Answer: The correct option is
(A) [tex]P(X)\times P(Y)=P(X\cap Y).[/tex]
Step-by-step explanation: We are given to consider a situation in which X and Y are two events such that
[tex]P(X)=\dfrac{4}{5},~P(Y)=\dfrac{1}{4},~P(X\cap Y)=\dfrac{1}{5}.[/tex]
We are to select the statement that best describes the events X and Y.
We know that
any two events A and B are said to be independent if
[tex]P(A)\times P(B)=P(A\cap B).[/tex]
We have, for events X and Y,
[tex]P(X)\times P(Y)=\dfrac{4}{5}\times\dfrac{1}{4}=\dfrac{1}{5}=P(X\cap Y)\\\\\\\Rightarrow P(X)\times P(Y)=P(X\cap Y).[/tex]
Thus, X and Y are independent because [tex]P(X)\times P(Y)=P(X\cap Y).[/tex]
Option (A) is CORRECT.
Evaluate M2/P2 for M = 10, N = -5, and P = -2?
A.-5
B.5
C.-25
D.25
Answer:
(10)^2/(-2)^2 = 100/4= 25
the answer is d
3(6+5y)=2(-5+4y) help huhu
Answer:
-4 = y
Step-by-step explanation:
3(6+5y)=2(-5+4y)
18 + 15y = -10 + 8y
+10 +10
28 + 15y = 8y
- 15y -15y
28 = - 7y
28/-7 = -4
-7y/-7 = y
Answer:
y = -4
Step-by-step explanation:
distribute both 3 and 2 through the parenthesis, move the variable to the left side and change its sign, move constant to the right side and change its sign, collect like terms, calculate the difference, divide both sides of the equation by 7, and your answer would be -4
What is the solution to
−4x+5y=−12
x−6y=22
Answer:
The solution to the system is S= (-2, -4).
Step-by-step explanation:
Given the system
−4x+5y=−12
x−6y=22
The first step is to solve x from the first equation for example, and substitute the expression in the second equation.
1) -4x + 5 y = -12 ⇒ -4x = -12 - 5y ⇒ x = (-12 - 5y)/-4 ⇒ x = 3 + (5/4)y
2) x - 6y = 22 ⇒ (3 + (5/4)y) - 6y = 22 ⇒ 3 + (5/4)y - 6y = 22
⇒ 3 - (19/4)y = 22 ⇒ (-19/4)y = 22- 3 ⇒ y = 19/(-19/4) ⇒ y =-4.
Finally, with the value obtained for "y", you have to return to the original equations and replace it to obtain the "x" value.
-4x + 5y = -12 ⇒ -4x + 5(-4) = -12 ⇒ -4x - 20 = -12 ⇒ -4x = -12 + 20
⇒ -4x = 8 ⇒ x = 8/-4 ⇒ x = -2.
Summarizing, the solution to this system is S = (-2, -4).
Terry,Sasha, and Harry each chose a number.Terrys number is 10x as much as Sasha’s. Sasha’s number is 0.4. What number did each person choose?
200 principal, 4% compounded annually for 5 years
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$200\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=200\left(1+\frac{0.04}{1}\right)^{1\cdot 5}\implies A=200(1.04)^5\implies A=243.33058048[/tex]
The equation 3w + 4j = 39 is used to determine the number of water bottles w and the number of juice bottles j that can be bought for $39. If you purchase 6 bottles of juice, how many bottles of water can you buy?
Juice bottles are J, replace j with 6 in the equation and solve for w:
3w + 4(6) = 39
3w + 24 =39
Subtract 24 from both sides:
3w = 15
Divide both sides by 3:
w = 15/3
w = 5
You can buy 5 water bottles.
Answer:
5
Step-by-step explanation:
The number of water bottles [tex]= w[/tex]
The number of juice bottles [tex]= j[/tex]
We have, [tex]3w + 4j = 39[/tex]
When we purchase 6 bottles of juice, [tex]j = 6[/tex]
So,
[tex]3w + 4j = 39[/tex]
[tex]3w + 4 \times 6 = 39[/tex]
[tex]3w + 24 = 39[/tex]
[tex]3w = 39 - 24[/tex]
[tex]3w = 15[/tex]
[tex]w = \frac{15}{3}[/tex]
[tex]w = 5[/tex]
Therefore, we can buy 5 bottles of water.
Please I need help?!
Answer:
1a. 460313
1b. 405040
1c. 100000 more
2a. 176960
2b. 12097
2c. 839000
2d. 452210
Step-by-step explanation:
2d. 442210
+ 10000
________
452210
2c. 849000
- 10000
________
839000
2b. 13097
- 1000
_______
12097
2a. 100000
+ 76960
________
176960
1c.
[tex] - 347077 + 447077 = 100000[/tex]
1b.
[tex]300000 + 90000 + 5000 + 40 = 395040 \\ \\ 10000 + 395040 = 405040[/tex]
1a.
[tex] -100000 + 560313 = 460313[/tex]
I am joyous to assist you anytime.
This equation graphed
I answered this question already.
a salesman receives a salary rs 1000 per month and 10%commission on sales in excess of rs 5000.what is the amount of sales if he earns rs.2000. in a particular month
Answer:
Amount of sales = rs 10,000.
Step-by-step explanation:
He earns 2000 - 1000 = rs 1000 from sales.
This equals 10% ( = 0.10 as a fraction) of his sales so his sales must have been 1000 / 0.10
= rs 10,000.
i need help whoever got this answer right gets brainlist
Using the appropriate constant of proportionality, provide the value in the table that makes the quantities proportional to one another. Answer format: 8/9 *
Answer:
3
Step-by-step explanation:
If you look closely every X is changing by 3 so 3·y=x
Answer:
The value in the table that makes the quantities proportional to one another is y = 3
Step-by-step explanation:
Two quantities x and y are proportional one to another if they can be expressed as
y = kx
where k is the constant of proportionality. We can find k using an specific point. Take the first one
y = kx
k= y/x with (3.1 )
k= 1/3
So
y =1/3x for this case
If the two quantities are proportional, this rule must be true for any point (x,y) . Lets prove it
Point 2 (6,2)
2 =1/3*(6)
2= 2 True
Point 4 (12,4)
4 =1/3*(12)
4= 4 True
So to accomplish the rule in point 3, and finally in all table we must have that
y =1/3x is true for Point 3 (9,y) Then
y = 1/3 (9) = 9/3 = 3
y= 3
Y must be 3
Sam has a total score of 500 on a game, compared to the maximum possible score of 1200.
Write this proportion as a percentage, correct to the nearest integer.
Julie is thinking about the product-54. Which expressions could result in this product? Select all that apply.
Ms. Thornton's class visited five freshwater lakes to learn more about the crocodiles and alligators living in them. The class counted the number of species in each lake as shown in the table.
Lake Crocodiles Alligators
A 4 5
B 21 35
C 3 9
D 6 16
E 24 30
The relationship between the number of crocodiles and the number of alligators is not proportional across all lakes. Only two of the lakes have crocodiles and alligators in the same proportion. Which two lakes are they?
A.
lake A and lake B
B.
lake B and lake C
C.
lake A and lake E
D.
lake C and lake D
Answer:
It's C. If you divide them you get 1.25 for both of them and its proportional
Y is inversely proportional to x. If y= 400 when x =2 find y when x= 200
Answer: 4
Step-by-step explanation:
Inversely proportional means xy = k, where k is the constant of proportionality
First, find k when x = 2 and y = 400 ----> 2(400) = k --> 800 = k
Then, find y when x = 200 (knowing that k = 800)
200y = 800
y = 4
Your watch Gains 0.5 minutes in 6hours. How much will it can in three days.
Answer:
6 Minutes
Step-by-step explanation:
3 days is 72 hours
72/6 = 12
12 * 0.5 = 6
Find the slope of the line passing through each of the following pair of points. (4, 0), (-2, 8)
Answer:
-4
-----
3
Step-by-step
x1,y1
(4,0),
x2,y2
(-2,8)
y2-y1/x2-x2
8-0/(-2)-4=8/-6= -4
-----
3
Use Order of Operations to simplify
8 + 7(4 exoponet 2 -3)
9x+11y=-14
6x-5y=-34
Resolver por regla de cramer
Answer:
x=-4 y=2
Step-by-step explanation:
y=-14-9x÷9
6x-5 (14-9x÷9)=-34
6x-(70+45x÷9)=-34
Take LCM
and then do it
2x+10 + 4x+1 pleasee help!!
2x+10 + 4x+1
2x+4x+10+1 ( combine like terms)
2x+4x=6x
10+1=11
Answer: 6x+11
Answer:
6x+11
Step-by-step explanation:
Collect the like terms and add them up.
2x+4x and 10+1
=6x+11
Have a nice day!!!!!!! :-)
KA
What is the greatest common factor of 19 and 18?
The greatest common factor of 19 and 18 is 1 since 19 is a prime number and has no other factors that divide 18.
Explanation:The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 19 and 18, we need to determine the factors of both numbers. Since 19 is a prime number, its only factors are 1 and itself (19).
The factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors of 19 and 18 are therefore just 1, as 19 has no other factors. Hence, the greatest common factor of 19 and 18 is 1.
A town has accumulated 3 inches of snow, and the snow depth is increasing by 6 inches every hour. A nearby town has accumulated 6 inches, and the depth is increasing by 3 inches every hour. In about how many hours will the snowfall of the towns be equal?
Answer:
1 hour
Step-by-step explanation:
set town one equation to 3 + 6x and town two equation to 6+3x
set these two equations equal to each other and solve for x
3 + 6x = 6 + 3x
3x = 3
x = 1
1 hour
Which function has the given graph?
Answer:
none of the above
Step-by-step explanation:
How many times greater is 0.000006 than 0.00000002
0.000006 is 300 times greater than 0.00000002.
Explanation:To find out how many times greater 0.000006 is than 0.00000002,
We need to divide 0.000006 by 0.00000002.
So, let's perform the calculation:
0.000006 ÷ 0.00000002 = 300
This means that 0.000006 is 300 times greater than 0.00000002.
Learn more about Division here:https://brainly.com/question/33969335
#SPJ2
Find the slope of the line with the equation 12x - 8y + 7 = 9.
-3/2
312
2/3
Final answer:
The slope of the line represented by the equation 12x - 8y + 7 = 9 is 3/2. To find this, the equation was rearranged into slope-intercept form, revealing the slope as the coefficient of x.
Explanation:
To find the slope of the line with the given equation 12x - 8y + 7 = 9, you first need to rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
First, subtract 12x from both sides of the equation to isolate terms with y on one side:
-8y = -12x + 2
Next, divide each term by -8 to solve for y:
y = (12/8)x - 2/8
Simplify the fractions:
y = (3/2)x - 1/4
Now the equation is in slope-intercept form, and you can see that the slope m is 3/2 or 1.5. Therefore, the slope of the line is 3/2.
If BD and AC are perpendicular , DBE = (2x - 1), and CBE = (5x - 42), find the value of x.
What is 8+w/4 when w =16
Answer:
12
Step-by-step explanation:
8 + w/4
w = 16
8 + 16/4
16/4 = 4
8 + 4
8 + 4 = 12
12
Hey!
------------------------------------------------
Steps To Solve:
~Substitute
= 8 + 16/4
~Solve using PEMDAS
= 8 + 4
= 12
------------------------------------------------
Answer:
[tex]\large\boxed{12}[/tex]
------------------------------------------------
Hope This Helped! Good Luck!
Which expression is the simplest form of -(2x+y)+3(x-4y)?
Answer:
x-13y
Step-by-step explanation:
Combine like terms and when you do x is by itself and you have 13 y
making the answer x-13y
Solve −2x2 − 16x − 44 = 0.
The solution to the quadratic equation -2x² - 16x - 44 = 0 are [tex]x = -4 -4\sqrt{6}i \ and \ x = -4 +4\sqrt{6}i[/tex]
Given the quadratic equation in the question:
-2x² - 16x - 44 = 0
To solve the quadratic equation -2x² - 16x - 44 = 0, we use the quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac} }{2a}[/tex]
From the equation:
a = -2, b = 16, c = -44
Plug these values into the above:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-(-16)\±\sqrt{(-16)^2 - 4(-2)(-44)} }{2(-2)} \\\\x = \frac{16\±\sqrt{256 - 352} }{-4} \\\\x = \frac{16\±\sqrt{-96} }{-4} \\\\x = \frac{16\±4\sqrt{6}i }{-4} \\\\x = -4 \±4\sqrt{6}i\\\\x = -4 -4\sqrt{6}i \ or \ x = -4 +4\sqrt{6}i[/tex]
Therefore, the values of x are [tex]x = -4 -4\sqrt{6}i \ and \ x = -4 +4\sqrt{6}i[/tex]
what is the answer to number 16
Answer:
b ≈ 13.80 in
Step-by-step explanation:
Since the triangle is right use the tangent ratio to solve for b
tan17.71° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{43.21}[/tex]
Multiply both sides by 43.21
43.21 × tan17.71° = AC, hence
AC = b ≈ 13.80 ( to 2 dec. places )
factor x squared-6x+3x-18 by grouping
Answer:
(x - 6)(x + 3)
Step-by-step explanation:
Given
x² - 6x + 3x - 18 ( factor the first/second and third/fourth terms )
= x(x - 6) + 3(x - 6) ← factor out (x - 6) from each term
= (x - 6)(x + 3)