Use the following information to find the surface area of the specified objects. Round to the nearest square unit. A sphere is a solid formed by all points in space that are the same distance from a fixed point (the center). The formula for the surface area of a sphere is S = 4πr², where r is the radius. The radius of a spherical soap bubble is 0.5 inch.

For the linear function $f(x)=-4 x+3$ Find the slope and y-intercept.

determine whether each x-value is a solution (or an approximate solution) of the equation. 4^2x-7 = 64. x = 2

Verify that x=7, y=19, and n=6 do not yield a solution to the equation

$$x ^ { n } + y ^ { n } = z ^ { n }$$

where z is a natural number.

The standard free energies of formation and the standard enthalpies of formation at 298 K for difluoroacetylene $\left( \mathrm { C } _ { 2 } \mathrm { F } _ { 2 } \right)$ and hexafluorobenzene $\left( \mathrm { C } _ { 6 } \mathrm { F } _ { 6 } \right)$ are

$$\begin{matrix} & \text{$\Delta G _ { \mathrm { f } } ^ { \circ } ( \mathrm { kJ } / \mathrm { mol } )$} & \text{$\Delta H _ { f } ^ { \circ } ( \mathrm { kJ } / \mathrm { mol } )$}\\ \hline \text{$\mathrm { C } _ { 2 } \mathrm { F } _ { 2 } ( g )$} & \text{191.2} & \text{241.3}\\ \text{$\mathrm { C } _ { 6 } \mathrm { F } _ { 6 } ( g )$} & \text{78.2} & \text{132.8}\\ \end{matrix}$$

For the following reaction: $\mathrm { C } _ { 6 } \mathrm { F } _ { 6 } ( g ) \rightleftharpoons 3 \mathrm { C } _ { 2 } \mathrm { F } _ { 2 } ( g )$ a. calculate $\Delta S ^ { \circ }$ at 298 K. b. calculate K at 298 K. c. estimate K at 3000. K, assuming $\Delta H ^ { \circ }$ and $\Delta S ^ { \circ }$ do not depend on temperature.

Find the divergence of the vector field. F(x,y,z)=xye^zi+yze^xk

Solve the inequality. Check your solution.

$$\frac { z } { 4 } + 7 \geq - 5$$

To find the percent of the tiles in Hi! that are in the H, first find either the fraction or the decimal that represents the number of tiles in the H out of the total number of tiles. a. Which is easier to find in this situation, a decimal or a fraction? Explain. b. Find the equivalent fraction to your answer in hundredths, since percent is a number out of 100. Then convert the hundredths to a percent. c. Write this percent as a decimal.

Find the exact value of each expression. Do not use a calculator.

$$\csc \left( \frac { 22 \pi } { 3 } \right)$$

Use properties of determinants to evaluate the given determinant by inspection. Explain your reasoning.

$$\left| \begin{array} { r r r } { 0 } & { 0 } & { 1 } \\ { 0 } & { 5 } & { 2 } \\ { 3 } & { - 1 } & { 4 } \end{array} \right|$$

Solve each system of equations.

$$\left\{ \begin{array} { l } { y = x ^ { 2 } + 2 x + 7 } \\ { y = 7 + x } \end{array} \right.$$

A student builds a series circuit with four 1.5-volt batteries, a 5-ohm resistor, and two 1-ohm resistors. a. What is the total resistance in the circuit? b. Use Ohm's law to find the value of the current in the circuit.

Simplify the expression. 6c + 4 + c + 8

$$\left( 3 x ^ { 5 } \right) ^ { 3 }$$