Complex numbers Questions and Answers

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.
Algebra
Complex numbers
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.
Algebra
Complex numbers
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.
Algebra
Complex numbers
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.)
Algebra
Complex numbers
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
Algebra
Complex numbers
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.
Algebra
Complex numbers
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.)
Algebra
Complex numbers
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
Algebra
Complex numbers
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.
Algebra
Complex numbers
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.
Algebra
Complex numbers
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.)
Algebra
Complex numbers
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
Complex numbers
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
Algebra
Complex numbers
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].
Algebra
Complex numbers
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.
Algebra
Complex numbers
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
Algebra
Complex numbers
(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
Algebra
Complex numbers
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.)
Algebra
Complex numbers
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
Algebra
Complex numbers
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)
Algebra
Complex numbers
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
Algebra
Complex numbers
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.)
Algebra
Complex numbers
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.)
Algebra
Complex numbers
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
Algebra
Complex numbers
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
Algebra
Complex numbers
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.)
=
Algebra
Complex numbers
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).
Algebra
Complex numbers
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.)
Algebra
Complex numbers
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
Algebra
Complex numbers
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:
Algebra
Complex numbers
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
Algebra
Complex numbers
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)
Algebra
Complex numbers
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
Algebra
Complex numbers
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.
Algebra
Complex numbers
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
Algebra
Complex numbers
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.)
Algebra
Complex numbers
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.
Algebra
Complex numbers
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)
Algebra
Complex numbers
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
Algebra
Complex numbers
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
Algebra
Complex numbers
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 =
Algebra
Complex numbers
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)
Algebra
Complex numbers
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
Algebra
Complex numbers
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?
Algebra
Complex numbers
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.
Algebra
Complex numbers
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.
Algebra
Complex numbers
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 =
Algebra
Complex numbers
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
Algebra
Complex numbers
The zero product property states the following: If a b 0, then either a = Type your answer here or b = Type your answer here
find the roots of a) Z^8 -16i=0
b) Z^8 +16i=0
Algebra
Complex numbers
find the roots of a) Z^8 -16i=0 b) Z^8 +16i=0
Select all that are True.
The Law of Sines works for most triangles but not for right triangles.
The Law of Cosines works for most triangles but not for right triangles.
The Law of Sines works for all triangles, including right triangles.
The Law of Cosines works for all triangles, including right triangles.
Algebra
Complex numbers
Select all that are True. The Law of Sines works for most triangles but not for right triangles. The Law of Cosines works for most triangles but not for right triangles. The Law of Sines works for all triangles, including right triangles. The Law of Cosines works for all triangles, including right triangles.