A toy manufacturer buys ball bearings from three different suppliers-50% of her total order comes from supplier 1, 30% from supplier 2, and the rest from supplier 3. Past experience has shown that the quality-control standards of the three suppliers are not all the same. Two percent of the ball bearings produced by supplier 1 are defective, while suppliers 2 and 3 produce defective bearings 3% and 4% of the time, respectively. What proportion of the ball bearings in the toy manufacturer’s inventory are defective?

Carlos is the last person to board a Ferris wheel that has a radius of 52 feet. The counterclockwise arc swept out by Carlos is measured from where he got on, at the bottom of the Ferris wheel. Since Carlos is the last one to board, the Ferris wheel starts up and doesn't stop again unit the ride is over. a. Draw a diagram that show's Carlos's location and the angle swept out by Carlos at an arbitrary moment in time. b. Define a function f that relates Carlos's vertical distance above the center of the Ferris wheel (measured in feet) as a function of the measure of the angle (in radians) swept out by Carlos. Over what interval of input will Carlos complete one revolution? c. Define a function g that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the measure of the angle (in radians) swept out by Carlos Over what interval of input will Carlos complete one revolution? d. Suppose Carlos's cart is traveling 0.3 radii per second on a circular path as the wheel rotates. Define a function h that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? e. Marilyn claimed that she saw Carlos's cart travel at a speed of 3.5 radii per second. Is that possible? Explain. (Hint: Determine the cart's speed in miles per hour. f. Suppose that Carlos's cart traveled at 0.4 radii per second. Define a function j that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? g. Suppose Carlos's cart is traveling 0.2 radii per second. Define a function k that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? h. Sketch a graph of each function defined in parts (d)-(g). Label your axes. Identify the interval of input over which Carlos completes one revolution.

Find all solutions for the given triangle, if possible. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree. $a=5, b=6, A=63^{\circ}$

Many programming teams work independently at a large software company. The management has been putting pressure on these teams to finish a project on time. The company currently has 18 large programming projects, of which only 12 are likely to finish on time. Suppose the manager decides to randomly supervise three such projects.

a. What is the probability that all three projects finish on time?

b. What is the probability that at least two projects finish on time?

Urn I contains three red chips and five white chips; urn II contains four reds and four whites; urn III contains five reds and three whites. One urn is chosen at random and one chip is drawn from that urn. Given that the chip drawn was red, what is the probability that III was the urn sampled?

Urn I contains three red chips and one white chip. Urn II contains two red chips and two white chips. One chip is drawn from each urn and transferred to the other urn. Then a chip is drawn from the first urn. What is the probability that the chip ultimately drawn from urn I is red?

Evaluate each expression. $\log _{10} 10$

At State University, 30% of the students are majoring in humanities, 50% in history and culture, and 20% in science. Moreover, according to figures released by the registrar, the percentages of women majoring in humanities, history and culture, and science are 75%, 45%, and 30%, respectively. Suppose Justin meets Anna at a fraternity party. What is the probability that Anna is a history and culture major?

A taxi company tests a random sample of 10 steel-belted radial tires of a certain brand and records the following tread wear: 48,000, 53,000, 45,000, 61,000, 59,000, 56,000, 63,000, 49,000, 53,000, and 54,000 kilometers. Find the standard deviation of this set of data by first dividing each observation by 1000 and then subtracting 55.

Urn I contains five red chips and four white chips; urn II contains four red and five white chips.Two chips are drawn simultaneously from urn I and placed into urn II. Then a single chip is drawn from urn II. What is the probability that the chip drawn from urn II is white?

The distance around Earth along a given latitude can be found using $C=2 \pi r \cos L$, where r is the radius of Earth and L is the latitude. The radius of Earth is approximately 3960 miles. Make a table of values for the latitude and corresponding distance around Earth that includes $L=0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}$, and $90^{\circ}$. Use the table to describe the distances along the latitudes as you go from $0^{\circ}$ at the equator to $90^{\circ}$ at a pole.

Find the exact value of each expression, if it exists. $\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

Find the value of k so that each remainder. is zero. $\frac{2 x^{3}-x^{2}+xk}{x-1}$

The brightness of two celestial bodies as seen from Earth can be compared by determining the variation in brightness between the two bodies. The variation in brightness V can be calculated by V=$2.512^{m_{f}-m_{b}}$, where $m_f$ is the magnitude of brightness of the fainted body and $m_b$ is the magnitude of brightness of the brighter body. The variation in brightness between Mercury and Venus is 5.25. Venus has a magnitude of brightness of -3.7. Determine the magnitude of brightness of Mercury.