)(cot(x) + 1)) / x².
The function is y = csc(x) / x.
To find the derivative of this function, we will use the Quotient Rule of Differentiation which is given as:
If y = u/v, thendy/dx = (v(du/dx) - u(dv/dx)) / v².
Using the above formula for our function y, we get:
u = csc(x) and
v = x
So,du/dx = -csc(x)cot(x) (derivative of csc(x) is -csc(x)cot(x))dv/dx
= 1 (derivative of x with respect to x is 1)
Now,dy/dx = (x(-csc(x)cot(x)) - csc(x)(1)) / x²
= -csc(x)cot(x) / x - csc(x) / x²
= (-csc(x)(cot(x) + 1)) / x²
Therefore, the required derivative is dy/dx = (-csc(x)(cot(x) + 1)) / x².
To know more about function visit;
brainly.com/question/31062578
#SPJ11
John, a roofing contractor, need to purchae aphalt hingle for a client’ roof. How many 4-x-4-inch hingle are needed to cover a roof that meaure 12 x 16 feet?
John will need 1728 4x4-inch shingles to cover the rectangular roof.
To calculate the number of 4x4-inch shingles needed to cover a roof measuring 12x16 feet, we need to convert the measurements to the same units.
Given that 1 foot is equal to 12 inches, we can convert the roof measurements as follows:
Length of the roof in inches: 12 feet × 12 inches/foot = 144 inches
Width of the roof in inches: 16 feet 12 inches/foot = 192 inches
Now, we can calculate the number of 4x4-inch shingles needed to cover the roof.
The area of one 4x4-inch shingle is 4 inches × 4 inches = 16 square inches.
To find the total number of shingles needed, we divide the total area of the roof by the area of one shingle:
Total number of shingles = (Length of the roof × Width of the roof) / Area of one shingle
Total number of shingles = (144 inches × 192 inches) / 16 square inches
Total number of shingles = 1728 shingles
Therefore, John will need 1728 4x4-inch shingles to cover the roof.
To know more about rectangular click here :
https://brainly.com/question/546921
#SPJ4
he Empirical Rule states that the approximate percentage of measurements in a data set (providing that the data set has a bell-shaped distribution) that fall within three standard deviations of their mean is approximately: A. 68% B. 99% C.95% D. 75% E. None of the above. All of the following statements are true about a normal distribution except: A. A normal distribution is centered at the mean value. B. The standard deviation is a measure of the spread of the normal distribution. C. A normal distribution is a bell-shaped curve showing the possible outcomes for something of interest. D. A normal distribution can be skewed either to the left or to the right. E. A normal distribution is characterized by the mean and standard deviation.
1)The answer to the first question is A. 68%. 2)The statement that is not true about a normal distribution is: D. A normal distribution can be skewed either to the left or to the right.
The Empirical Rule states that for a bell-shaped distribution (which is assumed to be a normal distribution), approximately 68% of measurements fall within one standard deviation of the mean, approximately 95% fall within two standard deviations of the mean, and approximately 99.7% fall within three standard deviations of the mean. Therefore, the answer to the first question is A. 68%.
Regarding the second question, the statement that is not true about a normal distribution is:
D. A normal distribution can be skewed either to the left or to the right.
A normal distribution is symmetric and not skewed. Skewness refers to the asymmetry of the distribution, and a normal distribution by definition does not exhibit skewness. Therefore, the answer is D. A normal distribution cannot be skewed either to the left or to the right.
Learn more about normal distribution here:
brainly.com/question/15103234
#SPJ11
Remark: How many different bootstrap samples are possible? There is a general result we can use to count it: Given N distinct items, the number of ways of choosing n items with replacement from these items is given by ( N+n−1
n
). To count the number of bootstrap samples we discussed above, we have N=3 and n=3. So, there are totally ( 3+3−1
3
)=( 5
3
)=10 bootstrap samples.
Therefore, there are 10 different bootstrap samples possible.
The number of different bootstrap samples that are possible can be calculated using the formula (N+n-1)C(n), where N is the number of distinct items and n is the number of items to be chosen with replacement.
In this case, we have N = 3 (the number of distinct items) and n = 3 (the number of items to be chosen).
Using the formula, the number of bootstrap samples is given by (3+3-1)C(3), which simplifies to (5C3).
Calculating (5C3), we get:
(5C3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3!) / (3! * 2) = (5 * 4) / 2 = 10
To know more about samples,
https://brainly.com/question/15358252
#SPJ11
what is the domain of the function graphed below?
The domain of the function in the given graph is:
D = (-2, 4] U [7, ∞)
What is the domain of the function graphed?The domain of a function is the set of possible inputs of the function.
To find the domain, we just need to look at the horizontal axis.
Here we can see that the graph starts at:
x = -2 with an open circle (so the value does not belong to the domain)
Then it goes until x = 4, this time with a closed circle (so this belongs to the domain).
Then we have another segment that starts at x = 7 and keeps going to the right.
So the domain is:
D = (-2, 4] U [7, ∞)
Learn more about domains at.
https://brainly.com/question/1770447
#SPJ1
The domain of the function graphed above include the following: B. (-2, 4] and [7, ∞).
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular relation or function is defined.
The horizontal section of any graph is typically used for the representation of all domain values. Additionally, all domain values are both read and written by starting from smaller numerical values to larger numerical values, which means from the left of a graph to the right of the coordinate axis.
By critically observing the graph shown in the image attached above, we can logically deduce the following domain:
Domain = (-2, 4] and [7, ∞).
Read more on domain here: brainly.com/question/31157648
#SPJ1
79,80,80,80,74,80,80,79,64,78,73,78,74,45,81,48,80,82,82,70 Find Mean Median Mode Standard Deviation Coefficient of Variation
The calculations for the given data set are as follows:
Mean = 75.7
Median = 79
Mode = 80
Standard Deviation ≈ 11.09
Coefficient of Variation ≈ 14.63%
To find the mean, median, mode, standard deviation, and coefficient of variation for the given data set, let's go through each calculation step by step:
Data set: 79, 80, 80, 80, 74, 80, 80, 79, 64, 78, 73, 78, 74, 45, 81, 48, 80, 82, 82, 70
Let's calculate:
Deviation: (-4.7, 4.3, 4.3, 4.3, -1.7, 4.3, 4.3, -4.7, -11.7, 2.3, -2.7, 2.3, -1.7, -30.7, 5.3, -27.7, 4.3, 6.3, 6.3, -5.7)
Squared Deviation: (22.09, 18.49, 18.49, 18.49, 2.89, 18.49, 18.49, 22.09, 136.89, 5.29, 7.29, 5.29, 2.89, 944.49, 28.09, 764.29, 18.49, 39.69, 39.69, 32.49)
Mean of Squared Deviations = (22.09 + 18.49 + 18.49 + 18.49 + 2.89 + 18.49 + 18.49 + 22.09 + 136.89 + 5.29 + 7.29 + 5.29 + 2.89 + 944.49 + 28.09 + 764.29 + 18.49 + 39.69 + 39.69 + 32.49) / 20
Mean of Squared Deviations = 2462.21 / 20
Mean of Squared Deviations = 123.11
Standard Deviation = √(Mean of Squared Deviations)
Standard Deviation = √(123.11)
Standard Deviation ≈ 11.09
Coefficient of Variation:
The coefficient of variation is a measure of relative variability and is calculated by dividing the standard deviation by the mean and multiplying by 100:
Coefficient of Variation = (Standard Deviation / Mean) * 100
Coefficient of Variation = (11.09 / 75.7) * 100
Coefficient of Variation ≈ 14.63%
So, the calculations for the given data set are as follows:
Mean = 75.7
Median = 79
Mode = 80
Standard Deviation ≈ 11.09
Coefficient of Variation ≈ 14.63%
To know more about Mean visit
https://brainly.com/question/17956583
#SPJ11
x−2y+10z=1
−5x+5y−30z=0
−8x+11y−60z=k
In order for the above system of equations to be a consistent system, then k must be equal to
In order for the system to be consistent, k must be equal to 23z + 11, where z is any real number.
To find the value of k that makes the system consistent, we can use Gaussian elimination to row-reduce the augmented matrix:
[1 -2 10 | 1]
[-5 5 -30 | 0]
[-8 11 -60 | k]
Performing the row operations, we get:
[1 -2 10 | 1]
[0 -5 20 | 5]
[0 -3 20 | k+8]
Next, we can use back-substitution to solve for the variables. From the second row, we get:
-5y + 20z = 5
Simplifying this equation, we get:
y - 4z = -1
From the third row, we get:
-3y + 20z = k + 8
Substituting y - 4z = -1, we get:
-3(-1 + 4z) + 20z = k + 8
Expanding and simplifying, we get:
23z + 11 = k
Therefore, in order for the system to be consistent, k must be equal to 23z + 11, where z is any real number.
Learn more about number from
https://brainly.com/question/27894163
#SPJ11
Suppose a company has fixed costs of $33,800 and variable cost per unit of1/3+x222 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1,548 - 2/3x dollars per unit.
(a) Form the cost function and revenue function (in dollars).
C(x) =
R(x) =
Find the break-even points. (Enter your answers as a comma-separated list.)
x =
The break-even point is 1000. Answer: x = 1000.
Given the fixed cost of a company is $33,800
Variable cost per unit = $1/3 + x/222
The selling price of its product = 1548 - (2/3)x dollars per unit
a) Cost function and Revenue function (in dollars)
Let x be the number of units produced by the company
Then,
Total variable cost of the company = Variable cost per unit * number of units produced
Variable cost per unit = 1/3 + x/222Number of units produced = x
Therefore, Total variable cost = (1/3 + x/222) * x = x/3 + x²/222
Total cost of the company = Total fixed cost + Total variable cost
Total cost function, C(x) = $33,800 + (x/3 + x²/222)And,
Total Revenue (TR) = Selling price per unit * number of units sold
Selling price per unit = 1548 - (2/3)x
Number of units sold = number of units produced = x
Total Revenue function, R(x) = (1548 - (2/3)x) * x
Let's solve for break-even points
b) Break-even points
The break-even point is the point where the total cost is equal to the total revenue
Therefore, we will equate the Total Cost function to Total Revenue function
i.e., C(x) = R(x)33,800 + (x/3 + x²/222) = (1548 - (2/3)x) * x
Let's solve for x222 * 33,800 + 222 * x² + 3x² = 1548x - 2x³/3
Collecting like terms,2x³ + 1332x² - 4644x + 2,233,600 = 0
Dividing both sides by 2,x³ + 666x² - 2322x + 1,116,800 = 0
It is given that x > 0
Let's check the options available
If we substitute x = 10, we get,
Cost function, C(10) = 33800 + (10/3 + (10²)/222) = 33800 + 10/3 + 50/111 = 33977.32
Revenue function, R(10) = (1548 - (2/3)*10)*10 = 1024
Break-even point when x = 10 is not a correct answer.
If we substitute x = 100, we get,
Cost function, C(100) = 33800 + (100/3 + (100²)/222) = 34711.71
Revenue function, R(100) = (1548 - (2/3)*100)*100 = 91800
Break-even point when x = 100 is not a correct answer.
If we substitute x = 1000, we get,
Cost function, C(1000) = 33800 + (1000/3 + (1000²)/222) = 81903.15
Revenue function, R(1000) = (1548 - (2/3)*1000)*1000 = 848000
Break-even point when x = 1000 is a correct answer.
The break-even point is 1000. Answer: x = 1000.
Know more about break-even point here:
https://brainly.com/question/21137380
#SPJ11
For real numbers t1 and y1, if φ(t) is a solution to the initial value problem
y′ = f(t,y), y(t0) = y0
then the function φ1(t) defined by φ1(t) = φ(t −t1 + t0) + y1 −y0 solves the IVP
y′ = f(t −t1 + t0,y −y1 + y0), y(t1) = y1
We call the two IVPs equivalent because of the direct relationship between their solutions.
(a) Solve the initial value problem y′ = 2ty, y(2) = 1, producing a function φ(t).
(b) Now transform φ to a function φ1 satisfying φ1(0) = 0 as above.
(c) Transform the IVP from part (a) to the equivalent one (in the sense of (*) above)
"with initial point at the origin" – ie. with initial condition y(0) = 0 – then solve it
explicitly. [Your solution should be identical to φ1 from part (b).]
The function [tex]φ1[/tex] satisfying
[tex]φ1(0) = 0 is \\\\φ1(t) = φ(t - φ⁻¹ (y1 - y0)) + y1 - y0[/tex]
a) The given initial value problem (IVP) is:
[tex]y′ = 2ty, y(2) = 1.[/tex]
We will use the method of separating the variables, that is, we will put all y terms on one side of the equation and all t terms on the other side of the equation, then integrate both sides with respect to their respective variables.
[tex]2ty dt = dy[/tex]
Integrating both sides, we get:
[tex]t²y = y²/2 + C[/tex], where C is the constant of integration.
Substituting y = 1 and
t = 2 in the above equation, we get:
C = 1
Then the solution to the given IVP is:
[tex]t²y = y²/2 + 1[/tex] .......(1)
b) To transform φ to a function φ1 satisfying [tex]φ1(0) = 0[/tex],
we put [tex]t = t + t1 - t0, y = y + y1 - y0[/tex]
in equation (1), we get:
[tex](t + t1 - t0)²(y + y1 - y0) = (y + y1 - y0)²/2 + 1[/tex]
Rearranging the above equation, we get:
[tex](t + t1 - t0)²(y + y1 - y0) - (y + y1 - y0)²/2 = 1[/tex]
Expanding the above equation and simplifying, we get:
[tex](t + t1 - t0)²(y + y1 - y0) - (y + y1 - y0)(y - y1 + y0)/2 - (y1 - y0)²/2 = 1[/tex]
Now, let [tex]φ1(t) = φ(t + t1 - t0) + y1 - y0[/tex]
Then, [tex]φ1(0) = φ(t1 - t0) + y1 - y0[/tex]
We need to choose t1 and t0 such that [tex]φ1(0) = 0[/tex]
Let [tex]t1 - t0 = - φ⁻¹ (y1 - y0)[/tex]
Thus, [tex]t0 = t1 + φ⁻¹ (y1 - y0)[/tex]
Then, [tex]φ1(0) = φ(t1 - t1 - φ⁻¹ (y1 - y0)) + y1 - y0[/tex]
= [tex]φ(- φ⁻¹ (y1 - y0)) + y1 - y0[/tex]
= [tex]0 + y1 - y0[/tex]
= y1 - y0
Hence, [tex]φ1(t) = φ(t + t1 - t0) + y1 - y0[/tex]
= [tex]φ(t - φ⁻¹ (y1 - y0)) + y1 - y0[/tex]
Therefore, the function [tex]φ1[/tex] satisfying[tex]φ1(0) = 0 is \\φ1(t) = φ(t - φ⁻¹ (y1 - y0)) + y1 - y0[/tex]
c) The IVP in part (a) is equivalent to the IVP with initial condition y(0) = 0, in the sense of the direct relationship between their solutions.
To transform the IVP [tex]y′ = 2ty, y(2) = 1[/tex] to the IVP with initial condition
y(0) = 0, we let[tex]t = t - 2, y = y - 1[/tex]
To know more about integration visit:
https://brainly.com/question/31744185
#SPJ11
What is the product? [7x2][2x3+5][x2-4x-9]
Answer:
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.
Step-by-step explanation:
To find the product, we need to multiply the terms inside the brackets:
[7x^2][2x^3 + 5][x^2 - 4x - 9]
First, let's multiply the terms inside the second set of brackets:
[7x^2][(2x^3)(x^2) + (2x^3)(-4x) + (2x^3)(-9) + (5)(x^2) + (5)(-4x) + (5)(-9)]
Simplifying further:
[7x^2][2x^5 - 8x^4 - 18x^3 + 5x^2 - 20x - 45]
Finally, let's distribute the remaining terms:
(7x^2)(2x^5) + (7x^2)(-8x^4) + (7x^2)(-18x^3) + (7x^2)(5x^2) + (7x^2)(-20x) + (7x^2)(-45)
Simplifying each term:
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
Therefore, the product is 14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.
You are going to roll a fair 6-sided die 170 times. What is the
probability (as a decimal rounded to 4 decimal places) that you get
22 to 35 sixes?
The probability (as a decimal rounded to 4 decimal places) that you get 22 to 35 sixes when you roll a fair 6-sided die 170 times is 0.0004.
Here's how to solve it: We have a fair 6-sided die and we are rolling it 170 times. We need to find the probability of getting 22 to 35 sixes.
Let X be the number of sixes obtained in 170 rolls. X is a binomial random variable with n = 170 and p = 1/6.
Let P(X = k) be the probability of getting exactly k sixes in 170 rolls.
Using the binomial probability formula, we have:
P(X = k) = nCk p^k (1-p)^(n-k)
where nCk is the binomial coefficient (number of ways to choose k items from n distinct items).
To find the probability of getting 22 to 35 sixes, we need to add up the probabilities of getting exactly 22, 23, 24,..., 35 sixes.
P(22 ≤ X ≤ 35) = P(X = 22) + P(X = 23) + ... + P(X = 35) ≈ 0.0004 (rounded to 4 decimal places)
Therefore, the probability (as a decimal rounded to 4 decimal places) that you get 22 to 35 sixes when you roll a fair 6-sided die 170 times is 0.0004.
Learn more about binomial probability visit:
brainly.com/question/12474772
#SPJ11
The cost of operating a Frisbee company in the first year is $10,000 plus $2 for each Frisbee. Assuming the company sells every Frisbee it makes in the first year for $7, how many Frisbees must the company sell to break even? A. 1,000 B. 1,500 C. 2,000 D. 2,500 E. 3,000
The revenue can be calculated by multiplying the selling price per Frisbee ($7) , company must sell 2000 Frisbees to break even. The answer is option C. 2000.
In the first year, a Frisbee company's operating cost is $10,000 plus $2 for each Frisbee.
The company sells each Frisbee for $7.
The number of Frisbees the company must sell to break even is the point where its revenue equals its expenses.
To determine the number of Frisbees the company must sell to break even, use the equation below:
Revenue = Expenseswhere, Revenue = Price of each Frisbee sold × Number of Frisbees sold
Expenses = Operating cost + Cost of producing each Frisbee
Using the values given in the question, we can write the equation as:
To break even, the revenue should be equal to the cost.
Therefore, we can set up the following equation:
$7 * x = $10,000 + $2 * x
Now, we can solve this equation to find the value of x:
$7 * x - $2 * x = $10,000
Simplifying:
$5 * x = $10,000
Dividing both sides by $5:
x = $10,000 / $5
x = 2,000
7x = 2x + 10000
Where x represents the number of Frisbees sold
Multiplying 7 on both sides of the equation:7x = 2x + 10000
5x = 10000x = 2000
For more related questions on revenue:
https://brainly.com/question/29567732
#SPJ8
(2 points) Find domnin and range of the function \[ f(x)=2 x^{2}+18 \] Domin: Range: Write the ancwer in interval notation. Note: If the answer includes more than one interval write the intervals sepa
the domain is `R` and the range is `[18,∞)` in interval notation.
The given function is, `f(x)=2x²+18`.
The domain of a function is the set of values of `x` for which the function is defined. In this case, there is no restriction on the value of `x`.
Therefore, the domain of the function is `R`.
The range of a function is the set of values of `f(x)` that it can take. Here, we can see that the value of `f(x)` is always greater than or equal to `18`. The value of `f(x)` keeps increasing as `x` increases. Hence, there is no lower bound for the range.
Therefore, the range of the function is `[18,∞)`.
Hence, the domain is `R` and the range is `[18,∞)` in interval notation.
Learn more about domain and range:
https://brainly.com/question/1632425
#SPJ11
Evaluate the integral ∫ (x+3)/(4-5x^2)^3/2 dx
The integral evaluates to (-1/5) * √(4-5x^2) + C.
To evaluate the integral ∫ (x+3)/(4-5x^2)^(3/2) dx, we can use the substitution method.
Let u = 4-5x^2. Taking the derivative of u with respect to x, we get du/dx = -10x. Solving for dx, we have dx = du/(-10x).
Substituting these values into the integral, we have:
∫ (x+3)/(4-5x^2)^(3/2) dx = ∫ (x+3)/u^(3/2) * (-10x) du.
Rearranging the terms, the integral becomes:
-10 ∫ (x^2+3x)/u^(3/2) du.
To evaluate this integral, we can simplify the numerator and rewrite it as:
-10 ∫ (x^2+3x)/u^(3/2) du = -10 ∫ (x^2/u^(3/2) + 3x/u^(3/2)) du.
Now, we can integrate each term separately. The integral of x^2/u^(3/2) is (-1/5) * x * u^(-1/2), and the integral of 3x/u^(3/2) is (-3/10) * u^(-1/2).
Substituting back u = 4-5x^2, we have:
-10 ∫ (x^2/u^(3/2) + 3x/u^(3/2)) du = -10 [(-1/5) * x * (4-5x^2)^(-1/2) + (-3/10) * (4-5x^2)^(-1/2)] + C.
Simplifying further, we get:
(-1/5) * √(4-5x^2) + (3/10) * √(4-5x^2) + C.
Combining the terms, the final result is:
(-1/5) * √(4-5x^2) + C.
To learn more about derivative click here
brainly.com/question/25324584
#SPJ11
Apply Theorem B.3 to obtain the characteristic equation from all the terms:
(r-2)(r-1)^2(r-2)=(r-2)^2(r-1)^2
Therefore, the characteristic equation from the given equation is: [tex](r - 2)(r - 1)^2 = 0.[/tex]
According to Theorem B.3, which states that for any polynomial equation, if we have a product of factors on one side equal to zero, then each factor individually must be equal to zero.
In this case, we have the equation:
[tex](r - 2)(r - 1)^2(r - 2) = (r - 2)^2(r - 1)^2[/tex]
To obtain the characteristic equation, we can apply Theorem B.3 and set each factor on the left side equal to zero:
(r - 2) = 0
[tex](r - 1)^2 = 0[/tex]
Setting each factor equal to zero gives us the roots or solutions of the equation:
r = 2 (multiplicity 2)
r = 1 (multiplicity 2)
To know more about characteristic equation,
https://brainly.com/question/32615056
#SPJ11
Which expression is equivalent to 22^3 squared 15 - 9^3 squared 15?
1,692,489,445 expression is equivalent to 22^3 squared 15 - 9^3 squared 15.
To simplify this expression, we can first evaluate the exponents:
22^3 = 22 x 22 x 22 = 10,648
9^3 = 9 x 9 x 9 = 729
Substituting these values back into the expression, we get:
10,648^2 x 15 - 729^2 x 15
Simplifying further, we can calculate the values of the squares:
10,648^2 = 113,360,704
729^2 = 531,441
Substituting these values back into the expression, we get:
113,360,704 x 15 - 531,441 x 15
Which simplifies to:
1,700,461,560 - 7,972,115
Therefore, the final answer is:
1,692,489,445.
Learn more about expression from
https://brainly.com/question/1859113
#SPJ11
The odtitude (or height ) of a plane landing at an airport changes at a rate of -450 meters per minute. At that rate, how many minutes will it take tor the plane's altitude to change by -5,400 meter
It will take 12 minutes for the plane's altitude to change by -5,400 meters.
To calculate the number of minutes it would take for the altitude of a plane landing at an airport to change by -5,400 meters at a rate of -450 meters per minute, we can use the formula:Time = Change in distance/RateLet's substitute the given values into the formula and solve for time:Time = -5,400/-450Time = 12Therefore, it will take 12 minutes for the plane's altitude to change by -5,400 meters.
Learn more about distance :
https://brainly.com/question/28956738
#SPJ11
The heat index is calculated using the relative humidity and the temperature. for every 1 degree increase in the temperature from 94∘F to 98∘F at 75% relative humidity the heat index rises 4∘F. on a summer day the relative humidity is 75% the temperature is 94 ∘F and the heat index is 122f. Construct a table that relates the temperature t to the Heat Index H. a. Construct a table at 94∘F and end it at 98∘F. b. Identify the independent and dependent variables. c. Write a linear function that represents this situation. d. Estimate the Heat Index when the temperature is 100∘F.
a) The linear function that represents the relationship between the temperature (t) and the heat index (H) in this situation is H = 4(t - 94) + 122.
b) The estimated heat index when the temperature is 100∘F is 146∘F.
c) The linear function that represents this situation is H = 4(t - 94) + 122
d) When the temperature is 100∘F, the estimated heat index is 146∘F.
a. To construct a table that relates the temperature (t) to the heat index (H), we can start with the given information and calculate the corresponding values. Since we are given the heat index at 94∘F and the rate of change of the heat index, we can use this information to create a table.
Temperature (t) | Heat Index (H)
94∘F | 122∘F
95∘F | (122 + 4)∘F = 126∘F
96∘F | (126 + 4)∘F = 130∘F
97∘F | (130 + 4)∘F = 134∘F
98∘F | (134 + 4)∘F = 138∘F
b. In this situation, the independent variable is the temperature (t), as it is the input variable that we can control or change. The dependent variable is the heat index (H), as it depends on the temperature and changes accordingly.
c. To find a linear function that represents this situation, we can observe that for every 1-degree increase in temperature from 94∘F to 98∘F, the heat index rises by 4∘F. This suggests a linear relationship between temperature and the heat index.
Let's denote the temperature as "t" and the heat index as "H." We can write the linear function as follows:
H = 4(t - 94) + 122
Here, (t - 94) represents the number of degrees above 94∘F, and multiplying it by 4 accounts for the increase in the heat index for every 1-degree rise in temperature. Adding this value to 122 gives us the corresponding heat index.
d. To estimate the heat index when the temperature is 100∘F, we can substitute t = 100 into the linear function we derived:
H = 4(100 - 94) + 122
H = 4(6) + 122
H = 24 + 122
H = 146∘F
To know more about linear function here
https://brainly.com/question/29205018
#SPJ4
