There are [tex]\binom62=15[/tex] ways of selecting any two fruit from the basket, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
If the baby picks out [tex]k[/tex] oranges, where [tex]k\in\{0,1,2\}[/tex], it can do so in
[tex]\dbinom 3k \dbinom3{2-k} = \dfrac{3!}{k!} \dfrac{3!}{(2-k)! (1 + k)!}[/tex]
ways.
Then the PMF (probability mass function) of [tex]X[/tex] is
[tex]P(X=x) = \begin{cases} \dfrac{\binom30 \binom32}{\binom62} = \dfrac3{15} & \text{if }x=0 \\\\ \dfrac{\binom31 \binom31}{\binom62} = \dfrac9{15} & \text{if }x = 1 \\\\ \dfrac{\binom32 \binom30}{\binom62} = \dfrac3{15} & \text{if }x=2 \\\\ 0 &\text{otherwise}\end{cases}[/tex]
Need number 2 please!!
Answer:
A
Step-by-step explanation:
note that i = [tex]\sqrt{-1}[/tex]
given
- 1 + 2i[tex]\sqrt{3}[/tex]
= - 1 + [tex]\sqrt{2^2(-1)3}[/tex]
= - 1 + [tex]\sqrt{-12}[/tex]
ABC is an isosceles triangle, with AB = AC. find X
Answer:
67.13°
Step-by-step explanation:
First separate triangles then you use Pythagoras theorem to get the third side and then apply the sine rule
Somebody please assist me here
The base case of [tex]n=1[/tex] is trivially true, since
[tex]\displaystyle P\left(\bigcup_{i=1}^1 E_i\right) = P(E_1) = \sum_{i=1}^1 P(E_i)[/tex]
but I think the case of [tex]n=2[/tex] may be a bit more convincing in this role. We have by the inclusion/exclusion principle
[tex]\displaystyle P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1 \cup E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1) + P(E_2) - P(E_1 \cap E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le P(E_1) + P(E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le \sum_{i=1}^2 P(E_i)[/tex]
with equality if [tex]E_1\cap E_2=\emptyset[/tex].
Now assume the case of [tex]n=k[/tex] is true, that
[tex]\displaystyle P\left(\bigcup_{i=1}^k E_i\right) \le \sum_{i=1}^k P(E_i)[/tex]
We want to use this to prove the claim for [tex]n=k+1[/tex], that
[tex]\displaystyle P\left(\bigcup_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]
The I/EP tells us
[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cup E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right)[/tex]
and by the same argument as in the [tex]n=2[/tex] case, this leads to
[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1})[/tex]
By the induction hypothesis, we have an upper bound for the probability of the union of the [tex]E_1[/tex] through [tex]E_k[/tex]. The result follows.
[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^k P(E_i) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]
Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of .
4cm
4cm
4cm
The diagram is not drawn to scale.
Help with this math problem
Answer:
The minimum cost of the X-ray machines is 12,197dollars.
Step-by-step explanation:
First, we check whether it’s a Quadratic Equation or not
The general form of the Quadratic equation [tex]f(x) =[/tex] [tex]ax^{2} + bx + c[/tex]
Let’s compare it with the given equation, we get
a = 1
b = -520
c = 79,79
Hence, it’s a quadratic equation.
Now, we will use the VERTEX FORMULA as we are asked to find the ‘minimum’ unit cost.
X = [tex]\frac{-b}\[2a[/tex] = [tex]\frac{-(-520)}\[2(1)[/tex] = [tex]260[/tex]
So , number of X-ray machines are = 260 (value of x)
To find the minimum unit cost, plug the value of x into the given equation, and we get
[tex]f(260) = (260)^{2} -520(260) + 79,797[/tex]
[tex]=12,197[/tex]
Learn more about quadratic equation here: https://brainly.com/question/23511870
#SPJ10
Question 5 of 50
Perpendicular lines are best defined as which of the following?
OA. Lines that intersect
O B. Lines that meet to form a right angle
OC. Lines that are not coplanar
O D. Lines that never intersect
A
❗️URGENT❗️
Chase has won 80% of the 30 football video games he has played with his brother, Jacob. If Chase and Jacob continue to play the video game, how many more games in a row goes Chase have to win to achieve an 85% win percentage?
Answer:
10
Step-by-step explanation:
24/30 = 0.8
24+x/30+x =0.85
10=x
If you want more clarification just ask
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
We can write the total number game won by Chase as -
w = 80% of 30
w = 80/100 x 30
w = 4/5 x 30
w = 24
Assume that he wins {x} games after winning 24 games to achieve 85% win percentage. Now, we can write that out of (30 + x) number of games played, Chase won (24 + x) games to achieve 85% win percentage. So, we can write that -
(24 + x)/(30 + x) = 85/100
(24 + x)/(30 + x) = 0.85
(24 + x) = 0.85(30 + x)
24 + x = 25.5 + 0.85x
0.15x = 1.5
x = 10
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
To solve more questions on percentage, visit the link below-
https://brainly.com/question/19034579
#SPJ2
If f(x)=x+2 and g(x)=x2+1 find:a. f(g(x)) b. g(f(x))
Answer:
Step-by-step explanation:
Answer:
x² + 3 and x² + 4x + 5
Step-by-step explanation:
(a)
to find f(g(x)) substitute x = g(x) into f(x)
f(g(x))
= f(x² + 1)
= x² + 1 + 2
= x² + 3
(b)
to find g(f(x)) substitute x = f(x) into g(x)
g(f(x))
= g(x + 2)
= (x + 2)² + 1 ← expand factor using FOIL
= x² + 4x + 4 + 1
= x² + 4x + 5
Match the scatter plot with its description
weak and positive
moderate and negative
strong and negative
strong and positive
weak and negative
moderate and positive
A line of best fit was drawn for 16 data points. What is the maximum number
of these data points that may not actually be on the line?
OA. 14
OB. 13
O C. 15
OD. 16
The maximum number of data points that may not actually be on the line is 16. so, the correct option is D.
How to find the line of best fit?We know that a line of best fit is basically a straight line drawn for a given data that may or may not pass through data points.
It is given that the line is drawn for 16 data points.
Hence, the line may or may not pass through all these 16 points.
Therefore, the maximum number of data points that may not actually be on the line is 16.
so, the correct option is D.
Learn more about line here;
https://brainly.com/question/10165160
#SPJ1
Simplify:
(x-1)+(12–7.5x)
Answer:
[tex]-6.5x+11[/tex]
Step-by-step explanation:
Expand The Brackets:
[tex]x-1+12-7.5x[/tex]
[tex]=x+(-1)+12+(-7.5x)[/tex]
Combine Like Terms:
[tex]=x+(-1)+12+(-7.5x)[/tex]
[tex]=(x+-7.5x)+(-1+12)[/tex]
Answer:
[tex]-6.5x+11[/tex]
I Hope This Helps
5
The recursive formula for a geometric sequence is given below. What is the third term in the sequence?
f(1) = 2
f(n) = 3f(n − 1)
-
OA. 18
OB. 54
OC. 162
OD. 12
Reset
Submit
[tex]\Large{ \boxed{ \tt{ \blue{A}}}}\Large{ \boxed{ \tt{ \pink{N}}}}\Large{ \boxed{ \tt{ \green{S}}}}\Large{ \boxed{ \tt{ \purple{W}}}}\Large{ \boxed{ \tt{ \red{E}}}}\Large{ \boxed{ \tt{ \pink{R}}}}[/tex]
[tex] \: \: [/tex]
A. 18[tex] \: \: [/tex]
[tex]\Large{ \boxed{ \tt{ \blue{S}}}}\Large{ \boxed{ \tt{ \pink{O}}}}\Large{ \boxed{ \tt{ \green{L}}}}\Large{ \boxed{ \tt{ \purple{U}}}}\Large{ \boxed{ \tt{ \red{T}}}}\Large{ \boxed{ \tt{ \pink{I}}}}\Large{ \boxed{ \tt{ \blue{O}}}}\Large{ \boxed{ \tt{ \pink{N}}}}[/tex]
[tex] \: \: [/tex]
[tex] \mathtt{f(1) = 2}[/tex][tex] \tt{f(2) \: = \: 3f \: (1) \: = \: 3(2) \: = \: 6}[/tex][tex] \tt{f(3) \: = \: 3f(2) \: = \: 3(6) \: = \: 18}[/tex][tex]\color{pink}─────────────────────────────────────[/tex]
keep learning
A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures the distance from the tree at 14 m and the angle of elevation to the tree at 88°. What is the height of the tree to the nearest tenth of a meter
Answer:
400.9 m
Step-by-step explanation:
According to American Airlines, flight 71098 from New York to Los Angeles is on time 88.9% of the time. Assume that we randomly select 150 flights, use the normal approximation to the binomial to do the following:
a) approximately the probability that exactly 124 flights are on time.
b) approximate the probability that between 113 and 130 flights ,inclusive, are on time.
Using the normal approximation to the binomial, it is found that the probabilities are given as follows:
a) 0.0055 = 0.55%.
b) 0.2296 = 22.96%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters of the binomial distribution are given as follows:
n = 150, p = 0.889.
Hence the mean and the standard deviation of the approximation are:
[tex]\mu = E(X) = np = 150 x 0.889 = 133.35[/tex].[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150(0.889)(0.111)} = 3.8473[/tex]Item a:
Using continuity correction, the probability is P(123.5 < X < 124.5), which is the p-value of Z when X = 124.5 subtracted by the p-value of Z when X = 123.5, hence:
X = 124.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{124.5 - 133.35}{3.8473}[/tex]
Z = -2.3
Z = -2.3 has a p-value of 0.0107.
X = 123.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{123.5 - 133.35}{3.8473}[/tex]
Z = -2.56
Z = -2.56 has a p-value of 0.0052.
Hence the probability is 0.0107 - 0.0052 = 0.0055 = 0.55%.
Item b:
The probability is P(112.5 < X < 130.5), which is the p-value of Z when X = 130.5 subtracted by the p-value of Z when X = 112.5, hence:
X = 130.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130.5 - 133.35}{3.8473}[/tex]
Z = -0.74
Z = -0.74 has a p-value of 0.2296.
X = 112.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{112.5 - 133.35}{3.8473}[/tex]
Z = -5.42
Z = -5.42 has a p-value of 0.
Hence the probability is 0.2296 - 0 = 0.2296 = 22.96%.
More can be learned about the normal approximation to the binomial at https://brainly.com/question/14424710
#SPJ1
find Y if AB bisects DAC and CB bisects ACE
Answer:
L1 and L2 are parallel
BAC = 58° as it is given in the question that AB bisects DAC
similarly BCE = y°
angle B = 90° ( from figure)
Y + 58° + 90° = 180 ( angle Sum property of a triangle).
Y + 148° = 180°
Y = 180 - 148
Y = 32°
quest
The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On
which day would you expect that number to be reached?
D)
10
Days People
1
26
2
30
3
34
4
38
5
42
6 46
og php?totalQuestions-10&testid-5
strand-5716&element-18789&condition-random #
Answer:
Day 5 ................
11. Calculate the weight on earth of an object with a mass of 48 kg. Gravitational acceleration (a) = 9.81 m/s ² Show all steps and formulae used. (3) ✓
Answer:
470.88 N
Step-by-step explanation:
F = ma
48 ( 9.81) = 470.88 N ( 105.958 lbs)
Hi can someone please help me with this geometry problem? Thanks!
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The triangles ΔEST and ΔEFD are similar triangles, therefore, we can write,
[tex]\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}[/tex]
Since S and T are midpoints of EF and ED, the lines will be divided into two equal parts. Therefore,
[tex]\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}= \dfrac12[/tex]
Therefore, we can write it as,
[tex]FD = 2 (ST)[/tex]
In ΔEST and ΔTDR
∠T ≅ ∠T {Vertical angles}
ET ≅ TD {T is the midpoint of ED}
∠SET ≅ ∠TDR {Alternate interior angles}
Therefore, ΔEST ≅ ΔTDR.
Since the two triangles are equal we can write,
ST ≅ TR
Further, it can be written as,
FD = 2(ST)
FD = ST + ST
FD = ST + TR
FD = SR
Hence, FD≅SR.
Learn more about Triangle:
https://brainly.com/question/2773823
#SPJ1
what is the length of the squares side?
Answer:
side ≈ 4.24= [tex]\frac{6}{\sqrt{2} }[/tex]
Step-by-step explanation:
sides a = b
[tex]6^{2} =a^{2} +a^{2}[/tex]
[tex]6^{2} =2a^{2}[/tex]
[tex]a^{2}= \frac{6^{2} }{2} =\frac{36}{2} =18[/tex]
[tex]a=\sqrt{18} =4.24=\sqrt{(9)(2)} =\frac{6}{\sqrt{2} }[/tex]
Hope this helps
Refer to the figure to complete the following item.
Given:
If m = 60° and m = 30°, then 3 =
45
15
30
If m VB = 60° and m BS = 30°, then m ∠3 =15°.
What is tangent?A tangent is a line passing by touching the perimeter of the circle, perpendicular to the line joining the center and touch point.
Given, PB tangents PV, PU secants
If m VB = 60° and m BS = 30°, then m ∠3 =
The measurement of the external angles is the semi difference of the arcs it consists.
∠3 = 1/2 (60 - 30)
∠3 = 15°
Thus, If m VB = 60° and m BS = 30°, then m ∠3 =15°.
Learn more about tangent.
https://brainly.com/question/23265136
#SPJ1
Given any two events, E, and E₂, what does the probability P(E, U E₂) represent?
Answer:
P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)
Step-by-step explanation:
As we know that, if A and B are two events then
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
⇒ P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)
A sells an article to B at profit of 20% and B sells it to C at a profit of 25%. If C buys it for Rs.225, what did A pay for it?
Answer:
A pay 120 for itLet the cost price be X
A Sells to B
profit = 20%
= cost price + 20%
= X + 20/100 of X
= 6x/ 5
B sells to C
profit = 25%
= Cost price + + 25%
= cost price + 25%
= 6x/5 + 25/100*6x/5
= 6x/5.+ 3x/10.
= 3x/2
3x/2 = 225.
3x = 450
x = 150.
sp = C. p + profit
S. p - profit = C. p
X - X/5
4x/5
4(150)/5.
120
Managerial Accounting
Answer:
1400 units
$26,600
1700 units
$32,300
Step-by-step explanation:
yw :))
The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript negative 3?
Applying the negative exponent, the equivalent expression [tex]3^{-3}[/tex] is 1/27.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator.
Hence, the equivalent expression is:
[tex]3^{-3} = \dfrac{1}{3^3} = \dfrac{1}{27}[/tex]
More can be learned about exponents at
brainly.com/question/1773695
#SPJ1
factorise 4ab +6bn-2a-3n
Answer:
(2b - 1)(2a + 3n)
-----------------------------------------------
Given polynomial
4ab + 6bn - 2a - 3nFactorize it as below:
4ab + 6bn - 2a - 3n =
(4ab - 2a) + (6bn - 3n) = Regroup
2a(2b - 1) + 3n(2b - 1) = Factorize each group using common factors
(2b - 1)(2a + 3n) Factorize using common factor
Answer:
[tex](2b-1)(2a+3n)[/tex]
Step-by-step explanation:
Given expression:
[tex]4ab+6bn-2a-3n[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2b(2a+3n)-1(2a+3n)[/tex]
Factor out the common term (2a + 3n):
[tex]\implies (2b-1)(2a+3n)[/tex]
can someone find the value of x?
Answer:
[tex]\boxed{\sf x=12}[/tex]
Step-by-step explanation:
By applying Similar Triangles Theorem:-
[tex]\sf \cfrac{x}{6} =\cfrac{6}{3}[/tex]
We'll multiply both sides of the equation by 6, the LCM of 6,3.
[tex]\sf x=2 \times 6[/tex]
[tex]\sf x=12[/tex]
Which number produces a rational number when added to 1/2?
Answer:
Another rational number.
Step-by-step explanation:
For example, [tex]\pi[/tex] is incorrect because It is a irrational number
you must add another rational number to 1/2 to make the sum rational.
Rational number are numbers that can be converted into a fraction.
all natural numbers, whole numbers, integers, are rational.
and all rational and irrational numbers are real numbers
three-quarters of a pile of bricks were used for a certain project. when two thirds of the reminder had been used, 50 bricks were left. how many bricks were there in the original pile?
Answer:
sorry I don't know the answer
Which of the following best describes the set of complex numbers?
OA. The set of all numbers of the form a+bi, where a and bare any
real numbers and i equals -1
B. The set of all numbers of the form abi, where a and bare any real
numbers and i equals 1
C. The set of all numbers of the form a+bi, where a and b are any
real numbers and i equals √-1
OD. The set of all numbers of the form abi, where a and b are any real
numbers and / equals -1
Answer:
C
Step-by-step explanation:
The correct statement is option C.
What is complex number?A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, i = √-1 and both a and b are real numbers.
Since we know that
Complex number is of the form a+ib
Where,
a is real number belongs to real axis
And b is also a real number belongs to imaginary axis.
And the value of i = √-1
Thus,
The set of all numbers of the form a+bi, where a and b are any
real numbers and i equals √-1 is the correct statement.
To learn more about complex numbers visit:
https://brainly.com/question/27940074
#SPJ7
the segments ab and cd are graphed on a coordinate plane. The endpoints of ab are at (9,4) and (9,20). CD is parallel to the x-axis, and one of its endpoints is at (5,8). if ab=cd and cd is entirely in the first quadrant, what is the other endpoint of cd
Answer:
21, 8
Step-by-step explanation:
The second endpoint is of the form (X, 8) since it's parallel to the x axis.
Given the congruence of the two segments, we can tell that its length is 16 units (since [tex]|4-20| = |-16|= 16[/tex])
At this point the two possible endpoints for the segment are [tex](5-16; 8)[/tex] or [tex](5+16, 8)[/tex]. The fact that the segment has to sit in the first quadrant rules out the first option (it's endpoint will be at (-11, 8) which will set most of it in the second quadrant) and we're left with (21, 8)
