23. Show that for any numbern, n andn+1 are coprime.
28. Show that if (a,b)=1 and c divides a, then (c,b)=1.
In: Math
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 7%probability that a nonsmoker will begin smoking a pack or less per day, and a 3% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 6% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)
A) in 1 month
non-smokers --------------------------- people
1 pack/day or less---------------------people
more than 1 pack/day ----------------people
B) in 2 month
non-smokers --------------------------- people
1 pack/day or less---------------------people
more than 1 pack/day ----------------people
C) in 1 year
non-smokers --------------------------- people
1 pack/day or less---------------------people
more than 1 pack/day ----------------people
In: Math
Communication is considered an important component of
mathematics education in order for deep learning to occur.
1. Choose a specific algebra concept (SeeM2.Fractions and
Mixed Numbers or M4.Intro to Algebra in MFL) that you
think you understand well, and explain it in your own words.
2. Then, present a math problem for your classmates to solve,
making use of this concept (the one you selected). Remember
to make your initial post prior to the close of Wednesday of each
week.
In: Math
1. If (1, -1) is an eigenvector of A with associated eigenvalue -2, and (1, 1) is an eigenvector of A with associated eigenvalue 4, then what the entries of A ,a11 , a12, a21 and a22 ?
2. If A has a repeated eigenvalue, the A definitely isn't diagonalizable. (True or False)
In: Math
use the two-phase method and big.M method to solve the LPP: min z=x1-2x2 st: x1+x2>=2 -x1+x2>=1 x2<=3 x1,x2>=0 (two method!)
In: Math
Determine the student's Level of Van Hiele Model of Geometric Thought based on the response given. For example: Is the student at Level 1 (Basic Level): Visualization, Level 2: Analysis, Level 3: Informal Deduction, Level 4: Formal Deduction, or Level 5: Rigor? Explain your decision.
Miss Gonmez gave her students a paper polygon and asked them to identify the given shape and explain how they decided which polygon it was.
James responded that the shape was a rectangle. He decided this because he folded the polygon in half length-wise and found that it had opposite sides the same length.
He compared the corners of the polygon by placing them on top of each other and found they were all the same. He concluded they must all be right angles.
In: Math
A land surveyor places two stakes 500 ft apart. He locates the midpoint between the two stakes and creates a perpendicular to the line that connects these two stakes. He needs to place a third stake 100 ft away along this perpendicular line. To apply the Perpendicular Bisector Theorem, the land surveyor would need to identify
the location of the third stake as equidistant from the original two stakes
the location of the third stake as closer to one of the original two stakes
a line parallel to the line connecting the two stakes
a line congruent to the line connecting the two stakes
In: Math
Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $3.00. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day. Because of a backlog of orders for model A grates, Kane's manager had decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit?
In: Math
How many 5-card hands have at least one pair?
In: Math
Chloe is buying souvenirs on vacation. She wants to spend 70 dollars at most, but only has 60 cubic inches of space available in her luggage. If bracelets cost 7 dollars and take up 3 inches of space and t-shirts are 5 dollars but take 15 inches of space, write and graph a system of four inequalities that model Chloe's possible purchases.Let x=the number of bracelets and y=the number of t-shirts. Use a scale of 2 on both axes.
So my inequalities are as follows: x >= 0
y >= 0
7x+5y<=70
3x+15y<=60
Can you please check if my inequalities are correct and show me how to graph them? Thanks!
In: Math
a) For the following polynomial; a. Use the Rational Zero Test to list all possible rational roots b. Use Descartes Rule of Signs to provide the possible numbers of positive and negative real roots c. Factor the polynomial completely. ? 3 + 4? 2 + 9? + 36
b) For the following polynomial; d. Use the Rational Zero Test to list all possible rational roots e. Use Descartes Rule of Signs to provide the possible numbers of positive and negative real roots f. Factor the polynomial completely. ? 4 + 3? 3 − 7? 2 − 27? − 18
In: Math
75 million people died in World War 2 spread over 6 years. Right now in the World 13 000 people have died due to the pandemic. If the doubling time is 5 days (many people think it will decrease to 3 days) how long before the death toll will be greater than World War 2?
In: Math
For the following exercises, assume α is opposite side a,β is opposite side b, and γ is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth.
1) α=119°,a=14,b=26
2) a=7, c=9, α= 43°
In: Math
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (-2,-5) and parallel to the line whose equation is y=-4x+2
In: Math
There are 2 different catalogs sent to customers. One of the catalogs costs 50 cents to make and is 50 pages long. The conversion rate for the catalog is 5% and each customer brings in 315 dollars. The second catalog costs 95 cents to make, is 100 pages long and each customer brings in 300 dollars from it. The profit margin is 30%. What should the conversion rate for the second catalog be to make at least the same amount of profit as the first one.
In: Math