Answer:
Probability of missing two passes in a row is 0.08.
Step-by-step explanation:
Event E = A football player misses twice in a row.
P(E) = ?
Event X = Football player misses the first pass
P(X) = 0.4
Event Y = Football player misses just after he first miss
P(Y) = 0.2
Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:
P(E) = P(X).P(Y)
P(E) = 0.4*0.2
P(E) = 0.08
Answer:
Probability of missing two passes in a row is 0.08.
Step-by-step explanation:
Event E = A football player misses twice in a row.
P(E) = ?
Event X = Football player misses the first pass
P(X) = 0.4
Event Y = Football player misses just after he first miss
P(Y) = 0.2
Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:
P(E) = P(X).P(Y)
P(E) = 0.4*0.2
P(E) = 0.08
In a given week, it is estimated that the probability of at least one student becoming sick is 17/23. Students become sick independently from one week to the next. Find the probability that there are at least 3 weeks of no sick students before the 2nd week of at least one sick student.
Answer:
0.614
Step-by-step explanation:
Let the time be given by = t
and P(S ) = probability that a person is sick
P(s) = probability that a person is not sick
P(s) = [tex](\frac{17}{23})^{23}* (1-\frac{17}{23})\\[/tex]
Then the probability for that there are at least 3 weeks of no sick students before the 2nd week of at least one sick student is given by:
[tex](\frac{17}{23})(\frac{17}{23})(\frac{17}{23})(\frac{17}{23}) + \frac{6}{23} + 3(\frac{17}{23})^{3}\\ = 0.614[/tex]
Ten of 16 students in Nyack's class are girls. His teacher selected two helpers by randomly drawing names. He drew a boys name first and then a girls names. Nyack thinks that the probability of this happening is 15/64. Is he correct? If not, Explain his error.
[tex]|\Omega|=16\cdot15=240\\|A|=6\cdot10=60\\\\P(A)=\dfrac{60}{240}=\dfrac{1}{4}[/tex]
He's wrong.
The formula to find the period of orbit of a satellite around a planet is T2=(4π2GM)r^3 where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant. If you are given all the values except r, how do you rewrite the formula to solve for r?
Answer:
[tex]r=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}}[/tex]
Step-by-step explanation:
Divide by the coefficient of the r factor, then take the cube root.
[tex]T^2=\dfrac{4\pi^2}{GM}r^3 \qquad\text{given formula}\\\\\dfrac{T^2GM}{4\pi^2}=r^3 \qquad\text{divide by the coefficient of the r factor}\\\\r=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}} \qquad\text{cube root}[/tex]
Answer:
The formula to solve r is [tex]r=\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}[/tex].
Step-by-step explanation:
Consider the provided formula:
[tex]T^{2}=\frac{4\pi^{2}r^{3}}{GM}[/tex]
Where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant.
Multiply both side by GM.
[tex]T^{2}GM=4\pi^{2}r^{3}[/tex]
Further solve the above equation.
[tex]\frac{T^{2}GM}{4\pi^{2}}=r^{3}[/tex]
[tex]\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}=r[/tex]
Hence, the formula to solve r is [tex]r=\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}[/tex].
A man steps out of a plane at a height of 4,000m above the ground falls 2,000m very quickly and then opens his parachute and slowly falls the remaining 2000m to the ground what height above the ground would be the best Choice for a reference point
Answer:
Step-by-step explanation:
A man steps out of a plane at 4,000m of height above the ground.The point at which he jumps out of the plane would make a good reference point. However, if his acceleration is going to change as a result of him opening his parachute 2000m above the ground, a good reference point would be there. Keep in mind though, that his velocity at that instant would need to be known for it to be useful- otherwise the airplane reference point would be just as good with appropriate modeling....
Answer:4000m easy !!
Find the equation for the horizontal line and the vertical line passing through ( − 10 , 7 )
Answer:
Step-by-step explanation:
Horizontal lines have the form " y = " where vertical lines have the form " x = ".
Horizontal lines run parallel to the y = 0 line, the x-axis, so horizontal lines are found in the y coordinate of the point. Therefore, the horizontal line at that point is y = 7.
The vertical lines run parallel to the y-axis, which is the line x = 0. The vertical lines are found then in the x coordinate of the point. Therefore, the vertical line at that point is x = -10
The two rectangles are similar. Which is the correct proportion for corresponding sides? (12)
Answer:
The answer is
D.
GD/MJ = DE/JK
Answer:
GD/MJ = DE/JK
Step-by-step explanation:
This answer is correct because GD and MJ are similar sides and DE and JK are similar sides as well
One zero of the polynomial function f(x) = x3 + x2 + 20x is x = 0. What are the zeros of the polynomial function?
0, −5, −4
0, −5, 4
0, 5, −4
0, 5, 4
The zeros of the polynomial function f(x) = x^3 + x^2 + 20x are 0, -5, -4.
Explanation:The zeros of a polynomial function are the values of x that make the function equal to zero.
We are given that one zero of the polynomial function f(x) = x^3 + x^2 + 20x is x = 0.
To find the other zeros, we can use polynomial long division or synthetic division to factor out x = 0 and find the remaining quadratic equation.
Factoring the quadratic equation, we find that the zeros are x = -5 and x = -4.
Therefore, the correct answer is 0, -5, -4.
Final answer:
The zeros of the polynomial function f(x) = x^3 + x^2 + 20x are 0, -5, and -4.
Explanation:
The zeros of a polynomial function are the values of x that make the function equal to zero. Given that one zero of the polynomial function f(x) = x^3 + x^2 + 20x is x = 0, we need to find the other zeros. To do this, we factor the polynomial using synthetic division or long division. In this case, the factored form of the polynomial is f(x) = (x)(x + 5)(x + 4). Therefore, the zeros of the polynomial function are 0, -5, and -4.
For 20 Points.
============
Answer:
D) 33
Step-by-step explanation:
The sum of the lengths of the segments is equal to the overall length:
(3x -5) + 8 = 4x -7
10 = x . . . . . . . . . . . . add 7-3x to both sides
Then the overall length is ...
MO = 4·10 -7 = 33
Answer:
Step-by-step explanation:
(3x -5) + 8 = 4x -7
10 = x what you wnat to do is add 7-3x to both sides
= 4·10 -7 = 33
and that should be your answer 33
A piece of thread is 52,000 nanometers thick. How many meters thick is the
thread? Write your answer in standard form.
1 nanometer = 1.0 x 10 meters
Answer:
0.000052
1 nanometer = .000000001 meters
.000000001 x 52000 = 0.000052
To convert 52,000 nanometers to meters, divide by the conversion factor of 1,000,000,000 nanometers per meter, resulting in a thickness of 5.2 x 10-8 meters in standard form.
To convert the thickness of a piece of thread from nanometers to meters, we need to use the conversion factor that 1 meter equals 1,000,000,000 nanometers, or 1 m = 109 nm.
Using this conversion factor, we can set up the following calculation:
Thickness in meters = Thickness in nanometers \/ Conversion factor
Thickness in meters = 52,000 nm \/ (109 nm/m)
Thickness in meters = 52,000 nm \/ 1,000,000,000 nm/m
Thickness in meters = 0.000000052 m or 5.2 x 10-8 meters when expressed in standard form.
Find the distance between the points given
(0, -6) and (9, 6)
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-0]^2+[6-(-6)]^2}\implies d=\sqrt{(9-0)^2+(6+6)^2} \\\\\\ d=\sqrt{9^2+12^2}\implies d=\sqrt{225}\implies d=15[/tex]
Six pairs of data yield r = 0.444 and the regression equation y = 5x + 2. also, y = 18.3. what is the best predicted value of y for x = 5?
The best predicted value of y for x = 5 is 27.
Explanation:A regression equation is a mathematical model that represents the relationship between a dependent variable and one or more independent variables. It expresses the linear or nonlinear association between these variables and is derived from statistical methods like linear regression analysis.
To predict the value of y for x = 5 using the regression equation, you can substitute x = 5 into the equation y = 5x + 2:
y = 5(5) + 2 = 27
Therefore, the predicted value of y for x = 5 is 27.
The best predicted value of [tex]\( y \) for \( x = 5 \) is \( y = 27 \).[/tex]
To find the best predicted value of [tex]\( y \) for \( x = 5 \),[/tex]we substitute [tex]\( x = 5 \)[/tex] into the regression equation:
[tex]\[ y = 5x + 2 \] \[ y = 5(5) + 2 \] \[ y = 25 + 2 \] \[ y = 27 \][/tex]
To reconcile this discrepancy, if we assume that the provided value of [tex]\( y = 18.3 \)[/tex] corresponds to [tex]\( x = 5 \),[/tex] then we would set the regression equation equal to 18.3 and solve for \( x \):
[tex]\[ 18.3 = 5x + 2 \] \[ 16.3 = 5x \] \[ x = \frac{16.3}{5} \] \[ x = 3.26 \][/tex]
Fred and Gina are playing tennis. The first player to win 2 sets wins their match. Fred has a 3/5 chance to win each set while Gina has a 2/5 chance. What is the probability that the match is decided in only two sets?
From the information below the games is over in 3 sets. For Gina to win the match there are 3 possibilities.
1) Gina wins the first 2 sets with probability
2)Gina wins the first set. Looses the next set. Wins the third set.
3)Gina looses the first set. Wins the next 2 sets.
The required probability that Gina wins is the sum of the above 3 probabilities . That is the probability that Gina wins the match is
Answer:[tex] P=\frac{9+4}{25}=\frac{13}{25}[/tex]
Step-by-step explanation:
Given
Fred has a chance of 3/5 to win
and Gina has a chance of 2/5 to win
Probability(P) that the match is decided in only two sets is when
Either Fred or Gina win both matches continuously
P=P(Fred win both match)+P(Gina win both match)
[tex]P=\frac{3\times 3}{5\times 5}+\frac{2\times 2}{5\times 5}[/tex]
[tex] P=\frac{9+4}{25}=\frac{13}{25}[/tex]
⊙M≅⊙N and AB=31.8. Identify PQ, rounded to the nearest tenth.
Answer:
[tex]PQ=9.6\ units[/tex]
Step-by-step explanation:
In this problem
If AB=31.8 units
then
ZY=31.8 units
ZP=PY=31.8/2=15.9 units
In the right triangle MZP
we have
[tex]ZP=15.9\ units[/tex]
[tex]MZ=18\ units[/tex] ----> the radius of the circle
Applying Pythagoras Theorem Find MP
[tex]MP^{2}=MZ^{2}-ZP^{2}[/tex]
substitute
[tex]MP^{2}=18^{2}-15.9^{2}[/tex]
[tex]MP^{2}=71.19[/tex]
[tex]MP=8.4\ units[/tex]
Find the value of PQ
we know that
[tex]MQ=MP+PQ\\ PQ=MQ-MP[/tex]
we have
[tex]MQ=18\ units[/tex]
[tex]MP=8.4\ units[/tex]
substitute
[tex]PQ=18-8.4=9.6\ units[/tex]
Simplify the following? (x^4y)^3
Answer:
(x^12y)
Step-by-step explanation:
= (x^4y)^3
= (x^12y)
Answer:
The simplified form of given expression is x¹²y³
Step-by-step explanation:
Points to remember
Identities
(xᵃ)ᵇ = xᵃᵇ
xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
To find the simplified form
It is given that, (x⁴y)³
By using the above identities we can write (x⁴y)³ as,
(x⁴y)³ = (x⁽⁴ * ³ ⁾ * y³
= x¹² * y³
= x¹²y³
Therefore the simplified form of given expression is x¹²y³
Select the correct answer.
Which table shows a proportional relationship between x and y?
Answer: The answer would be choice C because there is a constant rate of change of 3 :)
Step-by-step explanation:
Answer:
C.Step-by-step explanation:
If x and y are proportional then the ratio y/x is constant.
[tex]A.\\\\\dfrac{4}{2}=2,\ \dfrac{6}{3}=2,\ \dfrac{9}{4}\neq2\\\\B.\\\\\dfrac{4}{3},\ \dfrac{16}{9}\neq\dfrac{4}{3}\\\\C.\\\\\dfrac{12}{4}=3,\ \dfrac{15}{5}=3,\ \dfrac{18}{6}=3\ \qquad\bold{CORRECT}\\\\D.\\\\\dfrac{4}{1}=4,\ \dfrac{8}{2}=4,\ \dfrac{15}{3}=5\neq4[/tex]
Which expression is equivalent to (10x)–3?
The given expression evaluates to 1/(1000x^3).
Option (C) is correct.
What are exponents?The exponent of a number of says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.
As per the given data:
The given expression is (10x)^(–3)?
We can write the expression as:
= [tex]\frac{1}{(10x)^3}[/tex]
= [tex]\frac{1}{10^3x^3}[/tex]
= [tex]\frac{1}{1000x^3}[/tex]
= 1/(1000x^3)
Hence, the given expression evaluates to 1/(1000x^3).
To learn more about Exponents, click:
brainly.com/question/30066987
#SPJ7
(The given question is incomplete, the complete question is given below)
Which expression is equivalent to (10x)^-3?
a. 10/x^3
b. 1000/x^3
c. 1/(1000x^3)
d. 1/10x^3
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance.
Answer:
the music is both dubstep and trance
On December 31, 2016, Osborn Company purchased 30% of Shea Company’s common stock for $220,000. During 2017, Shea Company had a net income of $75,000 and paid cash dividends of $30,000. What would the balance of Osborn’s Equity Investment (Shea) account be at the end of 2017 if they use the equity method?A. $242,500 B. $211,000 C. $220,000 D. $233,500
Answer:
the balance of Osborn’s Equity Investment (Shea) account be at the end of 2017 is $233,500
Step-by-step explanation:
Given data
Acquistion price = $220000
purchased = 30%
net income = $75,000
cash dividends = $30,000
to find out
the balance of Osborn’s Equity Investment (Shea) account be at the end of 2017
solution
we will find out balance of investment i.e. given by formula
balance of investment = Acquistion price + share of income - share of dividend .................1
so here
share of income = 30% of net income
share of income =30% × 75,000 = $22500 ..............2
and
share of dividend = 30% of cash dividends
share of dividend = 30% × 30000 = $9000 ...............3
put equation 2 and 3 in equation 1 and we get
balance of investment = Acquistion price + share of income - share of dividend
balance of investment = 220000 + 22500 - 9000
balance of investment = $233,500
Sue graphed the formula for converting temperatures from Fahrenheit to Celsius. If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius
Answer:
Second Option (10° Celsius)
Step-by-step explanation:
There is a formula to convert the temperature which is in degree Celsius into degree Fahrenheit and vice versa. The formula to convert the temperature in degree Fahrenheit into degree Celsius is:
C° = (F° - 32) * 5/9.
It is given that the temperature is 50° Fahrenheit. Therefore, F° = 50°. Substituting F° = 50° in the formula gives:
C° = (50° - 32) * 5/9.
Further simplification results in:
C° = 18 * 5/9. Therefore, C° = 10°.
So the correct answer is 10° Celsius!!!
PLEASE HELP ASAP!!
At a frozen yogurt store, customers can purchase gelatin spheres as a yogurt topping. Each sphere contains 100.48/3 cubic millimeters of gelatin. Which statements about the measurements of the sphere are true? Check all that apply. (Use 3.14 for π. Recall that the formula for the volume for a sphere is V= 4/3πr³ .)
The radius of a sphere is 8 millimeters.
The radius of a sphere is 2 millimeters.
The circumference of the great circle of a sphere is 9.42 square millimeters.
The surface area of a sphere is 50.24 square millimeters.
The circumference of the great circle of a sphere is 12.56 square millimeters.
The surface area of a sphere is 25.12 square millimeters.
Answer:
The radius of a sphere is 2 millimeters
The surface area of a sphere is 50.24 square millimeters.
The circumference of the great circle of a sphere is 12.56 millimeters.
Step-by-step explanation:
Verify each statement
case A) The radius of a sphere is 8 millimeters
The statement is false
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=100.48/3\ mm^{3}[/tex]
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]100.48/3=\frac{4}{3}(3.14)r^{3}[/tex]
[tex]r^{3}=(100.48)/(4*3.14)[/tex]
[tex]r=2\ mm[/tex]
case B) The radius of a sphere is 2 millimeters
The statement is True
(see the case A)
case C) The circumference of the great circle of a sphere is 9.42 square millimeters
The statement is false
The units of the circumference is millimeters not square millimeters
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]C=2(3.14)(2)[/tex]
[tex]C=12.56\ mm[/tex]
case D) The surface area of a sphere is 50.24 square millimeters.
The statement is True
Because
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]SA=4(3.14)(2)^{2}[/tex]
[tex]SA=50.24\ mm^{2}[/tex]
case E) The circumference of the great circle of a sphere is 12.56 millimeters.
The statement is true
see the case C
case F) The surface area of a sphere is 25.12 square millimeters
The statement is false
because the surface area of the sphere is [tex]SA=50.24\ mm^{2}[/tex]
see the case D
Answer:
B, D,E
Step-by-step explanation:
Sakura speaks 150 words per minute on average in Hungarian, and 190 words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent 555 minutes in total giving both instructions, and spoke 270 more words in Polish than in Hungarian. How long did Sakura speak in Hungarian, and how long did she speak in Polish?
Answer:3 minute
Step-by-step explanation:
Sakura speaks hungarian =150 words per minute
Sakura speaks polish =190 words per minute
and it is given she speaks 270 more words in polish than in hungarian
She speaks for a total of 5 minutes
let she speaks hungarian for t mins
therefore [tex]150\times t+270=190\left ( 5-t\right )[/tex]
t=2 mins
therefore sakura speaks hungarian for 2 mins and polish for 3 mins
Sakura speaks hungarian for 2 mins and polish for 3 mins
What must the total momentum of the system be after the train cars collide?
Answer:
The total momentum of the system remains the same.Momentum before collision is equal to momentum after collision
Step-by-step explanation:
Momentum is defined as the product of mass and velocity of the bodies.According to the law of conservation of momentum, a collision that occurs in an isolated system, the momentum before collision equals that after collision.After collision, the bodies can move in the same direction thus their momentum is combined.
Answer:
The total momentum must remain the same.According to the law of conservation of momentum, in a system where particles collide, the momentum loss on one particles is gained by the other one. This is what create an reaction during the collision, for example, if two bodies collide, one will decrease its speed while the other will increase its speed, that's why the momentum is conserved.
So, basically, after the train cars collide, the momentum must be conserved, remaining the same.
I’m confused. Please help?
Step-by-step explanation:
[tex] f(x) = \log_a x [/tex]
[tex] \dfrac{f(x + h) - f(x)}{h} = [/tex]
[tex] = \dfrac{log_a(x + h) - \log_a x}{h} [/tex]
[tex] = \dfrac{log_a \dfrac{x + h}{x}}{h} [/tex]
[tex] = \dfrac{1}{h}log_a ( 1 + \dfrac{h}{x} ) [/tex]
[tex] = log_a ( 1 + \dfrac{h}{x} )^{\frac{1}{h}} [/tex]
What is the equation of the midline for the function f (x)?
f (t) = 3 cos (x) – 2.5
Answer:
y = -2.5
Step-by-step explanation:
For such a problem as this, you can replace all sine or cosine functions with their midline value of 0. Then you have ...
f(x) = 0 -2.5
which simplifies to ...
f(x) = -2.5
You can leave the equation like this, or write it as ...
y = -2.5
_____
Perhaps you can see that the midline is the value of any constant added to a sine or cosine function.
Answer: y=-2.5
Step-by-step explanation:
HELP!!!!
Select the correct answer.
What is the volume of this cone in terms of ?
Answer:
168.75π cm^3 is your answer.
Volume of a cone is 1/3 πr^2h.
Here, radius is given 7.5cm and height is given 9cm. So by using the formula we get the above answer.
For this case we have that by definition, the volume of a cone is given by:
[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]
Where:
h: It's the height
r: It is the cone radius
According to the data we have:
[tex]h = 9cm\\r = 7.5cm[/tex]
Substituting:
[tex]V = \frac {\pi * (7.5) ^ 2 * 9} {3}\\V = \frac {\pi * 56.25 * 9} {3}\\V = 168.75\pi[/tex]
Thus, the volume of the cone is [tex]168.75 \pi \ cm ^ 3[/tex]
Answer:
Option C
Ana, Mateo, and Elena are arguing about who has to give the dog a bath. How
can they make a fair decision?
Select all the correct answers
A. Roll a number cube. If the number rolled is 2 or 4, Ana bathes the
dog. If the number is odd, Elena bathes the dog. If it lands on any
other number, Mateo bathes the dog.
B. Put each person's name on a separate piece of paper in a bag
Randomly draw a name. The person whose name is chosen
bathes the dog
c. Flip a coin twice. If both tosses are heads, Ana bathes the dog. If
one is heads and one is tails, Mateo bathes the dog. If both are
tails, Elena bathes the dog
D. Roll a number cube. If the number rolled is 1 or 2, Ana bathes the
dog, If the number is 3 or 4, Mateo bathes the dog If the number
Answer:
B and D.
Step-by-step explanation:
B This is a fair method. There is an equal chance for all 3 people because picking one of the three is random.
D. I can't see all of it but it looks like it will be ' if the number is 5 or 6 Elena will bathe the dog. This is fair because the probabilities are all 1/3.
Method D is a fair method because the probability of each is equal.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
Ana, Mateo, and Elena are arguing about who has to give the dog a bath.
Then a fair decision will be
A. Roll a number cube. If the number rolled is 2 or 4, Ana bathes the dog. If the number is odd, Elena bathes the dog. If it lands on any other number, Mateo bathes the dog.
This is not a fair method because the probability of each is not equal.
B. Put each person's name on a separate piece of paper in a bag Randomly draw a name. The person whose name is chosen bathes the dog.
This is not a fair method because the number of pieces of paper is not given.
C. Flip a coin twice. If both tosses are heads, Ana bathes the dog. If one is headed and one is tail, Mateo bathes the dog. If both are tails, Elena bathes the dog.
This is not a fair method because the probability of each is not equal.
D. Roll a number cube. If the number rolled is 1 or 2, Ana bathes the dog. If the number is 3 or 4, Mateo bathes the dog. If the number rolled is 5 or 6, Elena bathes the dog.
This is a fair method because the probability of each is equal.
Then the correct option is D.
More about the decision-making link is given below.
https://brainly.com/question/3369578
#SPJ2
I know that these answers are correct, but I don't understand how to get it using the De Moivere Theorem. Can someone please explain in detail? Thank you so much!
Step-by-step explanation:
10.
First, convert 1+i from Cartesian to polar.
r = √(1² + 1²)
r = √2
θ = atan(1/1), θ in first quadrant
θ = 45°
Therefore:
(1+i)²⁰ = (√2 (cos 45° + i sin 45°))²⁰
(1+i)²⁰ = 1024 (cos 45° + i sin 45°)²⁰
Now applying the De Moivre theorem:
1024 (cos (20×45°) + i sin (20×45°))
1024 (cos (900°) + i sin (900°))
1024 (-1 + 0)
-1024
11.
Repeat the same steps from Question 10. First, convert to polar:
r = √(1² + (-1)²)
r = √2
θ = atan(-1/1), θ in fourth quadrant
θ = 315°
Therefore:
(1−i)¹⁰ = (√2 (cos 315° + i sin 315°))¹⁰
(1−i)¹⁰ = 32 (cos 315° + i sin 315°)¹⁰
Now applying the De Moivre theorem:
32 (cos (10×315°) + i sin (10×315°))
32 (cos (3150°) + i sin (3150°))
32 (0 − i)
-32i
The following chart represents the record high temperatures recorded in Phoenix for April - November. Select the answer below that best describes the mean and median of the data set ( round answers to the nearest tenth)
A. The mean is 114.5F and the median is 111.9F.
B. The mean is 121F and the median is 118.5F.
C. The mean is 111.9F and the median is 114.5F.
D. The mean is 118.5F and the median is 121F
Answer:
C. The mean is 111.9F and the median is 114.5F.
Step-by-step explanation:
The mean is 111.9 given that (105 + 113 + 122 + 121 + 116 + 118 + 107 + 93)/8 = 111.875 which can be rounded to 111.9 F.
Organizing the values we have:
[93, 105, 107, 113, 116, 118, 121, 122]
We find that the median is going to be between 113 and 116. Therefore:
(113 + 116) / 2 = 114,5
Therefore, the correct answer is option C.
The answer would be "C"
mean = 111.9F
median = 114.5F
For the mean, we would add up all the numbers in the data. In this case, we would add...
105 + 113 + 122 + 121 + 116 + 118 + 107 + 93 = 895
Next, we would divide the sum by the number of bars we have in the graph. There are 8 bars in the graph with 8 different temperatures so we would divide 895 by 8 and we will get a quotient of 111.875. 111.875 rounded to the nearest tenths place is 111.9F
For the median, we would first place all the numbers in order from least to greatest.
least to greatest- 93,105,107,113,116,118,121,122
next, we need to find the two middle numbers because there is no middle number in an even set of data.
The two middle numbers in the data set are 113 and 116. The halfway point between 113 and 116 is 114.5 so our median would be 114.5
Solve: e^2x + 5 = 4
help pls
Answer:
The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex] ⇒ 3rd answer
Step-by-step explanation:
* Lets explain how to solve this problem
- The function f(x) = e^x is called the (natural) exponential function
- The natural logarithm (㏑), or logarithm to base e, is the inverse
function to the natural exponential function
∵ [tex]e^{2x+5}=4[/tex] is an exponential function
∴ We can solve it by using the inverse of e (㏑)
- Remember:
# [tex]ln(e)=1[/tex]
# [tex]ln(e^{m})=m(ln(e))=m[/tex]
- Insert ln in both sides
∴ [tex]ln(e^{2x+5})=ln(4)[/tex]
∵ [tex]ln(e^{2x+5})=(2x+5)ln(e)=2x+5[/tex]
∴ 2x + 5 = ㏑(4)
- Subtract 5 from both sides
∴ 2x = ㏑(4) - 5
- Divide both sides by 2 to find x
∴ [tex]x=\frac{ln(4)-5}{2}[/tex]
* The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex]
Answer:
Answer is C on edge
Step-by-step explanation:
x= (ln 4)- 5/2