Math Questions

3 A grocery store worker has to collect all the shopping carts left out in the parking lot He collects 4 carts and measures the length of the 4 carts he is pushing to be 51 inches He collects another cart for a total of 5 carts and measures the length of the 5 carts to be 57 inches a He sees that there are a total of 21 carts in the parking lot How long will the line of 21 carts be

A tunnel is constructed with a semielliptical arch The width of the tunnel is 70 feet and the maximum height at the center of the tunnel is 20 feet What is the height of the tunnel 10 feet from the edge Round your answer to the hundredths place 19 17 feet 16 41 feet 014 01 feet 10 30 feet

1 URE For f x x 6 and g x x 7 find the following functions a fog x b gof x c fog 3 d gof 3 a fog x Simplify your answer

Sheila works in a bookstore and sold 100 books She sold 28 more paperback books than hardback books How many of each type of book were sold Sheila sold 36 hardback books and 64 paperback books Sheila sold 72 hardback books and 28 paperback books Sheila sold 64 hardback books and 36 paperback books Sheila sold 28 hardback books and 72 paperback books

What does this math statement tell us AABC AXYZ B A X Z A Triangles ABC and XYZ are congruent this means their side lengths are equal to each other B Triangles ABC and XYZ are similar this means their side lengths are proportional to each other C Triangles ABC and XYZ are different they have different angles and their sides aren t

Based on probability and if it is appropriate for a decision to be left up to chance choose every situation that is both statistically fair an morally fair Situation 1 Situation 2 A high school student is deciding whether to first clean his room or do his homework He decides by picking a tile at random from a bag of lettered tiles If he picks a consonant he will clean his room and if he picks a vowel he will do his homework Situation 3 There are four candidates eligible for a vacancy at a company Ignoring qualifications and experience the recruitment manager decides which candidate to hire by writing their names on pieces of paper shuffling the papers and drawing one at random Five cousins are deciding which board game to play They each write their preferred game on a different section of a spinner that has five equally sized sections They spin the spinner and will play the game written on the section where the spinner lands To determine who can choose the spot for a picnic Kate picks a tile at random Situation 4 from a collection of five tiles numbered 2 through 6 Kate chooses the spot if she picks a prime number and Charles chooses if Kate picks a composite number Five roommates all want to attend an event but they only have four invites To decide who will attend they shuffle a set of five cards consisting of four aces and a king Each roommate is randomly dealt a card The ones dealt an ace will attend Situation 5 the event

The prescribed dosage of a drug is 10 mg kg daily meaning that 10 milligrams of the drug should be administered daily for each kilogram of a patient weight How many 400 milligram tablets should be given each day to a patient who weights 175 pounds Use the fact that 1 lb is approximately 0 45 kg

Convert the two way table to a relative frequency table Has siblings Does not have siblings Rides the bus to school Does not ride the bus to school Has siblings Does not have siblings Has siblings 122 10 Does not have siblings Rides the bus to school Value here Does not ride the bus to school Value here Rides the bus to school Value here Does not ride the bus to school Value here 64 4 1 0 32 2 0 02 3 0 25 4 0 10 5 0 05 6 0 45 7 0 75 8 0 61

Easton is working two summer jobs making 18 per hour tutoring and 9 per hou learing tables Last week Easton worked 4 times as many hours tutoring as he worked hours clearing tables hours and earned a total of 162 Graphically solve a ystem of equations in order to determine the number of hours Easton worked utoring last week a and the number of hours Easton worked clearing tables last veek y 20 19 18 17 16 45 14 13 12 11 10 9 Click twice to plot each line Click a line to delete it

3 In a large city a transportation engineer wants to estimate the proportion of residents who use the bus system regularly Out of a random sample of 2000 residents 1220 use the bus regularly Construct and interpret the 99 confidence interval P hat 1220 2000 61 Q hat 1 61 39 Standard Error 010906 with a Z score of 2 5758 for the 99 confidence interval 61 2 5758 010906 6380 61 2 5758 010906 5819 5819 6380 So with a confidence interval of 99 the true proportion of residents who use the bus system regularly is between 58 19 and 63 8 Suppose we wanted the margin of error for the 90 confidence level to be exactly 2 How many residents 2

This table represents values of a cubic polynomial function X y 2 12 1 0 0 1 7 5 2 6 3 3 6 Based on the information in the table which sentence best describes the interval 2 1 The function is decreasing on the interval 2 1 The function is constant on the interval 2 1 The function is increasing on the interval 2 1 The function is both increasing and decreasing on the interval 2 1 O A O B O C OD

Suppose 13 people qualify for a college cheerleading squad five women and eight men How many six member squads can be selected if exactly two of the members are male Select one O a 715 b 140 OG 1417 d 33

1 There are 7 125 000 000 people on earth Represent this number in scientific notation a x 10 2 Heinz ketchup sells 1 1E10 packets of ketchup every year Represent this number in standard form 3 The distance to Mars is 38 000 000 miles away from Earth Represent this number in scientific notation a x 10 4 The width of a single piece of paper is 5E 5 meters thick Represent this number in standard form 5 A single M M weighs 0 0007776 kilograms Represent this number in scientific notation ax 10 Type the caret when representing an exponent Example 10 should be typed as 10 3 Question 1 type your answer Question 2 type yo

Write the equation of the line in fully simplified slope intercept form 12 11 10 987 d y 543 4 21 12 11 10 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7890 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 x

Approximate the measures of center for following GFDT Data Frequency 70 74 75 79 80 84 85 89 90 94 a mode Report mode and median accurate to one decimal place Report the mean accurate to two decimal places or enter as a fraction b median 2 1 11 c mean 21 10

Triangle DEF is shown on the xy coordinate plane 10 9 the perimeter of AD E F 161 5 4 2 2 S 6 The triangle will be rotated 180 clockwise around point 4 8 to create AD E F Which characteristic of AD E F will NOT be the same for the corresponding characteristic of ADEF the coordinates of D O the coordinates of F O the area of AD E F

ABCD QRST Find the missing side length m B 10 C 13 12 A 22 5 15 D m Rm S 5 2 4 8 9 6 T Enter

7 Tara is solving an equation Her first step is shown below Solve 4y 8 y 2 6 Step 1 4y 8y 16 6 Which property justifies Tara s first step O Distributive Property O Subtraction Property of Equality O Identity Property

Andy who loves to cook makes apple cobbler for his family The recipe serves 6 calls for 2 pounds of apples 3 cups of flour cup of margarine 3 cups of sugar and 2 teaspoons of cinnamon Since guests are coming Andy wants to make a cobbler that will serve 15 increase the recipe 2 times How much of each ingredient should Andy use Use of apples Use of sugar Use of flour Use of cinnamon Use of margarine pounds cups cups teaspoons cup

Consider two fire towers in the Canadian wilderness Tower B is 40 miles due East of tower A The guards notice a fire that appears at a bearing of 70 degrees from Tower A and a bearing of 310 degrees miles from the tower B the closer of from Tower B The fire is at a distance the two towers Hint Draw a picture

A table lamp emits light in the shape of a hyperbola If the hyperbola is modeled by the equation 25x 144y 2 3 600 0 which of the following equations represents the boundaries of the light Oy 5 12 5 x and y 12 X Oy 12x and y 12x 5 5 5 Oy x and y x X 13 13

est They Zoologists are studying two newly discovered species of Insects in population of Insect A to be 1 3 million and the current population of Insect B to be 2 1 million As development is encroaching on the section a rain forest where these insects live the zoologists estimate the populations of Insect A to be reducing at a rate of 3 8 and insect B to be reducing at a rate of 4 6 If Prepresents the population of each species of insect in millions and trepresents the elapsed time in years then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal OA O B SOC OD P 1 3e 0 038t P 2 1e 0 0461 P 1 3e 0 38t P 2 1e 0 461 P 1 3e0 0381 P 2 1e0 0461 P 1 3e0 381 P 2 1e0 46t

emand TWO iness students decided to open a small company together to sell the own brand of sheakers After doing some research they estimated that the wholesale price of their product p in dollars would be related to the monthly supply X in hundre airs by the equation 5 x p 4700 ow fast is the quantity demanded changing when the unit price per pair of sneakers is 40 dollars the monthly supply is x 15 and the unit price is increasing at a rate of 4 dollars per month ote Enter your solution as a decimal rounded to four 4 decimal places without units

2 A company produces and sells electric cars The company s profit P in thousands of dollars changes based on the number of cars x they produce per month The rate of change of their profit from producing x electric cars is modelled by dP 1 6x 48 x 0 dx The company makes a profit of 260 thousand dollars when they produce 15 electric cars a Find an expression for P in terms of x P P 10 441 200 000 1605 43

Suppose you wish to install a drip sprinkler system and need to run a drip water line to five areas as shown in the given graph The numbers show the distances in feet What is the smallest number of feet of drip hose necessary to install 80 A The smallest number of feet of drip 126 ft B The smallest number of feet of drip 111 ft The smallest number of feet of drip 216 ft 43 40 70 72 40 45 46 48

Question 1 of 14 3 points Attempt 1 of 1 View question in a popup 2h 44m Remaining Traveler Spending The data show the traveler spending in billions of dollars for a recent year for a sample of the states Round your answers to two decimal places 20 3 33 2 22 58 4 23 6 110 4 30 1 24 4 74 9 60 2 Send data to Excel Part 0 3 Part 1 of 3 Find the range The range is Part 1 3 Part 2 of 3 Find the variance The variance is Part 2 3 Part 3 of 3 X 3 2 Secti 5

4a 2 marks Series Sequence Mia baked a very large apple pie that she cuts into slices to share with her friends The smallest slice is cut first The volume of each successive slice of pie forms a geometric sequence The second smallest slice has a volume of 30cm The fifth smallest slice has a volume of 240cm Find the common ratio of the sequence 4b 2 marks Find the volume of the smallest slice of pie 4c 2 marks The apple pie has a volume of 61425cm Find the total number of slices Mia can cut from this pie

The graph shows the population of black toads in a forest reserve since their introduction It also includes functions drawn by different researchers to estimate the change in population of the toads Which function best models the researchers data Black Toads thousands 16 14 12 10 0 A B OC On function A function B function C function D 2 Black Toad Population D B A 4 6 Years Since Introduction 8 X 10

A ball bounces to a height of 6 7 feet on the first bounce Each subsequent bounce reaches a height that is 81 of the previous bounce What is the height in feet of the sixth bounce Round your answer to the thousandths place 1 892 ft

The magnitude and direction of vectors t u and v are shown in the table Vector Magnitude Direction 5 250 t u V 335 305 155 1 0213 6 What is the direction of t u v Round to the nearest degree 12 60 330

A vector has a magnitude of 50 and a direction of 30 Another vector has a magnitude of 60 and a direction of 150 What are the magnitude and direction of the resultant vector Round the magnitude to the thousandths place and the direction to the nearest degree 55 678 99 FESTO PU

Meals with Clients Breakfast 20 per person Lui Total meals expensed must not exceed allowed expenses based on rates given Question Decide if total meal reimbursement requests should be approved Meal Employee Breakfast Client Lunch Client Dinner Total Approval Status Andrew of People 2 3 3 Brianna Cost 26 53 75 45 150 04 252 02 Carlos

A saleswoman wants to visit eastern cities New York City Boston Cleveland and Washington D C Driving distances are as shown in the figure below What is the shortest trip starting in New York that visits each of these cities if r1 486 r2 473 Find a solution using any method A 1814 mi B 1813 mi C 1810 mi D 1811 mi Cleveland 712 667 Wash D C Boston 235 197 NYC

What is the measure of AC Enter your answer in the box A B 75 1 2 3 4 C 5 6

4 Person A is breathing five times as fast as person B Compare the graphs of the breathing of the two people over time O The period of the graph for person A is 2 times longer than the period of the graph for person B O The period of the graph for person A is 5 times shorter than the period of the graph for person B O The period of the graph for person A is 5 times longer than the period of the graph for person B O The period of the graph for person A is 2 times shorter than the period of the graph for person B

Scientists are measuring a distant planet s temperature The graph shows the temperature in C versus the height in kilome above the planet s surface Temperature C 40 36 32 28 24 20 16 12 8 4 0 Height kilometers a Choose the statement that best describes how the height and temperature are related Then fill in the blank O As the height increases the temperature decreases At what rate is the temperature decreasing C per kilometer O As the height increases the temperature increases At what rate is the temperature increasing C per kilometer b What is the temperature at 0 kilometers

0 A survey asks 1500 workers Has the economy forced you to reduce the amount of vacation you plan to take this year Forty one percent of those surveyed say they are reducing the amount of vacation Twenty workers participating in the survey are randomly selected The random variable represents the number of workers who are reducing the amount of vacation Decide whether the experiment is a binomial experiment If it is identify a success specify the values of n p and q and list the possible values of the random variable x spolity and value 1 TELL CHRIVE USUW aitu sirmarry die DASS I your VILE A n 20 OB This is not a binomial experiment Specify the value of p Select the correct choice below and fill in any answer boxes in your choice OA p B This is not a binomial experiment Type an integer or a decimal

15 O a 2b a 2b a 2b N Given The coordinates of rhombus WXYZ are W 0 4b X 2a 0 Y 0 4b and Z 2a 0 Prove The segments joining the midpoints of a rhombus form a rectangle As part of the proof find the midpoint of YZ a 2h W Y X

6 13 points Ben walks at a rate of 3 miles per hour He runs at a rate of 5 miles per hour In one week the combined distance that he walks and runs is 170 miles Write a linear model that relates the number of hours that Ben walks to the number of hours Ben runs O O 3x 5y 170 y 3x 170 3x 5y 170 3x 5y 170 84 Previous Next

gardener is starting a new square garden and will enclose it with 100 meters of fencing He wants to determine the area of this garden Let A represent the area of the garden in square meters Move an equation to the first blank and a number to the second blank to complete the sentences An equation that can be used to determine the area A of the garden is The area of the garden is 5 100 A square meters 10 100 4 A 20 625 100 VA 10 000

Solve the absolute value inequality and put the answer in interval notation img class equation image title mid7 7x mid 28 src equation images 255Cmid7 7x 255Cmid 253C28 alt mid7 7x mid 28 O 3 00 O 3 U 5 O 8 5

The function V t 3500t 19000 where V is value and t is time in years can be used to find the valu a large copy machine during the first 5 years of use a What is the value of the copier after 2 years and 6 months After 2 years and 6 months the copier is worth b What is the salvage value of the copier if it is replaced after 5 years After 5 years the salvage value of the copier is c State the domain of this function d Sketch the graph of this function t

Which statement is true OB OA A sample statistic can never be equal to the population parameter Point estimates are defined for both samples and populations OC To calculate a sample proportion we need to know the population size OD To calculate a point estimate we need to know the sample size

The positions on a lacrosse team are called defenders D midfielders M and attackers A One player is chosen at random to lead the team in exercises before each game The letters MDD mean that a midfielder was chosen at the first game and a defender was chosen at the next two games The list of all possible outcomes is shown where each outcome has equal probability of occurring AAA AMA ADA MAA MMA MDA AAM AMM ADM MAM MMM MDM AAD AMD ADD MAD MMD MDD What is the probability that a defender is chosen at least once given that a midfielder is chosen at the first game O A O B 19 DAA DMA DDA DAM DMM DDM DAD DMD DDD 113

2 Chang a store employee asked each of 50 customers which 1 of 4 shirt colors the customer perferred The number of customers who preferred each color is given in the table below Color Number of customers Red White Blue Gray Total 525896 15 22 50 Chang will order 500 shirts in their proportions by color in the table How many graw shirts will he order Show Your Work A 8 B 16

Which statement about weight loss is NOT true A Fad diets are not a healthy way to lose weight B Losing weight too fast is not healthy C Losing weight will not decrease your health risks D You don t have to exercise strenuously to lose weight

The function graphed to the right is of the form y c cos x y c sinx y cos x d or y sin x d where d is the least possible positive value Determine the equation of the graph y N 1 1 2 X

Yolanda has a job transporting soft drinks by truck Her truck is filled with cans that weigh 14 ounces each and bottles that weigh U ounces each There is combined total of 800 cans and bottles in her truck Let x be the number of 14 ounce cans in her truck Write an expression for the combined total weight in ounces of the cans and bottles in her truck total weight in ounces 0 DO

A company that m jeans estimates that the profit for selling a particular style is given by the equation P 250x 1 505x 300 for 0 x 6 where P is profit in tens of thousands of dollars and x is the advertising expense in tens of thousands of dollars What does an x intercept mean in the context of the problem B C D the number of times the company spent zero dollars on advertising the profit when the company spent zero dollars on advertising the advertising expense when the company had the most profit the advertising expense when the company s profit was zero dollars

3 Identify the statement as true or false and justify your answer Plane M is perpendicular to line s through point Q Therefore it is the only plane perpendicular to s through point Q M 2 a False If a line is perpendicular to a plane any line perpendicular to that line at the point of intersection of the line and the plane is contained by the plane b True If a line is perpendicular to a plane any line perpendicular to that line at the point of intersection of the line and the plane is contained by the plane c True Given a point on a line there is one and only one plane perpendicular to the line through that point d False Given a point on a line there is one and only one plane pondia