Questions

Assume that you have agreed to use a cellular plan that charges a price of p 4q 500 dollars for using q GB of data Determine a formula for a that describes the amount of data you can use in terms of the amount of money that you are willing to spend Answer

Given the following voltage and current i t 5 sin 377t 57 A u t 10 cos 377t 41 V Determine the phase relationship between i t and u t Notes on entering solution Enter your solution with respect to V leads i by Enter your solution in degree Do not include units in your answer ex 5 is entered as 5

The shaded region between the graphs of y 2x 20 and y 3x 15 is displayed 25 F 6 141 below in orange The shaded region lies between 2 5 40 and 3 5 A typical rectangle is shown in the diagram located at position x What is the height of this rectangle in terms of Now find the total area of the orange shaded region

Find the area of the region enclosed by y 1 25x and x 5 72 2 1 2 3 Use horizontal strips to find the area that is integrate with respect to y First find the y coordinates of the two points where y 1 25z meets 2 5 y lower limit c upper limit d and To find the area of the enclosed region from to d we will integrate C where g y d g y dy

Consider the function In 1 72 00 Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms For example if the series were 3 you would write 1 322 32z 33 3z Also indicate the radius of convergence Partial Sum Radius of Convergence 7

1 Find c 0 such that the area of the region enclosed by the parabolas y x c and y c x is 90

4 A reporter from the Sacramento Bee claims that more than 14 of California workers say it is likely they will quit working this year In a simple random sample of 250 California workers 18 said it is likely they will quit working this year At the significance level of 5 is there enough statistical evidence to support the report s claim Simple Random Sample Requirements 1 2 3 P 14 P214 Step 1 State the hypothesis Ho P 14 P 14 Tall Ha n 250 Step 2 Draw your distribution and find critical number s Step 3 Compute the test statistics Step 4 Make a Decision Step 5 Summarize the result Restate the level of significance and discuss the claim

Find the first five non zero terms of power series representation centered at x 0 for the function below f x ln 6 x Answer f x In 3 1 2 18 What is the radius of convergence Answer R 3 81 4 x 324 1215

A factory selling cell phones has a marginal cost function C x 0 01x 3x 229 where represents the number of cell phones and a marginal revenue function given by R x 429 2x Find the area between the graphs of these curves and x 0 What does this area represent total profit for 200 cell phones sold total profit for more than 200 cell phones sold total revenue for 200 cell phones sold for 200 cell phones cold

There is a line through the origin that divides the region bounded by the parabola y 8x 3x and the x axis into two regions with equal area What is the slope of that line

Sketch the region enclosed by y 5x y 7x and x 1 Find the area of the e region

Set up the definite integral required to find the area of the region between the graph 15 and y 3x 13 of y x da

Find c 0 such that the area of the region enclosed by the parabolas y x 2 and y c x is 460

Determine which graph corresponds to the area enclosed by the curves y 4x and y x 3 6 8 65 5 4 3 2 1 23 5 4 3 2 1 1 2 3 4 2 Find the area of the region between y 4x and y x 3

Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Then find the area of the region 2y 3 y 3 and 2y 3x 6

4 A reporter from the Sacramento Bee claims that more than 14 of California workers say it is likely they will quit working this year In a simple random sample of 250 California workers 18 said it is likely they will quit working this year At the significance level of 5 is there enough statistical evidence to support the report s claim Requirements 1 2 Simple Random Sample Binomial 3 np 250 Step 1 State the hypothesis Ho Ha Tail Step 2 Draw your distribution and find critical number s Step 3 Compute the test statistics Step 4 Make a Decision Step 5 Summarize the result Restate the level of significance and discuss the claim

c Write down the minimum height of point P 1 Later the cat is tired and it takes twice as long for point P to complete one revolution at a new constant rate d Write down the new value of b

74 90 1 01 M n 0

A rectangular soccer field has dimensions 70 yards by 110 yards as shown in the figure A sprinkler placed at point P rotates 15 and sprays across the entire field as shown in the figure What percent of the soccer field is watered by thi one sprinkler Round to the nearest hundredth P 95 yd 15 110 yards 70 yards

8 Wayne wants to plant a triangular garden in his backyard and he will enclose the garden with 204 feet of fencing a Give two possible sets of side lengths for the garden one making an acute triangle and one making an obtuse triangle b Find the semiperimeter of each garden c Find the area of each garden d Wayne decides that he will have one side length of the garden be 50 feet If another side length is x write an expression for the 3rd side length e Write an equation in terms of x for the area of the garden f Use technology to find the lengths of the sides of the garden that give the maximum area and state the maximum area

If you reflected the point 3 4 across the x axis what would be the coordinates of the new point The new coordinates would be Select Select Select 3 4 3

Two planes leave the Atlanta airport at the same time and fly for three hours Flight 1504 flies 34 West of North at 245 miles per hour and Flight 168 flies 70 East of North at 271 miles per hour After 3 hours how far apart are the planes Round to the nearest hundredth 34 N 70

A statistics lab required students to draw cards numbered between 1 and 6 and track the results Drawing a number between 1 and 6 xx 1 2 3 4 5 6 Number drawn How many students drew a number greater than 4 students Submit

2 The figure shows ABRO B 18 9 R 13 a Find the semi perimeter of ABRO b Find the area of ABRO Round to the nearest tenth

While working as a summer camp counselor Jessica monitored how many candy necklaces each child made Making candy necklaces 12 x 01 3 x 234 56 Candy necklaces made How many children are there in all children

If a point in Quadrant IV is reflected across the y axis which quadrant will the new point appear in O Quadrant I O Quadrant II O Quadrant III O Quadrant IV

What is the x coordinate for Point A TYPE THE NUMBER ONLY 6 y 6 4 2 4 2 XA 0 2 4B 6 2 A 4 C 6

4 AVMN has sides of lengths v n and m a Write an expression for the height of the triangle h in terms of the measures of the sides and angles of the triangle b Write an expression for the area of AVMN V m n N

1 In AACD AC 25 inches and DC 18 inches a Find ED to the nearest tenth b Find the area of AACD D

Explain how you would plot the point 1 5 on a coordinate plane

B Find the area of AMPO Round to the nearest hundredth M 14 66 O P 17 5

Which quadrant is the point 2 3 located in Quadrant I O Quadrant II O Quadrant III O Quadrant IV

What is the y coordinate for Point C TYPE THE NUMBER ONLY Ay 6 9 4 2 4 2 0 2 XA 2 AB 6 A 4 C 6

Which quadrant is the point 3 2 located in O Quadrant I O Quadrant II O Quadrant III O Quadrant IV

5m

A point in the figure shaded region A l W 4 17 m 8 m

Tuberculosis TB is one of the 13th leading cause of death worldwide Although a leading cause it is both preventable and treatable According to the World Health Organization WHO TB incidence is falling at about 2 per year In the year 2020 there were approximately 10 million incidences of TB globally Q2 1 Part a 15 points Use of TB globally where I is in millions of people and t is in terms of years since 2020 Show all work Define variables Put a box around the final answer Upload a PDF file in the correct orientation for credit Q2 2 Part b 15 points Graph this function in an appropriate window from the year 2020 to 2070 Include axes and scale Label your axes Include units Upload a PDF file in the correct orientation for credit

ethane DDT pesticide in Lake Michigan has been declining exponentially for many years In 1971 the DDT concentration was 13 00 ppm parts per million In 1984 the DDT concentration was 2 22 ppm Q1 1 Part a 20 Points Use the data points provided in question 1 to determine the exponential decay function D f t Ce that models the DDT concentration in Lake Michigan in ppm as a function of t years since 1971 Define all variables Include units Round r to four decimal places Show all work Put a box around your answer Upload a PDF of your work in the correct orientation

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