Complex numbers Questions and Answers

Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true? Removing the outlier will not change the spread of the graph of the data set. Removing the outlier will not change the variance of the data set. Removing the outlier will increase the variance of the data set. Removing the outlier will decrease the spread of the graph of the data set.

Sighting the top of a building, a surveyor measured the angle of elevation to be 27°. The transit (this is the piece of equipment used to measure the angles) is 5 feet above the ground and 325 feet from the building. Find the building's height to the nearest foot.

Zachary completes a hypothesis test and finds that he rejects the null hypothesis. Which statement gives a reason for rejecting the null hypothesis? The z-statistic is less than 0. The z-statistic lies in the critical region. The z-statistic lies outside the critical region. The z-statistic is greater than 0.

A real estate agent is working for a developer who claims that the average commute time to downtown is 20 minutes with a standard deviation of 7 minutes. Stephon is an independent real estate agent and wants to check the times for his client. He took a random sample of 15 commute times and found an average of 26 minutes. He did hypothesis testing using a significance level of 5%. Which conclusion could he make? The z-statistic is 0.22, so the null hypothesis should not be rejected. The z-statistic is 1.69, so the null hypothesis should not be rejected. The z-statistic is 3.32, so the null hypothesis should be rejected. The z-statistic is 3.67, so the null hypothesis should be rejected.

3) Evaluate f F dr, where F = x²i+xyj; C: r(t) = 3 cos ti + 3 sin tj.

Find the slope of the line x = 1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The slope is OB. The slope is undefined. (Type an integer or a simplified fraction.)

The set of solutions to ¹ = √2-√√2i is mi © {e = = * O ri O , e 28 mi 2 17 15 28 mi °{e="₁e₁e¹,e²,e#",e#"} mi : e 28 wi ₁ e ²₁ e ²₂ e ²², Ti mi ,e 15 " > , e 28 wi mi ez " 5 28 15 e 28 ri " mi ²₂ e = ¹²₁ e ²² ³²₁ e ² ^²} mi mi 23 28 > e 22 39 19 28 15 28 23 , e 28 O None of the other options. 31 Ⓒ {et, e#,e,e,e",e", 28 wi 23 28 28 23 ₁₂e™ } e 28 ni ‚e ² } , e 28 55 c#"₁e²"} 28 ○ {e, ei, ei, ei, ei, ei, e m} 15 31 47 28 28 28

Choose TRUE or FALSE for each statement below. (1 point each) 6. An even degree polynomial function whose y-intercept is positive, must have at least two real zeros. 7. A fifth degree polynomial function must have at least one real zero. 8. If 4 is a zero of a polynomial function, then (x + 4) is a factor. 9. The function g(x) = 3x4 + 5 has no real zeros.

6-(-5+5i)-(-5-i) 6-(-5+5i)-(-5-i)=| (Simplify your answer. Type your answer in the form a + bi.)

FLUENCY 1. If f(x)=10sin(x)-3 (1)-√3/2-3 (2) 2 COMMON CORE ALGEBRA II HOMEWORK 2. If f(x)=2x and g(x)= cos(x) then g ¹8 (¹())= ² (1) 1 (2) sin then f(30)=? (3)-¾ mic 3. Which of the following represents a rational number? (1) sin that cos (B)=- E- (3) 0 (3) cos (4) cos 4. When drawn in standard position, an angle 3 has a terminal ray that lies in the third quadrant. It is known 8 Which of the following represents the value of sin (B)? (3) sia 29 5m 15

Use a Laplace transform to solve y' − 3y – 4y = 0, y(0) = 1, y/′ (0) = 5.

Determine algebraically the zeros of f(x) = 3x³ + 21x² + 36x.

Write the number in scientific notation. 0.00000165 0.00000165= (Use the multiplication symbol in the math palette as needed.)

Divide and express the result in standard form. 4 i 9-3 i *** 4 i 9-3i (Simplify your answer. Type your answer in the form a +bi. Use integers or fractions for any numbers in the expression.)

Algebra determine the inverse z-transform of the following sign: z(2z+3) (z+1)(z-2)²

For the polynomial function f(x) = 7 (x²+4)²(x-3)3 answer the following questions. (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of [x].

Identify the intercepts. 6 IN A Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept(s) is/are (0.– 5) (Type an ordered pair. Use a comma to separate answers as needed.) There are no y-intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. B. A. The x-intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no x-intercepts.

(5 points) In a college meal plan you pay a membership fee, then all of your meals are at a fixed price per week. If 30 meals cost $153.5 and 60 meals cost $281, answer the following questions: a) Find C(n), a function for the cost of a meal plan in dollars, where n is the number of meals. C(n) = b) What is the membership fee? $ c) What is the price per meal? $ d) Find the cost for 45 meals. $ e) Determine the maximum number of meals you can buy on a budget of $300. Maximum number of meals implies if you find that n = 3.9, then you can buy a maximum of 3 meals. You must truncate any decimal solutions (which is different from rounding). 11= meals per meal

Evaluate the expression if x = −3, y = 5, and z = −2. (If an answer is undefined, enter UNDEFINED.) x+y+z 4y²x

Find the slope of the line x = 3. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is OB. The slope is undefined. (Type an integer or a simplified fraction.)

Evaluate the expression if x = -2, y = 5, and z = -3. (If an answer is undefined, enter UNDEFINED.) x²y Z

2. Determine the point of intersection for the graphs y = 2(3*) and y = 6(2*). Round your answer to one decimal place. (5 marks)

A child is holding the end of a 31 meter string attached to a kit. The string has an angle of elevation of 71° . Determine the elevation of the kite. Give your answer rounded to the nearest whole number. meters high. The kite is

Solve the equation using any method. 4x² +7=29x The solution set is {}. (Simplify your answer. Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)

Solve the following inequality. 3x + 1 - 3 X (Simplify your answer. Type an integer or a simplified fraction.)

Solve the following equation for z E C (and write z in the form x + jy): (z+j/z-j)3+(z-j/z+j)3 = 0

Solve the formula for the variable h. f=5gh

Divide and express the result in standard form. 5i/ 2-3i 5i/ 2-3i (Simplify your answer. Type your answer in the form a + bi. Use integers or fractions for any numbers in the expression.) =

26.(10 pts.) If the linear system [2a x₁ + X₂ = 1 3a x₁ +6a x₂ = 2 has a unique solution, then determine the values of the parameter ", and then find the solution (express in terms of a).

Fill in the blanks with the appropriate numbers or expressions related to the following equation. V 54 8 V-5 V + 3 v²-2v-15 = a. The restrictions on the variable are smaller number in the first blank.) Type your answer here If not, enter none. Write your response here... and Type your answer here b. When you solve the equation, do you get any extraneous solutions? If so, enter the value of the extraneous solution in the blank. c. The solution set of the equation is Write your response here... (Enter the (Enter the solution set notation. If there is more than one answer, separate the solutions by a comma and list the numbers in order from smallest to largest.)

Let y with respect to x. The following ODE (ysinx+cosx)dx + [(x+y)sinx]dy=0 has the following special integrating factor Isin(x) cot(x)] |csc(x)| None of these

For each polynomial, find all zeros and completely factor over the complex numbers. You can use whatever method you'd like, but show your work. a. g(x) = x³- 3x² + 4x - 12 Show work here: b. f(x) = 4x³-4x² - 7x-2 ZEROS: COMPLETE FACTORIZATION: ZEROS:

Divide and simplify to the form a + bi. 156 i/5+ i

Evaluate the function f(x) = 8x + 5 at the given values of the independent variable and simplify. a. f(-4) b. f(x + 1) c. f(-x)

Divide and express the result in standard form. 7/4-i

Let = (-6, 7, 2) and u = (0.6, 0, 0.8). Compute the vector components of parallel and perpendicular to unit vector u. Enter your answer as vectors using bracket notation, (v₁, v2, v3), and writing compenents as fractions if necessary.

Solve the equation. Enter the solution set in the blank. Write the solutions separated with a comma in order from smallest to largest with no spaces. 2/x = x/4x-6

Subtract. 7-(-6+7i)-(-2-i) 7-(-6+7i)-(-2-i)= (Simplify your answer. Type your answer in the form a + bi.)

Solve and check the linear equation. 4(x-2) +9=3(x+3) What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { B. The solution set is {x|x is a real number}. C. The solution set is Ø.

What is the mass of a piece of copper that displaces 3.0 mL of water and has a density of 9.0 g/cm3? mass = density x volume mass = [?] g Mass (g)

Perform the indicated operation and express the result as a simplified complex number. 3+24i/3

Evaluate 4x + y for x = 1 and y = -25. The result is

Write using exponential notation. 8.8.2.2.2.2 8.8.2.2.2.2 =

Find the exact value of the following trigonometric expression. Do not use any trigonometric functions on a calculator or other technology, as they will not provide you with exact answers. Decimal approximations will be marked wrong. sin [2 arctan (-15/8)

Perform the indicated operation : (-13-7i) + (-28 +24i) -41 +17i -41-17i 41-17i -41 - 18i

Z11²×13² how many quadratic non residues does this have? how many of those are units? and how many are not?

Let a, b, c be nonzero real numbers such that a + b + c = 0 and a³ + b³ + c³ = a³ + b³ + c³. Find the value of a² + b² + c².

Suppose that F = 3t8i+2t j + 2 t² k, G=7sinh(t) i— 2 cos(t)j+5(t+2)2 k. Let (F x G)' = hx (t)i+hy (t)j + hz(t)k. Enter only the expression in t for hæ in the box below using Maple syntax.

Find all distinct roots (real or complex) of z²-2iz+(-22+20i). Enter the roots as a comma-separated list of value of the form a+bi. Use the square root symbol '' where needed to give an exact value for your answer. z =

The zero product property states the following: If a b 0, then either a = Type your answer here or b = Type your answer here