Antacids are compounds that neutralize stomach acid. Write the equations that show how Milk of Magnesia, Alka-Seltzer, and Tums remove excess acid. a. Milk of Magnesia:

$$Mg(OH)_2$$

b. Alka-Seltzer:

$$KHCO_3$$

and

$$NaHCO_3$$

c. Tums:

$$CaCO_3$$

$$\begin{aligned} 4 x+y & \leq 20 \\ 3 x+5 y & \leq 37 \\ x & \geq 0 \\ y & \geq 0 \end{aligned}$$

As per the above system of linear inequalities solve the below statement Is the point $(4,5)$ in the solution region?

How does an aristocracy differ from an oligarchy?

Sketch the solid region whose volume is given by the iterated integral, and evaluate the iterated integral. ∫_0^2π∫_0^π∫_2^5 ρ² sin Φ dp dΦ dθ

Find the length of one side of a square inscribed in a circle that has a radius of 4 cm.

$$A. 4 cm$$

$$B. 4 \sqrt { 2 } \mathrm { cm }$$

$$C. 8 cm.$$

$$D. 8 \sqrt { 2 } \mathrm { cm }$$

As per the above system of linear inequalities solve the below statement

$$\begin{aligned} 5 x+y & \leq 32 \\ 7 x+4 y & \geq 45 \\ x & \geq 0 \\ y & \geq 0 \end{aligned}$$

Is the point $(6,2)$ in the solution region?

Use Pascal's triangle to expand the expression.

$$\left(\frac{1}{x}-\sqrt{x}\right)^5$$

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region.

$$\left. \begin{array} { l } { y \geq | x + 1 | - 2 } \\ { 0 \leq y \leq 6 } \\ { - 6 \leq x \leq 2 } \\ { x + 3 y \leq 14 } \\ { f ( x , y ) = 5 x + 4 y } \end{array} \right.$$

Graph each feasible region.

$$\left\{\begin{array}{l}y \geq-1 \\ x \geq-2 \\ y \leq-2 x+10 \\ y \leq \frac{1}{2} x+5\end{array}\right.$$

The sides of a triangle are in the ratio 2:3:5. The perimeter is 35 cm. Find the length of each side.

a) Sketch the graph: $y=\cos ^{-1} x$

b) Differentiate: $f(x)=\sec ^{-1} 3 x$

c) Integrate: $\int \tan ^{-1} 5 x d x$

d) Find the area of the region in Quadrant I bounded by the graph of $y=\cos ^{-1} x$.

How does aristocracy differ from an oligarchy?

Determine which value best approximates the area of the region between the x-axis and the graph of the function over the given interval. f(x) = 2x / x²+1, [0, 4] (a) 3 (b) 7 (c) -2 (d) 5 (e) 1

The lengths of courgettes are normally distributed with a mean of 16 cm and a standard deviation of 0.8 cm. a. Find the percentage of courgettes that have a length between 15 cm and 17 cm. b. Find the probability that a courgette is longer than 18 cm. The lengths of 100 courgettes are measured. c. Calculate the expected number of courgettes that have a length less than 14.5 cm.