Given:
The expression is:
[tex]\dfrac{1}{2}(\cos (72)+i\sin (72))^5[/tex]
To find:
The [tex]a+bi[/tex] form for the given expression.
Solution:
According to De Moivre's theorem,
[tex](\cos \theta+i\sin \theta)^n=\cos (n\theta )+i\sin (n\theta )[/tex]
We have,
[tex]\dfrac{1}{2}(\cos (72)+i\sin (72))^5[/tex]
Using De Moivre's theorem, we get
[tex]=\dfrac{1}{2}(\cos (72\times 5)+i\sin (72\times 5))[/tex]
[tex]=\dfrac{1}{2}(\cos (360)+i\sin (360))[/tex]
[tex]=\dfrac{1}{2}(1+i(0))[/tex]
[tex]=\dfrac{1}{2}+0i[/tex]
It is the [tex]a+bi[/tex] form of the given expression. Here, [tex]a=\dfrac{1}{2},\ b=0[/tex].
Therefore, the required expression is [tex]\dfrac{1}{2}+0i[/tex].
Find the missing value in the ratio table. Then write the equivalent ratio
Answer:
The missing value in shirts is 28, and the missing value in jackets is 14.
Step-by-step explanation:
100/a = 25
i think its 2500 but I'm not sure
Answer:
a=4
Step-by-step explanation:
100/a=25
100/25 =a
a=4
9 in
4 in
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
Answer:
9.8in
Step-by-step explanation:
i think this right
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)6
are
A. 0, 6, 15, 20, 15, 6, 0
B. 1, 6, 15, 15, 6, 1
C. 1, 6, 15, 20, 15, 6, 1
D. 0, 1, 6, 15, 15, 6, 1,0
Omar, Hala and Lujain got paid a total of $240 for cleaning neighborhood cars. They split the money in the ratio of 5: 9: 10. How much money did Omar earn?
Answer:
Total amount Omar earn = $120
Step-by-step explanation:
Given:
Total amount Omar, Hala and Lujain got paid = $240
Ratio of money Omar, Hala and Lujain got paid = 5:9:10
Find:
Total amount Omar earn
Computation:
Total amount Omar earn = [Total amount Omar, Hala and Lujain got paid][Omar'ratio / Total ratio]
Total amount Omar earn = [240][5 / (5+9+10)]
Total amount Omar earn = [240][5 / (24)]
Total amount Omar earn = [24][5]
Total amount Omar earn = $120
PLEASE I need help really bad I only have 10 minutes left to turn it in!! I’ll mark you as brainliest please!!!
Answer:
Area=76.8
Perimeter=49.6
Good luck!
In 2013 the Los Angeles Dodgers opening
day payroll was about $2.16 10^8 and the
Houston Astros opening day payroll was
about $2.4 x 10^7. How much higher was
the Dodgers' payroll?
Please help, I’m bad at math.
Answer: 1.92 x 10^8
Step-by-step explanation:
Solve equation by using the quadratic formula.
15x^2 + 13x = 0
Answer:
0 and - 13/15
Step-by-step explanation:
Order the following numbers from least to greatest. Put the lowest number on the left. 2 -2 5 -5
Answer:
-5,-2,2,5
Step-by-step explanation:
According to the Oxnard College Student Success Committee report in the previous year, we believe that 18% of students struggle in their classes because they don't spend more than 8 hours studying independently outside of a 4-unit class. For this year, you would like to obtain a new sample to estimate the proportiton of all Oxnard students who struggle in their classes because they don't study enough outside of the classrooms. You would like to be 99% confident that your estimate is within 5% of the true population proportion. How large of a sample size is required
Answer:
A sample size of 392 is required.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
18% of students struggle in their classes because they don't spend more than 8 hours studying independently outside of a 4-unit class.
This means that [tex]\pi = 0.18[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
You would like to be 99% confident that your estimate is within 5% of the true population proportion. How large of a sample size is required?
A sample size of n is required.
n is found when M = 0.05. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 2.575\sqrt{\frac{0.18*0.82}{n}}[/tex]
[tex]0.05\sqrt{n} = 2.575\sqrt{0.18*0.82}[/tex]
[tex]\sqrt{n} = \frac{2.575\sqrt{0.18*0.82}}{0.05}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575\sqrt{0.18*0.82}}{0.05})^2[/tex]
[tex]n = 391.5[/tex]
Rounding up:
A sample size of 392 is required.
How do you find the area under a curve?
Answer:
The area under a curve between two points can be found by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive.
Step-by-step explanation:
Question 7
A cylindrical water tank carries a volume of 150 L when it is full. The water tank has a base surface
with a diameter of 140 cm. What is the height of the water tank? Round your answer to three decimal
digits.
Answer:
Volume of a Cylinder:
In geometry, a cylinder is a three-dimensional shape with a circular base, a circular top and straight sides. It is the solid figure that you get when you rotate a rectangle about one of its sides. In most cases when we talk about the volume of a cylinder, we are talking about how much liquid it can hold.
The strictly correct way of saying it is "the volume surrounded by a cylinder" - the amount of liquid it holds. But many textbooks simply tell "the volume of a cylinder" to mean the same thing.
Remember that the radius and the height must be in the same units - convert them if necessary.
The resulting volume will be in those cubic units. So if the height and radius are both in centimeters, then the volume will be in cubic centimeters.
The volume of a cylinder is found by multiplying the area of its top or base by its height and is defined as: V = π· r2· h
Example 1: A cylindrical water storage tank has an inside base radius of 7m and depth of 11 m. Find the capacity of the tank in kiloliters (1kl = 1m3).
Solution:
Base radius: r = 7 m
Height: h = 11 m
The water storage tank is in the shape of the cylinder. So using the volume of cylinder formula we can find the volume of it.
V = π· r2· h
V = π· 72· 11
V = 1692.46 m3 = 1692.46 kl
Example 2: Find the volume of a cylinder whose base radius is 6 cm and height is 4 cm.
Solution:
Base radius: r = 6 cm
Height: h = 4 cm
V = π· r2· h
V = 3.14· 62· 4
V = 452.16 cm3
Example 3: If the capacity of a cylindrical tank is 1848 m3 and the diameter of its base is 14 m, find the depth of the tank.
Solution:
Let the depth of the tank be h metres. Then we have:
V = π· r2· h
h = V / π· r2
h = 12 m
Example 4: A conical vessel, whose internal radius and height is 20cm and 50 cm respectively, is full of liquid. Find the height of the liquid if it is put into a cylinder whose base radius is 10 cm.
Solution:
The volume of the vessel is:
V = π ∙ r2 ∙ h / 3
V = π · 202· 50 / 3
V = 20944 cm3
The volume of the liquid is the same no matter it is in the vessel or in the cylinder, therefore we have:
V1 = V2, where V1 is the volume of the vessel and V2 is the volume determined using the formula for a cylinder.
20944 = π · 102 · h
Thus:
h = 20944 / (π · 102)
h = 66.67 cm
Example 5: Find the volume of a right circular cylinder whose curved surface area is 2640 cm2
And the circumference of its base is 66 cm.
Solution:
To begin with we need to determine the base radius using the formula for circular perimeter (circumference).
P = 2 · π ·r
r = P /(2 · π) = 66 / (2 · π) = 10.50 cm
Now we will find the height of the cylinder using the formula for surface area of a cylinder.
SA = P · h
h = SA / P = 2640 / 66 = 40 cm
The volume of the cylinder is therefore:
V = π· r2· h
V = π· 10.502· 40
1. Use a straightedge to construct a line that goes
through points A and B. Label the line l.
2. Which axis is parallel to line l?
10
Which axis is perpendicular to line l?
3
Plot two more points on line l. Name them Cand D.
51
4. Give the coordinates of each point below.
B.
A:
B:
С.
D:
0
5
10
5. Give the coordinates of another point that falls on line l with a y-coordinate greater than 20.
My
Answer: A
2". 1. 0 a. Put a square box at the origin of the number line. b. Plot point C so it is located at 2 ... d. Plot a point at the midpoint of C and E. Label it H. Lesson 2. 1. Name the ... 2. Line & passes through point H and is parallel to the y-axis. Construct line l.
Step-by-step explanation:
Step-by-step explanation:
Name the 4Ps of marketing.
Answer:
Product – Attributes of an organization or offering within this segment include delivery system design, technology, quality, services provided and their availability.
Price – This silo of the marketing mix includes costs to users/supporters, payment periods, arrangements and terms. Note: Some have also argued “costs” are more than dollars … a full cost analysis should include emotional (for those seeking greater purpose, advancements, victory), sacrificial (for people giving time, energy, focus) and relational (what does one’s association with an organization do for their relationships … will people think more or less of them).
Place – An often-overlooked part of the marketing mix, this “P” covers strategy and executional elements surrounding service distribution channels, coverage, locations, logistics and e-services.
Promotion – Likely the most known aspect of the marketing mix, this piece considers strategies and tactics related to advertising, logo/identity and promotions. But it also covers development/fundraising, communications, events and public relations as they are all tools to be considered and deployed as part of the greater marketing and branding strategy.
ion
What is the total surface area of a pyramid with a square base with sides of 12 cm, where the faces
have a slant height of 15 cm?
15 cm
On this side.
A
= 0.3333333
12 cm
O A 144 cm?
OB 234 cm
OC 360 cm
OD 504 cm?
Answer: 504
Step-by-step explanation:
Area: 4 triangles + square
Triangle area = 1/2 x b x h
Square = side x side
4(1/2 x 12x 15) + 12x12
= 504
Why are blurring the answers
Answer:
? sorry what?
Step-by-step explanation:
The Venn diagram shows the number of students that exercise in different ways. What number should go in the highlighted box below?
Answer:
50
Step-by-step explanation:
Add up all the numbers
what is the volume if a hemisphare with a diameter of 10cm
Answer:
volume of hemisphere=2/3πr³
2/3×22/7×5³261.90cm³hope it helps.
Help me plsssssssssssssssssssssssssss
number 7 is as follows Answer: C18.9
Step-by-step explanation:
The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. so (5.65x2)+(3.8x2)=18.9 cm
Answer:
2 is F. 768 because all you have to do is mulltiply base times height oh and 7 is C
Step-by-step explanation:
Wyatt is going to invest $28,000 and leave it in an account for 5 years.
Assuming the interest is compounded quarterly, what interest rate, to the
nearest hundredth of a percent, would be required in order for Wyatt to end
up with $31,000?
Answer:2.04 %
Step-by-step explanation:
The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000)
1 9 8.1 7 8 7.6
2 7 6 8 11 8
3 11 3.6 9 10 8
4 12 4 10 12 6
5 8 5 11 6 8.6
6 7 10 12 6 8
Required:
a. Determine the regression equation.
b. Estimate the selling price of a 10-year-old car (in $000).
c. Interpret the regression equation (in dollars).
Answer:
ŷ = -0.47876X + 11.17724
$6.4
Step-by-step explanation:
Given the data :
Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000)
1 9 8.1 7 8 7.6
2 7 6 8 11 8
3 11 3.6 9 10 8
4 12 4 10 12 6
5 8 5 11 6 8.6
6 7 10 12 6 8
The estimated regression equation using a linear regression calculator is :
y = -0.47876X + 11.17724
With - 0.47876 being the slope ; and 11.17724 being the intercept
y = predicted variable (price of car) ; x = predictor variable (Age of car)
Selling price of a 10 year old car : x = 10
ŷ = -0.47876(10) + 11.17724
Price = 6.38964
About 6.4(000) dollars ($6,400)
According to the regression equation : The starting price of cars is about $11.18 (intercept) with the proved of cars declining by a value of $0.479(negative slope value) each year.
A group of friends wants to go to the amusement park. They have no more than $310 to spend on parking and admission. Parking is $9, and tickets cost $35 per person, including tax. Write and solve an inequality which can be used to determine xx, the number of people who can go to the amusement park.
Answer:
9 + 35x = 310
Step-by-step explanation:
What is the domain for this function, (x+2)/(x-3)? *
all real numbers except x=2
all real numbers except x=-2
all real numbers except x=3
all real numbers except x=-3
Answer:
C
Step-by-step explanation:
x-3≠0
x≠3
so C
Answer:
it is C
Step-by-step explanation:
i just took the test
She didn't see him either. (into affirmative)
Answer:
i Don't know this but other's can help you.
Find the product for each of the following.
Answer:
1 10/17
Step-by-step explanation:
make 45 a fraction by putting a denominator of 1
3/85 * 45/1
3*45 = 135
85*1 = 85
Simplify 135/85 = 1 10/17
What is the value of 1 / 5 (6 + 8.5)?
pls help ill give branliest
c(x)=2x^3+3x^2-1 find rational zeros
Answer:
1/2
Step-by-step explanation:
The Rational Root Theorem says that any rational root has
1. a numerator that is a factor of the constant term
2. a denominator that is a factor of the leading coefficient (that's attached to the highest-power term)
Numerator: [tex]\pm 1[/tex]
Denominator: [tex]\pm 2[/tex]
That means there are only two possible rational roots: [tex]\pm \frac{1}{2}[/tex]
Try them both by plugging them into the polynomial.
[tex]2\left(\frac{1}{2}\right)^3 + 3\left(\frac{1}{2}\right)^2 -1= \frac{1}{4}+\frac{3}{4}-1 =0[/tex]
Aha! The negative one-half value does not produce 0
Which of the following can be used to evaluate the series?
Answer put the question smarty
Step-by-step explanation:
F(x) =-6-3x/2. g(x)=2x+4
Answer:
correct
Step-by-step explanation:
my brain be smart