Answers
Given:
For two events X and Y,
[tex]P(X)=\dfrac{2}{3}[/tex]
[tex]P(Y)=\dfrac{2}{5}[/tex]
[tex]P(X|Y)=\dfrac{1}{5}[/tex]
To find:
The probabilities [tex]P(Y\cap X), P(Y)\cdot P(X)[/tex].
Solution:
Using the conditional probability:
[tex]P(X|Y)=\dfrac{P(Y\cap X)}{P(Y)}[/tex]
[tex]P(X|Y)\times P(Y)=P(Y\cap X)[/tex]
Substituting the given values, we get
[tex]\dfrac{1}{5}\times \dfrac{2}{5}=P(Y\cap X)[/tex]
[tex]\dfrac{2}{25}=P(Y\cap X)[/tex]
And,
[tex]P(Y)\times P(X)=\dfrac{2}{5}\times \dfrac{2}{3}[/tex]
[tex]P(Y)\times P(X)=\dfrac{4}{15}[/tex]
Therefore, the required probabilities are [tex]P(Y\cap X)=\dfrac{2}{25}[/tex] and [tex]P(Y)\times P(X)=\dfrac{4}{15}[/tex].
Related Questions
A dot plot with an axis marked from 0 to 10 at increments of 1 is shown. Plot shows 8 dots at 0, 7 dots at 1, 5 dots at 2, 4 dots at 3, 2 dots at 4, and 1 dot at 10.
A)
The mean is equal to the median and the data are symmetric.
B)
The peak is equal to the median and the data are skewed.
C)
The data are skewed and there is an outlier.
D)
The data are symmetric and there is an outlier.
Answers
Answer:
C) The data are skewed and there is an outlier.Step-by-step explanation:
Its clear from the dot plot that:
There is an outlier at 10, since majority of data are concentrated at 0-4 interval with only one far away.The data are skewed, since most data concentrated to one side of the median.So, the correct choice is C
The given information in the dot plot is,
i) An outlier is present at 10.
ii) The data's majority are concentrated at 0 to 4 interval.
iii) 10 is the only one, which is far away.
iv) We confirm that the data are skewed.
v) Because the most data is concentrated in one median's side.
Then the final answer will be,
C) The data are skewed and there is an outlier.
Therefore, option (C) is the answer.
A rectangular floor of area 360 m2 is going to be tiled. Each tile is rectangular, and has an area of 240 cm2. An exact number of tiles can be put into the space. How many tiles will be... Solve quickly
Answers
Answer:
1500
Step-by-step explanation:
The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,
[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]
And , the number of tiles required will be ,
[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]
Hence the required answer is 1500 .
AB is tangent to circle C. Find the value of r. Please answer Asap
Answers
Answer:
3
Step-by-step explanation:
a tangent to a circle makes right angle with the radius at that point ( here the point is B)
thus,
ABC is a right angled triangle
AC being the hypotenuse AB being the adjacentBC being the oppositeBy Pythagoras theorem :-
By Pythagoras theorem :-AC² = AB² + BC²
(r + 2)² = 4² + r²
r² + 4 + 4r = 16 + r²
subtracting r² from both sides and taking 4 common
4(1 + r) = 16
diving both sides by 4
1 + r = 4
r = 3 units
The value of r is,
⇒ r = 3 units
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
AB is tangent to circle C.
Now,
By Pythagoras theorem, we get:-
AC² = AB² + BC²
(r + 2)² = 4² + r²
r² + 4 + 4r = 16 + r²
subtracting r² from both sides and taking 4 common
4(1 + r) = 16
diving both sides by 4
1 + r = 4
r = 3 units
Thus, The value of r is,
⇒ r = 3 units
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Find all possible values of α+
β+γ when tanα+tanβ+tanγ = tanαtanβtanγ (-π/2<α<π/2 , -π/2<β<π/2 , -π/2<γ<π/2)
Show your work too. Thank you!
Answers
Answer:
[tex]\rm\displaystyle 0,\pm\pi [/tex]
Step-by-step explanation:
please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation
===========================
we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first
cancel tanγ from both sides which yields:
[tex] \rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma ) [/tex]
factor out tanγ:
[tex]\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)[/tex]
divide both sides by tanαtanβ-1 and that yields:
[tex]\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}[/tex]
multiply both numerator and denominator by-1 which yields:
[tex]\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)[/tex]
recall angle sum indentity of tan:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta ) [/tex]
let α+β be t and transform:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( t) [/tex]
remember that tan(t)=tan(t±kπ) so
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi ) [/tex]
therefore when k is 1 we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi ) [/tex]
remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal which yields:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm \pi [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }[/tex]
when is 0:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 ) [/tex]
likewise by Opposite Angle Identity we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal therefore:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm 0 [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }[/tex]
and we're done!
Answer:
-π, 0, and π
Step-by-step explanation:
You can solve for tan y :
tan y (tan a + tan B - 1) = tan a + tan y
Assuming tan a + tan B ≠ 1, we obtain
[tex]tan/y/=-\frac{tan/a/+tan/B/}{1-tan/a/tan/B/} =-tan(a+B)[/tex]
which implies that
y = -a - B + kπ
for some integer k. Thus
a + B + y = kπ
With the stated limitations, we can only have k = 0, k = 1 or k = -1. All cases are possible: we get k = 0 for a = B = y = 0; we get k = 1 when a, B, y are the angles of an acute triangle; and k = - 1 by taking the negatives of the previous cases.
It remains to analyze the case when "tan "a" tan B = 1, which is the same as saying that tan B = cot a = tan(π/2 - a), so
[tex]B=\frac{\pi }{2} - a + k\pi[/tex]
but with the given limitation we must have k = 0, because 0 < π/2 - a < π.
On the other hand we also need "tan "a" + tan B = 0, so B = - a + kπ, but again
k = 0, so we obtain
[tex]\frac{\pi }{2} - a=-a[/tex]
a contradiction.
plz help ASAP with explanation
Answers
Answer:
(in image attached)
Step-by-step explanation:
A.
Left: 6×-3
Right: -3×-2
Bottom: 6×-2
B.
48÷6 = 8
-42÷6 = -7
-56÷8 = -7
-56÷-7= 8
Find sin 0. Please and thank you
Answers
Answer:
the correct answer is C....I hope
John read 10 books in 12 months. What was his rate of reading in months per book?
Answers
Answer:
1.2 books per month
12/10
Step-by-step explanation:
foiuhgfdknsmlaeszxcyfvugbihnoj
Answers
Answer:
Given : A=(1,2)≡(x
1 ,y
1
) and B=(3,−2)≡(x
2
,y
2
)
Let M=(x,y) be the midpoint of AB
x=(
2
x
1
+x
2
) and y=(
2
y
1
+y
2
)
Then, x=
2
1+3
and y=
2
2−2
⟹x=2 and y=0
∴M=(2,0)
∴ Coordinates of the midpoint of AB is (2,0)
Step-by-step explanation:
BRAINLEST IF CORRECT!!!!which of the d-values satisfy the following inequality? d/5>4
Answers
Answer:
d = 25
Step-by-step explanation:
[tex]\frac{d}{5} >4[/tex]
The value of d has to satisfy the inequality
so replace d with one of the given options
[tex]\frac{25}{5} >4[/tex]
We have to simplify the fraction first
[tex]\frac{25}{5} =5>4[/tex]
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
7 cm and 2 cm
8 cm and 9 cm
Answers
Answer:
8 cm and 9 cm
Step-by-step explanation:
Hi there!
The sum of the lengths of two sides of a triangle must always be greater than the length of the third side.
5 cm and 8 cm ⇒ 5+8=13; not greater than 13
6 cm and 7 cm ⇒ 6+7=13; not greater than 13
7 cm and 2 cm ⇒ 7+2=9; not greater than 13
8 cm and 9 cm ⇒ 8+9=17; greater than 13
Therefore, the last set of two sides is possible for the lengths of the the other two sides of this triangle.
I hope this helps!
5+8=13
6+7=13
7+2=9
8+9=17
Use two unit multipliers to convert 36 inches to miles.
Answers
Answer:
36 inches = 0.000568182 miles
Lines A and B are parallel
NEED HELP, IF ITS RIGHT ILL MAKE YOU BRAINLIEST
Answers
130 is your answer! Look at line A. 130 degrees. now if A and B are parallel then 5 on line B will also be 130 degrees.
I hope this helps!
Look at pic for question and answer choices.
Answers
A fire extinguisher releases 27/4  liters of carbon dioxide in 9/16 minutes what is the speed in terms of liters per minute
Answers
Answer:
12 liters per min
Step-by-step explanation:
Math
27/4 = x
9/16 1
27/4=(9/16)x
Divide both sides by 9/16
12=x
Mrs Nu paid $2083 for 2 smiler laptops and 3 similar earphones. Each laptop cost of each earphones?
Answers
Answer:
Step-by-step explanation:
The information given is incomplete :
Answer:
x = 1/2(2083 - 3y)
y = 1/3(2083 - 2x)
Step-by-step explanation:
Let
Laptop cost = x
Earpiece cost = y
Number of laptops= 2
Number of earpiece = 3
2x + 3y = $2083
The cost per laptop :
2x = 2083 - 3y
Divide both sides by 2
x = (2083 - 3y) / 2
x = 1/2(2083 - 3y)
Or
3y = 2083 - 2x
y = (2083 - 2x) / 3
y = 1/3(2083 - 2x)
What is important to remember when multiplying radicals?
Answers
Answer:
A radical is basically a fractional exponent and is denoted by the radical sign (√). The expression x2 means to multiply x by itself (x × x), but when you see the expression √x, you're looking for a number that, when multiplied by itself, equals x. Similarly, 3√x means a number that, when multiplied by itself twice, equals x, and so on. Just as you can multiply numbers with the same exponent, you can do the same with radicals, as long as the superscripts in front of the radical signs are the same. For example, you can multiply (√x × √x) to get √(x2), which just equals x, and (3√x × 3√x) to get 3√(x2). However, the expression (√x × 3√x) can't be simplified any further.
The slope of the lines that passes through the points (-10,0) and (-13,3)
Answers
Answer:
-1
Step-by-step explanation:
The formula to find the slope of a line is:
[tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
where (x1, y1) and (x2, y2) are points on the line. We can substitute the points (-10, 0) and (-13, 3) into the formula and simplify:
[tex]\frac{3-0}{-13-(-10)} =\frac{3}{-13+10} =\frac{3}{-3} =-1[/tex]
This means the slope of the line is -1.
what is the answer of this questoin 2c-3b+6+7b-2b+11?
Answers
Answer:
[tex]2c+2b+17[/tex]
Step-by-step explanation:
-----------------------
Given:
[tex]2c-3b+6+7b-2b+11[/tex]
---------->>>>
Collect like terms.
[tex]2c+(-3b+7b-2b)+(6+11)[/tex]
---------->>>>
Simplify
[tex]2c+2b+17[/tex]
------------------------
Hope this is helpful.
Answer:
2c-2b+17 if using algebra
Step-by-step explanation:
firstly group like terms 2c+(-3b)+7b-2b+6+11
2c-2b+17
Do anyone know this
Make sure is the correct answer please
Answers
9514 1404 393
Answer:
(a) P = 44 cm + 18 cm + 18 cm = 80 cm
(b) 396 cm²
(c) (i) see attached: radius = 7 cm; height ≈ 16.58 cm; slant height = 18 cm
(c) (ii) 7 cm
Step-by-step explanation:
(a) The length of arc PQR is given by the formula ...
s = rθ . . . . . where r is the radius and θ is the angle in radians
The angle θ in radians is (140°)(π/180°) = (140)(22/7)/(180) = 22/9
So, the arc length is ...
PQR = (18 cm)(22/9) = 44 cm
Then the perimeter of the figure is ...
P = PQR +RO +OP = 44 cm + 18 cm + 18 cm
P = 80 cm
__
(b) The area of a sector is given by ...
A = 1/2r²θ = 1/2(rs)
A = (1/2)(18 cm)(44 cm) = 396 cm² . . . area of the sector
__
(c) (i) A drawing of the cone is attached. The "slant height" is 18 cm. The radius is found in part (ii) as 7 cm. The height is given by the Pythagorean theorem:
height = √((slant height)² - radius²) = √(18² -7²) = √275
height ≈ 16.58 . . . cm
(ii) The length of arc PQR is the circumference of the base of the cone, given by ...
C = 2πr . . . . where r is the radius of the base of the cone
Filling in the known values, we find ...
44 cm = 2(22/7)r
(44 cm)(7/44) = r = 7 cm . . . . . multiply by 7/44 to find r
The radius of the base of the cone is 7 cm.
Find x. Round your answer to the nearest hundredth
Answers
Answer:
5.86
Step-by-step explanation:
Answer:
x = 5.86
Step-by-step explanation:
x / 15 = cos67°
x = 15cos67°
x = 5.86
what is the length of segment QV ?, NO LINKS.
Answers
Answer:
44 units
Step-by-step explanation:
TS = TQ
2x + 8 = 40
2x = 32
x = 16
QV = SV
QV = 3x - 4
QV = 3(16) - 4
QV = 48 - 4
QV = 44
which relation is a function?
Answers
The first one because there is only one y value for every x value. The correct option is first.
To determine if a relation is a function, use the vertical line test: If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. On the other hand, if every vertical line intersects the graph of the relation at most once, then the relation is a function.
In first relation is considered a function, because each input x-value is associated with exactly one output y-value. In other words, for every x-value in the domain of the relation, there can be only one corresponding y-value in the range. Each x-value should not have more than one y-value associated with it.
Therefore, each x-value should not have more than one y-value associated with it. The correct option is first.
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HURRY I NEED HELP. ASAP.
What are the coordinates of the quadrilateral STUV when reflected over the X-axis.
S(3,4), T(3,1), U(-2,1, V(-2,4)
Answers
Step-by-step explanation:
here is the answer friend
nate and laura picked 20 apples laura picked 1/2 of what nate picked
how many did nate pick?
Answers
Answer:
10
Step-by-step explanation:
20÷2=10 the half of 20 is 10 simple as that
Answer:
ok so together they picked 20 apples so
20=y+1/2y
y=40/3 or 13 1/3
thats how many nate picked and we divide by 2
6 2/3
Hope This Helps!!!
Step 3: Let LM = x. We know the lengths of the radii of each circle, so KL = 12 +
8 = 20. Add the length of KL to the diagram.
J
12 K
20
L
X
M
12
00
8
N
Answers
Answer:
Step-by-step explanation:
Step 3:
Let LM = x
OK = KP = 12 units [Radii of circle K]
LN = LP = 8 units [Radii of circle L]
Therefore, KL = KP + PL
KL = 12 + 8
= 20 units
Step 4:
Since, ΔKOM and ΔLNM are the similar triangles,
By the property of two similar triangles, corresponding sides of these similar triangles will be proportional.
[tex]\frac{OK}{NL}=\frac{KM}{LM}[/tex]
[tex]\frac{12}{8}=\frac{x+20}{x}[/tex]
12x = 8(x + 20) [By cross multiplication]
12x = 8x + 160
12x - 8x = 160
4x = 160
x = 40
6. Find the value of x to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
[tex]Cos \ 39 = \frac{adjacent \ side}{hypotenuse}\\\\0.7771 = \frac{7}{x}[/tex]
x * 0.7771 = 7
[tex]x =\frac{7}{0.7771}=9.007[/tex]
x = 9
(5^3)^5 please need help on this one
Answers
Answer:
Step-by-step explanation:
[tex](5^3)^5=5^{15}[/tex] which is absolutely huge. In scientific notation it is
3.051757813 × 10¹⁰
Answer:
(5×5×5)=125
125^5=30,517,578,125
final answer=30,517,578,125
a square number and a multiple of 3 have a total of 90 what r the 2 numbers
Answers
Hello,
Let's x² the square number
and 3*y the multiple of 3.
[tex]x^2+3y=90\\\\\boxed{y=-\dfrac{1}{3} x^2+30}\\\\[/tex]
2 solutions : for (x,y) as integers : (-6,18) and (6,18)
but one solution for (x²,3y) as integers : (36,54)
HELPPP
___
Thank you
Answers
Answer:
11.0.0035
12.39×10^-4
13.)0.00031
14.59800
15.3.6×10^9
Step-by-step explanation:
This year, Carlos planted 6 more than one-third of the cucumber plants he planted last year. How many cucumber
plants did he plant this year if last year he planted 12 plants?
06
09
O 10
12
Answers
Answer:
10
Step-by-step explanation:
last year he planted 12.
1/3 of that is 12/3 = 4.
6 more than that is 4 + 6 = 10.
Answer: C.) 10
Step-by-step explanation: