What is the product of 3rad3cis(pi/8) and 3rad5cis(2pi/3)
Answers
Answer:
[tex]9\sqrt{15}*cis(\dfrac{19\pi}{24})[/tex]
Step-by-step explanation:
To multiplying complex numbers in polar form, follow these steps:
Multiply the polar magnitudes of the complex numbers.Add the angles of the complex numbers.Given the two complex number in polar form
[tex]3\sqrt{3}\:cis(\dfrac{\pi}{8})\:\:and\:\:3\sqrt{5}\:cis(\dfrac{2\pi}{3})\\\\3\sqrt{3}\:cis(\dfrac{\pi}{8})*3\sqrt{5}\:cis(\dfrac{2\pi}{3})=(3\sqrt{3}*3\sqrt{5})*cis(\dfrac{\pi}{8}+\dfrac{2\pi}{3})[/tex]
[tex]=9\sqrt{15}*cis(\dfrac{3\pi+8*2\pi}{24})\\\\=9\sqrt{15}*cis(\dfrac{19\pi}{24})[/tex]
Answer: 34.86cis (2.49)
Step-by-step explanation: I took the quiz.
Related Questions
please help with this
Answers
Answer:
Width = 3x^2 + 5
Step-by-step explanation:
Area = Length*Width
(6x^2+10)=2*Width Divide both sides by 2
3x^2+5 = Width
Answer:
3x^2 +5
Step-by-step explanation:
Take the pink area 6x^2 and divide by 2
6x^2/2 = 3x^2
Take the blue area and divide by 2
10/2 = 5
Add them together to find the width
The width is 3x^2 +5
Carol rolled a dice 150 times she rolled a 6 29 times use carols data to estimate the probability of rolling a six with this dice give your answer as a fraction
Answers
This is because she rolled a 6 29 times out of a possible 150 times
You can afford $1,000 per month as a house payment. If you can get a home loan at 5.3% interest for 15 years (paid monthly), how expensive of a home can you afford? In other words, what amount loan can you pay off with $1,000 per month for 15 years?
Answers
Answer:
You can afford $1,000 per month as a house payment.
You can get a home loan at 5.3% interest for 15 years (paid monthly).
Then, after 15 years, the price of house that you can afford would be:
A x (1 + (5.3/100)/12)^(12 x 15) = 2.2 x A
With payment of 1000$ per month in 15 years, then we have
2.2 x A = 1000 x 12 x 15 = 180000
=> The price of house that you can afford now, would be:
A = 180000/2.2 = 81818.2$
Hope this helps!
:)
A repeated-measures study comparing two treatments with n = 4 participants produces MD = 2 and SS = 75 for the difference scores. What is the estimated standard error for the sample mean difference? Group of answer choices 25 25/4 = 6.25 5 2.5
Answers
Answer:
2.5
Step-by-step explanation:
n = 4 participants
MD = 2, SS = 75
Estimated standard error, s² =[tex]\frac{SS}{n-1}[/tex]
= [tex]\frac{75}{4-1}[/tex] = 25
Standard error = [tex]\sqrt{\frac{Estimated standard error}{n} }[/tex] = [tex]\sqrt{\frac{25}{4}}[/tex] = 2.5
In a recent study of statistics students, a random sample of students were asked to provide the number of hours per week they spend studying for their statistics class. The results were used to compute confidence intervals for the population mean hours per week spent studying for statistics. The 95% confidence interval for the population mean hours per week that students spend studying for statistics was (6.83, 8.27). In this confidence interval, what is the sample mean (x bar) hours per week spent studying for statistics? Provide your answer as a number rounded to two decimal places.
Answers
Answer:
The sample mean hours per week spent studying for statistics is 7.55 hours.
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The 95% confidence interval for the population mean hours per week that students spend studying for statistics was (6.83, 8.27).
Compute the sample mean hours per week spent studying for statistics as follows:
[tex]\frac{\text{UL + LL}}{2}=\frac{(\bar x+ z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}})+(\bar x- z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}})}{2}\\\\\frac{8.27+6.83}{2}=\frac{2\cdot \bar x}{2}\\\\7.55=\bar x[/tex]
Thus, the sample mean hours per week spent studying for statistics is 7.55 hours.
PLEASE HELP ?
Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
Answers
Step-by-step explanation:
-2m - 5m - 8 = 3 + (-7) + m
Solving like terms
-7m - 8 = 3 - 7 + m
-7m - 8 = - 4 + m
Option 2 4 and 5 are equivalent
I need to know what –5(–2) equals.
Answers
Answer:
10
Step-by-step explanation:
Simplify the expression by combining like terms. Write the terms in alphabetical order of the variables.
X+20y-2z+19x-2y+19z
Answers
Answer: [tex]20x+18y+17z[/tex]
Step-by-step explanation:
[tex]x+20y-2z+19x-2y+19z\\(x+19x)+(20y-2y)+(-2z+19z)\\20x+18y+17z[/tex]
Find the volume of the cylinder below (using 3.14 for p).
- Include the equation you are using.
- Show all work to get your answer.
- Round your answer to the nearest tenth.
Make sure to label your answer appropriately.
Answers
==========================================================
Work Shown:
d = 8.4 is the diameter
r = d/2 = 8.4/2 = 4.2 is the radius
h = 14.5 is the height
V = pi*r^2*h = volume of cylinder
V = pi*(4.2)^2*14.5
V = pi*255.78
V = 255.78pi = exact volume in terms of pi
V = 255.78*3.14
V = 803.1492
V = 803.1 ... round to one decimal place
The units for the volume are in cubic meters which we can abbreviate as "m^3"
Simplify to create an equivalent expression.
8(10 - 6q) + 3(-7q - 2)
Answers
Answer:
27q + 74
Step-by-step explanation:
=80 - 48q -21q - 6
=27q + 74
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 5000 subjects randomly selected from an online group involved with ears. 717 surveys were returned. Use a 0.01 significance level to test the claim that the return rate is less than 15%.
Answers
Answer:
As the P-value (0.086) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the return rate is less than 15%.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the return rate is less than 15%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.15\\\\H_a:\pi<0.15[/tex]
The significance level is 0.01.
The sample has a size n=5000.
The sample proportion is p=0.143.
[tex]p=X/n=717/5000=0.143[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.15*0.85}{5000}}\\\\\\ \sigma_p=\sqrt{0.000026}=0.005[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.143-0.15+0.5/5000}{0.005}=\dfrac{-0.007}{0.005}=-1.366[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-1.366)=0.086[/tex]
Answer:
[tex]z=\frac{0.1434 -0.15}{\sqrt{\frac{0.15(1-0.15)}{5000}}}=-1.307[/tex]
Now we can calculate the p value with the following probability:
[tex]p_v =P(z<-1.307)=0.0956[/tex]
For this case the p value is lower than the significance level provided of 0.1 so then we can reject the null hypothesis and we can conclude that the the return rate is significantly less than 15%.
Step-by-step explanation:
Information provided
n=5000 represent the random sample taken
X=717 represent the surveys returned
[tex]\hat p=\frac{717}{5000}=0.1434[/tex] estimated proportion of urvyes returned
[tex]p_o=0.15[/tex] is the value to verify
[tex]\alpha=0.01[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the return rate is less than 15% the system of hypothesis are.:
Null hypothesis:[tex]p \geq 0.15[/tex]
Alternative hypothesis:[tex]p < 0.15[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.1434 -0.15}{\sqrt{\frac{0.15(1-0.15)}{5000}}}=-1.307[/tex]
Now we can calculate the p value with the following probability:
[tex]p_v =P(z<-1.307)=0.0956[/tex]
For this case the p value is lower than the significance level provided of 0.1 so then we can reject the null hypothesis and we can conclude that the the return rate is significantly less than 15%.
On a map, 4 inches represents an actual distance of 24 miles. If the actual distance between two cities is 126 miles, how many inches apart will the two cities be on the map
Answers
Answer:
21 inches
Step-by-step explanation:
1 inch = 6 miles
126/6 = 21
is 2x^2+y =3x - 1 a function quadratic
Answers
Answer:
Step-by-step explanation: yes because when rewritten in standard form the x term will still be raised to the 2nd power.
Data was collected for 226 randomly collected 10 minute interval. For each Tim and I are in a rule the number of people entering the atrium of a large mall were recorded. The data is summarized in the table below
What is the width for this GFDT?
Number of guest. Frequency
60-64. 57
65-69. 39
70-74. 7
75-79. 36
80-84. 87
Answers
Answer:
The class width of this grouped frequency distribution (GFDT) = 5.
The total width of the distribution = 25, that is, from 60 to 84.
Step-by-step explanation:
The class width of a GFDT (grouped frequency distribution) is obtained by dividing the range by the number of classes required and then rounding up.
Note that rounding up is different from rounding off as 4.2 is rounded up to 5 and rounded off to 4.
The class width is the span of each of the class in the grouped frequency distribution.
For this distribution,
Maximum value = 84
Minimum value = 60
Range = (Maximum value) - (Minimum value) = 84 - 60 = 24
Number of classes required = 5
Class width = (24/5) = 4.8 = 5 (rounded up).
The total width of the distribution is given as
Total width = Range + 1 = 24 + 1 = 25.
Hope this Helps!!!
As an estimation we are told £3 is €4.
Convert €52 to pounds.
Answers
Answer:
£69.33
Step-by-step explanation:
4/3=1.33333333333 so that 52*1.33333333333 would convert 52 euros into 52 pounds
Will mark u brainliest
15 points!!!!
Class 9 math
Answers
Answer:
[tex]\frac{3375}{512}[/tex] or ≈6.59
Step-by-step explanation:
We can first begin by simplifying each of the numbers with exponents. Recall that in a fraction exponent, the numerator is the power, while the denominator is the root.
Take [tex]25\frac{3}{2}[/tex] for example. The '2' in the fraction means we must take the square of 25. √25 = 5.
The '3' in the fraction means we take the power, which means we must cube '5'.
5³ = 125. Therefore, [tex]25\frac{3}{2}[/tex] = 125. Use this process for the other numbers:
[tex]25^{\frac{3}{2} } = 125\\243^{\frac{3}{5} } = 27\\16^{\frac{5}{4} } = 32\\ 8^{\frac{4}{3} } = 16[/tex]
The new fraction would look like:
[tex]\frac{125 * 27}{32 * 16}[/tex]
Which simplifies to:
[tex]\frac{3375}{512}[/tex] or ≈6.59
Answer:
Step-by-step explanation:
(25) raise to 3/2 = (5^2) raise to 3/2 and 2 gets cancelled when the bracket is opened which leaves 5^3.
(243) raise to 3/5 = (3^5) raise to 3/5 and 5 gets cancelled when the brackets are opened which leaves 3^3.
(16) raise to 5/4 = (2^4) raise to 5/4 and 4 gets cancelled when the bracket is opened which leaves 2^5.
(8) raise to 4/3 = (2^3) raise to 4/3 and 3 gets cancelled when the brackets are opened which leaves 2^4.
5^3 * 3^3 divided by 2^5 * 2^4
= (5 x 3)^ 3 / 2^5+4 [∵a^m x b^m = (ab)^m] & [a^m x a^n = a^m+n]
15^3 / 2^9
This when simplified gives 6.591.
So, 15^3 / 2^9 is approximately equal to 6.59
PLS MARK IT AS BRAINLIEST
Mark ordered a square pizza that has a side length of 12 inches Rodney ordered a round pizza with a 12 inch diameter each of them paid seven dollars for their pizza you got the better deal
Answers
Answer:
Square pizza is the better deal.
Step-by-step explanation:
The better deal will be the one that has larger area of pizza. So, find the area of pizza in the case of square pizza and in the case of round pizza.
Below is the calculation of area of pizzas.
[tex]\text{Area of square pizza} = (Side)^{2} \\\text{Area of square pizza} = (12)^2 \\\text{Area of square pizza} = 144 \ in^2 \\[/tex]
[tex]\text{Now area of round pizza.} \\\text{ The area of round pizza} = \pi r^{2} \\\rm Diameter = 12 \\So, \ radius = \frac{12}{2} = 6 \\\text{ The area of round pizza} = \pi r^{2} \\= \frac{22}{7}\times (6)^2 \\= 113.1 \ in^2[/tex]
Since the area of square pizza is greater than round pizza. Thus, square pizza is better deal.
What are the zeros of f(x) = x2 + x - 20?
A. X = -5 and x = 4
B. X = - 4 and x = 5
C. x = -2 and x = 10
D. x = -10 and x = 2
Answers
Answer:
A. x = -5, 4
Step-by-step explanation:
0 = x^2 + x -20
0 = (x + 5)(x - 4)
x = -5, 4
Answer: x=-4 and x=5
Step-by-step explanation:
0 = x^2 + x -20
0 = (x + 5)(x - 4)
then to find the zeros we should switch the signs so the answer is :
-4,5
Write the least common multiple of 10 and 30
Answers
Answer:
30
Step-by-step explanation:
Multiples of 10 = 10,20,30
Multiples of 30= 30,60,90
The smallest one is 30
Answer:
30
Step-by-step explanation:
GCF(10,30) = 10
LCM(10,30) = ( 10 × 30) / 10
LCM(10,30) = 300 / 10
LCM(10,30) = 30
What’s the correct answer for this?
Answers
Answer:
D.
Step-by-step Explanation:
In the attached file
Ms. Wong's class had 11 girls and 14 boys. What is the probability that a girl will get the infection first and then a boy ?
Answers
Answer: 25,67%
Step-by-step explanation:
We have 11 girls and 14 boys, this is a total of 11 + 14 = 25 students.
If all the students have the same probability of being infected, the probability that a girl will get infected first is equal to the number of girls dividedthe total number of students:
p1 = 11/25
Now we get a boy infected, the number of boys is 14, and the total number of students is now 24 (because we already have a girl infected)
this probability is p2 = 14/24
The probability for both events is equal to the product of the probabilities:
P = p1*p2 = (11/25)*(14/24) = 0.2567
or 25,67%
Evaluate 2x^3 + 5x^2 + 4x + 8 when x = -2
Answers
Answer:
4Step-by-step explanation:
Given the function 2x³ + 5x² + 4x + 8. In order to evaluate the value of the function at x = -2 we will substitute the value of x given into the function as shown;
F(x) = 2x³ + 5x² + 4x + 8
at x = -2
f(-2) = 2(-2)³ + 5(-2)² + 4(-2) + 8
f(-2) = 2(-8) + 5(4) +(-8) + 8
f(-2) = -16+20-8+8
f(-2) = -16+20
f(-2) = 4
The value of the function when x = -2 is 4
Guys please help it’s easy but idk
Answers
Answer:
51
Step-by-step explanation:
Volume can be calculated by [tex]\frac{4}{3}\pi r^{3}[/tex]
In this situation, your r (radius) is 2.3. Put 2.3 in to the equation for r, and you get 50.97. Round that to the nearest tenth to make it 51!
Suppose that a magazinemagazine predicted that Candidate A would defeat Candidate B in a certain election. They conducted a poll of telephone directoriestelephone directories with a response rate of 23%. On the basis of the results, the magazinemagazine predicted that Candidate A would win with 57% of the popular vote. However, Candidate B won the election with about 62% of the popular vote. At the time of this poll, most households with telephoneshouseholds with telephones belonged to the party of Candidate A. Name two biases that led to this incorrect prediction.
Choose the correct answer below.
A.
Sampling bias Using an incorrect frame led to undercoverage.
Response bias: The way the poll was administered showed bias
B.
Sampling bias: Using an incorrect frame led to undercoverage
Nonresponse bias: The low response rate caused bias
C.
Nonresponse bias: The low response rate caused bias.
Response bias: The way the poll was administered showed bias.
Answers
Answer:
im pretty sure its B
Step-by-step explanation:
Marissa bought 60 horns for her New Year’s Eve party for $83.40.
She needs to purchase an additional 18 horns for the party at the same unit rate.
Choose True or False for each statement.
Answers
Answer:
We don't have the statements but I can tell you the following info:
Step-by-step explanation:
83.4/60= $1.39 for each horn
18*1.39= $25.02 for the 18 additional horns.
$83.40+25.02= $108.42 for the total 78 horns
what is the circumference of this circle?
Answers
Answer:
12π
Step-by-step explanation:
C = Dπ
C = 12π
Answer:
37.68
Step-by-step explanation:
Trust me
Make me brainleist
A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and, of these 312 men, 102 died from causes related to heart disease. Calculate the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease. (A) 0.115 (B) 0.173 (C) 0.224 (D) 0.327 (E) 0.514
Answers
Answer:
The correct option is (B) 0.173.
Step-by-step explanation:
The law of total probability states that:
[tex]P(A)=P(A\cap B)+P(A\cap B^{c})[/tex]
The conditional probability of an event A given that another event B has already occurred is:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
Then the probability of intersection of A and B is:
[tex]P(A\cap B)=P(A|B)\cdot P(B)[/tex]
Denote the events as follows:
H = a man died from causes related to heart disease.
X = a man had at least one parent who suffered from heart disease
The information provided is:
[tex]P(H)=\frac{210}{937}\\\\P(X)=\frac{312}{937}\\\\P(H|X)=\frac{102}{312}[/tex]
The probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease is, [tex]P(H|X^{c})[/tex].
Compute the value of [tex]P(H|X^{c})[/tex] as follows:
[tex]P(H)=P(H|X)\cdot P(X)+P(H|X^{c})\cdot P(X^{c})[/tex]
[tex]\frac{210}{937}=[\frac{102}{312}\cdot \frac{312}{937}]+[P(H|X^{c})\cdot (1-\frac{312}{937})]\\\\\frac{210}{937}-\frac{102}{937}=[P(H|X^{c})\cdot \frac{625}{937}]\\\\\frac{108}{937}=P(H|X^{c})\cdot \frac{625}{937}\\\\P(H|X^{c})=\frac{108}{937}\times \frac{937}{625}\\\\P(H|X^{c})=0.1728\\\\P(H|X^{c})\approx 0.173[/tex]
Thus, the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease is 0.173.
The correct option is (B).
What is the simplest form of StartRoot StartFraction 126 x y Superscript 5 Baseline Over 32 x cubed EndFraction EndRoot ?
Answers
Answer:
b
Step-by-step explanation:
Answer:
The Correct Answer is b
Step-by-step explanation:
Correct on Edg 2020
heart and give me a good rating if you dont mind ;)
There are 11 small jars on a table.
3 are Honey.
8 are Jam.
Rosie take 2 at random.
Work out the probability that she takes at least on jar of honey.
Answers
Answer:
There are 11 small jars on a table and 3 of 11 are jars of honey.
=> Probability that Rosie takes at least 2 jars honey:
P = P(Rosie picks 1 jar of honey) + P(Rosie picks 2 jars of honey)
= (3/11) x (8/10) + (8/11) x (3/10) + (3/11) x (2/11) = 0.486 = ~0.49
Hope this helps!
:)
Answer:
Step-by-step explanation:
you can use a treee diagrammm so the answer ist goeig to be 0.49 thums up
what is the area of a trapezoid where one base is 6 cm the second base is 4cm and the height is 8cm?
Answers
Answer:
40 cm
Step-by-step explanation:
To find the area of a trapezoid, you have to do...
(4+6)times 8 divided by 2
so its 10 times 8 which is 80 divided by 2 is 40 cm!!
hope this helps!!
48 + 32 divided by 2 is 40
Step-by-step explanation:
The area is 40