Probability of an event measures its chance of occurrence. P(Green in first draw) = 5/14, P(Red in second draw) = 2/14. P(Green in first and red in second draw) = 5/98
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
What is chain rule in probability?For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is probability of occurrence of A given that B already occurred.
How to find if two events are independent?Suppose that two events are denoted by A and B.
They are said to be independent event if and only if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
It is because
[tex]P(A|B) = P(A)\\P(B|A) = P(B)[/tex]
and therefore, using chain rule and above facts gives:
[tex]P(A \cap B) = P(A)P(B)[/tex]
The question is missing some informations, which are:
Total marbles in the bag = 14Total red marbles = 5Total green marbles = 2rest of the 7 marbles are of some other colors.The result of first draw and the second draw are independent of each other as Deepak replaces the marble after first draw, therefore, making no changes in the count of balls of each color in the considered bag, which decides the probability needed.
Now, let we take:
A = probability that Deepak picks green ball in first draw
B = probability that Deepak picks red ball in the second draw
Then, we get:
[tex]P(A) =\dfrac{5}{14}\\\\P(B) = \dfrac{2}{14}\\\\P(A \cap B) = P(A)P(B) = \dfrac{5 \times 2}{14^2} = \dfrac{5}{98}[/tex]
(there are 14 ways to select a ball, but 5 favorable ball for event A to occur, and 2 favorable balls for event B to occur,therefore the aforesaid probabilities.)
Thus, for this case, we get:
P(Green in first draw) = 5/14, P(Red in second draw) = 2/14. P(Green in first and red in second draw) = 5/98Learn more about probability here:
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A train travels 150 miles in 3 hours. At this same rate, how many miles will it travel in 8 hours?
Answer:
400 miles
Step-by-step explanation:
150---3
x --- 8
x= (150)(8) / 3 = 1200/3 = 400
Hope this helps
Answer:
x=400 miles
Step-by-step explanation:
A toy manufacturing organization manufactures two types of toys A and B. Both the toys are sold at birr 25 and birr 20 respectively. There are 2000 resource units available every day from which the toy A requires 20 units while toy B requires 12 units. Both of these toys require a production time of 5 minutes. Total working hours are 9 hours a day. How much is the maximum profit?
Answer:
The answer is B I did this already
Simplify 2(-3n - 5) + 5n
Answer:
-1n-10
Step-by-step explanation:
EXPLANATION:
Use PEMDAS it will show u from where to start first and you will end up with the right result
PEMDAS : Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
2(-3n-5) + 5n
distribute 2 in the parantheses
-6n-10+5n
-1n-10
What is the answer of two times two (2x2=)
Answer:
=> 2 × 2 = 4
Step-by-step explanation:
two times two is four
Answer:
2x1=1
2x2=4
so the answer is 4
Step-by-step explanation:
subtract R from 6. Then add 3
8/7 as a mixed number
Answer:
[tex]1\frac{1}{7}[/tex]
Worth 41 points!
A camp counselor buys lunch for her campers at a nearby fast food restaurant. On Monday, she purchased 5 hamburger meals and 6 chicken nugget meals, for a total of $39. On Thursday, she purchased 9 hamburger meals and 2 chicken meals, for a total of $35. Which pair of equations could be used to determine the cost of each type of meal?
Answer:
4x+3y=23
Step-by-step explanation:
4x+3y=23
2x+6y=34 multiply equation by 2 to get x values equivalent, so
4x+12y=68 now subtract firs equation from this
-(4x+3y=23)
so 9y=45 and y=5
now find x:
4x+3(5)=23
4x+15=23
4x=8
x=2
So, hamburgers cost $2 and chicken nuggets $5.
the GCF factor the given expression: 21xy + 14y
7(3xy + 2y)
7y(3x + 2)
3(7xy + 14y)
7xy(3 +2)
NEXT
Answer:
7y
Step-by-step explanation:
GCF for 21xy+14y is: 7y
because GCF is greatest common factor. y is common for both units so take it out and greatest number that both numers can divide by is 7,
so 7y.
Check:
7y(3x+2)
7y*3x + 7y*2
21yx + 14y
true
Between 3 pm and 6 pm the temperature dropped from 88 degrees to 60 degrees frond the percent of decrease
Answer:
31.81%
10.60% per hour
Step-by-step explanation:
88 - 60 = 28
28/88 = .31818181818
.31818181818 = 31.81%
.31818181818/3 = .10606060606
.10606060606 = 10.60%
Choose the method of pay that would result in the most earnings for one month on sales of $60,000. a. straight commission of 6% on all sales. b. monthly salary of $1,500 plus 3% commission on all sales. c. graduated commission of 4% on the first $50,000 in sales and 10% on anything over that. d. graduated commission of 5% on the first $40,000 in sales and 9% on anything over that. please select the best answer from the choices provided a b c d
The method of pay that would result in the most earnings is: Option d. graduated commission of 5% on the first $40,000 in sales and 9% on anything over that.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
We're specified that:
One month sales of $60,000 occurs.Calculating the earnings from all the options:
Option a: straight commission of 6% on all sales.That means, we get:
Earning = 6% of 60,000 = [tex]\dfrac{60000}{100} \times 6 = 3600[/tex] (in dollars)
That means:
Earning = 1500 + 3% of 60,000 = [tex]1500 +\dfrac{60000}{100} \times 3 = 1500 + 1800 = 3300[/tex] (in dollars).
Option c : graduated commission of 4% on the first $50,000 in sales and 10% on anything over thatThat means, we get:
Earning = 4% of 50,000 + 10% of 10,000 (as total 60,000 dollars sales was done).
Earning = [tex]\dfrac{50000}{100} \times 4 + \dfrac{10000}{100} \times 10 = 2000 + 1000 = 3000[/tex] (in dollars)
Option d: graduated commission of 5% on the first $40,000 in sales and 9% on anything over that.That means:
Earning = 5% of 40,000 + 9% of 20,000 (as 40000 + 20000 = 60000)
or, we get:
Earning = [tex]\dfrac{40000}{100} \times 5 + \dfrac{20000}{100} \times 9 = 2000 + 1800 = 3800[/tex] (in dollars).
Thus, option D provides the method for max earning.
Thus, the method of pay that would result in the most earnings is: Option d. graduated commission of 5% on the first $40,000 in sales and 9% on anything over that.
Learn more about percent here:
https://brainly.com/question/11549320
Answer:
D
Step-by-step explanation: i took the test
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!
Answer:
See below ~
Step-by-step explanation:
Finding m∠HCG
HE is the diameter line [= 180°]∠ECF + ∠FCG + ∠HCG = 180°60° + 75° + ∠HCG = 180°∠HCG = 180° - 135°∠HCG = 45°Finding m∡DF
∠ECF + ∠DCE60° + 45°105°Answer:
m∠HCG = 45°
m∡DF = 105°
Step-by-step explanation:
m∠ECD + m∠ECF + m∠FCG
= 45° + 60° + 75°
= 180°
As angles on a straight line always sum to 180°, we can conclude that the line DG is a straight line and the diameter of the circle, and the Point C is the center of the circle.
Assuming that line EH is also a straight line, using the vertical angles are always congruent theorem, m∠ECD = m∠HCG.
Therefore, m∠HCG = 45°
We always measure arcs in a counterclockwise direction.
⇒ m∡DF = m∡DE + m∡EF
= 45° + 60°
= 105°
what is the solution of the system of equation? y=2x-3 , 4x-3y=31
Answer:
Use Substitution.
Plug in 2x-3 in place of y in the second equation.
4x - 3(2x-3) = 31
4x - 6x + 9 =31
-9 -9
-----------------------
-2x=22 so x=-11
Then, y=2(-11)-3, so y=-25
So the solution would be (-11,-25).
Step-by-step explanation:
is the variable alone?
No
what is it attached to?
you always do adding or subtracting first so it is attached to 3
How is it attached?
by subtraction
what is the inverse operation?
it is addition
then all you do is the same thing but with multiplication or division
Hi!
We can solve this using the substitution method.
Given:
[tex]y=2x-3\\4x-3y=31[/tex]
Using the first question, we know that [tex]y[/tex] is equal to [tex]2x-3[/tex], so we can simply plug that value in to the second equation, like so:
[tex]4x-3(2x-3)=31[/tex]
Now, we can algebraically solve this for [tex]y[/tex]
[tex]4x-3(2x-3)=31[/tex]
Distribute.
[tex]4x-6x+9=31[/tex]
Add like terms.
[tex]-2x+9=31[/tex]
Subtract [tex]9[/tex] from both sides.
[tex]-2x=22[/tex]
Divide both sides by [tex]-2[/tex]
[tex]x=-11[/tex]
Now plug in that value to the first equation:
[tex]y=2(-11)-3[/tex]
Multiply.
[tex]y=-22-3[/tex]
Subtract.
[tex]y=-25[/tex]
The solution is (-11, -25)
The model is shaded to represent the remaining one-half of a cake. Three friends will each receive an equal amount of the remaining cake until it is all gone.
Which equation can be used to determine the fraction of the whole cake each friend will receive?
Answer:
The model is shaded to represent the remaining one-half of a cake. Three friends will each receive an equal amount of the remaining cake until it is all gone.
cake
An equation that is true for all values of the variables in its domain is _____.
a property
a function
an identity
a formula
An equation that is true for all values of the variables in its domain is an identity
Hope that helps!
Carmen earns 3% a year on money in her savings account. She had $354 in her account last year how much interest did she earn
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3\% of 354}}{\left( \cfrac{3}{100} \right)354}\implies 10.62[/tex]
What’s The Answer Of This? PLEASE HELP
Answer: 68 degrees
Step-by-step explanation:
Find the 12th term of the geometric sequence 2, -8, 32,
Answer:
what kind of term is this
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
C. 5 1/2
Step-by-step explanation:
Hope this helps!
Have a blessed day!!
Marco and Juan entered a trivia competition. When they miss a question,they lose points.
Find the LCM by first finding the prime factor.
Answer:
Step-by-step explanation:
3(x² - y²) = 3(x + y)(x -y)
x² - 2xy + y² = (x - y)²
LCM = 3(x + y)(x - y)²
At a school assembly, there are 150 students. If the students are to be dismissed in groups of 10, how many groups will be made?
Answer:
15 groups would be made.
Explanation:
150 divided by 10 = 15
Find the area of the figure.
Step-by-step explanation:
such problems are always the combination of areas of simple figures.
in our case here the simplest way seems to me to calculate the area of the whole 15×15 square (the side lengths are 15 and 9+6 = 15) and then subtract the small 6×6 square (top left), the small 6×3 triangle (bottom right) and the larger 6×9 triangle (top right).
we know that the left side of the main square is 9+6 = 15.
we know that the missing side piece (top right) is also 6 (like its left side). and the right side piece is 15-6-6 = 3.
that is how we know the side lengths of the missing pieces.
so,
15×15 = 225 cm²
the small square is
6×6 = 36 cm²
the large triangle is
6×9/2 = 3×9 = 27 cm²
the small triangle is
6×3/2 = 3×3 = 9 cm²
so, the total area of the figure is
225 - 36 - 27 - 9 = 153 cm²
Sharon bought 4/5 pound of flour for $1. What is the cost of 1 whole pound of flour?
what is x and y?
2x-2y=-4
2x+y=11
Is there infinitely many solutions, 1 solution, or nosolution
Let's solve your system by substitution.
2x−2y=−4;2x+y=11
Rewrite equations:
2x+y=11;2x−2y=−4
Step: Solve2x+y=11for y:
2x+y=11
2x+y+−2x=11+−2x(Add -2x to both sides)
y=−2x+11
Step: Substitute−2x+11foryin2x−2y=−4:
2x−2y=−4
2x−2(−2x+11)=−4
6x−22=−4(Simplify both sides of the equation)
6x−22+22=−4+22(Add 22 to both sides)
6x=18
6x/6 = 18/6
(Divide both sides by 6)
x=3
Step: Substitute3forxiny=−2x+11:
y=−2x+11
y=(−2)(3)+11
y=5(Simplify both sides of the equation)
Answer:
x=3 and y=5
solve for N.
8/10 = 4/N
Answer:
5
Step-by-step explanation:
Cross multiply
8n = 40
N = 5
Answer:
n= 5
Step-by-step explanation:
1. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8/10-(4/n)=0
2. Simplify 4/n = after that the equation will be 8/10 - 4/n = 0
3. Simplify 4/5 = after that the equation will be 4/5 - 4/n = 0
(Please answer, 100 points)
Find the circumference of each of the following circles. Use 3.14 for π.
(The last one is 25 mi across.)
These were my answers, are they correct:
6a. 53.38
6b. 100.48
6c. 122.46
6d. 78.5
use the formula 2πr
106.76 300.962×3.14×(1/2)×39 = 122.4678.5the c bit I did the whole process cuz the diameter is given and for the d bit i thought what you were trying to say is 25 diameter.
hope it helps and don't forget to put the units wherever necessary.!!!!
Milani's teacher draws students names at random, calls on the student, and replaces the name so that students know they should always be prepared to respond. There are 202020 students in Milani's class. Let XXX be the number of names it takes for the teacher to draw Milani's name.
Find the probability that the teacher first draws Milani's name as the 7^{\text{th}}7
th
7, start superscript, start text, t, h, end text, end superscript name.
You may round your answer to the nearest hundredth.
P(X=7)=P(X=7)=
Using the binomial distribution, it is found that there is a 0.0368 = 3.68% probability that the teacher first draws Milani's name as the 7th student.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, there are 20 students, hence in each question the probability that Milani's name is called is p = 1/20 = 0.05.
The probability that the teacher first draws Milani's name as the 7th student is P(X = 0) when n = 6(none during the first six) multiplied by 0.05(called during the seventh), hence:
P(X = 7) = (0.95)^6 x 0.05 = 0.0368.
0.0368 = 3.68% probability that the teacher first draws Milani's name as the 7th student.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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The length of a rectangle is 8 feet more than its width. the area of the rectangle is 97 ft.² determine the length and width of the rectangle
Answer:
L = [tex]\sqrt{113}[/tex] +4
W = [tex]\sqrt{113}[/tex] -4
or L = 14.63 ft, and W = 6.63 ft
Step-by-step explanation:
Let L be the length and W the width.
We are told that the "length of a rectangle is 8 feet more than its width:"
L = W+8
Area of the rectangle is given by L*W, and is 97 [tex]ft^{2}[/tex]
L*W = 97
Substituting L=W+8, we get:
(W+8)W=97 [tex]ft^{2}[/tex]
[tex]W^{2}[/tex] + 8W = 97
[tex]W^{2}[/tex] + 8W - 97 = 0
The roots to this equation are:
-4-[tex]\sqrt{113}[/tex], and[tex]\sqrt{113}[/tex] -4Only the second gives a positive value, so W = [tex]\sqrt{113}[/tex] -4
Since L=W+8, the length, L, is [tex]\sqrt{113}[/tex] -4 + 8 or [tex]\sqrt{113}[/tex] +4
In decimal:
L = 14.63 ft, and W = 6.63 ft
For which equation is 0 not a solution?
x - 5 = 4
6 x + 4 = 4
3 x = 0
x + 9 = 9
I think its the third one
WILL MARK BRAINLIST!!!
Answer:
[tex]3/4[/tex]
Step-by-step explanation:
We are asked to find the difference which means we will be using subtraction.
We are given two numbers to use [tex]4\frac{1}{12}[/tex] (Houston to Dallas) & [tex]3\frac{1}{3}[/tex] (San Antonio to Houston).
To be able to subtract, we need to have the same denominator on both fractions, which we can do by multiplying 1/3 by 4
[tex]\frac{1}{3} * 4=\frac{4}{12}[/tex]
now we can subtract the numbers and simplify!
[tex]4\frac{1}{12} -3\frac{4}{12} =\frac{9}{12} =\frac{3}{4}[/tex]