Questions

m Determine the power output of a certain speaker if the intensity is approximately 0 0782 and the distance from the center of the sphere is 5 meters Round your answer to 3 decimal places Upload a PDF of your work in the correct orientation Only PDFs will be given credit Show all work Provide units

Use properties of logarithms to solve for x 15 points log y 3 log 2y 2 log y A y 2 1 only B y 2 only C y 1 only D y 1 2 only E y 2 only

The length X of a fish from a particular mountain lake in Idaho is normally distributed with 8 2 inches and 1 5 inches a Is X a DISCRETE or a CONTINUOUS random variable b Write the event a fish chosen has a length equal to 6 2 inches in terms of X I am expecting an inequality such as X 3 c Find the probability of this event d Find the probability that the length of a chosen fish was at most 9 2 inches e Find the probability that the length of a chosen fish was between 6 2 and 9 2 inches

Use properties of logarithms to solve for x 15 points 0 log 4x 3 log7 x 2 The value of x is The value of x is A Less than 1 B Between 1 and 2 5 C Between 2 5 and 4 D Between 4 and 5 5 E More than 5 5

A portable boombox advertises a sound output power of 50 Watts W Determine the intensity in W m and in decibels for a person who is standing 4 meters from the boombox Round your answer to 3 decimal places Upload a PDF of your work in the correct orientation Only PDFs will be given credit Show all work

Use properties of logarithms to rewrite as a single logarithm in the form log P where P is an algebraic expression 10 points log3 x 3 log3 y 7log3 2 A logs 3x 3y 7 x B log C logs D log 1 3 x 3y 7

For each statement select True or False from each pull down menu 1 In the normal distribution the right half of the curve is slightly larger than the left half 2 The z score such that the area to the left of it is 0 05 is located to the left of zero on the z axis 3 All normal distributions have a mean of zero 4 If X is a normal random variable and c is a constant then P X c 0 5 In the normal distribution the tails of the graph get closer and closer to the horizontal axis but never crosses it

Fluorescent lighbulbs have lifetimes that are normally distributed with a mean of 5 9 years and a standard deviation of 1 6 years The figure below shows the distribution of lifetimes of fluorescent lightbulbs Calculate the shaded area under the curve Express your answer in decimal form with at least four decimal places Answer 4 828 9 1 Lifetines of Fluorescent Lightbulbs

The top selling Red and Voss tire is rated 60000 miles which means nothing In fact the distance the tires can run until they wear out is a normally distributed random variable with a mean of 73000 miles and a standard deviation of 5000 miles a What is the probability that the tire wears out before 60000 miles Probability b What is the probability that a tire lasts more than 76000 miles Probability

B a Given triangle ABC and circle CA centered at A with radius AC and circle Cg centered at B with radius BC how many intersection points do the two circles have and where are the intersection point s located b If two circles centered at A and B intersect in a single point C then describe all of the possible relationships between AB BC and AC Explain your answer

A math textbook explains probability by showing a set of cards numbered 4 through 9 and showing the number of people who might draw each card Drawing a card between 4 and 9 xx xxx 456789 Number drawn Which number was drawn the most times

y f x R S 10 1 Let f be the function given by f x x 3cos x Let R be the shaded region in the second 2 quadrant bounded by the graph of f and let S be the shaded region bounded by the graph of and line l the line tangent to the graph of at x 0 as shown above a Find the area of R

The area of the region between the graph of y 2x 6 and the x axis

0 5 y 0 5 0 70 0 5 0 34 0 94 An angle is shown State another angle that has the same cos value but a different sin value 0 5 X Check

TT VE 0 5 y 0 5 0 866 The angle 60 is shown in the unit circle Draw in another angle that has the same sin value 0 5 0 60 0 5 0 5 X

Belle figured out the scores at the end of a card game Scores in a card game x x x x x X8 x x x 4 5 6 7 8 9 10 Score How many people scored more than 6 people

DUE MONDAY APRIL 15th YOU 2004 AP CALCULUS AB FREE RESPONSE QUESTIONS y g x 2 Let f and g be the functions given by f x 2x 1 x and g x 3 x 1 x for 0 x 1 The graphs of and g are shown in the figure above a Find the area of the shaded region enclosed by the graphs of f and g y f x g x 0 1 Let f and g be the functions given by f x 1 sin 2x and g x e 2 Let R be the shaded region in the

y 0 5 Give an example of an angle b with a negative cos value and a sin value that is between 0 5 and 0 9 You can use trial and error here type an angle and see its coordinates 0 5 0 0 5 0 5 X Check

Some students in a biology class compared how many times they went to the park last week to work on their plant research projects Trips to the park last week 012 3 4 5 Number of trips How many students went to the park fewer than 4 times students

0 5 y 0 5 0 95 0 312 1 Move the blue point to a place on the unit circle so that sin 0 0 8 2 State the value of cos 0 based on where you placed the point 0 0 5 0 5 X Submit

0 5 0 866 y 0 5 0 866 The angle shown in red has the same sin value as sin 60 What is the size of the red angle 0 5 0 5 0 60 0 5 0 5 X Submit

0 5 y 0 34 0 94 0 5 0 70 0 5 0 5 X The angle 70 is shown on the unit circle together with its coordinates State another angle that has the same sin value but a different cos value Check

A Solve for the missing angle to 400 50 5 degrees 12 7 degrees 36 9 degrees 72 2 degrees 300

Susan is flying a kite which gets caught in the top of a tree Use the diagram to estimate the height of the tree 63 6 ft 1 59 ft 74 2 ft 86 9 ft string 44 90 feet

sin 8 and cos 6 both positive Match in groups of three When it s correct the title will change 330 230 sin 0 and cos 0 both negative sin 0 is positive and cos 8 is negative cos 8 is positive and sin 8 is negative 40 135 D

y 0 5 The angle 310 is shown on the unit circle Which two of the statements below are true Select two statements cos 310 is negative sin 310 is negative 0 5 310 sin 310 is positive 0 5 X cos 310 is positive 0 5 0 643 0 766

y Give an example of an angle a which has a cos value between 0 1 and 0 5 You can use trial and error here type an angle and see its coordinates 0 5 0 5 0 0 5 X 0 5 Check

0 5 For each of the four quadrants give an example of an angle that is in that quadrant Quadrant 1 2 0 5 0 0 5 3 0 5 Check Example Angle

What is the volume of the pyramid below 112 116 4

3x 2y z 5 2x 5y z 2 Given the system what would be the resulting equation if you combined these equations to eliminate the variable z Type a response

On a given day the number of people in thousands that have entered a museum is modeled by the function h given by h t 4 217 tan 0 7t 0 026 where t is measured in hours and 0 t 8 Based on the model at what time t did person number 4000 enter the museum ROUND your answer to 3 Decimal Places 4000 people in this scenario is represented by the number 4 since the model is in thousands Type your answer

y Find the value of the variable 450 450 y 60

Exercise 6 6pt Detrmine derivatives of the following functions a f x x e b f x ln 5x 2 COS I c f z d f x sin f x 9 x I

Exercise 5 13pt Find the maximal domain and all the asymptotes of the following function 2x 7 a f z 3 b f x 1612 9

5 Rewrite each expression as a single logarithm a 5 log x log 2y 3 4log 3z 2 b 4lnx ln x 3 3 log x 1 c logx log 4x 3 2 log 5x 1

Use the definition of the logarithmic function to find x A log5x 0 B logx 25 2 C log3 x 2 D logx 8

Evaluate the logarithmic expression by using the properties of logarithm 1 A log5 54 B logs 125 C log55 1 D logs 125 E logs 5 F 5logs 4

Find the area of the region between the graphs of y 12 2 and y 7x 4 ove the interval 6 x 5 The area is

A University works with community groups to organize volunteer opportunities for students A researcher suspects that some faculties are overrepresented with regards to the number of volunteers they yield The researcher would like to determine whether she has statistical evidence that warrants rejecting the null hypothesis that the faculties at her university yield equal numbers of volunteers Using the observed values in the table below by hand i determine the expected frequencies and calculate x and ii calculate the degrees of freedom Show all your work Health Sciences Education Humanities Math Science Social Science

Express using a negative exponent Z Type exponential notation with negative exponents Z 9

The area of the region between the graph of y 2 7x 30 and the x axis is

Simplify mh er 3 m h x3 15 xf5 9 3 mh Simplify your answer Use positive exponents only

now bout Exponents Simplify lestion 20 4n5 4n5 6 Simplify your answer Use positive exponents only

Type your answer using exponential notation Use positive exponents only N Divide and simplify 28 28 24

Multiply and simplify 7v 7v 7v 7v Type exponential notation with positive exponents

Compute by hand the i Pearson correlation and corresponding ii degrees of freedom for the data below Show all your work please X Y 2 3 3 4 4 5 2

Simplify Assume a b 0 ab 4 Choose the simplified form of ab 4 OA 1 a4b 4 OC ab 4

Simplify w 5 8 1 w 5 8 Simplify your answer Type exponential notation using positive exponents

The average discharge at the mouth of the Amazon River is 4 700 000 cubic feet per second How much water is discharged from the Amazon River in one hour in one year ft3 of water is discharged in one hour Round to the nearest thousandth as needed Use scientific notation Use the multiplication symbol in the math palette as needed ft3 of water is discharged in one year assuming it is not a leap year Round to the nearest thousandth as needed Use scientific notation Use the multiplication symbol in the math palette as needed

Multiply Write the result using scientific notation 5 9x107 6 9 103 5 9 107 6 9 103 Simplify your answer Use scientific notation Use the multiplication symbol in the math palette as needed