Answer:
P(AUB)'=2/15
Step-by-step explanation:
According to the Question,
Given That, A and B be two independent events. If P(A)=3/5 and P(B')=1/3.So, P(B)=1-P(B') ⇒ P(B)=1-(1/3) ⇔ P(B)=2/3
The Product Rule of Probability says For independent events P(A∩B)=P(A)×P(B)P(A∩B)=3/5 × 2/3 ⇒ P(A∩B)=2/5
We know, P(AUB)=P(A)+P(B)-P(A∩B)Thus, P(AUB)= 3/5 + 2/3 - 2/5
P(AUB)=1/5 + 2/3
P(AUB)=(3+10)/15 ⇔P(AUB)=13/15
Now, The Value Of P(AUB)'=1-P(AUB) ⇔ 1 - 13/15 ⇒ P(AUB)'=2/15Let f be a function of two variables that has continuous partial derivatives and consider the points
A(8, 9),
B(10, 9),
C(8, 10),
and
D(11, 13).
The directional derivative of f at A in the direction of the vector AB is 9 and the directional derivative at A in the direction of
AC is 2. Find the directional derivative of f at A in the direction of the vector AD.
(Round your answer to two decimal places.)
Answer:
The directional derivative of f at A in the direction of [tex]\vec{u}[/tex] AD is 7.
Step-by-step explanation:
Step 1:
Directional of a function f in direction of the unit vector [tex]\vec{u}=(a,b)[/tex] is denoted by [tex]D\vec{u}f(x,y)[/tex],
[tex]D\vec{u}f(x,y)=f_{x}\left ( x ,y\right ).a+f_{y}(x,y).b[/tex].
Now the given points are
[tex]A(8,9),B(10,9),C(8,10) and D(11,13)[/tex],
Step 2:
The vectors are given as
AB = (10-8, 9-9),the direction is
[tex]\vec{u}_{AB} = \frac{AB}{\left \| AB \right \|}=(1,0)[/tex]
AC=(8-8,10-9), the direction is
[tex]\vec{u}_{AC} = \frac{AC}{\left \| AC \right \|}=(0,1)[/tex]
AC=(11-8,13-9), the direction is
[tex]\vec{u}_{AD} = \frac{AD}{\left \| AD \right \|}=\left (\frac{3}{5},\frac{4}{5} \right )[/tex]
Step 3:
The given directional derivative of f at A [tex]\vec{u}_{AB}[/tex] is 9,
[tex]D\vec{u}_{AB}f=f_{x} \cdot 1 + f_{y}\cdot 0\\f_{x} =9[/tex]
The given directional derivative of f at A [tex]\vec{u}_{AC}[/tex] is 2,
[tex]D\vec{u}_{AB}f=f_{x} \cdot 0 + f_{y}\cdot 1\\f_{y} =2[/tex]
The given directional derivative of f at A [tex]\vec{u}_{AD}[/tex] is
[tex]D\vec{u}_{AD}f=f_{x} \cdot \frac{3}{5} + f_{y}\cdot \frac{4}{5}[/tex]
[tex]D\vec{u}_{AD}f=9 \cdot \frac{3}{5} + 2\cdot \frac{4}{5}[/tex]
[tex]D\vec{u}_{AD}f= \frac{27+8}{5} =7[/tex]
The directional derivative of f at A in the direction of [tex]\vec{u}_{AD}[/tex] is 7.
For each 70 mm of coloured fabric Alex uses to make his curtains, he also uses 20 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.
Answer:
20×10=200mm
70:200
70/10=7
200/10=20
7:20 is your answer in it's simplest form
Use the graph to determine the input value for which f(x) equals G(x) is true x=0.5,x=1, x=1.5,x=2
Step-by-step explanation:
1.5 is the answer I just tried it and got it correct
Answer:
1.5 I just got the correct answer on edge
Simplify 3a²b³x 4a³b
Proving the Converse of the Parallelogram Side Theorem
GONIN
roce UNO Salam
seat of argam
20N
3.
Nad NL
are atrages
SININ
S.
WONIN
i hope you guys didn't have to suffer thru the rest like I did c,:
here is THE REST OF THE ANSWERS!
Step-by-step explanation:
THE ENTIRE PICTURE ABOVE IS CORRECT, BUT AFTER THAT THE NEXT ANSWERS ARE.....
8. angle LNO is congruent to angle NLM because of CPCTC
9. segment ON is parallel to segment LM because of converse of the alt. int. angles theorem
10. segment LO is parallel to segment MN because of converse of the alt. int. angles theorem
11. LMNO is a parallelogram because of the def. of a parallelogram
I just did all of these on edg. 2022 and they're correct. have a great day/night you guys and good luck!
We will use the converse of alternate interior angles theorem to prove LMNO is a Parallelogram.
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are of equal measure.
The proof is as follows:
Statements Reasons
1) LO ≅ MN Given
2) ON ≅ LM Given
3) LN ≅ LN Reflexive property
4) Δ LON ≅ Δ NML SSS congruency rule
5) ∠ NLO ≅ ∠ LNM CPCTC
and ∠ MLN ≅ ∠ LNO
6) LM ║ ON and LO ║ MN converse of alternate interior angles theorem
7) LMNO is a Parallelogram Property of Parallelogram
For more references on Parallelogram, click;
https://brainly.com/question/29147156
#SPJ2
Find RS. See image below
Step-by-step explanation:
since both cords are equal, so are arc length
4x + 18 = 7x - 51
3x - 21 = 0
x = 7
arc RS = 4(7) + 18
The ratio of teachers to students at Happy Hill School is 2:29 , which means that for every 2 teachers there are students. There are 7 doctors and 27 nurses at Happy Hill Hospital. The ratio of doctors to nurses is, therefore, 7 7:_.
Question from Venn diagram solving... plz solve. Worth 15 points
Answer:
For this type of problem, it is best to use Venn diagrams as shown in the picture. The areas where the circles intersect are the mutual events that occur together. The area where all circles intersect is denoted as x. These are the students who play all sports. Assuming all of the students play sports in the school, all of the numbers in the circles should add up to 405. The remaining area would be the difference. The solution is as follows:
Students who play tennis and hockey: 45 - x
Students who play hockey and softball: 60 - x
Students who play only tennis and softball: 39 - x
Students who only play tennis:
251 - 45 + x - 39 +x -x = x + 167
Students who only play hockey:
157 - x - 45 + x - 60 + x = x + 52
Students who only play softball:
111 - x - 60 + x - 39 + x = x + 12
The sum of all of these should be 405:
45-x+60-x+39-x+x+167+x+52+x+12 = 405
Solving for x,
x = 30
Therefore, there are 30 pupils who play all sports; 15 pupils who play tennis and hockey; 30 pupils who play hockey and softball; 9 pupils who play tennis and softball; 197 pupil who only play tennis; 82 pupils who only play hockey; and 42 pupils who only play softball.
Step-by-step explanation:
Hope this is correct, if it is wrong then please feel free to critique me and I wil correct my mistake(s). I'm sorry in advance if it is incorrect.
please answer I need this answer fast please
D
its just a basic logarithmic law.
Busco amigos o amigas :D
Jasmine ran 5 miles in 42.5 minutes. Caroline ran 3 miles in 26.4 minutes. Who ran at a faster pace?
A) Jasmine because she ran 0.8 minute faster per mile.
B) Jasmine because she ran 0.3 minute faster per mile.
C) Caroline because she ran 0.7 minute faster per mile.
D) Caroline because she ran 0.2 minute faster per mile
Answer:
B
Step-by-step explanation:
For this problem, let us find the respective speeds of Jasmine and Caroline and compare the two. All we have to do is divide #minutes by #miles to find the time spent per one mile.
Jasmine:
[tex]\frac{42.5}{5} =\\\\[/tex]
[tex]8.5[/tex] minutes per mile
Caroline:
[tex]\frac{26.4}{3} =\\[/tex]
[tex]8.8[/tex] minutes per mile
Since Caroline takes longer to run a mile than Jasmine, We now know that Jasmine ran at a faster pace:
[tex]8.8-8.5=0.3[/tex]
B. Jasmine ran at a faster pace because she ran 0.3 minutes faster per mile.
I hope this helps! Let me know if you hae any questions :)
Adam builds model rockets. Where he lives, his backyard is 12 feet below sea level. When he ignites his rocket, it flies a maximum of 350 feet straight up into the air before releasing its parachute. What is the altitude of Adam’s rocket at its highest point, as measured from sea level
Answer:
338 feet
Step-by-step explanation:
350 - 12 = 338
An exam has 20 exercises.For every exercise solved correctly you get 8 points and for every exercise solves wrong are taken off 5 points.Ben had 13 points.How many exercises did he solve?
Answer:
13 exercises
Step-by-step explanation:
The number of exercises in the exam = 20
The points received for questions solved correctly = 8 points
The points taken off for exercises solved wrong = 5 points
The number of points Ben has = 13 points
Let 'c' represent the number of exercises he solved correctly and let 'w' represent the number of exercises he solved wrong, we have;
0 < c + w ≤ 20...(1)
8·c - 5·w = 13...(2)
Given that 5·w has either a 0 or 5 as the unit digit, and x3 = x8 - 5, such as 13 = 18 - 5, we have that the last digit of 8·c is 8, and the last digit of 5·w is 5
The products of 8 with '8' as the unit are, 8 × 6, 8 × 11, and 8 × 16
Therefore, when c = 6, and w = 7, we get;
8 × 6 - 5 × 7 = 13
The number of exercises Ben solved, c + w = 6 + 7 = 13 < 20
When c = 11, we get;
8 × 11 - 5 × 15 = 13
11 + 15 = 26 > 20
The number of exercises Ben solved = 13 exercises
I need to find the value of x. Help please
Answer:
[tex]x=68[/tex]
Step-by-step explanation:
In the figure, we shown all four exterior angles of the polygon. The sum of the exterior angles of any polygon is equal to [tex]360^{\circ}[/tex].
Therefore, we have:
[tex]79+(x+10)+(x-1)+(2x)=360,\\79+x+10+x-1+2x=360,\\88+4x=360,\\4x=272,\\x=\boxed{68}[/tex]
What is the value of x in the triangle?
45°
7
X
45°
A. 7
B. '14
C. 72
D. 7V2
2
Answer:
c
Step-by-step explanation:
the value of x can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
The triangle is an isosceles triangle
An isosceles triangle has two opposite sides. If the two angles are equal , it means the triangle is an isosceles. Thus the value of the base is also 7
7² + 7²
49 + 49
= 98
√98 = 9.899 = 7√2
Need help on this question asap pleasee
Answer:
15 cm
Step-by-step explanation:
[tex]\frac{12}{24}[/tex] = [tex]\frac{x}{30}[/tex]
cross multiply and solve for x
or just notice that the fraction reduces to 1/2 and 15 is half of 30
the answer is in the picture
PLEASEEEEEEEE HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Question 1 of 5
Which data set has a variation, or mean absolute deviation, similar to the data
set in the given dot plot?
Answer:
It is A because it is pretty similar to the data set in the given dot plot.
What is the area of the triangle in centimeters
squared?
Answer:
A = 112cm²
Step-by-step explanation:
Area of a triangle = (bh) / 2
b = base length and h = height
The triangle shown has a given base length of 14cm and a given height of 16cm
Hence area = ( 16 * 14 ) / 2
16 * 14 = 224
224 / 2 = 112
A = 112cm²
the length of rope P is three times the length of rope Q. After 10cm of rope is cut from rope P and rope Q respectively, the length of rope P is four times the length of Q. Calculate the original length, in cm, of rope P before it is cut.
Answer:
150 cm
Step-by-step explanation:
The information in the question includes;
The length of rope P = 3 × The length of rope Q
The length of rope P - 10 cm = 4 × (The length of rope Q - 10 cm)
Let p represent the original length of rope P and let q represent the original length of rope Q, we have;
p = 3·q...(1)
p - 10 = 4·(q - 10)...(2)
Expanding equation (2) gives;
p - 10 = 4·q - 40
∴ p = 4·q - 40 + 10 = 4·q - 50
p = 4·q - 50...(3)
Equating the values of p in equation (1) and equation (3) gives;
p = 3·q, and p = 4·q - 50, therefore, by the substitution property of equality, we have;
3·q = 4·q - 50
50 = 4·q - 3·q = q
q = 50
p = 3·q
∴ p = 3 × 50 = 150
The original length of P before it was cut, p = 150 cm.
PLEASE HELP THANK YOU EVERYBODY
Answer:
150 in^2
Step-by-step explanation:
Answer:
Step-by-step explanation:
Givens
L = 9
W = 4
H = 3
Formula
SA = 2*L*w + 2*L*H + 2 * H * W
Solution
SA = 2 * 9*4 + 2*9*3 + 2*3 * 4
SA = 72 + 54 + 24
SA = 150 in^2
Mila is a teacher and takes home 31 papers to grade over the weekend. She can grade at a rate of 8 papers per hour. Write a recursive sequence to represent how many papers Mila has remaining to grade after working for n hours.
four terms in the sequence an are a3=15, a4=19, a5=23, and a6=27 which function can be used to find the nth term in the sequence
Answer:
an = 4n + 3
Step-by-step explanation:
Help ASAP!!!!!!!!!!!!!!
Jen wants to finish half of her book. She is on page 24. The book has 68 pages. The equation shown represents this situation. 24+□=68÷2 Which is the missing number that represents how many more pages Jen must read to finish half of her book?
68Answer:
10
Step-by-step explanation:
68/2=34
24+10=34
I need help pleaseeee
Answer:
A. 70°
Step-by-step explanation:
There are two ways to solve this problem:
(1) The sum of all the angles of a quadrilateral equals 360°.
The equation for this problem would be:
110° + 110° + 70° + m∠A = 360°
Simplify:
290° + m∠A = 360°
m∠A = 70°
(2) Trapezoid ABCD is an isosceles trapezoid, because m∠B and m∠C, opposite angles of the same base of the trapezoid, are congruent.
Therefore m∠A and m∠D must also be congruent.
m∠A = m∠D = 70°
does anyone know the answer?
Answer:
multiply the bottom equation by 6
The length of a rectangle is 18 cm and the width is 6 cm. A similar rectangle has a width of 2 cm.What is the length of the second rectangle? pls help im solving hw ._.
Answer:
Length = 6cm
Step-by-step explanation:
You would get 6cm as the length, because 6 ÷ 3 = 2, that is your width. So in the same way, you would divide 18 by 3 and get 6, thus the length of the second rectangle is 6 centimeters
Hope it helps :D
6 cm po tama to mag quandary pi akyu
Please help
Sketch the graph of y = (x – 1)2 + 2 and identify the axis of symmetry.
Answer:
The axis of symmetry is (0,0)
Step-by-step explanation:
This is the picture
I need help please no links
Answer:
A and D
Step-by-step explanation:
Look at the answer choices as (x,y) so if you multiply the x for the x spot and the y for the y spot, you make sure the it is greater than or equal to 3 and if it is, select that answer.
