Questions

Write v as a linear combination of u and w if possible where u 3 2 and w 3 1 Enter your answer in terms of u and w If not possible enter IMPOSSIBLE V 6 1 V

4 g x 5 at x 4 X

Factor the following perfect square trinomial 0 Gm 1

Factor the following perfect square trinomial 2 9x 6x 1

2 The density of water is 997 kg m Convert the density of water to units of pounds per cubic foot lb ft Show your work and make sure your final answer has appropriate units U 03 U 04 U 05 U 13

An open box is made from a square piece material with sides 3 feet by 3 feet by cutting equal squares from each corner Find the dimension of the box of maximum volume draw a diagram

Which of the trinomials below is a perfect square of a binomial Select the correct answer below Ox 12x 9 9x 6x 1 O4x 16x 2 x 6x 4 x 4x 16 BART

As a surveyor you are responsible for subdividing regular and irregular shaped lots into areas of equal size Your services have been requested by a family that needs to divide a trapezoidal lot Here are the details of your task The lot has bases measuring 60m and 35m The perpendicular depth of the lot is 110m The lot is to be subdivided into two equal lots by a line parallel to the bases Given this information find the distance from the 60m base to the line parallel to both bases 1 Draw an accurate representation of the information provided included all the 3 points given measurements and any variables you need In the space below show all work used to solve the problem 7 points

Factor the following

If the r value or correlation coefficient of a data set is 0 908 what is the coefficient of determination to three decimal places O A 0 908 OB 0 924 OC 0 824 OD 0 808

which one of the follwoing is a valid and correct method overloading A public int sum int a int b public int sum int a int b B public double sum int a int b public int sum int a int b C I public int sum int a int b int c public int sum int a int b D public static void sum int a public int sum int a double b

In at x 0 2

Which statement about residual plots is not true A If there is an obvious pattern the model is probably reasonab OB The x axis appears in the middle of the graph C The sum of the residuals is 0 OD The vertical axis shows residuals

Given the table of values of x and y find the slope and the y value of the y intercept X 2 6 11 y 20 40 65 a Slope b y intercept

Instructions Write your answers neatly on blank sheet s of paper and upload your solutions to Grade scope You may also write your solutions on a tablet When submitting to Gradescope you must indicate where each question appears in your solution If you do not have a solution to a question then write no solution for that question on your paper Leave all final numerical answers exact unless otherwise specified Show your steps work Box or circle your final answer 1 Suppose A is an m x n matrix such that the equation AF 6 has a solution for every bRm a If m n what if anything can you determine about the linear dependence independence of the columns of A b If m n what if anything can you determine about the linear dependence independence of the columns of A c Is it possible that m n You must justify each answer you may use theorems stated in class 2 Suppose a linear transformation T R2 R satisfies Determine T ED T H B and T 2

Choose the correct logarithmic forms for the following equations a 54 625 o log 4 5 625 o log 4 625 5 o log 625 4 o log 5 625 4 b 6 216 O log 216 3 O log6 216 3 o log 3 216 6 o log 3 6 216

16 Use the table to the right to find the equation of the tangent line of the function r x 0 5f x 3g x at x 2 X f x f x g x 2 12 2 4 4 10 1 15

x tan cos x at x 1

Evaluate 8 log 4 64 7

What does it mean to say that a data point has a residual of 1 OA The x coordinate of the point is 1 OB The point lies 1 unit below the regression line OC The point lies 1 unit above the regression line OD The point lies directly on the regression line

Divide the polynomial 49 x by 7 x Reduce your answer to lowest terms 0 7 x 07 x 0 14 x

a A 5 20 O Quadrant I O Quadrant II O Quadrant III O Quadrant IV b B 3 12 O Quadrant I O Quadrant II O Quadrant III O Quadrant IV c C 6 12 O Quadrant I O Quadrant II O Quadrant III O Quadrant IV

Solve the system of equations by using either the Substitution or the Elimination method X 8 y 0 0 8x 0 2y 0 9 0 6x 0 4y 0 4

The perimeter and area of an envelope are known to be 68 cm and 64cm respectively We can find the dimensions by solving the equation x 34x 64 0 Factored the left side of this equation gives O x4 x 16 O x 2 x 17 O x 2 x 32

Factor fully 9x 121 0 3x 11 3x 11 O 3x 11 3x 11 O 3 11x 3 11x

Solve for x by rewriting in exponential form log 14 x 2 x

A regression line was calcul measure the height of a plant in inches over time in days The residual plots for each set are shown Based on the residuals which data set is best fit by the regression line A y 10 HA O A Data set A B Data set B OC Data set C 10 y C 10 y B

2m 12x 30 0 is

Express the following expression as a single natural logarithm Choose the correct answer 2 ln 2 3 ln 3 2 In 5 O 0 In 3 Oln 07 O In In 108 25 31 25

Determine expression is simplified P 9 m n the coefficients p and q and exponents m and n when the following III 3 4x3 5y5 Pxm qy

Simplify the expression x y 6 x 4 What s the sum of the coefficients of x and x

Factor fully 32x y 56x y O x4y 32y 56x O 8x4y 4x 7y O 8x4y 4y 7x 08 4x4y 7x5y

Simplify the algebraic expression Ex 6 x 5 2x 18

The residuals for data set A and data set B were calculated and plotted on separate residual plots If the residuals for data set A do not form a pattern and the residuals for data set B form a pattern what can be concluded O A Data set A is not linear and data set B is not linear OB Data set A is not linear and data set B is linear C Data set A is linear and data set B is not linear D Data set A is linear and data set B is linear

for crop B costs 20 per acre The farmer can spend at most 800 on seed If crop B brings in a profit of 90 per acre and crop A brings in a profit of 160 per acre how many acres of each crop should the farmer plant to maximize her profit acres of crop A

Veterinarians use different medications to treat fleas in dogs Once administered the medication typically decays exponentially One treatment decays by half each week A dog receives 4 mL of medication and the function f gives the number of mL of medicine left after w weeks 1 Find the amount of medication in the dog s bloodstream 1 week 2 weeks and 3 weeks after it is administered 2 Write an expression to represent the amount of medication in its bloodstream 1 day after it is administered 3 Explain what f means in this context

Determine whether the points are coplanar 1 3 7 1 3 7 1 3 7 1 3 7 coplanar O not coplanar

What is the value of 2 for the following data to three decimal places OA 0 930 OB 0 659 OC 0 964 OD 0 852 X 1 2 5 y 2 4 7 7 10 10 20

0 y 36 y 8y 12 y 2x 35 y 9y 14

x 1 x 5 x 3 x 6x 5

9 11a 24 6a 18 3a 15 a 6a 1

x 3 x 2 6x 7 x 2 x 1

8 6 x 3 4x 11 x 9

4x x 2 x 3 x 2

x 1 x 1 2 x x

4 2 x 3 5x 7 x 3

3 7x 8 2 x 5 3x 2 2 x 5

1 a 9 4a 3 6a 4a 3

6 Sy 2y 1 y 3 2 1

y 2 y 2 3 y 2