Basic Math Questions and Answers

Eugene has fifteen songs on his playlist If he uses the random mode on the music app to play all the songs which of the following represents the number of possible ways to order the songs Assume that the random mode does not play the same song more than once in a cycle O 15 O 1515 0 15 15 15

IV A light display has three colored lights each of which flashes on for an instant at regular intervals The yellow one flashes 15 times per minute the blue one flashes 6 times per minute and the red one flashes 12 times per minute You see all three lights flash on simultaneously How much longer must you wait before the three lights flash on simultaneously again The correct answer is 20 seconds Solve this problem and explain each step of your process so that a 5th grader will understand

Complete the following chart Standard Form 5700300 Word Form five thousand three hundred seventy thirty nine thousand seven hundred one

A rectangle will be rotated 360 about a line that contains the point of intersection of its diagonals and is parallel to a side What three dimensional shape will be created as a result of the rotation O A a cube OB a rectangular prism O C a cylinder D a sphere

Goldie Esparza buys 4 paper lanterns at 14 95 each 2 pi atas for 19 95 and 2 strings of white lights at 19 99 each The sales tax rate is 4 Norma Engel buys an inflatable canoe for 194 94 2 paddles for 44 95 and 9 energy hare 0 90 PTE

A force F with a magnitude length of 10 Newtons is applied to the point P at an angle of TT FS F with the horizontal as shown below Fv p FH Using trigonometry determine the horizontal component FH and the vertical component FV of the force Note that the triangle shown is a right triangle OFH 5 3 Newtons and Fy 5 Newtons OFH 5 Newtons and Fy 5 3 Newtons FH 5 2 Newtons and Fy 5 2 Newtons FH 5 3 Newtons and Fy 5 2 Newtons FH 5 2 Newtons and Fy 5 3 Newtons

9 Jenny is sitting on a sled on the side of a hill inclined at 15 What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds Show work

Here is a graph of the function Use the graph to find the following If there is more than one answer separate them with commas a All local minimum values of b All values at which has a local minimum DO X

4 2 1 You have saved 400 350 and 340 so far After your next and final week of saving you want to have saved an average of 375 per week How much do you have to save to get a four week average of 375 per week

ABCD is a parallelogram and EF is parallel to AB Select all triangles are similar to triangle AEX 12 cm 8 cm D 2cm E O Triangle ADC Triangle CDA Triangle XFC Triangle CFX X B

Carl is making a garden that is half as long as it is wide He wants to cover 271 square feet with the garden Which equation best represents the situation if x represents the length of the garden Ox 2x 271 Oxx 271 Ox x 271 Ox 2x 271

The measurement of a side of a square is found to be 9 centimeters with a possible error of 0 05 centimeter a Approximate the percent error in computing the area of the square X b Estimate the maximum allowable percent error in measuring the side if the error in computing the area cannot exceed 2 9 1 15

Select the correct answer Each statement describes a transformation of the graph of f x 3 which statement correctly describes the graph of y fx 7 3 OA It is the graph of ftranslated 3 units up and 7 units to the left OB It is the graph of ftranslated 7 units down and 3 units to the right It is the graph of ftranslated 7 units up and 3 units to the right It is the graph of ftranslated 3 units up and 7 units to the right OC O D Reset Next

The hawk population in a county is declining at a rate of 1 4 per year The population was 3800 in the year 2016 Which answer is the best prediction of the population in the year 2020 O 3541 O 3592 O 3643

You wake up one morning and find yourself wearing a toga and scarab ring Always a logical person you conclude that you must have become an Egyptian pharoah You decide to honor yourself with a pyramid of your own design You decide it should have height h 4470 and a square base with side 1210 S To impress your Egyptian subjects find the volume of the pyramid using integration

From December 2007 through March 2012 researchers at the University of Pittsburgh studied a new medication to treat osteoporosis in frail elderly women The researchers administered a daily dose of the medication or a placebo by injection along with calcium and vitamin D supplements Then the researchers measured the hip and spine bone density of each patient at 12 and 24 months Results were published in the Journal of the American Medical Association JAMA in April 2015 This is an example of which type of study observational study experiment

arble jar below Assuming that you keep each marble after you pick one out what is the probability of pulling out a yellow marble then a blue and then a red YOU MUST SHOW WORK TO RECIEVE FULL CREDIT a 1 point work shown 1 point correct final answer 27 TOTAL 30 ON FILL

G H For this question make sure to type your answers using proper notation symbols capitalization as needed and include the word Point or Plane accordingly 1 Name three points that are not collinear 2 Name two opposite rays 3 Give another name for JH 4 Name two different planes that contain HL 5 Use Desmos Geometry tool to sketch two planes that intersect with each other at a side Label your planes using the points on each plane Save your image drawing and include it here with your workcheck

3 0 d Solve SHOW YOUR WORK Solve SHOW YOUR WORK Camille has 20 stuffed cats and 15 stuffed Bila and Clarence are training for a marathon dogs which she wants to divide into identical Lila runs 12 kilometers at a time while Clarence with no stuffed animals left over prefers to run in blocks of 3 kilometers At the end of a month they realize that they have run same total number of kilometers What is the smallest number of kilometers that each must have run groups What is the greatest number of groups Camille can place her stuffed animals into HINT GCF Find the factors of 15 then the factors of 20 This will give you the GCF This is the answer T Gef 5 Wor HINT LCM Find the least common multiple of 12 and 3 The answer to this is the answer to the problem 1cm 121m O

For the following distribution decide whether you expect the mean median or mode to give the best representation of the center of the distribution and explain why Daily snowfall in Omaha in January Choose the correct answer below OA The mean because it takes into account all days regardless of the amount of snow OB The median because it is easier to calculate C The mode because it will find the most common snowfall amount s OD The mean because it is the most commonly understood measure of center OE The median because it is unaffected by outliers such as extreme storms OF The mode because there can be more than one

In the diagram below MN is parallel to JK If MN is 3 more than JM ML 14 and JK 15 find the length of JM Figures are not necessarily drawn to scale State your answer in simplest radical form if necessary L M J N K O

Jon has quarters dimes and nickels in his pocket The value of his money is 1 75 There are two more dimes than quarters and twice as many nickels as dimes How many nickels does he have Inickels

Use the median home values in Mississippi and Hawaii adjusted for inflation shown in the table below Assume that the house values are changing linearly Year 1950 2000 Mississippi 25 200 71 400 Hawaii 74 400 272 700 In what state have home values increased at a higher rate Select If the trends were to continue what would be the median home value in Mississippi in 2010 Select If we assume the linear trend existed before 1950 and continues after 2000 the two states median house values will be equal in what year Select

1 Angle 3 and Angle 6 are examples of which type of angle pair Lines A and B are parallel lines cut by a transversal Use the lines and the angles formed to answer the questions below Corresponding angles 4 Which of the following angles would not be congruent o the measure of 27 42 23 26 Alternate interior angles Same side interior angles Vertical angles 28 f the m27 115 find the asure of 115 0 115 2 Angle 1 and Angle 5 are examples of which type of angle pair ABIGAIL The two angles must be on opposite sides of the transversal Same side exterior angles Alternate interior angles Vertical angles Corresponding angles 5 Which of the following is an example of corresponding angles 28 and 24 25 and 27 21 and 27 D 23 and 25 8 If the m25 is 63 find the measure of 43 MALIK The two angles could be corresponding angles A B m27 3 Angle 6 and Angle 7 are examples of which type of angle pair Alternate exterior angles Same side interior angles Vertical angles 27 and 28 22 and 23 21 and 27 26 and 24 Corresponding angles 6 Which of the following is not an example of supplementary angles lejandro drew two parallel lines cut by a transversal He measured two of the angles that both measured 86 Circle the name of any student who made a true statement wo angles 9 If the mz1 is 57 find t measure of 26 FLETCHER The two angles coule be a linear pair

A hospital has been tracking the number of incidents of heart disease it treats each year for several years The data is shown below Year Heart Disease Incidents 2012 2013 2014 2015 80 83 84 89 a The data is approximately linear Use the data from 2012 and 2015 to find an equation for the linear model Use these variables t years after 2010 so 2015 would be t 5 n number of heart disease incidents b Using this model predict the year in which the number of heart disease incidents will reach 107 The year

Order Sandostatin octreotide acetate 40 mcg subcut Q 6h Read the label in the figure If the recommended dose is 100 600 mcg d in 2 4 divided doses titrate to response is the prescribed dose safe If the prescribed dose is safe how many milliliters will you administer Select one O a Yes 0 8 mL O b No the dosage is not safe O c Yes 0 5 ml O d Yes 1 2 mL

5 34 Husbands and wives The mean height of American women in their twenties is about 64 3 inches and the standard deviation is about 2 7 inches The mean height of men the same age is about 69 9 inches with standard deviation about 3 1 inches Suppose that the correlation between the heights of husbands and wives is about r 0 5 310 a What are the slope and intercept of the regression line of the husband s height on the wife s height in young couples Interpret the slope in the context of the problem b Draw a graph of this regression line for heights of wives between 56 and 72 inches Predict the height of the husband of a woman who is 67 inches tall and plot the wife s height and predicted husband s height on your graph c You don t expect this prediction for a single couple to be very accurate

apital Expansion Jester s Burger Hut plans to expand by opening several new restaurants e chain operates two types of restaurants drive through and full service A drive through restaurant costs 111 000 to construct requires 7 employees and has an expected annual revenue of 205 000 A full service restaurant costs 184 000 to construct requires 17 employees and has an expected annual revenue of 565 000 McJester s has 3 250 000 in capital available for expansion Labor contracts require that they higher no more than 325 employees Licensing restrictions require that they open no more than 25 new restaurants Let x be the number of drive through restaurants and let y be the number of full service restaurants in this expansion Let R be the expected annual revenue in dollars resulting from the expansion McJester s wants to maximize the expected revenue Set up the linear programming problem Answer the following questions about this linear programming problem for some values a and b Find a and b Round to the nearest integer a Select 325 25 b 205000 184000 17 565000 111000 7 The objective function is R ax by a for some values a and b Find a and b Round to the nearest integer Select b Select 184000 205000

Choose each answer that is a possibility for the solution set of a system involving an absolute value equation and a linear equation The picture below only shows one possibility as an example Do not limit your responses to the system graphed below Consider all of the ways any line can interact with an absolute value function Choose 4 8 7 6 5 Oinfinite solutions one solution Othree solutions O two solutions no solution y 2 f g

A scientist went hiking and took water samples at the top of a mountain and did an isotopic analysis of the oxygen atoms in the sample and recorded the average atomic mass The data is shown below Location Mountain Top Average Atomic Mass of the Sample 17 869 amu Based on the information in the chart which of the following conclusions can be made about the abundance of isotopes at the top of the mountain There is an abundance of oxygen 16 because the average atomic mass is 17 869 amu There is an abundance of oxygen 18 because the average atomic mass is 17 869 amu There is an abundance of oxygen 16 because the average atomic mass is 16 000 amu There is an abundance of oxygen 18 because the average atomic mass is 16 000 amu

Kyla applied m To 3 to triangle ABC What mistakes did she make Check all that apply C She applied the rotation to the triangle first She applied the reflection to the triangle first She changed the size of the triangle instead of just applying a translation She translated the triangle down instead of just applying a reflection rotation instead of a reflection

Select the correct shapes Jenna is making a shape for art class using craft sticks The shape must include two pairs of parallel sides Look at the shapes below Select all the shapes that Jenna could make

The country of Shyaway includes an adult population of 450 000 people Of those 245 000 are working full time and another 70 000 work part time If there are 100 000 people either retired or not in the labor force what is the labor force participation rate

1 Identify the color of each of the following aspects of the figure a The three perpendicular bisectors b The three angle bisectors c The inscribed circle d The circumscribed circle 2 Identify the point that gives each of the following aspects of the figur a The circumcenter b The incenter H G

A polynomial has been factored below but some constants are missing 2x 8x 24x ax x b x c What are the missing values of a b and c a 2 b 2 and c 6 O a 1 b 4 and c 6 O a 1 b 4 and c 6

Jan is looking at a map of Roaring River The map was created using the scale 1 inch 25 miles If the river is 5 5 inches long on the map then it is actually miles long

Car Value The equation V 28500 0 93 represents the value in dollars of a car t years after its purchase Use thi equation to complete the statements below The value of this car is Select an answer The purchase price of the car was Question Help Post to forum at a rate of Select an answer Select an answer Y

Population N Managers 21 Employees 29 Population Mean 95 CI 60 52 4 23 52 79 5 90 Managers Employees Median Mean 60 57 Write a 350 to 700 word response to the following What does the mean median mode and standard deviation tell us about the managers and employees Include answers to the following questions in your explanation of each What do they mean in our data What additional questions does it make you ask about the data Mode Median 70 68 Standard Deviation 9 28 15 52 Mode Standard Deviation

Mia has a conical container filled with chocolates She knows that the volume of the container is equal to one third of the product of the square of the radius of the base of the container and the height of the container Mia measured the height of the container and found it to be 14 centimeters She also measured the radius of the base of the container and found it to be 4 centimeters If Vrepresents the volume of the conical container then which of the following equations can be used to calculate the volume of the container OA 4 4 14 3V 7 SO B 4 3x 14V O C OD 147 4 4

1 point Sarah left Minneapolis heading east on the interstate at a speed of 60 mph Her sister followed her on the same route leaving 3 hours later and driving at a rate of 75 mph How long will it take for Sarah s sister to catch up to Sarah Round to the nearest tenth Time needed to catch up hours help numbers

Find the surface area of this sphere Round to the nearest tenth Formulas for Spheres S A 4nr V nr 7 in in Enter

Students want to investigate this question Is there a relationship between the number of hours high school students spend each week on Facebook and their high school GPA grade point average Which study design is most appropriate Send out a survey to your friends on Facebook Ask them to take the survey and to forward it to their Facebook friends In the survey ask two questions How many hours do you spend on Facebook each week What was your GPA in high school Collect at least 100 responses Divide high school students into two groups Flip a coin to decide who is in each group One group goes onto Facebook for 5 minutes then takes a short quiz The other group just takes the short quiz Go to a local high school and survey students during study hall In the survey ask students to estimate the hours they spend on Facebook each week Obtain the GPA data for these students from the high school counselor

2 Using the following figures determine closing book inventory not all information given may be needed Opening inventory 89 760 Gross purchases 43 620 RTV 860 Cash discounts 320 Markdowns 5 246 Markdown cancellations 318 Employee discounts 784 Gross sales 49 318 Customer returns 2 945 Net markups 760

Francisco needs the three pieces of glass shown below to complete a stained glass window The shapes two triangles and a trapezoid are measured in inches 12 13 12 15 13 9 12 6 15 5 20 Glass can be purchased in rectangular sheets that are 12 inches wide What is the minimum length of a sheet of glass in inches that Francisco must purchase in order to have enough to complete the window

elect the statement that is not equivalent to the following statement It is not true that Snoopy did not dance a jig and Charles Schultz wrote a sonat O If Snoopy did not dance a jig then Charles Schultz did not write a sonata Snoopy danced a jig and Charles Schultz did not write a sonata O Snoopy danced a jig or Charles Schultz did not write a sonata If Charles Schultz wrote a sonata then Snoopy danced a jig

The population of Centerville increases each year The function C t P 1 r represents the population of Centerville at year t where Pis the initial population and ris the rate of increase Select the correct statement O A The factor 1 r is the percentage by which the population grows each year OB The value of C depends only on the starting population and the year C ris less than 0 D Prepresents the population in year 0

Given ABC is bisected by ray BD m ABD 7x 12 and mzDBC 48 2x Statement 1 Ray BD bisects 2 m ABD m DBC Prove m ABD 40 3 m ABD 7x 12 4 m DBC 48 2x 5 7x 12 48 2x 7x 36 2x 7 9x 36 8 x 4 ABC Reason 1 Given 2 Definition of Angle Bisector 3 Given 4 Given 5 Substitution 6 Subtraction Property of Equality 7 Addition Property of Equality 8

4 The volume of the box is 6480 cubic inches What are the lengths of the sides of the squares that are cut out Give the equation to solve this problem Use the expanded form of the volume Get one side equal to zero Divide out any whole number you can from the expression i e A 3 can be factored out so 0 6x 15x 60 so divide both sides by three to get the new equation 0 2x 5x 20 Do this to make it easier to find roots

City water which is slightly chlorinated is being used to flush a tank of heavily chlorinated water The concentration C C t of the chlorine in the tank t hours after flushing begins is given by the following formula C 0 3 2 76e 0 35t C milligrams per gallon a What is the initial concentration of chlorine in the tank mg gal b Express the concentration of chlorine in the tank after 8 hours using functional notation Calculate the concentration of chlorine in the tank after 8 hours Round your answer to two decimal places mg gal

Instruction Find the average rate of change for the scenario below Jenna has a part time job at the ice cream shop She saves 60 every two weeks for a new car Find her rate of change After two weeks she will have I After six weeks she will have Jenna s rate of change is per week