The product of the complex number z₁ = 7(cos15° + isin15°) and z₂ = 2(cos110°+isin110°) is z₁z₂ = 14(cos(125) + isin(125)]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
z₁ = 7(cos15° + isin15°) and z₂ = 2(cos110°+isin110°)
z₁z₂ = (7 * 2)[cos(15 + 110) + isin(15 + 110)]
z₁z₂ = 14(cos(125) + isin(125)]
The product of the complex number z₁ = 7(cos15° + isin15°) and z₂ = 2(cos110°+isin110°) is z₁z₂ = 14(cos(125) + isin(125)]
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An employer wants to determine the amount of job satisfaction experienced by his employees. Which sampling
method is most likely to result in undercoverage?
Answer:
C: Employees are assigned to one of four pay scales. Randomly select a pay scale and survey every employee in that pay scale
Step-by-step explanation:
Looking at the given options, the one that will likely result in undercoverage will be option C. This is because even after assigning employees to any of the 4 payscales, when randomly selecting for survey, he picked only one pay scale and surveyed every on there. Since he didn't include at least one person in the other pay scales, he will not have covered every pay scale which he will need to make a conclusion on job satisfaction experienced by his employees.
If the similarity ratio of two similar solids is 3 : 13, what is the ratio of their
corresponding areas? What is the ratio of their corresponding volumes?
Answer:
Below in bold.
Step-by-step explanation:
Ratio of areas is 3^2 : 13^2
= 9 : 169.
Ratio of volumes = 3^3 : 13^3
= 27 : 2197.
Give an example of tangents in the real world that have not been presented in this lesson.
Explain how you know the tangent and the radius in your example are perpendicular.
This is in relation to tangent lines and not cosine, sine, etc!
My example is attached via photo!
Answer:
Hey! Sorry im too late lol but here-
Step-by-step explanation:
Example of tangent in the real world-
When a stone gets tied at one end of a string & the other end is rotated, then the stone will form a circle.
How you know the tangent and radius are perpendicular:
The radius is formed vertically and is completely straight, while the tangent is completely straight but horizontal. You can draw a right triangle angle between the radius and tangent line by adding a third line, and a right angle is 90 degrees. So, this forms a perpendicular line.
Hope this helped :))
Part A: The path of the ball in relation to the curved path of the thrower
Part A: The path the ball takes is perpendicular to the hand, bat or feet at the point of last contact
Reason for the selection:
Part A
A real world example of tangents is the direction of a ball immediately it is released and the circular path of the motion, that provides the force input that is given to the ball to cause it to move in the required direction
The tangent is the path the ball takes immediately it is moving without contact to the bat, hand or feet that causes it to move
The circular path is the motion of the hand, leg, bat or feet that makes before the ball is released
The radius is the hand, leg, or bat that rotates in a circular path, so as to move the ball
Part B
How the radius is perpendicular to the tangent
The radius, such as the leg kicking a ball is perpendicular to the tangent of the which is the path of the ball because a kick to send the ball into air, the orientation of leg at the point the ball leaves is perpendicular to the angle of elevation with which the ball is launched
Learn more about tangents here:
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A graph of a linear equation passes through (-2,0) and (0,-6).
Is 3x - y = -6 an equation for this graph?
Select one:
Yes
No
Out of a group of 120 students that were surveyed about winter sports 28 said they ski 53 said they snowboard Sixteen of the students who said they ski said the also snowboard. If a student is chosen at random P ( snowboard I ski)
Answer:
P ( snowboard I ski) = 0.5714
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Ski
Event B: Snowboard.
28 out of 120 students ski:
This means that [tex]P(A) = \frac{28}{120} = 0.2333[/tex]
16 out of 120 do both:
This means that [tex]P(A \cap B) = \frac{16}{120} = 0.1333[/tex]
P ( snowboard I ski)
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1333}{0.2333} = 0.5714[/tex]
So
P ( snowboard I ski) = 0.5714
An object is launched at 24.5 meters per second from a platform that is 68.6 meters tall. The equation for the object's height in meters, h, at t seconds after the launch is shown below.
h =-4.9t2 + 24.5t + 68.6
Find the length of Arc YWV, if line XZ=12 meters. (Round to the nearest hundredth)
Answer:
53.62 m
Step-by-step explanation:
Length of arc = θ/360 × 2πr
r = XZ = 12 m
m<XYZ = 180 - 108 = 72° (angles on a straight line)
θ = 85° + 72° + 108° = 265°
Length of arc YWV = 256/360 × 2 × π × 12
= 53.6165146 ≈ 53.62 m (nearest hundredth)
Tropical islands have many rainstorms during the afternoon heat. One particular tropical island has a 79% chance of a rainstorm on any given afternoon. Abraham is planning a weeklong stay on this tropical island. Let X represent the number of days there is an afternoon tropical storm that week. What are the mean and standard deviation of X?
Mu Subscript x Baseline = 1.47, Sigma Subscript x Baseline = 1.16
Mu Subscript x Baseline = 3.5, Sigma Subscript x Baseline = 1.16
Mu Subscript x Baseline = 5.53, Sigma Subscript x Baseline = 1.08
Mu Subscript x Baseline = 7, Sigma Subscript x Baseline = 3.5
the fact is you cant copy and paste it you have to take screenshot or picture and attach it i don't understand the the computers substitution for unknown characters
Answer:
3.5, 1.16
Step-by-step explanation:
if the digit in one’s place of a number is 2 then the last digit of its cube will be?
Answer:
Thus , if the digit in one's place of a number is 2, then the last digit of its cube will be unit digit of . Since the last digit of cube of 2 is 8. Hence, if the digit in one's place of a number is 2, then the last digit of its cube will be 8
Step-by-step explanation:
Which function is shown in the table below?
(1) f(x) = 3x
(2) f(x) = x+3
(3) f(x) = -x^3
(4) f(x) = 3^x
Answer:
4. f(x)=[tex]3^{x}[/tex]
Step-by-step explanation:
Sorry if I'm wrong
Find the circumference of a circle that has a diameter of 26 ft. (Round to the nearest hundredth)
Your answer
Answer:
C = 81.69 ft
Step-by-step explanation:
Given the following data;
Diameter = 26 ft
To find the circumference of a circle;
Mathematically, the circumference of a circle is given by the formula;
Circumference of circle, C = πd
Where;
d represents the diameter of the circle.
Substituting into the formula, we have;
C = 3.142 * 26
C = 81.69 ft
From a bag containing 6 white balls, 3 black balls and 13 red balls, two balls are drawn at random. What is the probability that they are both red without replacement?
a) 26/77
b) 9/10
c) 1/2
d)5/77
Answer:
Probability [Both ball red without replacement] = 26 / 77
Step-by-step explanation:
Given:
Number of white ball in beg = 6 balls
Number of black ball in beg = 3 balls
Number of red ball in beg = 13 balls
Find:
Probability [Both ball red without replacement]
Computation:
Probability of first red ball = Number of red ball in beg / [Total balls in beg]
Probability of first red ball = 13 / [6 + 3 + 13]
Probability of first red ball = 13 / 22
Probability of Second red ball = Number of remaining red ball in beg / [Total balls in beg without replacement]
Probability of Second red ball = [13 - 1] / [6 + 3 + 12]
Probability of Second red ball = 12 / 21
Probability [Both ball red without replacement] = [Probability of first red ball][Probability of Second red ball]
Probability [Both ball red without replacement] = [13/22][12/21]
Probability [Both ball red without replacement] = 26 / 77
Help with this problem pls
Based on the figure below, find the value of x.
Answer:
The value of x = 9.Step-by-step explanation:
The figure shown is represented as a right triangle, which means that the sum of the angles within should add up to 90°. So if we take 32° (one of the angles given) and subtract it from 90°, we should be left with 58°.
This means that the value of the equation that contains "x" must equal 58°. Therefore, (6 x 9 + 4)° must equal 58.° Which means that the value of x = 9.
How many sixths are equal to 4/12? Write an equation to show.
Answer:
2/6
Step-by-step explanation:
divide 4/12 by two(top and bottom) to get 2/6. or multiple 2/6 by two (top and bottom) to get 4/12.
A room is 15 feet tall. An architect wants to include a window that is 6 feet tall. The distance between the floor and the bottom of the window is b feet. The distance between the ceiling and the top of the window is a feet.
This relationship can be described by the equation
a
=
15
−
(
b
+
6
)
a=15−(b+6).
The customer wants the window to have 5 feet of space above it. Is the customer describing a or b? What is the value of the other variable?
Answer:
2.5 feeeeeeeeeeeeeeeeeeeet i think
5 A circle has a radius of 12 in. Find an exact value for each measurement. (Hint: Use arc length formula to find angle)
a) an arc length with a central angle of 90°:
b) the area of a sector with a central angle of 90°:
Answer:
[tex](a)\ L = 18.84[/tex] --- arc length
[tex](b)\ A = 113.04[/tex] --- sector area
Step-by-step explanation:
Given
[tex]r = 12[/tex]
[tex]\theta = 90[/tex]
Solving (a): The arc length
This is calculated using:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{90}{360} * 2* 3.14 * 12[/tex]
[tex]L = 0.25* 2* 3.14 * 12[/tex]
[tex]L = 18.84[/tex]
Solving (b): The sector area
This is calculated using:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
So, we have:
[tex]A = \frac{90}{360} * 3.14 * 12^2[/tex]
[tex]A = 0.25 * 3.14 * 12^2[/tex]
[tex]A = 113.04[/tex]
Find the volume of this cone
Answer:
[tex]\frac{6400\pi}{3}\approx 6702.06\:\mathrm{cm^3}[/tex]
Step-by-step explanation:
The volume of a cone is given by [tex]V=\frac{1}{3}\cdot r^2\pi\cdot h[/tex].
In this specific cone, the entire height of the cone is not given. However, we do see that it is broken up into two separate cones. Since one cone is inside/part of the other, these cones must be similar. Therefore, we can set up the following proportion to find the height of the smaller cone.
Let [tex]h_s[/tex] be the height of the small cone:
[tex]\frac{5}{h_s}=\frac{20}{12+h_s},\\\\20h_s=5(12+h_s),\\\\20h_s=60+5h_s,\\\\15h_s=60,\\\\h_s=4[/tex]
Therefore, the height of the largest cone is [tex]12+4=16[/tex]. Now we have all necessary information to find the volume of the cone:
[tex]V=\frac{1}{3}\cdot 16\cdot 20^2\cdot \pi =\frac{6400\pi}{3}\approx \boxed{6702.06\:\mathrm{cm^3}}[/tex]
HELPPPPPP?????????????????,,,,,,,????
Answer:
280 is the correct answer
Step-by-step explanation:
5 x 8 = 40
40 / 2 = 20
20 x 14 = 280
Can someone please help me please!!!!!!
Answer:
the graph one is G and the second one is C hope this helps
The map at the right has an Euler Path in which you can pass through each doorway exactly once. Which 2 rooms must be a starting or ending
to the Euler path?
Answer choice.
a) Room A and the Outside
b) Room A and Room D
c) Room B and Room D
d) Room E and the Outside
Answer:I think the answer is d
Step-by-step explanation:
Find the area of the composite figure shown below.
A. 12 cm2
B. 36 cm2
C. 24 cm2
D. 18 cm2
Two cylinders are shown below. Find the volume of each cylinder. Use 3.14 for T. Round your answers to the nearest hundredth.
12 cm
4 cm
8 cm
..10.000.-
A
B
Cylinder A:
cm
Cylinder B:
cm3
Answer:
[tex]volume \ of \ cylinder = \pi r^2 h[/tex]
[tex]volume (A) = 3.14 \times 4 \times 4 \times 12 = 602.88 cm^3\\\\volume (B) = 3.14 \times 10 \times 10 \times 8 = 2512 cm^3[/tex]
I need the answer. Please help
Answer:
C = 25
a = 10.72
b = 11.83
Step-by-step explanation:
The easiest thing to solve for right now is C- all angles in a triangle add up to 180 degrees. So we can subtract 65 and 90 from 180 to get the measure of angle C, 25 degrees.
Then we can use trigonometric functions: SOH CAH TOA
sinC = opposite / hypotenuse
sin25 = 5 /hyp
5/sin25 = hyp
hyp (aka b) = 11.83
cosC = adjacent / hypotenus
cos25 = a/11.83
11.83*cos25 = a
a = 10.72
C = 25
a = 10.72
b = 11.83
One positive number is one-fifth of another number the difference between the two numbers is 180 find the numbers
9514 1404 393
Answer:
45 and 225
Step-by-step explanation:
Let x represent the larger number. Then ...
x - 1/5x = 180
x = 5/4(180) = 225
1/5x = 45
The two numbers are 45 and 225.
Read the excerpt from Lizzie Bright and the Buckminster Boy.
[Mr. Stonecrop] draped his arm around Turner's shoulders and drew him in, into his strength and power and presence. Turner felt as if he were moving in close to a mountain. But when he looked up into Mr. Stonecrop's face, he shuddered. Mr. Stonecrop was laughing, and his mouth was pulled into a grin, but his eyes were as dead as marbles, almost as if there were nothing behind them. He was like someone out of a ghost story, and Turner tried to draw away.
In this excerpt, Mr. Stonecrop is compared to a mountain. How does this description relate to Mr Stonecrop’s role in the main conflict of the story?
Mr. Stonecrop, like a mountain, is a fair and wise man whom others look up to for leadership about Malaga Island.
Mr. Stonecrop, like a mountain, is intimidating and strongly holds his position against the people of Malaga Island.
Mr. Stonecrop, like a mountain, changes with the seasons, and he changes his mind about the people of Malaga Island.
Mr. Stonecrop, like a mountain, is an elderly man who lets others decide what is best in reference to Malaga Island.
Answer:
C-:
Mr. Stonecrop, like a mountain, is intimidating and strongly holds his position against the people of Malaga Island.
Step-by-step explanation:
Answer:
B- "Mr. Stonecrop, like a mountain, is intimidating and strongly holds his position against the people of Malaga Island."
Step-by-step explanation:
got it on Edge
Label each statement True or False.
Need it fast will give 5 stars
Answer:
false
Step-by-step explanation:
The whole number between -1 and 1, with the symbol 0. Show’s that there is no amount:
Answer:
The number between -1 and 1 is 0 ( zero)
What is the Value of x
Answer:
42
Step-by-step explanation:
A skateboard ramp has a 158° entry angle. Find the measure of 1
Answer:
B. 68°
Step-by-step explanation:
The interior angles of the right triangle from the figure given are:
<1, right angle (90°), and (180° - 158°)
m<1 + 90° + (180° - 158°) = 180° (sum of triangle)
m<1 + 90° + 22° = 180°
m<1 + 112° = 180°
m<1 + 112° - 112° = 180° - 112°
m<1 = 68°
Answer: 68
Step-by-step explanation:
multiple choice test no explanation needed good luck