Answer:
Step-by-step explanation:
hello :
z⁴=1+i given : z² = t t is the complex number so : z⁴= (z²)² =t²
solve for t this equation : t² = 1+i
if : t = x+iy t² =(x+iy)² = x²+2xiy+(iy)² =x²-y²+2xyi ...... ( i² = -1)
t² = 1+i means : x²-y²+2xyi = 1+i
you have this system : x²-y² = 1.....(*)
2xy = 1.....(**)
slve for x and y you ca add this equation : ....(***)
( use : t² = 1+i
/t²/ = /1+i/ so :/t/² = /1+i/ .... (√(x²+y²))²=√(1²+1²) =√2 means x²+y² = √2)
the system is : x²-y² = 1.....(*)
2xy = 1.....(**)
x²+y² = √2 ....(***)
add (*) and (***) : 2x²= 1+√2
x² = (√2+1)/2
substrac (*) and (***) you have : y² = (√2-1)/2
use (**) the proudect xy is positif (same sign) so :
x=√( (√2+1)/2) and y = √( (√2-1)/2) so : t1 =√( (√2+1)/2)+i√( (√2-1)/2)
x= -√( (√2+1)/2) and y = -√( (√2-1)/2) so :t2= -t1
same method for equation : z² =t1 ..(2 solution ) and z² = t2..(2 solution )
select the best term from the box
________name same amount
(1) Equivalent fractions (2) common denominator
Solution:
1. Equivalent fractions name the same amount.
Equivalent fractions are the same value with different numerator and denominator.
Example:
These values are same.
2. A common denominator is a common multiple of two or more denominators.
Example:
Here 6 is a common multiple of 2 and 3.
Hence the answer is (1) Equivalent fractions (2) common denominator.
⻏尺闩讠㇄讠丂七 讠丂 闩尸尸尺⼕讠闩セᗪ
The values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-group 20 years to 30 years because they are either 1.5 times the interquartile range (IQR) greater than the upper quartile or 1.5 times the IQR less than the lower quartile. Using the same method for identifying outliers, which of the three values are identified as outliers for the age-group 40 years to 50 years
Answer:
Only 60 is an identified outlier
Step-by-step explanation:
Given
Age group: 40 to 50
[tex]Min = 60[/tex] [tex]Q_1 = 70[/tex] [tex]Median= 73[/tex]
[tex]Q_3 = 76[/tex] [tex]Max = 85[/tex]
Conditions for outlier
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]Value < Q_1 - 1.5 * IQR[/tex]
See attachment for complete question
Required
Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years
First, calculate the IQR of group 40 to 50.
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
Where:
[tex]Q_3 = 76[/tex] and [tex]Q_1 = 70[/tex]
So:
[tex]IQR = 76 - 70[/tex]
[tex]IQR = 6[/tex]
Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)
Testing 60
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]60 > 76 + 1.5 * 6[/tex]
[tex]60 > 76 + 9[/tex]
[tex]60 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]60 < 70 - 1.5 * 6[/tex]
[tex]60 < 70 - 9[/tex]
[tex]60 < 61[/tex] --- True
Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years
Testing 62
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]62> 76 + 1.5 * 6[/tex]
[tex]62 > 76 + 9[/tex]
[tex]62 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]62 < 70 - 1.5 * 6[/tex]
[tex]62 < 70 - 9[/tex]
[tex]62 < 61[/tex] --- False
Because both conditions are false, then 62 is not an outlier of group 40 - 50 years
Testing 84
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]84> 76 + 1.5 * 6[/tex]
[tex]84 > 76 + 9[/tex]
[tex]84 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]84 < 70 - 1.5 * 6[/tex]
[tex]84 < 70 - 9[/tex]
[tex]84 < 61[/tex] --- False
Because both conditions are false, then 84 is not an outlier of group 40 - 50 years
what number is the largest
15%
0.153
1/12
1/7
Answer:
0.153
Step-by-step explanation:
15% =0.15
0.153 = 0.153
1/12 =0.083
1/7=0.142
So the greatest one is 0.153
Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is . Each independently constructed a confidence interval based on the point estimate, but Jaime's interval has a lower bound of and an upper bound of , while Mariya's interval has a lower bound of and an upper bound of . Which interval is wrong? Why? Choose the correct answer below.
Complete question :
Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.13. Each independently constructed a confidence interval based on the point estimate, but Jaime’s interval has a lower bound of 0.097 and an upper bound of 0.163, while Mariya’s interval has a lower bound of 0.117 and an upper bound of 0.173. Which interval is wrong? Why?
Answer:
Mariya's interval
Step-by-step explanation:
Point estimate = 0.13
Mariya's confidence interval :
Lower boundary = 0.117
Upper boundary = 0.173
Jamie's confidence interval :
Lower boundary = 0.097
Upper boundary = 0.163
The correct confidence interval should have an average value equal to the value of the point estimate ;
Jamie's confidence interval average :
(0.097 + 0.163) / 2 = 0.26 / 2 = 0.13
Mariya's confidence interval average :
(0.117 + 0.173) / 2 = 0.29 / 2 = 0.145
Based on the confidence interval average obtained we can conclude that Mariya's interval is wrong as it the average obtained is greater than the point estimate.
0.145 > 0.13
The measures of two complementary angles are in the ratio 7:3. What is the measure of the smaller angle?
The speed of a boat in still water is 10 km/hr. The boat travels 24 km upstream, turns
around and comes back the same route. The entire trip takes 5 hours, What is the
speed of the current?
Answer:
rate of the current = 2 km/hr
Step-by-step explanation:
d = rt
Let c = rate of the current
Rate of boat downstream = 10 + c
Time going downstream = 24/(10 + c)
Rate of boat upstream = 10 - c
Time going upstream = 24/(10 - c)
Since the total time is 5 hr, then
24/(10 + c) + 24/(10 - c) = 5
24(10 - c) + 24(10 + c) = 5(10 + c)(10 - c)
240 - 24c + 240 + 24c = 500 - 5c^2
480 = 500 - 5c^2
5c^2 = 20
c^2 = 4
c = 2 or -2
Since a rate cannot be negative, the rate of the current = 2 km/hr
PLEASE ANSWER ILL GIVE HOU BRAU=INLIEXST
Answer:
4775.22
Step-by-step explanation:
V= πr2h
Input your numbers into the equation, and it will give you this answer.
HELP A FRIEND IN NEED
Answer:
Angle A = 68 degree
Angle B = 44 degree
Step-by-step explanation:
Sum of all interior angles = Angle A+Angle B+ Angle C
180 = 68+x+x-24
180 = 68+2x-24
180-68 = 2x-24
112+24 = 2x
136/2 = x
68 = x
Therfore, Angle A = 68 degree
Angle B = (x-24)
= (68-24)
= 44 degree
Mark as brainliest.
Please help!
Given that the glass can hold a maximum volume of 60 cm3, what is the height of the glass? Round to the nearest tenth of a centimeter.
Answer:
The volume of cone = Maximum holding of glass = 60 cube cm(cm^3)
Step-by-step explanation:
Cone formula:
[tex] v = \frac{1}{3} \pi \: r {}^{2} h[/tex]
The radius is 3cm and Volume is 60cm^3.
if pi =~ 3 So the "h" is 6.66 cm.
"h" is distance from cone's head to its base.
The "H"( height of glass) = 6.66 + 7 = 13.6 =~ 14
9514 1404 393
Answer:
13.4 cm
Step-by-step explanation:
The volume of the cone is given by ...
V = 1/3πr²h
For the given dimensions, we have ...
60 cm³ = 1/3π(3 cm)²h
20/π cm = h ≈ 6.37 cm . . . . . . . . . . . divide by the coefficient of h
The overall height of the glass, H, is 7 cm more than the value of h.
H = 7 cm +6.4 cm = 13.4 cm
The height of the glass is 13.4 cm.
i neeed help and quick its due at 3:15
Answer:
it c
Step-by-step explanation:
Ben wants to buy a guitar. The regular price of the guitar is $364.00. The sale peke of the guitar is 20% off of the regular price. Ben must pay 8.75 sales tax in addition to the sale price of the guitar. What is
the total amount ben must pay for the guitar?
Answer:
299.95
Step-by-step explanation:
you decide to go to a star gazing event there are 12 people in the group
Answer:
whts the question??
Step-by-step explanation:
what is the area of a sector of a circle with a diameter of 12 and a sector bou des by a 90degree arc?
Answer:
I worked it outf to be 3π in terms of π, apologies if this is wrong :/
Solve the following system of inequalities graphically on the set of axes below. State
the coordinates of a point in the solution set.
y < -x +4
y > 3x – 8
Answer:
[tex](x,y) = (3,1)[/tex]
Step-by-step explanation:
Given
[tex]y < -x + 4[/tex]
[tex]y > 3x - 8[/tex]
Required
Solve graphically
See attachment for graph;
The blue shade represents [tex]y < -x + 4[/tex]
While the green, represents [tex]y > 3x - 8[/tex]
Next, determine the intersection points between the two lines
From the attached graph, we have:
[tex](x,y) = (3,1)[/tex]
Hence, the solution is: [tex](3,1)[/tex]
Each side of the cube at the Discovery Science Center in Santa Ana is 64 feet long.
(a)
Find the volume (in cubic feet).
cu. ft
(b)
Find the surface area (in square feet).
Answer:
V = 262’144 ft^3, surface area = 24’576 ft^2
Step-by-step explanation:
The volume con be find with this formula =
V = side^3
V = 64^3 = 262’144 ft^3
For find the surface area we can proceed in this way: first of all we can find the area of a face.
A = side^2 = 4096 ft^2
a cube has 6 faces, so we have to the mutiply the value six times.
Surface area = 4096 x 6 = 24’576 ft^2
solve for x
3x + 7 = -2
Answer:
x = -3
Step-by-step explanation:
1. Write the equation
3x + 7 = -2
2. -7 from both sides
3x = -9
3. Divide 3 from both sides to get x alone
x = -3
Answer:
Hello There!!
Step-by-step explanation:
3x+7=-2 (-7 from both sides)
-7 -7
3x=-9 (divide by 3 from both sides)
÷3 ÷3
x=-3
hope this helps,have a great day!!
~Pinky~
a clothing distributor sold an $80 coat at a discount price of $73. what was the percentage of discount for the coat?
Answer:
91%
Step-by-step explanation:
The discount is $73 so we would get 73/80.
73/80 is also known as 73÷80
which would equal 0.9125
if we were to covert and round it to a percent, it would be 91%
In figure, if PQ = QR = 14cm, then find the length of the tangent RT.
gimme answer fastt pls
Step-by-step explanation:
When we observe the figure there are two semicircles , one of radius 14cm . And other will be of 14cm/2 = 7cm ( Since the 2nd semi circle is drawn taking radius of 1st semicircle as diameter.)
Now join T to the center of 2nd semi circle . Therefore , we have
[tex]\tt\to PR = 28cm \\\\\tt\to PQ + 14cm = 28cm \\\\\tt\to PM + MQ = 14cm \\\\\tt\to MQ = 14cm - 7cm \\\\\to\boxed{\orange{\tt MQ = 7cm }}[/tex]
Now , looking at the figure we know that radius is perpendicular to the tangent at point of contact . Here TR is tangent . Therefore ∆TRM is right angled triangle. Using Pythagoras Theorem we have,
[tex]\tt\to 21^2 = RT^2+7^2 \\\\\tt\to RT^2= 441 - 49 \\\\\tt\to RT =\sqrt{392}\\\\\tt\to\boxed{\orange{\tt RT = 19 .79 cm }}[/tex]
Ahmad took out a loan for 146 days and was charged simple interest at an annual rate of 12.5%.
The total interest he paid on the loan was $245.
How much money did Ahmad borrow?
Answer:
$488778
Step-by-step explanation:
For a for interest is;
i = PRT/100
Where;
R is rate
P is Principal
T is time
i is interest
We are given;
R = 12.5% = 0.125.
T = 146 days = (146/364) = 0.4011
i = $245
Thus;
245 = (P × 0.125 × 0.4011)/100
Thus;
P = (245 × 100)/(O.125 × 0.401)
P = $488778
PLS ASAP!! Thank You
Answer:
[tex]y = \frac{1}{2}x - 4[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{1}{2}x[/tex]
Required
Shift [tex]3\ units[/tex] down and [tex]2\ units[/tex] right
[tex]y = \frac{1}{2}x[/tex]
Shift 3 units down
The rule is: (x,y)=> (x,y-a)
Where a is the number of units shifted down
In this case: [tex]a = 3[/tex]
So, we have:
[tex]y = \frac{1}{2}x[/tex] == > [tex]y = \frac{1}{2}x - 3[/tex]
Shift 2 units right
The rule is: (x,y)=>(x-b,y)
Where b is the number of units shifted right
In this case: [tex]b = 2[/tex]
So, we have:
[tex]y = \frac{1}{2}x - 3[/tex] ==> [tex]y = \frac{1}{2}(x - 2) - 3[/tex]
Open bracket:
[tex]y = \frac{1}{2}x - 1 - 3[/tex]
[tex]y = \frac{1}{2}x - 4[/tex]
Hence, the new equation after the transformation is:
[tex]y = \frac{1}{2}x - 4[/tex]
joseph's lunch at a restraunt cost 13.00, without tax.
Answer:
Ok, what exactly is the question?
Step-by-step explanation:
find each angle or arc measure
Answer:
176
Step-by-step explanation:
The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.
SO JML is 88*2
Find the equation of the line with slope =-4 and passing through (2,-10) Write your answer in the form y=mx+b
Answer:
y= -4x -2
Step-by-step explanation:
-10=-4(2) -2
y= -4x -2
Part 3: The Space Inside! 1. Find the volume of the shipping box using the two methods and show your work: A. Packing cubes B. Using the volume formula 2. Explain how both methods provide the same measurement of volume for the shipping Let's ship. You are done! Penny and her classmates thank you, i really need help with the volume formula and the packing cubes
Answer:
Don't click the site its a scam and will give your phone a virus
Name the polygon. Then tell whether it is a regular polygon or not a regular polygon.
Answer:
pentagon
regular polygon
Step-by-step explanation:
A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center
what is 2 1/2 × 1/9 and how do i get the answer
Step-by-step explanation:
help me with this plzzzz
Answer:b c
Step-by-step explanation:
did it
The median value is ____
Answer:
45
Step-by-step explanation:
Help me please!!!! I really need this answer quickly
Answer:
X = 22
Step-by-step explanation:
This is a right triangle which means the angles add up to 90° total. So if 1 side is 15 and another side is 53 then 15 + 53 = 68 and 90 - 68 = 22 so X = 22 which is the missing side.
5/6 = 25/? Fractions
Answer:5/6=25/blank
Step-by-step explanation:so 5/6 the top is times five forget the bottom for now just think of 5 and 25
[5x5] equals 25 so you already got the top
now for the bottom since you multiply the top by five you have to do that to the bottom so that will be [6x5] that equals 30 so you got your answer
[25/30]
