Algebra Questions

Write the fraction as a terminating or repeating decimal 6 7 Choose the correct answer below OA 0 85714 OB 0 857142 OC 0 857142 OD 0 85714

Write the fraction as a decimal 6100 8

Find the prime factorization of the following number Write any repeated factors using exponents 392 The prime factorization of 392 is

Write the following fraction in lowest terms 10 77 Select the correct choice below and if necessary fill in the answ O A 10 The fraction written in lowest terms is 77 Type an integer or a simplified fraction OB The fraction 10 77 is already in lowest terms

Replace the with the correct symbol 59 6 11 6 11

Round the given number to the nearest hundredth 518 006 518 006 rounded to the nearest hundredth is

7 Write as a decimal 10 7 10 11

Write the fraction as a decimal 6 8 9

Rewrite the fraction 10 1 with 15 as the denominator 3

ill in the blank AAY AXD XAY XXD

Solve for y in the equation below Round your answer to the nearest hundredth Do not round any intermediate computations 9 6 11

A T ra y Rn Let x ER a ER and A Rnxn be a real symmetric positive semidefinite matrix Let B Prove that if B0 positive semidefinite then xe Range A noting that Range A Ac for c ER I

Consider a spiral curve C in the zy plane with parametrization r t cost sin t i cost sint j 0 1 7 2 a Use MATLAB to plot the curve b Find the work done by the force field F x y x y 1 i in moving a particle alon

vo angles are complementary angles if the sum of th solving the following system of equations A B 90 A 38 3B

3 When riding on a Ferris wheel your height h in meters above the ground in terms of time t in seconds can be represented by the graph shown below 15 Th 10 50 100 125 150 175 a Determine the diameter of the Ferris wheel b Determine the height of the center of the Ferris wheel c Determine a sine function and cosine modeled by this sketch show calculations 200 225 1 1 3 EN 1

12 Sketch period graphs to satisfy the given properties Shape 45 Period 135 1 Amplitude Equation of Axis 225 315 405 y 1 y 3 State the period amplitude and the equation of the axis for the given function Number of Cycles 2

Find the vector parametric equations for the line in the direction of the vector 7 7 5 and through the point 4 3 2 F t 1

The revenue R from the number of sales x of a certain videogame is described by the function R x 0 14x 420x

Find the dimension of the subspace spanned by the given vectors 1 2 3 5 9 4 14 7 3 11 The dimension of the subspace spanned by the given vectors is

a During Week 0 how many more specialty items were produced at the old factory than at the new factory Explain b Find and compare the growth rates in the weekly number of specialty items produced at each factory Show your work c When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory Explain

3 The function p w 230 1 1 represents the number of specialty items produced at the old factory w weeks after a change in management The graph represents the number of specialty items produced at the new factory during the same time period Number of specialty items 600 550 500 450 400 350 300 250 200 150 100 50 0 y 2 252 0 190 1 New Factory 4 337 1 220 2 B 7 505 6 440 3 290 5 380 6 8 X

1 Approximately plot the locus of roots using the basic rules 2 Describe in detail the application of the basic rules

When Hakeem runs the 400 meter dash his finishing times are normally distributed with a mean of 70 seconds and a standard deviation of 2 seconds Using the empirical rule determine the interval of times that represents the middle 68 of his finishing times in the 400 meter race

Write the letter of the statement in the Agree or Disagree column Explain why you put it there and justify your answer mathematically A radar is used to measure speeds of cars on Interstate 85 The speeds are normally distributed with a mean of 75 mi hr and a standard deviation of 5 mi hr What approximations can be made about the drivers on 1852 A 50 of drivers drive 75 mi hr or less on 185 C If you drive 69 mph you are in the 16th percentile E 50 of drivers are between 72 and 78 miles per hour Agree B 80 of drivers drive between 65 and 80 miles per hour D Only 0 47 of drivers are going faster than 88 mi hr F If an officer only pulls over the top 5 of speeders they will pull over everyone going 83 mph or higher Disagree

Given 3 unique non zero vectors in 2 space a b c what does the calculation a X b Xc determine O a Coplanar O b None of the other answers are correct Oc Parallel O d Orthogonal O e Area of a parallelpiped

not to scale Solve the triangle round to the nearest tenth drawing 24 a C C 36 16

11 Ms Warden needs 20 000 to go on her dream vacation in four years How much does she need to invest now in an account earning 8 5 annual interest compounded semi annually 3

1 Each of the following equations establishes a linear relationship between M and t i 2 81 10 t 1 10 10 M 4 14 10 M 3 14 ii 3 11 10 M t iii aM yt 3t c a y c 0 For each of the equations above identify the gradient and M intercept of the linear relationships

35 3 points Extra Credit The values below in column A list the weight in pounds of 10 different cars made in 2022 The values in column B are the corresponding gas mileage of each car Car Weight in lbs Car MPG 4000 2567 3945 3300 2140 4010 2565 3450 2900 3345 272272282 23 19 20 43 34 25 Develop a linear programming graph on your calculations file with the regression model and r squared value and answer Based on the LP that you have developed what does the graph tell us about the general relationship between these two variables Car weight and Car MPG As the weight of the car goes up the car s MPG goes up direct relationship As the weight of the car goes down the car s MPG goes up positive relationship As the weight of the car goes down the car s MPG goes down negative relationship As the weight of the car goes up the car s MPG goes down inverse relationship

b State the transformations and write the equation of the transformed cubic function Transformations reflec harizantel 1 0 to M 6 5 4 3 10 0 8 0 2 34 4 5 6 7 8 N 1 2 Hver Vest Crimso Equation Explain how you got the numbers for your equation Two possible correct equations can be written for the above transformed cubic function Why are there two possible equations for this function t JOT L

Which of the given subsets of R are subspaces a The set of all a a a2 a3 where a a 1 b a b c a 0 b 0 c x y z x 0 and y 0 d a b c a 0 and b c The sets in c and d The sets in a and b The sets in a and c O d The sets in b and d a O b C

The first step to determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I was to rotate the first rectangle 90 degrees clockwise about the origin What is the next step

Evaluate and write in lowest terms if necessary 5 17 24 2 6 10 LO 5 17 24

Evaluate and write in lowest terms 2 3 2 3 11 2 12 1 2 Type an integer or a simplified fraction

4 2 5 2 4 2 5 2 Type Type an integer or a decimal

f x h f x h 0 when f x 2x 4x 4 h C 2x 4 2h D 2x 4 2h E 4x 4 9 Simplify the difference quotient A 4x 4 2h B 4x 4 2h

Find the following difference and write it in lowest terms 7 16 7 1 16 16 1 16 Type an integer or a simplified fraction

5 45 6 5 operat 5 45 6 5 Type an integer Type an integer or a decimal

Perform the indicated operation 26 2 17 14 26 2 17 14

Perform the indicated operation 1 3 4 9 1 3 4 9

Perform the indicated operation 30 7 1 30 7 1 Type an integer or a decimal

Find the difference and write in lowest terms 33 10 33 10 33 6 33 Type an integer or a simplified fraction

Find the following sum and write it in lowest terms 21 1 8 9 2 2 21 8 Type an integer or a simplified fraction

12 Why is 0 6 a rational number

Find the difference and write in lowest terms 5 1 5 4

Evaluate and write in lowest terms if necessary 11 1 11 6 15 11 6 11 4 15 Type an integer or a simplified fraction

Find the quotient and write in lowest terms if necessary 23 2 3 3 3 3 Type an integer or a simplified fraction

Find the reciprocal of the rational number 2 The reciprocal of 2 is Type an integer or a simplified fraction

write each statement using the appropriate mathematical language 8 Even numbers are in the set of integers

The graph of h is shown 14 13 12 11 10 9 8 7 6 5 4 3 2 1 In interval notation the domain of his In interval notation the range of his 16 5 4 32 24 1234 a