Step-by-step explanation:
distance of (1,0) from the origin is,
√{(1-0)²+(0-0)²}
= √1
= 1
So the radius of the circle is 1,
now for the point (2/5,y) distance from origin should be the same since it's the radius
so,
√{(2/5-0)²+(y-0)²} = 1
or, √(4/25+y²)=1
or, 4/25+y²=1
or, y² = 1-4/25
or, y²=21/25
or, y=√(21/25)
or, y=√21/5
so, the simplest form of y is,
[tex] \frac{ \sqrt{21} }{5} [/tex]
Equation?
Slope?
Y-intercept?
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, 2) ← 2 points on the line
m = [tex]\frac{2-(-3)}{4-0}[/tex] = [tex]\frac{2+3}{4}[/tex] = [tex]\frac{5}{4}[/tex]
The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{5}{4}[/tex] - 3 ← equation of line
Critical Thinking: Empirical/Quantitative Skills
United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some
people with tickets don't show up. United will overbook by selling more than 180 tickets. If the flight is not
overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some
passengers are denied seats, the airline loses money from the compensation that must be given to bumped
passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the
flight. Also assume that the airline sells 200 tickets for the 180 seats that are available.
1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Show your calculation (ie. what you put in the calculator) and round to 4 decimals.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
Answer:
1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight.
This means that [tex]p = 0.905[/tex]
Also assume that the airline sells 200 tickets
This means that [tex]n = 200[/tex]
Question 1:
Exactly, so we can use the P(X = x) formula, to find P(X = 180).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]
0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Now we have to use the approximation.
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]
Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180.5 - 181}{4.15}[/tex]
[tex]Z = -0.12[/tex]
[tex]Z = -0.12[/tex] has a p-value of 0.4522.
0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So
[tex]p + 0.4522 = 1[/tex]
[tex]p = 1 - 0.4522 = 0.5478[/tex]
0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
11 + box equals 19 find box
Answer:
8
Step-by-step explanation:
11 + x = 19
Subtract 11 from each side
11+x -11 = 19-11
x = 8
Answer:
8
Step-by-step explanation:
11 + box = 19
=> box = 19 - 11
.°. box = 8
Pleasant help me out explanation need it
Answer:
for which question???????????????
Answer:
Ok please tell me your question because you forgotten the question your asking dor
f(x) = x2
g(x) = (x +4)^2 - 1
We can think of g as a translated (shifted) version of f.
Hurry I am in summer school and almost done I need help ASAP!
Answer:
down by 1 unit and left by 4 units
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Then
g(x) = (x + 4)² - 1
is f(x) shifted down by 1 unit and shifted left by 4 units
Mr. Johnson took up an appointment with Nestle Ghana as an accountant with an annual salary of $164 million. as part of his appointment, he was promised a yearly increment of $24 million. Mr Johnson got promoted to chief accountant after six years of work with an annual salary of $300 million and yearly increment of$36 million.
calculate a) Mr. Johnson's salary in the tenth year of service.
b). Mr. Johnson's total earnings at the end of the tenth year of service.
Answer:
300 million(1+ 36 million) y
Step-by-step explanation:
f(x) = −16x2 + 24x + 16
what is the vertex
Answer:
VERTEX: (0.75,25)
Step-by-step explanation:
the vertex will be at [-b/2a, f(-b/2a)]
−16x2 + 24x + 16
4(-4x^2 + 6x +4)
a = -4, b=6,c=4
-6/-8 = 3/4
f(3/4) = 25
A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
Write the sum using summation notation, assuming the suggested pattern continues.
2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
Step-by-step explanation:
An arithmetic sequence is of the form:
[tex]A_n = A_{n-1} + d[/tex]
While a geometric sequence is of the form:
[tex]A_n = A_{n-1}*r[/tex]
notice that first, we have a change of sign in our sequence, so we already can discard the arithmetic sequence.
In fact, the pattern is kinda easy to see.
The first term is:
A₁ = 2
the second term is:
A₂ = -10
notice that:
A₂/A₍ = r = -10/2 = -5
The third term is:
A₃ = 50
the quotient between the third term and the second term is:
A₃/A₂ = 50/-10 = -5
Whit this we can already conclude that the n-th term of our sequence will be:
[tex]A_n = A_{n-1}*(-5)[/tex]
Then the summation will be something like:
[tex]\sum_{n = 1} A_n = A_1 + A_2 + A_3 + ... = 2 - 10 + 50 - ...[/tex]
We can write:
[tex]A_n = A_{n-1}*(-5) = (A_{n-2}*(-5))*(-5)) = A_1*(-5)^{n-1} = 2*(-5)^{n-1}[/tex]
Then the summation is just:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
A boy's mother was 32 years old when he was born. Let a represent the boy's age and m represent the mother's age.
Complete the table using the relationship between a and m.
PLEASE ANSWER!!!!
see the picture attached
Use a calculator to find the mean of the data. {21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}
Answer:
The mean of the data is 21.41
Step-by-step explanation:
To find the mean of a data set you must...
Add up all data values to get the sum
Count the number of values in your data set
Divide the sum by the count
The mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have a data set:
{21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}
As we know from the definition of the mean:
The mean can be calculated using the formula:
Mean = sum of the data set/number of the data in the data set
Mean = 471/22
Mean = 21.409 ≈ 21.41
Thus, the mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.
Learn more about the mean here:
https://brainly.com/question/22871228
#SPJ5
3.3 A circle has a radius of 12cm. An angle of 3.2 radians is subtended at the centre by an arc. Calculate the length of the arc. (3)
Answer:
S = 38.4 centimeters.
Step-by-step explanation:
Given the following data;
Radius, r = 12 cmAngle = 3.2 radsTo find the length of the arc of a circle;
A full circle measures an angle of 360 degrees.
π = 180°
So; Angle, A = 360° = 2π
Therefore, a full circle is equal to 2π in terms of radians (rads).
Also, the circumference (the length of an arc) of a circle is equal to 2πr or Ar.
Mathematically, the length of the arc of a circle is given by the formula;
S = rA
Where;
S is the length of the arc.A is the angle measured in radians.Substituting into the formula, we have;
S = 12 * 3.2
S = 38.4 centimeters.
Wilbur spent $27 on a magazine and some notepads. If the magazine cost $3 and
each notepad cost $3, then how many notepads did he buy?
A) 11
B) 9
C) 8
D)12
Answer:
d 12
Step-by-step explanation:
27-3=24÷3=12 do the mathssssss
Answer:
If it was 11, it would be 33 dollars which is over the total so its not a.
It can't be b because that would be 27, and that would be on just notebooks not magazine
24 is correct because he baught one magazine so + 3 which is the total so it is C
Step-by-step explanation:
One month Ivanna rented 7 movies and 9 video games for a total of $80. The next month she rented 5 movies and 3 video games for a total of $34. Find the rental cost for each movie and each video game.
Answer:
each movie costs $2.75, each video game costs $6.75
Step-by-step explanation:
x = movies, y = video games
7x + 9y = 80
5x + 3y = 34
simplified to
x = 11/4 , y = 27/4
What is 10+2
Please I need help
Answer: 12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Check the picture below
Plz help, fill in the blanks in order
Alonzo finish history assignment and 5/8 hours then he completed his math assignment and 1/3 hours what was the total amount of time allowed to spend doing these two assignments
Step-by-step explanation:
The answer is 5/8 + 1/3
Answer = 5*3 /(8*3) +8/24 =23/24
Answer = 23/24
n-1 increased by 110%
Answer:
2.1n-2.1
Step-by-step explanation:
The increase is
1.10 (n-1)= 1.1n -1.1
Add this to the original amount
(n-1) + 1.1n - 1.1
2.1n-2.1
HELP ME PLS!!!!!
Which of the following is | 5-12i |?
A) -√119
B) √119
C) −13
D)13
Answer:
D) 13
[tex]\sqrt{169} = 13[/tex]
Step-by-step explanation:
Help with this please!
Answer:
A
Step-by-step explanation:
The correct answer is A
The length of a ladder leaning against a building is 60 feet. The ladder hits the building at the top of the building. The distance to the building from where the ladder touches the ground is 15 feet. What is the height of the building to the nearest foot?
A. 38ft
B. 48ft
C. 58ft
D. 68ft
Answer:
C. 58ft
Step-by-step explanation:
An imaginary triangle is described here. The hypotenuse is 60, and one of the other sides is 15.
60*60=3600
15*15=225
3600-225=3375
sqrt3375=58.09
round that to get 58ft
A canoeist traveling with the current traveled the 24 miles between two riverside campsites in 2 hours. The return trip against the current took 3 hours. Find the speed of the canoeist in still water and the speed of the current, both in miles per hour.
Answer:
Speed of canoiest is 10 miles/hour.
Speed of current is 2 miles/hour.
Step-by-step explanation:
Let the speed of canoiest is v and the speed of current is u.
distance = speed x time
24 = (v + u ) x 2
v + u = 12 ..... (1)
Now
24 = (v- u) x 3
v - u = 8 .... (2)
By solving (1) and (2)
2 v = 20
v = 10 miles/hour
u = 2 miles/hour
Which statements about the relationship between the two triangles below are true? Check all that apply,
Answer:
I don't know, because i really don't know
25% of £90
Work it out
Answer:
22.5
Step-by-step explanation:
percent is any number over 100, so 25% is 25 over 100, this means that 25% can be written as:
25100
Now, any number in fractional form (a number over a number) is the same as division so 25% can also be written as a decimal, we just move the decimal point 2 places to the right of 25, like this:
25100=0.25
Now we have two ways that we can solve this problem! I'll start with the fractional method of solving.
Eileen is reading a novel for her library’s summer reading program. Which question can Eileen ask herself to best form a personal connection with the text?
A. What symbolism does this novel share with other novels I have read?
B. How do the facts in the text add to what I already know about my research topic?
C. What connections can I build between the themes in this text and other modern stories?
D. How do the struggles of the characters compare with challenges I have faced in my own life?
Answer:
Step-by-step explanation:
To begin with the answer. This is very personal, but I would choose D. I think you have to relate things to what you know. How do other people live through the same problem? Does the author believe that the best path has been chosen, or does he/she believe that the central character is doomed to failure? And how do these comments relate to me. You are going to get the most out of any novel when you can relate to the central character or any of the characters for that matter.
I'm not concerned with C. You can read trash and what they say is likely consistent but that only means that trash is pandering to a clientele that does not want to think much. Whatever spin you put on C, agreement is not a terrific thing. It does not make you think.
I suppose B is important if you are reading non fiction. I'm not answering it that way.
A: not the answer. This is a very remote connection. Most of the time symbolism is not the main attraction of any novel nor especially of any non fiction writing. Moby D*ick is not a great novel because of its symbolism of which there is a huge amount. It is a great novel because the conflict is between man and nature and although that is symbolic, it is not as important as the character study of Ahab (who is himself a symbol). Nor or Ishmael for that matter. I will admit you have to have a Bible in one hand and Moby Di*ck in the other, but it is not critical. The theme is.
This is the question I am stuck on
Answer:
a^ 8 / b^12
Step-by-step explanation:
We know that x^y / x^z = x^ (y-z)
a^-5 b^-4
----------------
a^ -13 b^8
a^ (-5 - -13) b ^ (-4 -8)
a^ (-5+13) b^ (-4-8)
a^ 8 b^ (-12)
We know that x ^ - y = 1/ x^y
a^ 8 / b^12
Expand the following: 4(a + 3b - 5c).
Please help, I'm really struggling with expanding equations
Answer:
4a+12b-20c
Step-by-step explanation:
Use the distributive property, multiply the number on the outside to everythign on the inside.
4*a=4a
4*3b=12b
-5c*4=-20c
A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 49 feet less than the height of the pole. If the wire is to be 14 feet longer than the height of the pole, what is the height of the pole?
9514 1404 393
Answer:
105 ft
Step-by-step explanation:
Let x represent the height of the pole. Then (x -49) is the distance from the pole to the anchor point, and (x+14) is the length of the wire from the top of the pole to the anchor point.
The Pythagorean theorem gives us the relation ...
(x +14)² = x² +(x -49)²
x² +28x +196 = x² +x² -98x +2401 . . . . eliminate parentheses
x² -126x +2205 = 0 . . . . . . . . put in standard form
x² -126x +3969 -1764 = 0 . . . . "complete the square)
(x -63) = ±√1764 . . . . . . add 1764, take the square root
x = 63 +42 = 105 . . . . . . highest value root. The pole must be higher than 49 feet
The height of the pole is 105 feet.
What is the length of Line segment A C? Round to the nearest tenth.
Triangle A B C is shown. Angle A C B is 90 degrees and angle B A C is 55 degrees. The length of C B is 15 meters.
10.5 m
12.3 m
18.3 m
21.4 m
Answer:
10.5
Step-by-step explanation:
In the picture if you think about it, it has to be a number less than 15 since CB is 15. I picked 12.3 and got it wrong therefore it has to be 10.5.
Answer:
A) 10.5
Step-by-step explanation:
Find the intersection of the line and the circle given below
2x+y=-5
x^2+y^2=10
Answer:
There are two intersections.
(-3,1) and (-1,-3)
Step-by-step explanation:
Answer:
They intersect at (-3,1), and also (-1,-3)
Step-by-step explanation:
Graph:
