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
On Monday, a localamburger shop said a combined total of 225 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number
of hamburgers sold. How many hamburgers were sold on Monday?
hamburgers
х
?
Answers
Answer:
h = hamburgers sold
2h - 72 = 578
2h = 650
2 2
h = 325
There were 72 fewer cheeseburgers sold than hamburgers. That means cheeseburgers = 325 - 72
325 - 72 = 253
253 = cheeseburgers
325 = hamburgers
253 + 325 = 578
Hamburgers = 325
Hope this helps :)
Hi need help with this so plz help me
Answers
I can’t type your symbol, but will use =< instead.
So: 2=We are told x is an integer (whole number) so the possible solutions are the consecutive numbers from 2 to 8.
That is: x = 2, 3, 4, 5, 6, 7 or 8.
HELP HELP HELPPPP PLEASEEE
Directions: Determine if segments AB and CD are parallel, perpendicular, or neither.
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Answers
Given:
AB formed by (-2,13) and (0,3).
CD formed by (-5,0) and (10,3).
To find:
Whether the segments AB and CD are parallel, perpendicular, or neither.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
AB formed by (-2,13) and (0,3). So, the slope of AB is:
[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]
[tex]m_1=\dfrac{-10}{2}[/tex]
[tex]m_1=-5[/tex]
CD formed by (-5,0) and (10,3). So, slope of CD is:
[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]
[tex]m_2=\dfrac{3}{10+5}[/tex]
[tex]m_2=\dfrac{3}{15}[/tex]
[tex]m_2=\dfrac{1}{5}[/tex]
Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.
[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]
[tex]m_1\times m_2=-1[/tex]
Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.
Hence, the segments AB and CD are perpendicular.
Answer:
AB is perpendicular to CD.
Step-by-step explanation:
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Slope of a line passing through two points is
[tex]m= \frac{y''-y'}{x''- x'}[/tex]
The slope of line AB is
[tex]m= \frac{3- 13}{0+2} = -5[/tex]
The slope of line CD is
[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]
As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.
which equation represents a line parallel to the y-axis?
Answers
Answer:
B. x=4
Step-by-step explanation:
I hope this helps!
whats the equation of this horizantal line
Answers
Answer:
[tex]y=-7[/tex]
Step-by-step explanation:
Hope this helps you.
Answer:
y = — 7
Step-by-step explanation:
thanks for the pts
✌️❤️✌️
PLEASE HELP! Which point would be included in the solution set of this system of inequalities?
A. (-2,10)
B. (2,10)
C. (0,0)
D. (-2,-10)
Answers
Answer:
D
Step-by-step explanation:
-10 < -6 - 1
-10 < - 7 (ok)
-10 < -4 - 3
-10 < -7 (ok)
The answer is D (-2, -10)
Determine the area of an obtuse triangle with a height
of 11 cm and a base of 22 cm
Answers
Step-by-step explanation:
A
=
h
b
b
2
=
11
·
22
2
=
121
cm²
The area of the obtuse triangle with a height of 11 cm and a base of 22 cm is 121 cm².
To determine the area of an obtuse triangle, we can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
In this case, the height of the triangle is given as 11 cm and the base is given as 22 cm.
Substituting these values into the formula, we have:
Area = (1/2) * 22 cm * 11 cm
Calculating this expression, we get:
Area = (1/2) * 242 cm²
Simplifying further, we have:
Area = 121 cm²
The area of a triangle is calculated by multiplying half of the base by the height. In this case, the given height is 11 cm and the base is 22 cm. Substituting these values into the formula, the area of the obtuse triangle is calculated to be 121 cm².
To learn more about area click on,
https://brainly.com/question/8397982
#SPJ2
what is the slope of the graph?
Answers
Answer:
The slope is 1.5
Step-by-step explanation:
To get the slope of the graph, we proceed to select any two points lying on the given line, and applying the slope formula
The two selected points are as follows;
(x1,y1) = (-4,0)
(x2,y2) = (-2,3)
m = (y2-y1)/(x2-x1)
m = (3-0)/(-2-(-4)
m = 3/2 = 1.5
In a county containing a large number of rural homes, 60% of the homes are insured against fire. Four rural homeowners are chosen at random from this county, and x are found to be insured against fire. Find the probability distribution for x.
Answers
Answer:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]p = 60\%[/tex]
[tex]n = 4[/tex]
Required
The distribution of x
The above is an illustration of binomial theorem where:
[tex]P(x) = ^nC_x * p^x *(1 - p)^{n-x}[/tex]
This gives:
[tex]P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}[/tex]
Express percentage as decimal
[tex]P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}[/tex]
[tex]P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}[/tex]
When x = 0, we have:
[tex]P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}[/tex]
[tex]P(x=0) = 1 * 1 *(0.40)^4[/tex]
[tex]P(x=0) = 0.0256[/tex]
When x = 1
[tex]P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}[/tex]
[tex]P(x=1) = 4 * (0.60) *(0.40)^3[/tex]
[tex]P(x=1) = 0.1536[/tex]
When x = 2
[tex]P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}[/tex]
[tex]P(x=2) = 6 * (0.60)^2 *(0.40)^2[/tex]
[tex]P(x=2) = 0.3456[/tex]
When x = 3
[tex]P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}[/tex]
[tex]P(x=3) = 4 * (0.60)^3 *(0.40)[/tex]
[tex]P(x=3) = 0.3456[/tex]
When x = 4
[tex]P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}[/tex]
[tex]P(x=4) = 1 * (0.60)^4 *(0.40)^0[/tex]
[tex]P(x=4) = 0.1296[/tex]
So, the probability distribution is:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
Gabe went out to lunch with his best friend. The bill cost $16.40 before tax and tip. He paid a 9% tax and he left a 20% tip. How much did Gabe spend?
Hint: Tax and tip are both based on the original cost of the bill.
Don't forget to round to the nearest cent!
Answers
Explanation: First you want to take 9 percent of $16.40 using the equation 16.40 * 0.09 which is about $1.47. Then take 20 percent of $16.40 using the equation 16.40* 0.2 which is $3.28.
Now do 16.40+1.47+3.28 which equals $21.15
Help i give fre robuc and v bucc and gems
Answers
Answer:
x intercept is -7 and y intercept is 2
Step-by-step explanation:
Answer:
x intercept (-7,0)
y intercept (0,2)
Which value of w ww makes 14 = 11 + w 8 ⋅ 6 14=11+ 8 w ⋅614, equals, 11, plus, start fraction, w, divided by, 8, end fraction, dot, 6 a tru
Answers
Answer:
w=4
Step-by-step explanation:
Explain what the construction does and list the steps to creating the construction. Be as detailed as possible :D
Answers
Step-by-step explanation:
This construction bisects the pqr angle.
This is done by placing a compass on the pqr angle and marking construction lines at the points c and a.
Then at where the construction lines at points c and a meet the lines qr and qp draw 2 more from that placement.
Then draw a line running through angle pqr and where the construction lines meet at point b.
Hope this helps and good luck!
x + 2y when x = 1 and y = 4
Answers
Answer:
9
Step-by-step explanation:
x = 1
y = 4
x + 2y = 1 + 8 = 9
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
9
Step-by-step explanation:
x + 2y
subtitute:
1 + 2(4)
simplify:
1 + 8 = 9
The sides of the triangular base of prism are 10 cm 8 cm and 6cm respectively and it is 15 cm long .Find the total suface area of the prism.
Answers
Answer:
408 cm²
Step-by-step explanation:
the total SA = (2×½×6×8) + (10+8+6)×15
= 48 + 360
= 408 cm²
The total surface area of the prism that has a triangular base of 10 cm, 8 cm, and 6cm and it is 15 cm long is 408 cm².
What is a triangular base?In order to create the triangle base, the three triangular sides slant upward. A pyramid with a triangular base is also known as a tetrahedron since it is made up of four triangles.
The shape of a pyramid's base is often used to describe it. A hexagonal pyramid has a base that is a hexagon, as does a triangular pyramid, for example. Pyramids with triangular bases are called triangular pyramids.
A triangle's area is equal to half the sum of its base and height, according to the formula for triangular bases. Whether it be a scalene triangle, an isosceles triangle, or an equilateral triangle, this formula can be used to determine their properties.
The total surface area of the prism calculations are,
b = 6 cm, h = 8 cm, l = 10 cm, and L = 15 cm
[tex]Total\ Surface\ Area = (2\times \frac{1}{2} \times b \times h) + (l+h+b) \times \\ L=(2\times \frac{1}{2} \times 6 \times 8) + (10+8+6) \times 15\\= 48 + 360\\= 408 cm^2[/tex]
Therefore, total surface area of the prism that has a triangular base of 10 cm, 8 cm, and 6cm and it is 15 cm long is 408 cm².
Learn more about triangular base from here:
https://brainly.com/question/12434035
#SPJ2
Aaron's rear bicycle tire has too much air he removes 8 pounds of air so that his tire gauge now reads 53 pounds. How many pounds did he begin with? Use the equation p - 8 = 53
Answers
Answer:
61 pounds
Step-by-step explanation:
you rearrange the equation to make p the subject:
p-8=53
p = 8+53
p = 61
the question please i need help
Answers
Answer:
90g strawberry jelly
6 sponge fingers
315ml custard
135g tinned fruit
Step-by-step explanation:
----------------------------------------
Since those ingredients that are in the question say making a trifle for four people, let's divide each ingredient by four to find the ingredients for one person, and multiply by 3 to find the ingredients for 3 people.
So,
[tex]120/4=30[/tex]g strawberry jelly
[tex]8/4=2[/tex] sponge fingers
[tex]420/4=105[/tex]ml custard
[tex]180/4=45[/tex]g tinned fruit
There are the ingredients to make a trifle for one person.
-------------------->>>>
Now, let's multiply each of the ingredients for one person and multiply that by three to find the ingredients needed to make a trifle for four people.
[tex]30*3=90[/tex]g strawberry jelly
[tex]2*3=6[/tex] sponge fingers
[tex]105*3=315[/tex]ml custard
[tex]45*3=135[/tex]g tinned fruit
These are the ingredients needed to make a trifle for three people.
----------------------------------------
Hope this is helpful.
What is the value of x?
0 14
0 17
O 27
O 34
PLEASE HELP
Answers
To indirectly measure the distance across a lake, Nachelle makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter
Answers
Answer:
207.68 m
Step-by-step explanation:
From the diagram,
ΔDEC is similar to ΔFGC
Therefore,
(DE)/(FG) = (DC)/(FC).............. Equation 1
make line DE the subject of the equation
DE = [(DC)(FG)/(FC)]................ Equation 2
From the diagram,
Given: DC = 190 m, FG = 142.1 m, FC = 130 m
Substitute these values into equation 2
DE = (190×142.1/130)
DE = 207.68 m
Hence the distance across the lake is 207.68 m
Applying the similarity theorem, the distance across the lake to the nearest hundredth is: DE = 207.68 m
Recall:
The corresponding side lengths of two triangles that are similar are always proportional to each other.Thus:
ΔCDE and ΔCFG are similar to each other
FG = 142.1 m
FC = 130 m
DF = 60 m
DC = 130 + 60 = 190 m
Therefore:
DE/FG = DC/FC
SubstituteDE/142.1 = 190/130
Cross multiply[tex]DE = \frac{190 \times 142.1}{130} \\\\\mathbf{DE = 207.68 $ m}[/tex] (nearest hundredth).
Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is: DE = 207.68 m
Learn more about similar triangles here: https://brainly.com/question/11899908
20 Points- Which of the following is true for f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3?
There is a removable discontinuity at x = 3.
There is a non-removable discontinuity at x = 3.
The function is continuous for all real numbers.
Answers
Answer:
There is a non-removable discontinuity at x = 3
Step-by-step explanation:
We are given that
[tex]f(x)=\frac{x^2+9}{x-3}[/tex]
We have to find true statement about given function.
[tex]\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}[/tex]
=[tex]\infty[/tex]
It is not removable discontinuity.
x-3=0
x=3
The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.
Therefore, x=3 is non- removable discontinuity of function f(x).
Hence, option B is correct.
Dan invests £13000 into his bank account. He receives 2.3% per year simple interest. How much will Dan have after 4 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
=14237.90
Step-by-step explanation:
13000*1.023^4=14237.89832
=14237.90
Micheal is selling lemonade.He sold 6 large lemonades at $3 each and 5 small lemonades at $2 each. How much money did he earn ?
Answers
Answer:
$28
Step-by-step explanation:
Answer:
6=$3
5=$2
6x3=18
5x2=10
18+10= 28
=$28
Step-by-step explanation:
Which of the following statements is true?
A) All squares are rectangles.
B) All parallelograms are rectangles.
C) All rhombuses are squares.
D) All rectangles are squares. (D is Not the answer)
Answers
all sides are equal, opposite sides are equal, opposite sides are parallel, angles are equal, opposite angles are equal, and the sum of two adjacent angles is 180 degrees
A number ending in ___ is never a perfect square.
Answers
Answer:
2, 3, 7 or 8
Step-by-step explanation:
(-2x+1) (2x^2-1/3x+2)
Answers
Answer:
JHJHJHJHUJ3480945768
658768
Step-by-step explanation:
684867765543545
Ans x = 0.5
Step-by-step explanation:
[tex]= -4x^{3} + 2x^{2} +\frac{2}{3}x^{2} -\frac{1}{3}x-4x+2\\= -4x^{3}+\frac{8}{3}x^{2} -\frac{13}{3}x+2\\[/tex]
If the equation requires to find x, you can use Casio calculator to solve this by some basic formula:
Step 1: Type [tex]-4x^{3}+\frac{8}{3}x^{2} -\frac{13}{3}x+2[/tex]
Step 2: Press Shift SOLVE (CALC)
Step 3: Press "0" for Solve for X
-> You will find the x is 0.5
Help and explain please and thank you !!!!!!!
Answers
Answer:
[tex]q = 3[/tex]
Step-by-step explanation:
[tex]3q−2=7[/tex]
[tex]3q=7+2[/tex]
[tex]3q=9[/tex]
[tex]q = \frac{9}{3} [/tex][tex]q = 3[/tex]
Hope it is helpful....At a football stadium, 25% of the fans in the attendance were teenagers. If there were 190 teenagers at the football stadium, what was the total numbers of the people at the stadium?
Answers
Answer:
760
Step-by-step explanation:
25%= 190
100 = 25 × 4
100% (total number of people) = 190 × 4 = 760
Solve by factorisation.
3x² + 10x - 8 = 0
Answers
Answer:
3x²+12x-2x-8. = 0
3x(X+4)-2(X+4) = 0
(x+4)(3x-2) =0
[tex]x = (- 4) \: or \: x = \frac{2}{3} \: are \: the \: solutions[/tex]
The mean of 6 numbers is 8.
The numbers are in the ratio 1 : 1 : 2 : 2 : 3 : 3.
Find the median.
Answers
Answer: 8
Step-by-step explanation:
Given
Mean of the numbers is 8
If the ratio is 1:1:2:2:3:3
Suppose the numbers are [tex]x, x, 2x, 2x, 3x, 3x[/tex]
Write the mean of the numbers
[tex]\Rightarrow \dfrac{x+x+2x+2x+3x+3x}{6}=8\\\\\Rightarrow \dfrac{12x}{6}=8\\\\\Rightarrow x=4[/tex]
So, the numbers are [tex]4, 4, 8,8 ,12,12[/tex]
As the total numbers are even, median is the sum of the middle values
[tex]\Rightarrow \text{Median=}\dfrac{8+8}{2}\\\\\Rightarrow \text{Median=}8[/tex]
Write 8 as the ratio of two integer
Answers
Answer:
Step-by-step explanation: 7 1 16 37
8/1 8 divided by 1
16/2 16 divided by 2
24/3 24 divided by 3 I could go on, but won't
