students were surveyed on their current enrollment in Math, Biology, and Chemistry. The results are listed below. E students are enrolled in Math. 3 students are enrolled in Biology. O students are enrolled in Chemistry. 3 students are enrolled in Math and Bio. 4 students are enrolled in Bio and Chem. 26 students are enrolled in Math and Chem. 14 students are enrolled in all three courses. How many students were enrolled in at least one of the three courses?

Q: If 2n+3 a %3D 5n+8

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Q: 3. Evaluate: lim -) X-0 sinx

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Q: I would like to ask how 00 became 1? I think it is undefined.

A: Given;  Limx-0+Sinxtanx.

Q: Let u = 8i + 2j, v=i+j, and w =i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: Please do help me with this calculus questions. Please. I need the correct letter of the answer and…

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Q: Express the vector 4u + 5w in the form v = v,i+v½j+V3k if u = (3, - 2, 5) and w = (- 4, 5, – 4). 4u…

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Q: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

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Q: What is the absolute maximum value of the function f(x) = x - 3x2 on the interval [-2, 4] ? а. 16 O…

A: This question is based on application of derivative.

Q: The following series is divergent: 7n-2 \" Σ n+5 n =1 Select one: O True O False

A: We can solve this as follows:

Q: d E A. By power series, prove that: -cosx = -sinx dx

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Q: 1 Verify that tan?(csc-1(x)) = x2 – 1

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Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

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Q: please answer number  2 and follow the format of sample solution (include the rules/techniques used)

A: Here we have to find the integral

Q: 23 Given the ordered pair P, determine the requested sin, cos, or tan of angle . P(5,5) tan0 =…

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Q: The following series is divergent: 3n 3n Зп — 6. - 3 — 2п | n=1 Select one: O True O False

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Q: а. 4(е?) b. 4(e² – e*) с. 4(e* — е?) d. 4(e*) e. None of the above DA DE D.

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Q: Question 2 Construction Problem A farmer has 180 ft. of fencing to be used in the construction of…

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Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: Choose the quadrant in which the terminal side of this standard position angle is located: 105.7°…

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Q: A rectangular garden is fenced on three sides, and the house forms the fourth side of the rectangle.…

A: Explanation of the answer is as follows

Q: Differential Equation Classify the following differential equations.  - DEPENDENT VARIABLE -…

A: We have to classify the given differential equations.

Q: C. Find the derivative of each of the following functions using Differentiations Rule/Chain Rule. 1.…

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Q: Express the following vector in the form v = v,i+v2j+V3k. 3u - v if u = (4,6, – 8) and v = (2, –…

A: We can find the answer as below.

Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x2 + ax + B with…

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Q: lim 1 n- 00 n V1+x on [0, 2] 2/1 + x on [0, 2] 2/1-x on [0, 2] 2/1 + x on [-2, 2] Y1+X on [-2, 21 키

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: Given query is to find the antiderivative if the expression.

Q: 7. Determine whether the given integral is convergent or divergent dx? '1 x²+1 a. convergent b.…

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Q: x2 +y? +z? - 4x + 8y – 2z = - 12

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Q: Differentiate y = (9x- 11) log3 (1læ – 9). %3D A. y' = 9(11x-9)+11(9z-11) In(9r-11) (9x-11) In(3)…

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Q: Use back-substitution to solve the system of linear equations. X - 2y + z = 5 y + z = 8 Z = 3 (х, у,…

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Q: Solve for x and y the following system of simultaneous equations 2 In(x) = In(y) + In(25) e*e" = e5…

A: The given equations are;  2ln(x)=ln(y)+ln(25) exey=e5

Q: e 3x (d) lim X→0 5x+200

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Q: Find the domain and the vertical asymptotes, if any, of the following function x-9 x2+10x+21 ' a.…

A: Given

Q: It has to be one of the answer options.

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Q: 323. Evaluate: J tanV |1 – x |dx 1 + x

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Q: 3. Evaluate: lim ( ) X-0 sinx

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Q: -7 -3 A 87 23 Find the eigenvectors of the given matrix: -.1 1 1 i 3 - 15

A: Solution

Q: èrentiate f(x) = [(4x³ – 1)(8x² + 6x – 3)]° and solve f'(2).

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Q: Find and classify all the critical points of f(x, y) = 2x - 9y - xy + x2 + 5y2 .

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Q: why

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Q: For the function x-3 f(x) = 2x +5 etermine coordinates of the y-intercept of the inverse function…

A: We can find the coordinate of y-intercept inverse function as below.

Q: Use the Chain Rule to find dw/dt. w = xey/z,    x = t5,    y = 1 − t,    z = 3 + 7t

A: To find out dw/dt.

Q: (e) lim [p(x)]9(x) (d) lim [p(x)]^x) Xa INDETERMINATE Xa INDETERMINATE 9(x) (f) lim p(x) Xa

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Q: For the function x-3 f(x) =: 2x +5 Determine coordinates of the y-intercept of the inverse function…

A: We can find the inverse function and the required answer as below.

Q: For the points P1 (4,2,3) and P2(5,1,2), find the direction of P,P2 and the midpoint of line segment…

A: Given that coordinate of point P1 is (4,2,3) The coordinate of point P2 (5,1,2) We have to found the…

Q: The following series is not an alternating series. (-1)2n n=1 Vn2 + 6n Select one: O True O False

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: (i) What are the projections of the point (2, 3, 5) on the ry-, yz- and rz-planes? (ii) Write…

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Q: Give the range of the function f(x) = -x 2. all reals y ≤ 0 y ≥ 0

A: The given function is: f(x)=-x2

Q: 4. S(x² – 1) Vx + 4 dx

A: Solving

Q: do you have a solutuon for this?

A: Definite integral property : If f(x) is continuous on a,b and a<c<b ,then              ∫ab…