The number of red counters and the number of green counters that were in the bag originally is: 10 red and 8 green counters.
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.
For this case, let we had:
R numbers of red counters, and G number of green counters originally.
Then, total counters in the bag originally = R +G
One counter out of R+G counters can be chosen in R+G ways. But one green counter out of R+G counters can be chosen in G ways.
Thus, probability of taking green counter out in one random picking is:
[tex]\dfrac{G}{R + G}[/tex]
It is given that this probability is 4/9. Therefore, we get:
[tex]\dfrac{G}{R+G} = \dfrac{4}{9}\\\\\\9G = 4R + 4G\\\\5G = 4R[/tex](first equation)
When 4 more red counters and 2 more green counters were added, then:
One counter out of R+G+6 counters can be chosen in R+G+6 ways. But one green counter out of R+G+6 counters can be chosen in G+2 ways (since there are G+2 green counters in the considered bag) ways.
Thus, probability of taking green counter out in one random picking is:
[tex]\dfrac{G+2}{R + G+6}[/tex]
It is given that this probability is 10/23. Therefore, we get:
[tex]\dfrac{G+2}{R+G+6} = \dfrac{10}{23}\\\\\\23G + 46 = 10R + 10G + 60\\\\13G = 10R + 14[/tex](second equation)
Thus, we got a system of two linear equations as:
[tex]5G = 4R\\13G = 10R + 14[/tex]
From first equation, getting the value of G in terms of R,
[tex]G = \dfrac{4R}{5}\\[/tex]
Now, substituting this with G in the second equation, we get:
[tex]\\13\left(\dfrac{4R}{5} \right) =10R + 20\\\\52R = 50R + 20\\2R = 20\\R = 10[/tex]
From this value of R, and the value of G in terms of R, we get:
[tex]G = \dfrac{4R}{5}\\\\ = \dfrac{4 \times 10}{5} = 8[/tex]
Thus, R = 10 and G = 8.
Thus, the number of red counters and the number of green counters that were in the bag originally is: 10 red and 8 green counters.
Learn more about probability here:
brainly.com/question/1210781
favorite food pizza35 hotdog30 hamburger 200 whta percatage is all student's count
Answer:
265
Step-by-step explanation:
200+30=230
230+30=260
260+5=265
The access code for a car's security system consists of four digits. The second digit cannot be zero and the last digit must be odd. How many different codes are available?
Answer:
4,500 different codes.
how do you solve it tho
Answer:
solve what
Step-by-step explanation:
there's no question
Answer:
you forgot the picture lol
c) The area of a rectangle is 80 cm² and it is 8 m broad.In process
(i) Find its length (ii) Find its perimeter
11
Answer:
i) the length is 10cm
ii) the perimeter is 36 cm
Step-by-step explanation:
i) We know that Area of a rectangle can be found by using the following formula...
A = l x w
(where A is area of the triangle, l is the length of the triangle, and w is the width of the rectangle).
From this we know that
l = A/w
[tex]l = 80cm^{2} / 8cm = 10cm[/tex]
ii) Now that we know both the length and the width we know we can find the perimeter by using the following formula...
P = 2(l + w)
[tex]P = 2(10cm+ 8cm )\\P = 20cm + 16cm\\P = 36cm[/tex]
The half-life of a radioactive kind of iodine is 60 days. How much will be left after 240 days, if you start with 480 grams of it?
Answer:
30 grams
Step-by-step explanation:
half life is 60 days so every 60 days the amount 480 grams will be half
in 240 days will decay 240 /60 = 4 times
once 480 /2 = 240
twice 240 /2 = 120
trice 120 / 2 = 60
four times 60/2 = 30 grams will be left
NOBODY HAS HELPED ME TODAY ??? please help me !!!
25% of a number is 8.
What is the original number?
Answer:
B. 32
Step-by-step explanation:
25% is 1/4 of 100%, so you multiply 8 by 4.
Graph y+9=−3x. please help me
Well, first thing we need to do is put this in slope intercept form of y.
Subtract 9 from both sides to isolate "y".
y= -3x-9
Now we can graph the equation
Graph the point (0,-9) since it is the y-intercept.
To get the x intercept, isolate the "x" variable instead of "y".
y+9 = -3x
(Divide every number on both sides of the equation by -3 to isolate "x".)
y/-3 -3= x
now that this is in slope intercept form of x, plug in 0 for y to get the number for x when y is 0.
0/-3 -3 = x
-3 = x.
Graph (-3, 0). Connect this point to the point (0,-9) and you get have successfully graphed the equation y+9= -3x.
I hope this helped.
Write an algebraic expression for s decreased by nine
Answer:s-9
Step-by-step explanation: Decreased means subtract . and you are subtracting s from 9.
Hope it helps
Please help, pic attached!
Answer:
(y − 9) (y − 2)
Step-by-step explanation:
Factor y^2 − 11y + 18 using the AC method.
(y − 9) (y − 2)
The “AC” method or factoring by grouping is a technique used to factor trinomials. A trinomial is a mathematical expression that consists of three terms.
Please help me would be very appreciated.
Answer:
C
Step-by-step explanation:
On the blueprints for a building, 8 inches represents 28 feet. If the blueprints show a distance of 16 inches
between the two walls, how many feet separate the walls?
Answer:
56 feet
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
{(1, 7.6) (2, 7.2) (3, 6.8) (4, 6.4) (5, 6) (6, 5.6)}
Is this a function or no?
Answer:
Yes
Step-by-step explanation:
Let's put them vertically because that helps me explain this
x, y
1, 7.6
2, 7.2
3, 6.8
4, 6.4
5, 6
6, 5.6
For this to be a function there should be one output for every input, the y coordinates are our outputs and as you can see none of them repeat so this is a function.
Which property is demonstrated by the equation (5 + a) + 3 = (a + 5) + 3?
Answer:
Communitive Property
Step-by-step explanation:
Commutative property = 2 + 3 = 3 + 2 or 2(3) = 3(2)
Associative Property = (2 x 3) 5 = 2 (3 x 5) or (2 + 3) + 5 = 2 + (3 + 5)
Inverse Property = 2 + (-2) = 0 or (2/1)(½) = 1
Basic Definitions:
Commutative Property - Gives you the ability to switch the order of the numbers in an expression.
Associative Property - Let's you move the parenthesis in an expression but not the numbers.
Inverse - Uses numbers like 0 and 1.
Using these basic definitions and examples, we can summarize that the best answer would be Communitive Property
i don't need the work just the answer!!
hi, can you please do these? thanks for helping!
Answer:
i will answer you other if u rate me brainliest
Answer: (A) 1/10: 5 9/10 :5/6
(B) 3 3/4: -2 7/50
(C) 8 5/8 : 4/9
(D)2 2/5: 2 67/210: -2 2/3
(E)-1 1/2 : 81/128
Step-by-step explanation:
hopes this helps
Whos your favorite operator in rainbow six seige
Answer:
It has to be Maverick how about u
Step-by-step explanation:
Answer:
Niclas "Pengu" Mouritzen
Step-by-step explanation:
Find c.
Round to the nearest tenth:
2 cm
15°
105
Answer:
0.5cm
Step-by-step explanation:
Using the sine rule
Answer:
c = 0.5 cm
Step-by-step explanation:
Using the Sine rule in the triangle, then
[tex]\frac{c}{sin15}[/tex] = [tex]\frac{2}{sin105}[/tex] ( cross- multiply )
c × sin105° = 2 × sin15° ( divide both sides by sin105°
c = [tex]\frac{2sin15}{sin105}[/tex] ≈ 0.5 cm ( to the nearest tenth )
4/3=-6e-5/3
solve for "E" plz
Answer:
e=-1/2
Step-by-step explanation:
4/3=-6e-5/3
Multiply both sides by 3:
4=-18e-5
Add 18e to both sides:
18e+4=-5
Subtract 4 from both sides:
18e=-9
Divide both sides by 18:
e=-1/2
*You don't have to, but I am currently trying to reach the next level, and all I need is some more brainliest answers. If you think my answer was brainly enough, you can make my answer the brainliest, but no pressure. I just help people for fun! :) Thank you, have a great day!*
Write the slipe-intercept form of the equation of each line given the slope and y-intercept.
Please helppp!!!! i will give brainliest!!
Answer:
1. -1/2
2. 3/-2
3. 1/2/2
4. 7/2
Step-by-step explanation:
Hope it helped
Use the domain (1/2, 1, 2, 4, 8) to plot the points on the graph for the given equation. The grid marks represent one unit,
the horizontal red line represents the x-axis, and the vertical red line represents the y-axis.
y = log 2 x
According to values of a function we can plot the points on a graph.
What is domain?
Domain is the value which we used to enter in a function to get the value of a function.
How to plot the points on the graph?
We have been given the domain of the function and we have to plot the value in the graph.
F(1/2)=log1=0
F(1)=log2=0.3
F(2)=log4=0.6
F(4)=log8=0.9
F(8)=log16=1.2
Learn more about graphs at https://brainly.com/question/4025726
#SPJ2
(01.05)
What is the equation, in slope-intercept form, of the line that passes through (0, -2)
and has a slope of -3? (5 points)
O 1) y = -3x - 2
O 2 y=-3x+ 2
O3) y = –2x+3
O 4) y = -2x - 3
Answer:
O1
Step-by-step explanation:
Slope intercept form is y=mx+b, where m is the slope and b is the y intercept.
We are given a point: (0,-2) and a slope; -3.
we can substitute the numbers into the equation above, with what we know, to find b.
-2=-3(0)+b
multiply
-2=0+b
-2=b
so the y intercept is -2.
Since we know that the slope is -3, and the y intercept is -2, the equation is y=-3x-2
Therefore O1 is your answer
Hope this helps!
If DF=70, find the value of x.
Answer:
x = 12
Step-by-step explanation:
DE + EF = DF
2x - 1 + 5x - 13 = 70
7x - 14 = 70
7x = 70 + 14
= 84
x = 84 ÷ 7
x = 12
Answer: x=12
Step-by-step explanation:
2x-1+5x-13=70
Combine like terms
7x-14=70
Add 14 to both sides
7x=84
Divide both sides by 7
X=12
An airplane prepares for landing. When it begins its descent towards the airport, the plane's
altitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000
feet. Write an equation for the altitude of the plane. What will the altitude of the plane be after
descending for 12 minutes?
The required equation represents the descent motion of the airplane is y = 27000 - 1333.333x and 11000 feet.
Given that,
An airplane prepares for landing. When it begins its descent towards the airport, the plane's altitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000 feet. Write an equation for the altitude of the plane.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the motion of the airplane,
m = 27000 - 19000 / 6 = 1333.33
The equation of the plane is given as,
y - y₁ = m (x - x₁)
Substitute the value in the above equation,
y - 27000 = -1333.33[x - 0]
y = 27000 - 1333.33x
Now put x = 12 in above equation,
y = 27000 - 1333.33[12]
y = 11000
Thus, the required equation represents the descent motion of the airplane as y = 27000 - 1333.333x and 11000 feet.
Learn more about slopes here:
https://brainly.com/question/3605446
#SPJ2
Suppose there are 21 students in your class. If the teacher draws 2 names at random, what is the probability that you and your best friend will be chosen?
1/20
1/105
1/210
2/21
Answer:
2/21
Step-by-step explanation:
Probability = expected outcome/ possible outcome
Mmmm! I love apple cider punch this time of year, and so do all my neighbors. My recipe calls for two quarts of apple cyder, three teaspoon of cinnamon, and one pint of lemon-lime soda. This will make enough for 8 people to share. In my neighborhood, however, there are 36 people. How much do I need for each ingredient to make enough for everyone?
Answer:
j
Step-by-step explanation:
Which function shows a fabric with a price of $1.25 per square yard?
Answer:
D
Step-by-step explanation:
Pls help it due in a hour and show workings...
Need help with explicit rule. Please help.
Answer:
An = 74(1.07)^n-1
Step-by-step explanation:
Here, we want to get the explicit rule
We are told that the sequence is geometric
At hour 4, we have that this is the 4th term
With conformance to the rule of geometric progression;
T4 = ar^3
90 = ar^3
for the 6th hour, this is the sixth term
103 = ar^5
dividing the 6th term by the 4th term, we have that
103/90 = ar^5/ar^3
103/90 = r^2
r = 1.07
To get a, we simply use any of the terms to substitute
using;
ar^3 = 90
a = 90/r^3
a = 90/1.07^3
a = 73.5 which is approximately 74
So the explicit rule is as follows;
An = 74(1.07)^n-1
PLEASE HELP URGENT!!
An irregular polygon is shown below:
A: 21 Square Inches
B: 22 Square Inches
C: 26 Square Inches
D: 29 Square Inches
Answer:
[tex]26\:\mathrm{in^2}[/tex]
Step-by-step explanation:
The irregular polygon is made of a large rectangle with two smaller rectangles cut out of it. Therefore, we can find the area of the large rectangle and subtract these two smaller rectangles:
[tex]10\cdot 5-2\cdot3\cdot4=50-24=\fbox{$26\:\mathrm{in^2}$}[/tex].