Answer:
Step-by-step explanation:
To express 6√3 + 6i in polar form, we first need to find the magnitude and argument of the complex number.
The magnitude (or modulus) of the complex number is given by the formula:
|z| = √(a^2 + b^2)
where a and b are the real and imaginary parts of the complex number, respectively.
In this case, a = 6√3 and b = 6, so:
|6√3 + 6i| = √((6√3)^2 + 6^2) = √(108 + 36) = √144 = 12
The argument (or angle) of the complex number is given by the formula:
arg(z) = tan^-1(b/a)
In this case, arg(z) = tan^-1(6/6√3) = tan^-1(1/√3) = π/6
Therefore, the polar form of 6√3 + 6i is:
12(cos(π/6) + i sin(π/6))
or
12e^(iπ/6)
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that exactly 10 flights arrive on time.
Probability that exactly 10 flights arrive on time is 53.33%.
Given that,
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation.
Recently, Southwest Air had the best rate with 80% of its flights arriving on time.
Total number flights in sample = 15
Probability that exactly 10 flights arrive on time is,
P = 10/15 × 80%
= 0.5333
= 53.33%
Hence the required probability is 53.33%.
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25. Solve for the missing variables.
The missing angles in the cyclic quadrilateral are as follows:
a = 101°
b = 67°
c = 84°
d = 80°
How to find the angles in a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.
Opposite angles of a cyclic quadrilateral is supplementary.
c = 180 - 96
c = 84 degrees
d = 180 - 100
d = 80 degrees
100 = 1 / 2 (a + 99)
100 = 0.5a + 49.5
0.5a = 50.5
divide both sides by 0.5
a = 50.5 / 0.5
a = 101 degrees
84 = 1 / 2 (101 + b)
84 = 50.5 + 0.5b
84 - 50.5 = 0.5b
0.5b = 33.5
b = 33.5 / 0.5
b = 67 degrees
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Explain each step and answer 50 points
1 Yes the set of rational expressions is closed under subtraction
2. Yes the set of rational expressions is closed under multiplication
3. No the set of rational expressions is not closed under division
How to determine if the expression is closed
1. The subtraction of two rational expressions results in another rational expression.
= p(x)/q(x) - r(x)/s(x)= ((p(x)s(x) - r(x)q(x))/(q(x)s(x)))
this is also a rational expression.
2. The multiplication of two rational expressions results in another rational expression.
=(p(x)/q(x)) * (r(x)/s(x)) = ((p(x)r(x))/(q(x)s(x)))
this is a rational expression.
3. Division of two rational expressions may result in an expression that is not a rational expression.
= (p(x)/q(x)) / (r(x)/s(x)))
= ((p(x)s(x)) / (q(x)r(x)))
this may not be a rational expression if q(x)r(x) equals zero at some point, causing division by zero
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What is the strength of the association between the two
variables in the scatter plot?
Select from the drop-down menu to correctly complete the
statement.
The strength of association is Choose...
Strong or weak
A weak correlation between the two variables is depicted by the scatter plot in the supplied image.
The trend line's points are widely dispersed, which suggests that there is little correlation between the variables.
In a scatter plot, the degree of connection between the two variables can be classified as strong or weak.
A weak correlation indicates that there is a lot of scatter around the trend whereas a high relationship indicates that there is very little scatter in comparison to the trend's movement.
Thus, the given association is weak correlation.
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Subtract (8n-5)-(-2n-3)
Answer:
Step-by-step explanation:
( 8n - 5 ) - ( -2n - 3 )
( 8n - 5 ) + ( 2n + 3 )
8n - 5 + 2n + 3
10n - 2
What is the strength of the association between the two
variables in the scatter plot?
Select from the drop-down menu to correctly complete the
statement.
The strength of association is Choose...
Strong or weak
Consider polygon ABCD, shown below.
B
C
E
A
G
F
D
Select all the ways that describe rigid transformations that take AEFD to CFEB.
The rigid transformations that can take AEFD to CFEB are translation, rotation, and reflection.
To describe the rigid transformations that take polygon AEFD to CFEB, we need to identify the transformations that preserve the shape and size of the polygon. Here are some possibilities:
Translation: A translation involves moving the entire polygon without changing its orientation or shape. If we shift polygon AEFD to the right, it will align with polygon CFEB. Therefore, translation is one way to achieve this transformation.
Rotation: If we rotate polygon AEFD around a fixed point, such as the center of the polygon or a vertex, by a certain angle, it can align with polygon CFEB. A rotation preserves the shape and size of the polygon.
Reflection: A reflection involves flipping the polygon across a line, resulting in a mirror image. If we reflect polygon AEFD across a line of reflection, it can match polygon CFEB.
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The time (t) required to do a job varies inversely as the number of people (p) working on the job.
It takes 9 hours for 4 roofers to complete a certain job. How long would it take 6 roofers to complete the same job?
hours
Answer:
6 hours
Step-by-step explanation:
Varying inversely simply means using the "inverse proportion" methodSo therefore,
4 roofers= 1 hour
1 roofer= 9 * 4
= 36 hours
Why? Because the lesser amount of workers you have, the more time will be needed so as to complete the work.6 roofers= 36/6=6 hours
The more people you have, the lesser amount of time will be spent on completing the work.Which statements is true and justify your answer
Answer:
Step-by-step explanation:
Will mark it brilliant
40. What is mzWXY? How do you know?
W
X
69°
Z
Y
The value of the angle m<WXY is 69 degrees
How to determine angleWe need to know that the shape given is a parallelogram.
The properties of a parallelogram are given as;
Opposite sides of the shape are parallel.Opposite sides of the shape are congruent.Opposite angles of a parallelogram are equal.Same-Side interior angles are supplementary, that is sum up to 180 degrees.Each diagonal of a parallelogram separates it into two equal trianglesThe diagonals of a parallelogram bisect each other.From the information given, we have that;
Angel WZY and Angle WXY are opposite angles of the parallelogram
Then,
m<WXY = 69 degrees
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Simplify.
√n/18.
Answer choices:
A 1/6n √2.
B √1/9
C 1/6 √2n
Please explain the answer my radical calculator doesn't work on anything with letters in it.
Answer: C 1/6*√2n
Step-by-step explanation:
• Simplify √n/18 as (1/3)^2*n/2
• Multiply them under the radical so the squares 1/3 cancels out to 1/3*√n/2
• Multiply the √n/2 on both sides as √2*n/√2*√2 so it comes out to √2n/2
• Multiply √2n/2 with 1/3 to make √2n/6
√2n/6 is equal to 1/6*√2n
The radical expression √n/18 when simplified is 1/3√n/2
Simplifying the radical expressionFrom the question, we have the following parameters that can be used in our computation:
√n/18
Express 18 as 9 * 2
So, we have the following representation
√n/18 = √n/(9 * 2)
Rewrite as
√n/18 = √n/(2 * 9)
Take the square root of 9
This gives
√n/18 = 1/3 * √n/2
Evaluate the products
√n/18 = 1/3√n/2
Hence, the expression when simplified is 1/3√n/2
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A small square has length y cm
A large square has length 40 cm
The area of the small square is of
the area of the large square.
25
Work out the value of y.
Your final line must say, y = ...
y cm
40 cm
Total marks: 3
Answer:
Step-by-step explanation:
The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side of the square.
Let y be the length of the side of the small square.
Then, the area of the small square is y^2 cm^2.
According to the question, the area of the small square is 1/25 of the area of the large square.
Thus, the area of the large square is (25)(y^2) cm^2.
The length of a side of the large square is given by the formula s = √A.
Therefore, the length of a side of the large square is √(25y^2) = 5y cm.
Since the length of a side of a cube is equal to its height, width, and length, the dimensions of the cube are 5y cm x 5y cm x 5y cm = (5y)^3 cm^3.
Therefore, y = 40/5 = 8.
Thus, the dimensions of the cube are 40 cm x 40 cm x 40 cm.
100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
The values of the trigonometry functions are sin(θ) = 3/√13, cos(θ) = 2/√13, tan(θ) = 3/2, csc(θ) = √13/3, sec(θ) = √13/2 and cot(θ) = 2/3
Finding the values of the trigonometry functionsfrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse of the right triangle is calculated as
h² = 2² + 3²
When evaluated, we have
h = √13
The values of the trigonometry functions are then evaluated as
sin(θ) = 3/√13
cos(θ) = 2/√13
tan(θ) = 3/2
csc(θ) = √13/3
sec(θ) = √13/2
cot(θ) = 2/3
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Given f(x)=(1/4)^-x, Evaluate f(-2), f(1), and f(2).
When we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16.
To evaluate f(x)=(1/4)^-x for specific values of x, we can substitute the given values into the function expression and simplify the calculations.
Evaluating f(-2):
Substitute x = -2 into the function f(x):
f(-2) = (1/4)^-(-2) = (1/4)^2 = 1/16
Evaluating f(1):
Substitute x = 1 into the function f(x):
f(1) = (1/4)^-1 = 4^1 = 4
Evaluating f(2):
Substitute x = 2 into the function f(x):
f(2) = (1/4)^-2 = (1/4)^2 = 1/16
Therefore, the evaluations of f(-2), f(1), and f(2) are:
f(-2) = 1/16
f(1) = 4
f(2) = 1/16
In conclusion, when we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16. These values represent the corresponding outputs of the function for the given inputs.
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Susan borrows $1000 for 8 months at 7 1/8% per annum simple interest. What is the amount due?
Answer:
$1047.50-------------------------
Given:
principal (P) = $1000, time (t) = 8 months, and interest rate (r) = 7 1/8% per annum.Convert the interest rate to a decimal:
7 1/8% = 7.125% = 0.07125Convert the time from months to years:
8 months / 12 months per year = 2/3 years.Now, we can calculate the simple interest using the formula:
I = P * r * tI = $1000 * 0.07125 * (2/3) = $47.50Finally, add the interest to the principal to find the amount due:
Amount due = $1000 + $47.50 = $1047.50Susan's amount due for the loan is $1047.50.
The simple interest amount of Susan for time of 8 months is A = $ 1047.50
Given data ,
To calculate the amount due, we need to consider the principal amount borrowed, the interest rate, and the time period.
Principal (P) = $1000
Time (t) = 8 months
Interest rate (r) = 7 1/8% per annum
First, we need to convert the interest rate from a percentage to a decimal. To do this, we divide the given rate by 100:
r = 7 1/8% = 7.125% = 7.125/100 = 0.07125 (decimal)
Next, we can calculate the simple interest using the formula:
Simple Interest (I) = Prt
I = $1000 x 0.07125 x (8/12)
I = $1000 x 0.07125 x (2/3)
I = $47.50
Finally, to find the amount due, we add the principal amount to the simple interest:
Amount Due = Principal + Simple Interest
Amount Due = $1000 + $47.50
Amount Due = $ 1047.50
Hence , the amount is A = $ 1047.50
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Suppose you're making a soup that uses 5 cups of chicken broth for 8 servings. You need to make 12 servings of the soup. How much broth do you need?
A) 7.5 cups
B) 2.5 cups
C) 8.7 cups
D) 10 cups
please answer this question correctly.
The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.
Option C is the correct answer.
We have,
Profit = Amount Paid - Cost of Supplies
Given that the cost of supplies for each room is $32.50, we can represent the profit for each room as:
Profit per room = Amount Paid per room - $32.50
Zack wants to make a profit of more than $300 for painting 4 identical rooms.
The total profit for the 4 rooms should be greater than $300.
We can write this inequality as:
4 x (Profit per room) > $300
Substituting the expression for profit per room, we have:
4 x (Amount Paid per room - $32.50) > $300
Now, let's solve the inequality to find the dollar amount that Zack must be paid for each room:
4 x (Amount Paid per room - $32.50) > $300
4 x Amount Paid per room - 4 x $32.50 > $300
4 x Amount Paid per room - $130 > $300
4 x Amount Paid per room > $300 + $130
4 x Amount Paid per room > $430
Amount Paid per room > $430 / 4
Amount Paid per room > $107.50
Therefore,
The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.
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Find an angle in each quadrant with a common reference angle with 311°, from 0°≤θ<360°
Angles in each quadrant with common reference angle as 311° are :
First quadrant = 49°, second quadrant = 131°, third quadrant = 229° and fourth quadrant = 311°.
Given that,
Reference angle = 311°
We have to find an angle in each quadrant with this reference angle.
311° is in the fourth quadrant.
The equivalent angle on the first quadrant is,
360° - 311° = 49°
Equivalent angle on second quadrant is,
180° - 49° = 131°
Equivalent angle on third quadrant is,
360° - 131° = 229°
Hence the angles are found.
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Simplify the expression 5x2+6x+4+x2+x
.
Thank You!
The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.
The given expression is 5x²+6x+4+x²+x
Simplifying the given expression
5x²+6x+4+x²+x
Firstly, put the similar terms together
5x²+x²+6x+x+4
Adding the similar terms
6x²+7x+4
∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.
Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.
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Find the ordered pair solutions for the
system of equations.
f(x)=x²-3x - 10
f(x) = -x-2
([ ? ],
) and (
Enter the smallest x first.
Answer:
[tex]( - 2, 0 )\; and \; ( 4, - 6)[/tex]
Step-by-step explanation:
To find the ordered pairs set the right side expressions equal to each other and solve for x, then use those values for x to evaluate f(x) values
We get
x² - 3x - 10 = -x - 2
Moving -x - 2 to the left side gives
x² -3x - 10 + x + 2 = 0
(moving an expression from one side to another changes the signs of the terms)
Grouping like terms:
x² - 3x + x -10 +2 = 0
x² -2x -8 = 0
Expression on the left can be factored as (x + 2)(x-4)
This results in
(x + 2)(x - 4) = 0 giving
(x + 2) = 0 ==> x = -2 as one solution for x
(x - 4) =0 ==> x = 4 as the second solution
Plug in x = -2 into the second expression -x - 2 to get
f(-2) = -(-2) -2 = 2 - 2 = 0
So one ordered pair is (-2, 0)
Plug in x = 4 into -x - 2 to get
f(4) = - 4 -2 = -6
So (4, -6) is another ordered pair
A baseball player earns $3 million in 2015. During the next 15 years, the earning increase 4% each year.
Write an exponential growth model giving the earning y (in millions of dollars) t years after 2015. Write the base of the model as a decimal
The exponential growth model for the baseball player's earnings, in millions of dollars, t years after 2015 is[tex]y = 3 \times (1.04)^t,[/tex] with a base of 1.04.
To model the exponential growth of the baseball player's earnings, we can use the formula:
[tex]y = a \times (1 + r)^t[/tex]
where:
y represents the earning in millions of dollars
a represents the initial earning in millions of dollars (in this case, $3 million)
r represents the growth rate per year (4%, which can be expressed as 0.04)
t represents the number of years after 2015
In this case, we want to find the earning y (in millions of dollars) t years after 2015.
Since the initial earning in 2015 is $3 million, we can substitute a = 3.
Therefore, the exponential growth model for the player's earnings is:
[tex]y = 3 \times (1 + 0.04)^t[/tex]
Simplifying the expression further, we have:
[tex]y = 3 \times 1.04^t[/tex]
The base of the model is 1.04, which is the decimal representation of the growth rate (4%).
Using this model, we can calculate the player's earnings for any year after 2015 by plugging in the value of t.
For example, if we want to find the earnings 5 years after 2015, we substitute t = 5 into the equation:
[tex]y = 3 \times 1.04^5[/tex]
This will give us the projected earnings in millions of dollars for that particular year.
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In one part of a rainforest in South America, 3/5 of the frogs are poisonous. What fraction of the frogs are not poisonous?
2/5 of the frogs in that portion of the South American rainforest are not poisonous.
How to calculate the fraction of frogs that are not poisonous in South American rainforestOn the off chance that 3/5 of the frogs in a rainforest in South America are poisonous, at that point, the remaining division speaks to the frogs that are not poisonous.
To discover this division, we subtract the division of poisonous frogs from 1 (which speaks to the complete):
1 - 3/5 = 5/5 - 3/5 = 2/5
Hence, 2/5 of the frogs in that portion of the rainforest are not poisonous. This fraction represents the parcel of frogs that don't have poisonous characteristics.
It is important to note that this calculation expects that all frogs within the rainforest are either poisonous or notpoisonous, and there are no other conceivable outcomes or middle states.
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a cube with a surface area of 6 square inches is removed from the corner of a cube with a surface area of of 96 square inches.
questions
a. what do you think removing the smaller cube from largers cubes has on its surface area? explain your answer
b. find the surface area of the new solid.
a. The surface area of the cube is reduced .
b . The new surface area of the new solid is 90 in²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
a. The surface area of the original cube is 96 in² and a cube of another 6 in² is removed from the old cube.
This means that the surface area of the cube is reduced.
The surface area of a cube is expressed as;
SA = 6l²
where l is the side length of the cube.
b. The surface area of the new solid = surface area of big cube - surface area of old cube = 96-6
= 90 in²
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The shaded square has an area of 55 square units.
Enter the exact value of the side length of the square
and press "Try it."
I
units
Try It
The exact value of the side length of the square is √55 unit.
Given that the shaded square has an area of 55 square units.
We need to determine the exact value of the side length of the square,
To determine the exact value of the side length of the square, we can use the formula for the area of a square, which is given by the equation:
Area = side length²
In this case, the area is given as 55 square units. Therefore, we can set up the equation as follows:
55 = side length²
To solve for the side length, we need to find the square root of both sides of the equation:
√55 = √(side length)²
Simplifying further:
√55 = side length
Thus, the exact value of the side length of the square is √55 unit.
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100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!
The amplitude and the period of the function f(x) = 2cos[3(θ + 45)] + 2 are 2 and 2π/3
The Phase shift is 45 and the vertical shift is 2
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2cos[3(θ + 45)] + 2
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = A
Period = 2π/B
Phase shift = C
vertical shift = D
Using the above as a guide, we have the following:
Amplitude = 2
Period = 2π/2
Next, we have
Phase shift = 45
vertical shift = 2
Hence, the amplitude is 2 and the period is 2π/3
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Need help with pie chart
a. The category that was chosen as approximately 1/4 will be Cat.
b. The percentage that choose other or cat will be 35%.
c. The percentage that choose dog is 16%
a. It should be noted that to determine the category chosen by approximately one-fourth of the community, we need to look for the corresponding section of the pie chart. This shows the cat.
b. The percentage that choose other or cat will be:
= 10% + 25%
= 35%.
c. The percentage that choose dog is:
= 32% / 2
= 16%
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21. If AXYZ ≈ AJKL, which segment corresponds to KJ?
If triangles ΔXYZ is congruent to ΔJKL, then the segment which corresponds to KJ is YX.
Given that, two triangles ΔXYZ and ΔJKL are congruent to each other.
So the corresponding vertices are,
Vertex X of ΔXYZ corresponds to vertex J of ΔJKL
Vertex Y of ΔXYZ corresponds to vertex K of ΔJKL
Vertex Z of ΔXYZ corresponds to vertex L of ΔJKL
Now, the segment which corresponds to KJ in ΔXYZ will be the segment formed by joining the vertices that corresponds to K and J.
We already have,
K corresponds to Y and J corresponds to X.
So the equivalent segment is YX.
Hence the segment required is YX.
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Tara looks up hotel room prices for a holiday.
A hotel has a 25% off sale on its prices.
A VAT charge of 20% must be added on at the end of the transaction after any discount.
If the regular price of a room is £80 per night, how much will Tara pay for 5 nights?
Answer:
360
Step-by-step explanation:
80*5=400 and .25*400=100 so it costs 300 for five nights without tax, and adding on the tax raises the cost to 60 (300+(.2*300)=360)
sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2
Answer:
sin( 3pi/4 ) = -√2/2
So, B.
Graph the circle (x - 3)^2 + (y + 3)^2= 36.
The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.
To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.
The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.
Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.
Using this information, we can proceed to plot the circle on a graph:
Plot the center point: (3, -3).
From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.
Up: (3, -3 + 6) = (3, 3)
Down: (3, -3 - 6) = (3, -9)
Left: (3 - 6, -3) = (-3, -3)
Right: (3 + 6, -3) = (9, -3)
Connect the plotted points to form a circle.
The resulting graph should look like this:
| • (3, 3)
|
| •
| •
__|_____________________________
|
|
|
|
| • (3, -3)
The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.
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