In a survey of 200 students, 70 were taking mathematics and 50 were taking psychology. a) What is the least number of students who could have been taking both courses? b) What is the greatest number of students who could have been taking both courses? c) What is the greatest number of students who could have been taking neither course? a) The least number of students who could have been taking both courses is square

Write the equation for the plane. The plane through the points $P(5,4,-36),Q(-3,6,-16)$ and $R(-1,-5,42)$ A. $4x+6y+z=8$ B. $4x+6y+z=-8$ C. $6x+y+4z=-8$ D. $6x+y+4z=8$

Evaluate the expression. $\frac {C(8,6)\cdot C(9,7)}{C(13,9)}$ $\square $

Simplify the expression: $-5(-6+2x)=$ $\square $

Find the area of the region that lies inside both curves. $r=3sin(\Theta ),\quad r=3cos(\Theta )$

Note: You may need to assume the fact that $\lim _{M\rightarrow \infty }M^{n}e^{-M}=0$ for all n. Decide whether or not the given integral converges. $\int _{0}^{\infty }e^{-5x}dx$ The integral converges The integral diverges. If the integral converges compute its value. (If the integral diverges enter DNE.) $\square $

What is the slope of the line that passes through the points $(-5,-9)$ and $(-5,-13)$ ? Write your answer in simplest form. Answer $\square $

Evaluar la expresión para $b=1.6$ $2\cdot b+3\cdot b$

Solve the equation, and check the solution. $\frac {1}{4}(3x+5)-\frac {1}{5}(x+7)=7$

Find an equivalent expression for $3csc(x-\frac {\pi }{2})$ using the cofunction identities. $3csc(x-\frac {\pi }{2})=\square $ (Simplify your answer.)

Use the trigonometric function values of quadrantal angles to evaluate the expression below $(cos180^{\circ })^{2}-(sin0^{\circ })^{2}$