Given:
The complex number is:
[tex]z=1+i\sqrt{3}[/tex]
To find:
The argument of the given complex number.
Solution:
If a complex number is [tex]z=x+iy[/tex], then the argument of the complex number is:
[tex]\theta=\tan^{-1}\dfrac{y}{x}[/tex]
We have,
[tex]z=1+i\sqrt{3}[/tex]
Here, [tex]x=1[/tex] and [tex]y=\sqrt{3}[/tex]. So, the argument of the given complex number is:
[tex]\theta =\tan^{-1}\dfrac{\sqrt{3}}{1}[/tex]
[tex]\theta =\tan^{-1}\sqrt{3}[/tex]
[tex]\theta =\tan^{-1}\left(\tan \dfrac{\pi}{3}\right)[/tex]
[tex]\theta =\dfrac{\pi}{3}[/tex]
Therefore, the argument of the given complex number is [tex]\theta =\dfrac{\pi}{3}[/tex].
1. At an elementary school, it's picture day. Two picture packages are available. Package 1
contains one class picture and ten wallet-size pictures for a cost of $19. Package 2 contains two
class pictures and fifteen wallet-size pictures. The cost of Package 2 is $31. Find the cost of an
individual class picture and the cost of an individual wallet-size picture.
9514 1404 393Answer:
class picture: $5wallet-size: $1.40Step-by-step explanation:
Let c and w represent the per-picture cost of the class picture and a wallet-size picture, respectively. The two packages can be described by ...
c +10w = 19
2c +15w = 31
Subtracting the second equation from twice the first, we get ...
2(c +10w) -(2c +15w) = 2(19) -31
5w = 7
w = 1.40
Substituting into the first equation, we can find the cost of a class picture.
c + 10(1.40) = 19
c = 5 . . . . . . . . . . . subtract 14
A class picture costs $5; a wallet-size picture costs $1.40.
While in flight, some hummingbirds can flap their wings about 500 times in 10 seconds
Is this a true or false?
Answer:
50 times in 1 second
Step-by-step explanation:
I don't know what your specific question, but I'm guessing you wanted divide to see how many times they flap their wings in 1 second. :)
plz answer these questions without putting links and files
what is 3/4 multiplied by 1/2 then add 3/4
what is 1 and 1/8 multiplied by 1/2 then add 3/4
Answer:
11/8 and 21/16
Step-by-step explanation:
3 x 1 = 3
4 x 2= 8
3/8+3/4(convert to eighth's)
3/8+6/8=11/8
1 1/8 = 9/8
9 x 1 = 9
8 x 2 = 16
9/16+3/4(convert to sixteenth's)
9/16+12/16
21/16
---
hope it helps
=3/4 × 1/2 + 3/4
=3/8 + 3/4
=9/8
2nd questions ans
=1×1/2 + 3/4
=1/2 + 3/4
=5/4
The sides of a rectangle are in the ratio 2:5. If the longer side of the rectangle is 25.5
in., what are its width, perimeter, and area?
Answer: The width of the rectangle is 10.2 inches, the perimeter is 71.4 inches, the area is 260.1 inches.
Step-by-step explanation:
25.5/5=5.1
5.1*2=10.2
The width is 10.2 inches
25.5*2+10.2*2=71.4
The perimeter is 71.4 inches
20.5*10.2=260.1
The area is 260.1
1) The width of the rectangle is 10.2 in.
2) The perimeter of the rectangle is 71.4 in.
3) The area of the rectangle is 260.1 sq.in.
What is perimeter of rectangle?[tex]P=2\times(l+w)[/tex]
where, 'l' is the length of the rectangle
'w' is the width of the rectangle
What is the area of the rectangle?[tex]A=l\times w[/tex]
For given example,
The sides of a rectangle are in the ratio 2:5
The longer side of the rectangle is 25.5 in.
This means the length of the rectangle is [tex]l=25.5~in.[/tex]
Let 'x' represents the width of the rectangle.
⇒ [tex]\frac{2}{5} =\frac{x}{25.5}[/tex]
⇒ 2 × 25.5 = 5 × 'x'
⇒ 51 = 5x
⇒ x = 51/5
⇒ x = 10.2 in.
This means the width of the rectangle is 10.2 in.
⇒ [tex]l=25.5~in,~w=10.2~in.[/tex]
Using the formula of perimeter of the rectangle,
⇒ P = 2 × (25.5 + 10.2)
⇒ P = 2 × 35.7
⇒ P = 71.4 in.
Using the formula of area of the rectangle,
⇒ A = 10.2 × 25.5
⇒ A = 260.1 sq. in.
Therefore, the width of the rectangle is 10.2 in.
The perimeter of the rectangle is 71.4 in.
The area of the rectangle is 260.1 sq.in.
Learn more about rectangle here:
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What is the volume of a cylinder of a radius if 12cm and height 8cm
Answer:
V≈3619.11cm³
Step-by-step explanation:
Answer:
3619.11 cm³
Step-by-step explanation:
V = πr²h
π · 12² · 8
3619.11 cm³
amys older brother works 35 hours each week. if he works 18 dollars an hour how much does he earn in one week.
a 350
b 130
c 900
d 630
Answer:
He gets 630 dollars a week so the answer is D.
What two numbers multiply into (-24) and adds up to (-11)?
Answer:
-3 and -8
Step-by-step explanation:
Let the two numbers be called a and b respectively. We can say that ab=-24, and a+b=-11.
If a+b=-11, a=-11-b.
ab=-24
(-11-b)b=-24
b²+11b+24=0
(b+3)(b+8)=0
b=-3, b=-8
a=-11-b=-11+3=-8
a=-11-b=-11+8=-3
So the numbers are -3 and -8
What is the value of p(24)?
Answer:
24p
Step-by-step explanation:
I'm pretty sure that this is the answer because the question was "What is the value P(24)?" which means you have to use the commutative property to reorder the terms.
Hope this helped!
Three pounds of bananas cost $1.47 and 2 pounds of grapes cost $1.18. Which fruit is less expensive per pound? Explain how you know
Answer:
Grapes are less expensive
Step-by-step explanation:
First, find how much money 1 pound of each fruit is:
Bananas: $1.47 / 3 = $0.49
Grapes: $1.18 / 2 = $0.59
Compare:
0.49 < 0.59
So grapes are less expensive
The first step in solving a problem is to write a let statement
Answer:
whats this? can you provide more context?
Step-by-step explanation:
Write any two laws of indices in division and multiplication
Answer:
The first law: multiplication. If the two terms have the same base (in this case. ...
The second law: division. If the two terms have the same base (in this case. ...
The third law: brackets. If a term with a power is itself raised to a power then the powers are multiplied together. ...
Negative powers. ...
Power of zero. ...
Fractional powers.
Step-by-step explanation:
The hypotenuse of a right triangle measures 17 cm. One leg of the triangle measures 15 cm. Find the length of the other leg of the triangle.
Answer:
Step-by-step explanation:
8 cm
3.) 7:14. Find the value ofr
Answer:
1:2 all you have to do is simplify
A person invests $4000: part of the investment is at 10% interest and the rest at 12% interest. If she received $460 at the end of the year in interest, how much was invested at each rate?(whole number in dollars)
Let x be the amount invested at 10%;
SO we have;
.10x=amount invested at 10%
(4000-x).12=amount invested at 12%
So our equation would be;
.10x+(4000-x).12=460
Distribute the 12%;
.10x+480-.12x=460
Put like terms together so you can see them better;
.10x-.12x+480=460
-.02x+480=460;
subtract 480 from both sides;
-.02x=-20
Multiply each side by -.02;
x=1000
Now that we know what was invested at 10% we can subtract that from $4000 to get what was invested at 12%;
$4000-$1000=$3000
Hope you understand
=)
The price of a video game was reduced from $60 to $45. By what percentage was the price of
the video game reduced?
F 15%
G 25%
H 75%
4096
Someone please help
Answer:
G. 25%
Step-by-step explanation:
given : The price of a video game was reduced from $60 to $45 .
$60 - $45 = $15
then, the percentage was the price of the video game reduced :-
reduction in price/previous price x 100 = 15/60 x 100 = 25%
the percentage was the price of the video game reduced = 25%
line segment AB is a directed segment with endpoints A(2,2) and B(14,14). In two or more complete sentences, explain how you would verify that Point X, with a coordinate of (6,6), divides line segment AB in a 1:2 ratio?
Answer: Section formula
Step-by-step explanation:
Given
The line segment AB with endpoints [tex]A(2,2)[/tex] and [tex]B(14,14)[/tex] is divided by a point X in the ratio 1:2
To verify that X divides the line segment in the ratio 1:2, we will use section formula. Section formula tells the coordinates of the point which divide the line segment in the certain ratio or vice-versa.
We will assume that X divides AB in k:1 and insert the values in the section formula. If the ratio k:1 comes out to be 1:2, then it verifies the claim.
A survey asks students who walk or ride a bike to school whether they live more than one
mile from school. The results are shown in the table. Based on the results, which conclusion is
best?
Way to Get
to School
Walk
Bike
Total
Live More Than 1 Mile from School
Yes
No
Total
10
31
41
32
27
59
42
58
100
of the students who ride a bike, about 27% live
more than one mile away.
of the students who ride a bike, about 76% live
more than one mile away.
of the students who live more than one mile
away, about 32% ride a bike.
of the students who live more than one mile
away, about 76% ride a bike.
Answer:
of the students who live more than one mile
away, about 76% ride a bike.
Step-by-step explanation:
What is the product of 2r2 - 5 and 3r
Answer: 6r^3 - 15r
Step-by-step explanation:
(3r) (2r^2 - 5)
Distribute.
6r^3 - 15r
Hope this helped.
Joey opened a bank account 5 years ago with $100.
Today he has $1,000 in the account.
What is the percentage of increase?
_____%
how do I complete these questions a bit confused . (extra credit work )
Answer:
(1)
[tex]a = \frac{3\sqrt 3}{2}[/tex]
[tex]b = \frac{3}{2}[/tex]
(2)
[tex]a = \sqrt 6[/tex]
[tex]b = \sqrt 2[/tex]
Step-by-step explanation:
Solving (1):
Considering
[tex]\theta = 60^o[/tex]
We have:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(60^o) = \frac{a}{3}[/tex]
Solve for a
[tex]a = 3 * \sin(60^o)[/tex]
[tex]\sin(60^o) = \frac{\sqrt 3}{2}[/tex]
So:
[tex]a = 3 * \frac{\sqrt 3}{2}[/tex]
[tex]a = \frac{3\sqrt 3}{2}[/tex]
To solve for b, we make use of Pythagoras theorem
[tex]3^2 = a^2 + b^2[/tex]
This gives
[tex]3^2 = (\frac{3\sqrt 3}{2})^2 + b^2[/tex]
[tex]9 = \frac{9*3}{4} + b^2[/tex]
[tex]9 = \frac{27}{4} + b^2[/tex]
Collect like terms
[tex]b^2 = 9 - \frac{27}{4}[/tex]
Take LCM and solve
[tex]b^2 = \frac{36 - 27}{4}[/tex]
[tex]b^2 = \frac{9}{4}[/tex]
Take square roots
[tex]b = \frac{3}{2}[/tex]
Solving (2):
Considering
[tex]\theta = 60^o[/tex]
We have:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(60^o) = \frac{a}{2\sqrt 2}[/tex]
Solve for a
[tex]a = 2\sqrt 2 * \sin(60^o)[/tex]
[tex]\sin(60^o) = \frac{\sqrt 3}{2}[/tex]
So:
[tex]a = 2\sqrt 2 * \frac{\sqrt 3}{2}[/tex]
[tex]a = \sqrt 2 * \sqrt 3[/tex]
[tex]a = \sqrt 6[/tex]
To solve for b, we make use of Pythagoras theorem
[tex](2\sqrt 2)^2 = a^2 + b^2[/tex]
This gives
[tex](2\sqrt 2)^2 = (\sqrt 6)^2 + b^2[/tex]
[tex]8 = 6 + b^2[/tex]
Collect like terms
[tex]b^2 = 8 - 6[/tex]
[tex]b^2 = 2[/tex]
Take square roots
[tex]b = \sqrt 2[/tex]
If event A is certain to occur, what is P(A)?
Answer:
Unless I'm misunderstanding it should be 100% or 1/1 because something that is 100% likely to happen will always happen.
Step-by-step explanation:
If there is anything else that may change my understanding of this please send it otherwise I hope this helps.
The value of P(A) is 1 where A is the event that is certain to occur because the probability of any event is 1 which means that event is certain to occur.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
If event A is certain to occur.
As we know,
From the definition of probability, the ratio of the number of favorable outcomes to the total number of outcomes
The value of the probability lies between 0 to 1 or [0, 1]
If the probability of any event is 0 that means that event cannot happen.
If the probability of any event is 1 that means that event is certain to occur.
Event A is certain to occure.
P(A) = 1
Thus, the value of P(A) is 1 where A is the event that is certain to occur because the probability of any event is 1 which means that event is certain to occur.
Learn more about the probability here:
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The average salary for all 27 Arizona Diamondbacks in the 2005 baseball season was $2,308,488, with a standard deviation of $3,427,508. The population, all National League baseball players in 2005, earned an average salary of $2,585,804, with a standard deviation of $3,500,708. Does the average salary of the Diamondbacks players differ from that of all players in the National League
Answer:
The average salary of the Diamondbacks players does not differ from that of all players in the National League.
Step-by-step explanation:
1) Formulate null and alternate hypothesis
H0: u1= u2 Ha: u1 ≠ u2
The null hypothesis is that the average salary of the Diamondbacks players does not differ from that of all players in the National League
against the claim
that the average salary of the Diamondbacks players differ from that of all players in the National League
The data given is
x1`= $2,308,488, s1= $3,427,508 and n1 = 27
x2`= $2,585,804, s2=$3,500,708 and n2 = 27
2) The test statistic is
z= x1-x2/ sqrt( σ1 ²/n1 + σ2²/n2)
Putting the values
z = $2,308,488- $2,585,804/ sqrt( 3,427,508²/27 + 3,500,708²/27)
z= -0.294
3) The significance level is 0.05
The critical region is Z =±1.96
4) Since the calculated value of z= -0.294 is less than the z ∝=±1.96 we do not reject H0.
5) the P-value can be calculated using the calculator.
The p-value is p = 0.7687
The average salary of the Diamondbacks players does not differ from that of all players in the National League.
Simplify this please.
Answer:
The answer is in the picture I couldn't type it sorry.
Step-by-step explanation:
X
1 point
Mr.Boxer has organized the features of a credit card and a debit card into the table below. Which description is the best representation for the
missing detail?
CREDIT CARD
DEBIT CARD
?
purchases are withdrawn
immediately from bank
account
may not spend more than
your credit limit
may not spend more than
the balance of the
account
purchases are subject to
interest
no interest charged on
purchases
Answer:
Purchases are not withdrawn immediately from bank
Step-by-step explanation:
In case of credit cards, purchases are not withdrawn immediately from bank in fact the transaction needs approval and verification from the bank. Once the bank verify with the customer regarding the transaction requested, it will not allow money to flow from one account to other.
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then _______________________________________________.
Answer:
too difficult 99%(95%) fraction and decimal of 26.5 and (-36)
275436
divisible by 11
Your gross income is
$1945.63 of which you
get to keep 86% after
taxes.
Answer: You get to keep 1,673.24
You pay 272.38 in taxes.
the question is in the picture lol
Eleanor can type 10 pages in 22 minutes. At this rate, how long will it take her to type 93 pages?
Step-by-step explanation:
[tex]93 \times 22minutes = 2046 \\ \frac{2046}{10} = 204.6minutes[/tex]
A parabola y=x^2 is what type of function?
an even function
an odd function
an asymmetric function
a one to one function
Step-by-step explanation:
The parabola has a line of symmetry at x=0 so that means we can reflect the function across the y axis and it will remain unchanged so the answer is even function.