Indiana University professors investigated first-year college students’ knowledge of astronomy ( Astronomy Education Review, Vol. 2, 2003). One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 148 freshmen students, 37 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, would you be willing to state that more than 20% of all freshmen college students believe in the Big Bang theory? How confident are you of your decision?

Graph

$$y = \frac { ( \cos x ) ( 1 - \cos 2 x ) } { \sin 2 x }$$

to discover an identity. Then prove the identity.

Find the solution for the equation. Check your answer. $s + 3.5 = 3.7$

During a promotional event, a sporting goods store gave a free T-shirt to every 8th customer and a free water bottle to every 10th customer. Which customer was the first to get a free T-shirt and a free water bottle? A. the 10th customer B. the 20th customer C. the 40th customer D. the 80th customer

Use any problem-solving strategy to solve this problem. The length of Fun Center's go-kart track is 843 feet. If Nadia circled the track 9 times, how many feet did she travel?

Find the absolute maximum and minimum values of the function on the given interval. Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates. f(x) = -x - 4, -4 <= x <= 1

A rectangular field is 70 feet long and 30 feet wide. If fencing costs $8 per yard, how much will it cost to enclose the field?

Solve for y: 8y - 7x + 9y = 112x

Sketch a figure that has rotational symmetry. Describe the angle of rotation.

Two point charges are placed on the x-axis as follows: Charge $q _ { 1 } = + 4.00 n C$ is located at x = 0.200 m, and charge $q _ { 2 } = + 5.00 n C$ is at x = -0.300m. What are the magnitude and direction of the total force exerted by these two charges on a negative point charge $\mathrm { q } _ { 3 } = 6.00 nC$ that is placed at the origin?

Solve each equation, Write a justification for each step. $- \frac { x } { 3 } = 2$

Jason has a piece of wire that is 62.4 inches long. He cuts the wire into 3 equal pieces. Estimate the length of 1 piece of wire.

Convert from degrees to radians: (a)

$$1 ^ { \circ }$$

(b)

$$30 ^ { \circ }$$

(c)

$$25 ^ { \circ }$$

(d)

$$120 ^ { \circ }$$

Use each of the three terms below in a sentence that illustrates the meaning of the term. a. state bank b. national bank c. gold standard