Answer:
z = {1 +i, 1 -i, -1 +i, -1 -i}
Step-by-step explanation:
Using Euler's formula, you can write this as ...
z^4 = 4e^(i(π+2kπ))
Then the 4th root is ...
z = 4^(1/4)e^(i(π/4 +kπ/2)) = √2(cos(π/4+kπ/2) +i·sin(π/4+kπ/2))
for integers k in the range 0 to 3.
z = √2(±1/√2 ±i·1/√2) . . . signs are independent
z = ±1 ±i . . . . . . signs are independent; hence 4 solutions
z = {1 +i, 1 -i, -1 +i, -1 -i}
_____
Comment on roots of complex numbers
In the complex domain, each number has a number of roots equal to the index of the root. That is, there are four 4th roots. They all have the same magnitude, but their angles are separated by 360°/(root index) = 90°. Here, the principal fourth root of 4∠180° is 4^(1/4)∠(180°/4) = √2∠45° = 1+i.
Adding 90° is equivalent to multiplying by i, so the other 3 roots are √2∠135° = -1+i, √2∠225° = -1 -i, and √2∠315° = 1 -i.
z = {1 +i, 1 -i, -1 +i, -1 -i}
Adriana worked 38 hours last week. Her job pays $12 an hour. How much did she earn last week?
Multiply the hours by how much she makes per hour.
38 * 12 = $456
Therefore, she made $456 last week.
Best of Luck!
What percentage of the data in a standard normal distribution lies between x = .09 and x = 1.2?
Answer:
The percentage is [tex]P(0.09 < \mu < 1.2 ) = 34.9\%[/tex]
Step-by-step explanation:
From the question we are told that
The random number is [tex]x_1 = 0.09 \ and \ x_2 = 1.2[/tex]
Generally the mean of standard normal distribution is [tex]\mu = 0[/tex]
The standard deviation of a standard normal distribution is [tex]\sigma = 1[/tex]
The percentage of the data in a standard normal distribution lies between
[tex]x_1 = 0.09 \ and \ x_2 = 1.2[/tex] is mathematically represented as
[tex]P(x_1 < \mu < x_2 ) = P(\frac{x_1 - \mu}{\sigma } <\frac{X - \mu}{\sigma } < \frac{x_2 - \mu}{\sigma } )[/tex]
[tex]P(0.09 < \mu < 1.2 ) = P(\frac{0.09 - 0}{1 } <\frac{X - \mu}{\sigma } < \frac{1.2 - 0}{1 } )[/tex]
[tex]P(0.09 < \mu < 1.2 ) = P(0.09 <\frac{X - \mu}{\sigma } < 1.2 )[/tex]
The [tex]\frac{X - \mu}{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]
[tex]P(0.09 < \mu < 1.2 ) = P(0.09 <Z < 1.2 )[/tex]
[tex]P(0.09 < \mu < 1.2 ) = P (Z < 1.2 )- P( Z<0.09)[/tex]
From the z-table
[tex]P (Z < 1.2 )= 0.88493[/tex]
[tex]P( Z<0.09) = 0.53586[/tex]
So
[tex]P(0.09 < \mu < 1.2 ) = 0.88493 - 0.53586[/tex]
[tex]P(0.09 < \mu < 1.2 ) = 0.349[/tex]
Hence the percentage is
[tex]P(0.09 < \mu < 1.2 ) = 34.9\%[/tex]
In an 8 hour and 30 minute shift a patrolman drove 272 miles. What was his average rate(mph) during the shift?
Answer:
32 mph
Step-by-step explanation:
We want to find the patrolman's rate in miles per hour during the shift. Since we want to find miles per hour, we must divide the miles he drove by the number of hours.
rate = miles / hours
He drove 272 miles.
rate = 272 miles / hours
He drove for 8 hours and 30 minutes. There are 60 minutes in 1 hour. One half of 60 is 30. Therefore, we can also say he drove eight and a half, or 8.5 hours.
rate= 272 miles / 8.5 hours
rate = 32 miles / hour
rate= 32 mph
His average rate during the shift was 32 miles per hour.
Answer:
32 mph
Step-by-step explanation:
To answer this, find the average rate of change
272 mi
------------- = 32 mph
8.5 hr
Please help Please help
Answer:
Leg ED is adjacent to theta
find
the
radius of
the base of a
cylinder if the curved
surface
area is 100cm2 and
total surface
area is
408 cm2?
Answer:
7 cm.
Step-by-step explanation:
Area of the 2 bases = total area - area of curved surface
= 408 - 100 = 308cm^2.
So the area of 1 base = 154 cm^2.
If radius of the base = r:
pi r^2 = 154
r^2 = 154/pi
r = sqrt (154/pi)
r = 7.0014 cm
juan spent 10 min on his history homework and 3 min per question on his math homeowrk. which graph shows the total homework time t, related to the number of questions q
Answer:1st graph
Step-by-step explanation: did this question already
Answer: First option
Step-by-step explanation:
I did the lesson already
solve the equation 6 over x + 1 over 2 equals to 2
Answer:
x = 4
Step-by-step explanation:
6/x + 1/2 = 2
x(6/x + 1/2) = 2*x
x*6/x + x*1/2 = 2x
6 + x/2 = 2x
6 = 2x - x/2
6 = 4x/2 - x/2
6 = 3x/2
6*2/3 = x
12/3 = x
x = 4
probe:
6/4 + 1/2 = 2
3/2 + 1/2 = 4/2
how do I do this
plz help
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Use order of operations.
42/(15-2^3)
Exponents in Parentesis
42/(15-8)
Subtraction inParenthesis
42/7
Division
6
144 = m - 98 m = pls help
Answer:
43
Step-by-step explanation:
The solution to the equation 144 = m - 98 is m = 242 as per the PEMDAS rule.
To solve for m in equation 144 = m - 98, we can follow these steps:
Start with the given equation: 144 = m - 98.
To isolate the variable m, we need to eliminate the -98 on the right side of the equation. We can do this by adding 98 to both sides of the equation:
144 + 98 = m - 98 + 98.
Simplifying the equation, we get: 242 = m.
Now we have m = 242 as the solution to the equation.
Therefore, m = 242 is the value that satisfies the equation 144 = m - 98. By substituting m with 242 in the equation, we can verify that it holds true:
144 = 242 - 98.
144 = 144.
To learn more about the equation;
https://brainly.com/question/12788590
#SPJ6
The complete question:
144 = m - 98
Solve for m
Mary Watson gets a job as a waitress, at the Daily Grind. She earns $5.25 an hour plus tips. If tips are about 15% of the meal and she sold $452.97 worth of food during her 8 hour shift, what was her gross pay for the day?
Answer:
$109,9455
Step-by-step explanation:
8x5.25=42
452,97/100=4,5297
4,5297x15=67,9455
42+67,9455=109,9455
Answer:
$109.95
Step-by-step explanation:
rate = $5.25 per hour + tips
tips = 15% of the food sold during 8 hours shift.
Mary Watson will get:
$5.25 x 8 hours = $42
tips = 0.15 x $452.97 = $67.95
a total of $42 + $67.95 = $109.95
In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below: Please round your answer to 4 decimal places for the Relative Frequency if possible. # of Courses Frequency Relative Frequency Cumulative Frequency 1 20 Correct .3846 Correct 20 2 19 0.3654 39 Correct 3 13 0.25 52 What percent of students take exactly one courses? 51.61 Incorrect%
Answer:
The percentage of students taking exactly one courses is 38.46%.
Step-by-step explanation:
The frequency distribution table provided for the number of courses taken by part-time students is as follows:
# of Courses Frequency Relative Cumulative
Frequency Frequency
________________________________________________
1 20 0.3846 20
2 19 0.3654 39
3 13 0.2500 52
TOTAL 52 1.0000
The relative frequency is actually the probability or chance of the particular class or category of a frequency distribution.
The probability of students taking exactly one courses is 0.3846.
Then the percentage of students taking exactly one courses is:
0.3846 × 100% = 38.46%
Thus, the percentage of students taking exactly one courses is 38.46%.
What is the base of the rate is 16.1% and the portion is 454
The rate is 16.1% and the base is the final portion with the rate added on to it.
Chance the percentage into a decimal.
16.1% / 100 = 0.161
Multiply.
454 * 0.161 = 73.094
Add.
454 + 73.094 = 527.094 or 527.09
Therefore, the final base is roughly 527.09
Best of Luck!
agalar help mee agalar yardım
Answer: 510°
Step-by-step explanation:
1st. solution.
Draw the perpendicular EP ⊥FB.
So from quadrilateral FAEP we find the∡AEP ( sum of all angles in quadrilateral=360°)
∡AEP= 360°-∡FAE-∡AFP-∡FPE=360°-20°-90°-90°=160°
Draw CK ⊥FB
From triangle CKB we can find ∡BCK=180°-10°-90°=80°
From pentagon PEDCK (sum of PEDCK angles= 540°) we can find the sum of ∡PED+∡DCK= 540°-∡EPK-∡EDC-∡CKP= 540°-90°-90°-90°=270°
∡DEA+∡DCB=∡AEP+∡PED+∡DCK+∡KCB=160°+270°+80°=510°
Answer:
CEVAP 50ymis knk öyle dediler iwkwjskaoqkwjwhd
(10x² +34
+ 34x+ 30) = (2x+4)
Answer:
2 = 0
This equation has no solution.
Step-by-step explanation:
A a non-zero constant never equals zero
ab when a = 1/2 and b= 3/4
Answer:
3/8
Step-by-step explanation:
1/2*3/4
is
(1*3)/(2*4)
So it's 3/8
Answer:
Here,
a=[tex] \frac{1}{2} [/tex]
b=[tex] \frac{3}{4} [/tex]
Now,
[tex]ab \\ = \frac{1}{2} \times \frac{3}{4} \\ = \frac{3}{8} [/tex]
Which of the following are point-slope equations of the line going through (-3,4) and (2,1)? Check all that apply. A. y-1=-5/3(x-2) B.y-4=-5/3(x+3) C. y-1=-3/5(x-2) D.y+3=-3/5(x-4) E. y+2=3/5(x-1) F.y-4=-3/5(x+3) *I have been trying to find the right answers but i cant seem to get is right pls help !
Answer:
Step-by-step explanation:
(1-4)/(2+3)= -3/5 is the slope
y - 4 = -3/5(x + 3)
the solution is F
Convert without rounding 1/8 to a decimal
Answer:
.125
Step-by-step explanation:
.125 * 8 = 1
(7a^3 -2a-2)+(-5a+3)
Answer:
7a 3 −7a+1
Step-by-step explanation: I hope this help.
STEP
1
:
Equation at the end of step 1
((7a3 - 2a) - 2) + (3 - 5a)
STEP
2
:
Polynomial Roots Calculator :
2.1 Find roots (zeroes) of : F(a) = 7a3-7a+1
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 7 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,7
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 1.00
-1 7 -0.14 1.98
1 1 1.00 1.00
1 7 0.14 0.02
Polynomial Roots Calculator found no rational roots
Final result :
7a3 - 7a + 1
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{7 {a}^{3} - 7a + 1}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{(7 {a}^{3} - 2a - 2) + ( - 5a + 3) }[/tex]
When there is a ( + ) in front of an expression in parentheses, there is no need to change the sign of each term. That means, the expressions remains the same. Just, remove the parentheses
⇒[tex] \sf{7 {a}^{3} - 2a - 2 - 5a + 3}[/tex]
Collect like terms
⇒[tex] \sf{7 {a}^{3} - 2a - 5a - 2 + 3}[/tex]
⇒[tex] \sf{7 {a}^{3} - 7a - 2 + 3}[/tex]
Calculate
⇒[tex] \sf{7 {a}^{3} - 7a + 1}[/tex]
Hope I helped!
Best regards!!
(-6)^-1 without exponent
Answer:
-1/6
Step-by-step explanation:
[tex](-6)^-1\\=\frac{-1}{6}^1\\ =\frac{-1}{6}[/tex]
Now write the numbers 1 through 10 using exactly four 4s.
Value
Expression using four 4s
1
I
2
3
4
5
6
7
8
9
10
Step-by-step explanation:
By using exactly four 4s it is possible to write a few numbers: at least from 0 - 30.
=> For example, using exactly four 4s, we can write 1 as follows
1 = 44 / 44
The right hand side of the above equation has exactly four 4s and solving it will give 1.
=>Using exactly four 4s, we can write 2 as follows;
2 = (4/4) + (4/4)
Also, there are exactly four 4s in the right hand side of the above equation and solving it gives 2
=> Using exactly four 4s, we can also write 6 as follows;
6 = 4 x .4 + 4.4
The above equation also contains exactly four 4s which will give 6 when solved. i.e
(4 x .4) + 4.4 = (4 x 0.4) + 4.4 = 6
The expressions for numbers 1 through 10 using exactly four 4s have been tabulated and shown in the image attached to this response.
2!/0! = 2, 0 or undefined
Answer:
Undefined.
Step-by-step explanation:
Because there is a 0 in the denominator.
Answer:
Undefined
Step-by-step explanation:
Because you cant divide by 0
the surface area of a sphere whose radius is 0.5 cm is
Answer: The answer is 3.14 (also known as π)
Step-by-step explanation: The formula for the surface area of a sphere is:
A = 4πr^2
A = 4π (0.5)^2
A = 4π (0.25)
A = (4 x 0.25) π
A = 1π
A = π or A = 3.14
8. Compare the value of the 3 in 265,413 and 4.3.
Answer:
The three in the first number, 265,413 has the three in the ones place.
The three in the second number, 4.3 has the three in the tenths place.
So, the value of the three in the first number is ten times greater than the one in the second number.
Consider the system of linear equations.
x+y=9.0
0.50x + 0.20y = 4.05
Find the values of x and y.
x = 7.5
y = 1.5
Step-by-step explanation:x + y = 9.0 => x = 9 - y
0.50x + 0.20y = 4.05
0.5(9 - y) + 0.2y = 4.05
4.5 - 0.5y + 0.2y = 4.05
4.5 - 4.05 = 0.5y - 0.2y
0.45 = 0.3y
y = 0.45 : 0.3
y = 1.5
x = 9 - 1.5
x = 7.5
Does the following table represent a function? Explain.
Answer:
The table represents a function because each input corresponds to exactly one output.
Step-by-step explanation:
A table can be regarded as representing a function if and only if every input can only be mapped to exactly one output. In other words, it means, only 1 exact output can be assigned to an input. In a table of function, an input cannot have two different outputs. Although, two different inputs can be assigned to the same output.
From the table given, we see that every input has exactly one output. Although, we have different inputs that gives the same output.
Therefore, we can conclude that the table represents a function because each input corresponds to exactly one output.
The 10th term of an AP is -27 and the 5th term is -12, what is the 18th term?
Also find the sum of its 25 terms.
Answer:10th term: -27
5th term: - 12
d= -27+12/5
= -3
a+(n-1)d=-12
a+(5–1)d=-12
a+4d= -12
a=-12–4d
a=-12-(4×-3)
a=-12+12=0
18 term=a + (18–1)d
=0+(17×-3)
51
a+9d=-27......(1)
a+4d=-12.....(2)
make a the subject of equation 2 and put into equation 1
-12+4d+9d=-27
-12+13d=-27
d=-15\13
put d into equation 1
a+9(-15/13)=-27
a=16.6
a+17d=x
17+16.6(-15/13)
x=-2 is the 18th term
25÷2(16.6+15.6(-15/13)
=-208.4
Rehan paid 560p for 7 pencils.if the price of each pencil was the same.work out the price of 4 such pencils
Answer:
320p
Step-by-step explanation:
According to the question,
560p = 7 pencils
Therefore,
1 pencil = 560 / 7
= 80p
So, for 4 pencils it costs
4 * 80 = 320p
Answer:
easy piizzy lemon squeezyy!!
Step-by-step explanation:
i) 560/7
=80
ii) 80*4
=320
Which x values is the graph below discontinuous?
Answer: {...-3, -1, 1, 3, 5...}
Step-by-step explanation:
For a point to be discontinuous, the graph doesn't exist at that point. This means, it is represented with an open circle. All we have to do is to list out all the open circles on the graph.
{-3, -1, 1, 3, 5}
Answer:
b. {... –3, –1, 1, 3, ...}
Step-by-step explanation:
so basically it's b. the person above me is right they just added a 5 to the end
Finding Ordered Pairs from an Equation
For both equations below, x is the input and y is the output. Match the ordered pair with the correct equation by
dropping the ordered pair into the appropriate bin.
y = 3x - 4
y = (*2)X + 2
(4,4)
(3,5)
(5, 11)
(6, 14)
(2,3)
Answer:
In the y=3x-4 section it should be (3,5), (6,14), (5,11)
In the y= (1/2)x + 2 section it should be (4,4) , (2,3)
I hope this works!
Step-by-step explanation:
Find the value of 3/4 x 14
Answer:
21/2
Step-by-step explanation:
[tex]\frac{3}{4}\times\:14\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:14=\frac{14}{1}\\=\frac{3}{4}\times\frac{14}{1}\\\\\mathrm{Cross-cancel\:common\:factor:}\:2\\=\frac{3}{2}\times\frac{7}{1}\\\\=\frac{3\times\:7}{2\times\:1}\\\\=\frac{21}{2}[/tex]