Complex numbers Questions and Answers

the number of a certain type of bacteria y present in a culture is determined by the equation y 3000 2 where x is the number of days the culture has been growing Find the number of baclela fter 5 days After 5 days bacteria will be present

1 Find the derivative for each function below at x 1 Leave your answer in radical a f x 2x 1 x3 b y 3 3x 1

uppose you deposit your graduation cash gifts into an account that pays 4 annual interest compounded continuously If you are 18 when you graduate get 1000 in cash gifts and leave the money in the account until you are 30 how much money will you have Round to the nearest dollar At age 30 I will have S

10 Find all solutions of the equation z 8v2 1 i z2 z 1 0 Write the roots in exponential form and use principal values of their arguments

If the mean of a data set is 24 and the standard dev is 5 What percent of the values fall between 14 and 29 83 9 of the values fall between 19 and What value is 3 standard deviation to the left of the mean

Give the best letter A Nominal B Ordinal C Interval D Ratio Faculty titles like Professor Associate Professor Assistant Professor A variable that asks for birth year

What is the 2 decimal z value for an x value of 20 if the SD 3 and the mean is 22

What is the 2 decimal z value of a student who is 72 tall Part 3 of 3 2 16 X S If a student has a standard height of 2 5 what is their actual 1 decimal height 2 16 6

Part 1 of 3 A class has an average height of 54 with a standard deviation of 4 6 What is the 2 decimal z value of a student who is 49 tall Part 2 of 3 8 10 X What is the 2 decimal z value of a student who is 72 tall

Find each 2 decimal answer for the sample data 5 3 10 2 13 4 17 6 The mean Part 2 of 3 8 25 5 The standard deviation 8 X 0 0 6 8 10 662 0x0 5 6 3 ft mi

Find each for the data 10 16 22 29 33 31 18 26 15 Find Q1 Part 2 of 3 Find Q2 Part 3 of 3 2 16 X X

Part 1 of 3 The population of animals in a zoo was checked each week and the values are blew 121 144 133 155 111 144 153 150 What is the 1 decimal mean value of the population Part 2 of 3 2 16 X What is the 1 decimal population standard deviation of the data 9 10 5 X

What is the percent between 18 and 78 do not put the percent symbol 0 00

Find each quotient Simplify your answers 1 1 1 500 to check 4 58 2 43 55 6 5 3 2 1 121 120

Write an equation for the polynomial graphed below 5 3 2 1 6 5 4 3 2 1 1 2 3 4 5 6 1 2 3 A Preview uit 5

To test for any significant difference in the number of hours between breakdowns for four machines the following data were obtained Machine Machine Machine 1 2 3 6 4 7 9 5 3 7 5 8 4 7 1 9 0 7 7 9 7 10 2 9 4 9 8 10 8 Ho H H H3 H4 Ha H H H3 H4 10 0 9 4 10 1 Ho H H H3 H4 Ha H H H3 H4 8 9 8 4 Machine 4 9 7 12 8 12 0 10 6 11 1 a At the x 0 05 level of significance what is the difference if any in the population mean times among the four machines State the null and alternative hypotheses 11 6 O Ho Not all the population means are equal Ha H H H3 H4 O Ho At least two of the population means are equal Ha At least two of the population means are different Ho M H H3 H4 H Not all the population means are equal Find the value of the test statistic Round your answer to two decimal places Find the p value Round your answer to three decimal places

The table of data lists input output values for a function Complete parts a through c a Is the change in the inputs x the same Select the correct choice below and if necessary fill in the answer box to complete your choice OA Yes and it is equal to OB No X 11 28 96 113

Evaluate each expression show your work A 2c 4 when c 3 B 3 t 8 when t 4 C 43 x 2 when x 5

e From the zeros of the numerator and denominator of R x divide the x axis into intervals Determine where the graph of R is Above or Below the x axis by choosing a number in each interval and evaluating R there In short fill out the chart below and do an Interval Analysis as done in class 12 points Interval Number Chosen Value of f Location of graph Point on graph R x x 8x 12 X 9

What is the range of the function graphed below 3543 1 y 4 D 3 y 3 379199 44 5 B x

MATCH the indicated operation on the left with each simplified expression along the top Each row should contain exactly one check mark 1 7i a 2 3i 3 4 b 2 3i 3 4i c 2 3i 3 4i 2 3i 3 4i d THE 6 i O 5 1 0 24 0 68i 18 000 0 1

6 IG 3 Slape Find the slope of the line through e

Sketch the graph of each line 19 y x 4 43 75 10

2 a Graph the piece wise function For full credit add arrows to the ends that keep going Use a straight edge for x 3 for x 3 f x 2 3 1 a Evaluate f 2 b Evaluate 6 c Evaluate f 10 10 5 104 5 0 5 10 5

5 3 Intercept Form Worksheet 1 Y2 1 3 1 X X S Find the slope of each line 1 SIOR 2 3 1 5 3 573 2 4 Date 2 1 2024 Mr 33 1 3 1 2 y 1 1 x 3 X 12X 3 18th Period yuxur int Slope Farm Equation of Linely y SIOPE 1 X Yo 3 2 0 3 2 4 X Y X Y 313 32 x 0

16 through 0 4 and 1 4

3 2x 4x 2x

Consider the function f x 5 16 2x c What is f 2a d What is the domain of this function

x 5 2x 8 When you square both sides what is the resulting equation in the next step before you solve for x x 52x 8 x 5 x 5 4x 64 X 5 2x 8 2x 8

What is the period of the function f x 10 O5T O cos 10x

A quadratic equation is equal to 0 the constant is 16 the quadratic term s coefficient is 1 the linear term s coefficient is 6 What is are the solutions to the problem C 8 16

The inverse for matrix a b Select one O 1 ad bc c d b 1 ad bc c a d b a ad bcdc d b C a 1 d b

5 Here are three patterns with their first 5 terms listed For each pattern de way to produce each new term from the previous term a Pattern A 5 8 11 14 17 FM 5 F 2 F n f n 1 3 nzz R b Pattern B 1 2 4 8 f 1 1 2 f n f n 1 nzl c Pattern C 0 1 3 6 10 f 2 12 f n f n 1 3 1 b 2

Solve the inequality and graph the solution Write the answer in interval notation 2c 123 or 3c 6 1111 111 6 5 4 3 2 1 0 1 2 3 4 5 6 0 2 U 2 00 6 5 4 3 2 1 2 U 2 00 0 1 31 6 5 4 3 2 1 0 1 2 U 2 00 2 3 4 5 6 E 2 3 4 5 6

Rewrite the following radical function to identify its transformations from the parent graph f x 8x 24 Type a whole number j B The given function is stretched vertically by a factor of 2 from the parent function Type a whole number OC There is no stretch or compression Describe any horizontal translation Select the correct choice below and if necessary fill in the answer box within your choice unit s to the right from the parent function OA The given function is translated Type a whole number OB The given function is translated Type a whole number OC There is no horizontal translation www unit s to the left from the parent function

Helena is trying to write a radical function that is represented by the graph shown here Describe and correct the error Helena made in writing the radical function f x x 1 X Helena did not correctly account for the vertical stretch The correct function is f x vertical translation Ay s O OU

Use the equations represented in the graph to find the point of intersection The point of intersection is Type an ordered pair Type an integer or a simplified fraction 8 12 6 y 10 y 7 VI d

What radical function is represented in the graph f x Simplify your answer 3 Ay 21 1 2 X U

Part 1 of 4 Rewrite the following radical function to identify its transformations from the parent graph f x 8x 8x 8 Rewrite the function so that its transformations can be identified f x GEN

Use exponents to condense the expression below a b b b c C C C C C Answer Attempt 1 out of 2 Type the base then use the a button or use the symbol on your keyboard for the expone Condensed form

Write the function shown in the graph to the right Write the function that describes the graph above Simplify your answer y X C

Use exponents to condense the expression below Answer Attempt 1 out of 2 a c c Show Type the base then use the a button or use the symbol on your keyboard for the expon Condensed form Ta

tiplication to expand the expression below Then compute and or simplify 4c Answer Attempt 1 out of 2 Press the button or type the symbol on your keyboard to represent multiplication Using x for multiplication is inappropriate when x may be used as a variable For the answer type the base then use the a button or type the symbol for an exponent Expanded form

Divide 10 4 511 2 11 Select the correct choice below and fill in any answer boxes in your choice O A 10 4 571 211 11 Simplify your answer Type a whole number fraction or mixed number OB The quotient is undefined

Krisha can pick 4 pounds of coffee beans in an hour or gather 2 pounds of nuts Tom can pick 2 pounds of coffee beans in an hour or gather 4 pounds of nuts Each works 6 hours per day Assume that Tom and Krisha specialize according to their comparative advantage to produce coffee beans and nuts a Suppose that Krisha and Tom could buy or sell coffee beans and nuts in the world market at a price of 2 per pound for coffee beans and 2 per pound for nuts If each person specialized completely in the good for which he or she had a comparative advantage how much could they earn by selling all they produce Tom s earnings plus Krisha s earnings 36 per day b At the prices just described what is the maximum amount of coffee beans Krisha and Tom could buy each day in the world market with the income they earned The maximum amount of nuts Maximum amount of coffee beans that could be bought each day 36 pounds Maximum amount of nuts that could be bought each day 36 pounds wwwwwwwwwww Using the world market and the prices described above would it be possible for Krisha and Tom to consume 40 pounds of nuts and 8 pounds of coffee beans each day Yes c In light of their ability to buy and sell in world markets at the stated prices on the same graph as their PPC show all of the combinations of the two goods it would be possible for them to consume This is also known as their consumption possibilities curve

Use your Transformations Reference Sheet to follow the rules 1 3 5 7 Reflection across the x axis A V 5 4 3 2 2 8 7 6 5 4 3 2 1 D H 2 1 G Reflection across the line x 3 AY G D X 3 4 5 2 Reflection Across the y axis YA X X 2 4 6 8 Reflection across the line y 5 AV Reflection across the line y x AV K 5 4 3 2 41 1 1 3 4 21 Reflection Across Line y x YA X Reflection Across the line x 1 Reflection across the line y 1 YA AV I k 432 4 3 2 1 2 3 4 X X

Consider the expression 7 31 Which statement below is true about the expression A The expression 7 31 is an imaginary number B The expression 7 3i is a complex number where 7 is the real part and 31 is the imaginary part of the expression C The expression 7 31 is a complex number where 3i is the real part and 7 is the imaginary part of the expression D The expression 7 3i is not a number in the set complex numbers

32 Use the table below to evaluate i A 1 B 1 C i D I P 1 P A P i 1 f 1

2 Which of the following numeric expressions is a complex number A 2 B 41 C 5 21 D All of the above