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Mathematics Questions and Answers May 07, 2023

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Consider the set Dof vectors(1,2,3,4)4such that allare integers, and the sum1+2+3+4 is even. Find the non-zero elements ofwhich have minimal distance from the origin. Find inequalities defining the set of elements which are closer to the origin than any non-zero element of (Hint: By the Pythagorean theorem, a vector is on the hyperplane midway
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When you knit something using a pattern, each line of the pattern contains a stitch count. Depending on the weight of the yarn you want to use to make the project, you can use the number of stitches to calculate how much yarn you need to finish your project. The table below -ives the number of inches per stitch for the basic weights of yarn you
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3. An investor with $75,000 is weighing options between a 200-day GIC or two back-to-back 100- day GICs. The 200-day GIC has a posted simple interest rate of 1.4%. The 100-day GICs have a posted simple interest rate of 1.35%. The maturity value of the first 100-day GIC would be reinvested in the second 00-day GIC (assume the same interest rate
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Evaluate the function for the given value of x. f(x) = 5^xwhere x = 1 Evaluate the function for the given value of x f(x)= 2(5^x) where x = 2

5. (L37) Multiply 5 33 3 using fractional exponents

In which of the relations represented by the tables below is the output a function of the input? \f
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58. Which figure can serve as a counterexample to the conjecture below ? If one pair of opposite sides of a quadrilateral is parallel then the quadrilateral is a parallelogram . A ) rectangle B ) rhombus C ) square D ) trapezoid
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2) What are the return and risk characteristics of the Prolndex fund ?" For this analysis calculate the statistics outlined below . Prolndex S& P 500 Average Daily Return Annualized Daily Return Daily Standard Deviation Annualized Standard Deviation Correlation ( D ) Covariance ( D ) Beta ( D ) CAPM R Z ( D ) Sharpe Ratio ( A ) Market Sharpe Ratio
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holly searched for '' fire truck'' on the internet with quotation marks. Martina searched for fire truck without quotation marks. Did they get the same result. Explain.

The store is selling lemons at $0. 52 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make three 9-inch lemon pies, each requiring half a cup of lemon juice? 5C]
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Find the circumference and the area of a circle with radius 7cm. Use the value 3.14 for , and do not round your answers. Be sure to include the correct units in your answers.

I'd like the following questions to be solved as soon as possible. However, give nothing but accurate answers only. 1. Determine the number of possible 3 X 3 affine cipher transformations 2. Determine the size of that is gained after converting at most 448 bits into the subkey arrays through the blowfish algorithm's key. 3. Determine the number of

DILATIONS EXPLORATION Click here to access the GeoGebra exploration. Use the GeoGebra applet to answer questions 1-5. You can adjust the scale factor using the dark green slider. 1. Determine the ratio of CA' to CA. How does this ratio compare to the scale factor? 2. Use the dark green slider to change the scale factor to 3. Determine the ratio of
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If you try to use the spread sheet below to see when exponential growth at 5% catches linear you see that it's still behind at 20 years, which is as far as the table goes. Modify the spread sheet to determine when it catches up. Please help! I am not sure how to come up with the answer! Absolute and Relative Change Linear and Exponential Functions
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A telephone company charges a fixed monthly rate plus a rate per megabyte of data used. The company charges $135 for 100 megabytes of data and $375 for 500 megabytes of data. An equation can be written to show the relationship between the total megabytes used (x) and the total monthly charges (y). Which of the following best describes the steps to

1. The cost of running an assembly line can be modeled by the function, C(x)= 0.3x2 O.9x+ 1.675 , where C(x) is the cost per hour in thousands of dollars and x is the number of items produced per hour in thousands. The most economical production level occurs when 1500 items are produced. Verify this using the appropriate calculations for rate of
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Part B You will now perform the construction of a tangent to a circle using modern tools. Open GeoGebra ; and complete each step below. If you need help, follow these instructions for using GeoGebra. 1, Create a circle with a center at point A with a radius of your choice. 2. Now create a point outside of circle A, and label it point 8. Draw a
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Given 2x2 matrix: (a)Find eigenvector representation of H...find a 2x2 non-singular matrix U, its inverse, and a diagonal matrix D so that H = UDU -1 State U, U 1 and D. Then prove, by explicit matrix multiplication of your solution for U, D and U 1 , that the right-hand side of the foregoing equation is indeed equal to the left-hand side, given

Find the measure of both arc AB and arc APB, where \f
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Hi I need help with questions i got wrong from a study guide. Thank you 1.Jeffrey earned a gross income of $59,860 last year. He made $1,933.07 in student loan interest deductions, donated $3,702 to his favorite charities and paid $2,959.20 in home mortgage interest. Jeffrey claims a standard deduction of $11,400 for himself and his non-working

Please provide solution for each part asap to get a upvote 5. Find the following: a) log.(4) b) log.(1/64)
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What are the benefits of planning open-ended questions during math instruction to encourage students to provide rationales for their answers? How would asking "yes" or "no" questions hinder a student's ability to problem solve in the future? Provide two examples of open-ended questions about a specific math topic.

Problem: 2.49 Two-dimensional, steady-state conduction occurs in a hollow cylindrical solid of thermal conductivity k = 16W/m . K, outer radius r. = Im and overall length 22, = 5m, where the origin of the coordinate system is located at the midpoint of the center line. The inner surface of the cylinder is insulated, and the temperature
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The average cost per hour in dollars of producing x riding lawn mowers is given by the following. 2800 50c): 0.2x2 +21x- 273 + (a) Use a graphing utility to determine the number of riding lawn mowers to produce in order to minimize average cost. (b) What is the minimum average cost
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The circumference of the top rim of the cone-shaped paper cup is 7.12 inches, Find the least amount of paper that can form the cone-shaped cup. (Round your answer to two decimal places.) in3 C= 7.12 in 3.7 in Need Heiple Rain
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1.Identify the non-permissible value(s) for each of the following rational expressions. (xx) a. ( x + 1) ( x - 2) 3 ( x - 2) Answer: b. 10 x 2x - y Answer: c. 3 x 2 + xy - 2 y 2 9x2 - 4y 2 Answer: 2. Simplify the following rational expressions. Identify the non-permissible values. a. 4x2y 3 16 x 3 y Answer: b. 3ab 6a b - 12ab2 2 Answer: c. x 2 + 4

Ten thousand raffle tickets are sold. One first prize of $2000, 4 second prizes of $800 each, and 10 third prizes of $400 each are to be awarded, with all winners selected randomly. If you are given one ticket, what are your expected winnings? A) 92 cents B) 32 cents C) 152 cents D) 116 cents

Simplify your answer

Find the volume of the region in the first octant bounded by the coordinate planes and the planes x+ z =1, y +2 z =2 Set up and evaluate six different triple integrals, each equivalent to the given problem. (That is, by dzdydx, dzdxdy, dydzdx, dydxdz, dxdzdy, dxdydz) You can use a calculator to evaluate the triple integrals. Please show all work

I was asked to send a learning log for math final unit. It will be worth 15% of my final mark. The question went like this: Throughout the course you should have completed 4 submissions for your Learning Log and received feedback on each. This was to help you prepare for this culminating activity. Learning Log Requirements: five (5) entries (it

1. The acceleration of a particle is given by the equation: A 4 xt . If V= 9m / s at t 1 and S = 12m at t=1 sec Find S at t=2 sec Please show all steps in the equations and please write sentences in the explanation so I can better understand

Unit 7 - Activity 1 Homework 1. Calculate the average rate of change for the function g(x)= 4x2 - 5x +1 over each interval. a. 2 S x S 2.5 2. An emergency are is shot into the air. Its height, in meters, above the ground at various times in its ight is given in the following table. mum-m S m a) Determine the average rate of change in the height of
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Solve the problem. The function f(t) = -0.14t2+ 0.5t + 30.2 models the U.S. population in millions, ages 65 and older, where t represents years after 1990. The function g(t) = 0.53t2+ 11.96t + 107.1 models the total yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the functionrepresent? Find(10). Cost

Advance function 1 to 15 (4U) Question 1 (1 point) The graph of a polynomial function will appear to bounce off the xaxis at zeros that are of an even order. Question 2 (1 point) All cubic polynomial inequalities have innitely many solutions. Question 3 (1 point) When performing long division of a polynomial by a linear binomial, the degree of the
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The surface area of the cone is ] 7 square feet, Find the slant height of the co
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There is a 0.84 probability that MATH 23 students will correctly follow all instructions on the Final Exam. What is the probability that exactly 84 of the 100 students taking MATH 23 in a particular term correctly follow all Final Exam instructions? Round answer to the nearest ten thousandth (four places after decimal).

Find an equation of the line that is tangent to the graph of the function f (x) = 11 x and parallel to the line 1 1x + 2y -12= 0 O a, 1 1x + 2y -33= 0 O b. 1 1x + 2y -22=0 Ocox+y-12=0 O d, 6x +2y +6=0 O e. 1 1x +y +33=0
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You are the operations manager of a firm that uses the continuous-review inventory control system (Q system). Suppose the firm operates 52 weeks a year and has the following characteristics for its primary item: Demand = 25,000 units/year = 480 units / week Ordering cost = $30/order Holding cost = $8/unit/year A) Assuming constant demand and
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Midterm Review 3. Consider the following optimization problem for a function f : R2 - R. Minimize f(x) = y where T E n = 3 ER2 y > cos(2) (a Does * = NO satisfy the first-order necessary condition?\f\f\f
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Some one help? 1.3 Mapping from (x,y) to (R,B,G) 1.3.1 Task 1 Find numbers (u, v, w) so that uR+vB+wG=0 (7) Compute s = u + v + w (3) 1.3.2 Task 2 Find the 2 x 2 matrix A which sends I? to the coefcients of its representation as a linear combina- tion of R and B. That is, your matrix should have the following property: when we write X: (Z) =cR+dB
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(b) Passing through (4, 7) and perpendicular to the line whose equation is 2x4y3 = 0. Sketch both lines in the same axes and label it. 2. Determine the equation of each line and write your answer in General form. Then graph of each line. (a) Passing through (-4, 2) and parallel to the line whose equation is 2x - 3y + 7 = 0. Sketch both lines in
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In a random sample of 300 students from the 2001 fall semester there are 128 females and 172 males. What percentage of students in the sample are female?

saved and resumed later. only need the answers.....grade will determine tip Question 1 Find dy/dt. y=t 7 (t 5 - 6) 3 7t 6 (t 5 - 6) 2 (15t 5 - 6) 105t 33 (t 5 - 6) 2 t 6 (t 5 - 6) 2 (22t 5 - 42) t 7 (t 5 - 6) 2 (22t 4 - 42) 4 points Question 2 Write the function in the form y=f(u) and u=g(x). Then find dy/dx as a function of x. y=cot(6x- 6) y=cot

Problem #1: Find the values of a, b, and so that det(A) = ax? + bx +c. x -2 0 A=1|-2 x 2 3 -6 -4 Problem #1: : separate your answers with a comma | Just Save ' | Submit Problem #1 for Grading Problem #1 | Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #2: (a) Find the determinant of the following matrix. 3 0 2 0 2 3 0 -3 A=11 0 4
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Question: 1) Let A = [1 -2 1 1] [-1 2 0 1] [2 -4 1 0] a) Find all solutions of the system A [x y z w] T = [-2 6 -8] T . b) Find rank(A) and the dimension of the null space of A, {X :AX=0}. c) Find basis of row(A), the space spanned by the rows of A. d) Find basis of col(A), the space spanned by the columns of A. e) Find ker(A) ={X :AX=0}. f)Show

domain and range questoins The graph of f(x) = = is reflected about the y-axis and compressed vertically by a factor of -. What is the equation of the new function, g(x)? g ( x) = State the y-intercept of g(x). (x, y ) = State the domain and range of g(x). (Enter your answers using interval notation.) domain range 1) The graph of f(x) = - (4*-2 +
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TRANSFORMATIONS ASSIGNMENT 1. What is the image translation of triangle CAT with coordinates C(6,8), A(0, -4), and T(-1,-4) that is translated by the vector (3,-2)? 2. Point A(4,-3) has an image point of A'(-3,5) after a translation. Describe this translation. 3. Which of the following polygons has 45 degree rotational symmetry? A. Equilateral
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Help please!! on 3: Solving Radical Equations Graphically (12 marks) 4. Solve each equation graphically. Describe the function(s) you graphed and explain how you determined the solution from the graph. a. 2v5x + 32 =7 (5 marks) b. V3x2 - 11= x+ 1 (5 marks) Describe the difference between the roots of a radical equation and the x-intercepts of the
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Exercise 3 Why are the engines of all Russian sea planes so high up? A} To ensure stability whilst flying so lowI over water. H} To prevent water ingestion at the engines. C} To avoid blowing hot air over the wings. D} To keep the nose of the aircraft down and prevent the sea plane flying too high. Exercise 4 Why are helicopters so hard to fly? ["
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If u laid 9 bolts end to end that each measure 7/8 inch, how long would the row of bolts be?

1.... 2... 3... 4.... 5... 6.. 7

To implement INLI algorithm you will implement the following steps. 1. Read a batch of 100 tuples from TRANSACTIONS table as input data into a cursor. The Cursor is a user defined data type in PLSQL which works as a list and is used to store multiple records in memory for processing. 2. Read the cursor tuple by tuple and for each tuple retrieve
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.Given the following conditions for each problem, write an equation for the line in point-slope form, slope-intercept form, and standard form. Then graph the line that you created an equation for. please show all of your work for each problem 1)A line passing through (7,4)and(3,-4) in the graph find Point-Slope Form: Slope-Intercept Form: Standard

One way to describe the housing market is to divide the population of the country by the number of new housing starts. The ratios are listed in the following table for selected years. Answer the following. Year 2002 2007 2011 2013 Ratio 230 190 630 663 a. Find the interval(s) where R is increasing. If the function R is never increasing explain how

Pls help me to solve this TQ 2. Below are the result scores of 30 students in an English class. 67 67 72 68 9 0 71 TI 70 9 5 58 TI 64 (i) Determine the mode and the median of the scores. (4 marks) (ii) Calculate the mean and show the steps to achieve the standard deviation. (6 marks) (iii) Calculate the zscore and the t-score for the highest score
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The URLhttps://i.imgsafe.org/5d79876266.png contains the question. Please answer it, but only if you are certain that you are correct.

2. Determine the values of sin(20) and cos(20) given cose = uil w for 0
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Consider the two savings plans below. Compare the balances in each plan after 15 years. Which person deposited more money in theplan? Which of the two investment strategies isbetter? Yolanda deposits $50 per month in an account with an APR of 4%, while Zach deposits $600 at the end of each year in an account with an APR of 4%. The balance

Battery Wholesale Inc. sells about 4500 units of a particular type of battery a year at a uniform rate. The ordering cost is $120 per order. The annual holding cost is $10 per unit. The company operates 50 weeks a year. Order lead-time is 4 weeks and the standard deviation of weekly demand is 6 units. The company wants to maintain a 95% service
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Evaluate: 2 732,178 + 167 - 542,137 = 732,178 + 167= 732,345 732,178-542,137= 190,208 Answer: 190,208 . Evaluate: 2 26.45 + 4.79 + 120.02 - 3.20 = Type answer here 2. Add and write the fraction or mixed number in its 10 = Type answer here 13. Multiply and write the fraction or mixed number in X 7 = = Type answer here 14. Divide and write the
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When a seesaw is perfectly balanced, each person's distance, "d," from the fulcrum varies inversely as his weight, "w." If a 120-pound person sits 5 feet from the seesaw fulcrum, where must a 150-pound person sit to balance the seesaw?

Below are very challenging questions. Tackle all of them! 1. Determine the truth value given that in order to find the length of a suffix, N_sub = n + log_2(N/N_sub) is used. 2. Determine the number of addresses for a whole organizational network given that the organization is granted the block 130.34.12.64/26. 3. In the question above, determine

Compare the volume of the sphere to the volume of the cylinder The volume of the sphere is one-third the volume of the cylinder The volume of the cylinder is one-third the volume of the sphere. O The volume of the sphere is four-thirds the volume of the cylinder The volume of the cylinder is four-thirds the volume of the sphere. The volumes are
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At age 21, someone sets up an IRA(individual retirementaccount) with an APR of 8%. At the end of each month he deposits $100 in the account. How much will the IRA contain when he retires at age65? Compare that amount to the total deposits made over the time period.

Ryan borrowed $2400 from his parents. His parents have given him a choice of paying $100 in interest or 4% of the borrowed amount. Which should he choose

. Comics Plus has a current production level of 200,000 comics per month. Unit costs at this level are as follows: Direct materials $0.125 Direct labour 0.200 Variable overhead 0.075 Fixed overhead 0.100
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M,l9l -p2 ., Take Home Test 3 3.10 The smallest angle of a right triangle is 9 ' The leg opposite 9 is 2 units in length. The other leg is 3 units in length. (a) Sketch the triangle. (b) USC the inverse tangent function to express 6 in radians: 6 = (C) Express 6 in radians as a decimal accurate to hundredths: 9 = (d) Express 9 in degrees: 9 = (e)

The circumference of the top rim of the cone-shaped paper cup is 7.12 inches. Find the least amount of paper that can form the cone-shaped cup. (Round your answer to two decimal places.) in? C=712 in 3.7 in Need Help? Wissam
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15-11. Joe Levi bought a home in Arlington, Texas, for $140,000. He put down 20% and obtained a mortgage for 30 years at 52%. excel What is Joe's monthly payment? What is the total interest cost of the loan? LU 15-1(2, 3) 15-12. )If in Problem 15-11 the rate of interest is 72%, what is the difference in interest cost? LU 15-1(3) Xcer
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For this report, I was given two options either a histogram or a scatter plot and asked to select the one I believe gives the best visual for the distribution of points for Celtics between 2013-2015 and Bulls 1996-1998. For that reason, I have selected to use a histogram. Along with showing their dispersion histograms show which values are more
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A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program? A) 21 B) 35 C) 2520 D) 16,807

24 . What is missing from the oxygen in this ructural formula that would complete the Joctet in the Lewis structure
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The Fundamental Theorem of Matrix Representations. es and matrices of linear transformations LE zyBooks catalog LENGE ITY 5.7.2: The Fundamental Theorem of Matrix Representations. Jump to level 1 Let T : R2 - R2 be defined by I = 2a1 x1 - 202 . Let u = 121. B- {2. and Given Pc = [-2 3 , use the Fundamental Theorem of Matrix Representations to find
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A bank offers a CD that pays a simple interest rate of 8.5%. How much must you put in this CD now in order to have $1,000 for a home-entertainment center in 5 years? The present value that must be invested to get $1,000 after 5 years at an interest rate of 8.5% is $____________________

A student-faculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers. a. If one person from the group of volunteers is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a student? b. How many ways can the committee of four be formed if

Jocelyn owns perfume shop where she mixes her own brands- "Moonlight" and " sweetness". Moonlight gives her P25 an ounce and Sweetness gives her P16. These two brands are mixed from three ingredients: A, B, and C. Mixing requirements are: A B C Moonlight 0.2 oz 0.3 oz 0.1 oz Sweetness 0.1 oz 0.1 oz 0.4 oz Supply 25 oz 30 oz 54 oz Jocelyn has to

Use the quotient rule to simplify the given expression. StartFraction 4 a Superscript 4 Baseline g Superscript 5 Over 44 a Superscript 4 Baseline g squared EndFraction 4a4g5 44a4g2

"b" varies inversely as the square root of "c". If b = 1 when c = 16, find b when c = 6.

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Solve the equation below by completing the square and select the answer that contains all the solutions. 23. (L42) x 2 + 6x - 2 = 0

ZAP has coordinates Z (1, 5), A (1, 3), and P (2, 4). A translation maps point Z to Z' (1, 1). Find the coordinates of A' and P' under this translation. A' (4, 0); P' (1, 1) A' (3, 1); P' (0, 0) A' (1, 1); P' (4, 0) A' (0, 0); P' (3, 1)

Does the graph represent an efficient network?If it does, explain how you know.If it does not, tell which edges you could eliminate to make it more efficient. \f
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Find the specified domain and express it I. Interval notation.. for f(x)=x^2-1 and bx)=2x+3, what is the domain of {g/f}(x)

A store owner wants to mix cashews and almonds. Cashews cost 2 dollars per pound and almonds cost 5 dollars per pound. He plans to sell 150 pounds of a mixture. How many pounds of each type of nuts should be mixed if the mixture will cost 3 dollars?

6) In question 4, you estimated the time for lowering the surface of Happy Valley enough to account for the modern difference in elevation between the top of Mount Nittany and the bottom of the valley. In question 5, you saw that you could change that estimate a good bit. But, to make a 10-fold change in the estimate, you had to assume things that
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Definition of Reflection Consider the reflection of parallelogram PORS across the line of reflection, WY. If RR' = 14, then RZ = v If SX = 5, then v = 5
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Use the graph to determine a. open intervals on which the function is increasing, if any. b. open intervals on which the function is decreasing, if any. c. open intervals on which the function is constant, if any. 6-5-4-38- a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is
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Plz help. Make sure the answers are correct plz Problem #3: Consider the following matrix. a b A= d e f g h i Suppose that det(A) = 2. Let B be another 3 x 3 matrix (not given here) with det(B) = 3. Find the determinant of each of the following matrices. (a) a+2g -g -2d C=|b+2n -h =2e c+2i -i =2f (b) D=24"1B8T (c) E=-BA? (d) F=adj(B) Problem
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General journal Date Account and Explanation Post Ref. Debit Credit Record transaction entries below ..................... ............. ................ +............. .....................................................................................!! .............................. Record bank reconciliation entries on the next page
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Choose 1 topic You can include some or all of the following in point form: The introduction of your topic and research question Explanation of how you will represent your data (on a graph, chart, etc.) Explanation of how you will mathematically analyze your data (make a regression equation, make a prediction, etc.) Explanation of how you will
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4. [4 pts] Last year, Singh had $20,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 6% simple interest per year. After one year, he received a total of $1280 in interest. How much did he invest in each account
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Basic math discussion question. Please help me answer the discussion question bellow. Thanks DS1 What is the greatest common factor? How do you know when youhave found the greatest one? Why do we learn factoring? In which way factoring helps you in your real life? DS2 What one area from the readings in Week 2 are you most comfortable with? Why do

c. Suppose that over time consumers become more focused on stylistic differences among shoe brands. How would this change in attitudes affect each firm's price elasticity of demand? In the long run, how will this change in demand affect Sleek's price, output, and profits
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Multiply and divide to form a new function, h(x). State the domain. Let f(x) = 2x4 and g(x) = 6x 3. h(x) = f(x) * g(x) 3. __________________________ Domain: _____________________ 4. h(x) = f(x) 4. __________________________ g(x) Domain: _____________________

Hello, can anyone please help me with these math work questions? I would appreciate your help, thank you in advance. Factoring #1-4, 8, 10, 12, 17, 25, 32, 39, 55, 56 only. \f\fFactoring simple trinomials: ax + bx + c, a = 1 1. Factor, if possible. a) x' - 5x + 6 b) y' + 2y- 3 c) m' + 7m - 12 d) a + 6a + 5 e) x'- 9x - 10 () b2 - 76 + 10 g) y' - by
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The function s(t) = 1 17t 4 9\" describes the distance s from the origin at time of an object in rectilinear motion. Find the velocity v of the object at any time . (Use symbolic notation and fractions where needed.) When is the object at rest? (Use symbolic notation and fractions where needed.)
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LOCATION: PATIENT: Outpatient, Hospital Glory Ann Borden SURGEON: DIAGNOSIS: Mohomad Almaz, MD PROCEDURE Right carpal tunnel syndrome PERFORMED: Right carpal tunnel release PROCEDURE: The patient was placed in the supine position on the operating room table, where her right hand and forearm were prepped with Betadine and draped in a sterile
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The URLhttps://i.imgsafe.org/5cb623b46d.png contains the question. Only answer this question if you are certain that you are correct. Thanks!

3. The bookstore at SunTan U had a sale on school t-shirts. Thursday they sold 45 of the marked down t-shirts for a total of $406.50. If the women's shirts were on sale for $9.25 and the men's shirts were on sale for $8.50, how many of each was sold on Thursday? a. [2 pts] Write a system of equations that represents this information. b. [3 pts]
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A television manufacturing firm needs to design an open-topped box with a square base. The box must hold 32 in^3. Find the dimensions of the box that can be built with the minimum amount of materials. Please show ALL work.

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