there are only r red counters and g green counters in a bag. a counter is taken at random from the bag. the probability that the counter is green is 4/9 the counter is put back in the bag. 4 more red counters and 2 more green counters are put in the bag. a counter is taken from the bag. the probability that the counter is green is 10/23 find the number of red counters and the number of green counters that were in the bag originally. your final line must say, ... red and ... green counters.
Answers
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:
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Related Questions
A school purchases a used van that costs $10,000. The value, V(t), in dollars, of the van t years since its purchase is modeled by the exponential function V(t)=10,000(0.8)^t . Select ALL statements that are true regarding the value of the van. a.The value of the van decreases by 20% each year since its purchase. b.The value of the van decreases by 80% each year since its purchase. c.The value of the van decreases by $2,000 each year since its purchase. d.Each year since its purchase, the value of the van is 80% of the value of the previous year. e.Each year since its purchase, the value of the van is 0.8 times the value of the previous year.
Answers
Answer:
a.The value of the van decreases by 20% each year since its purchase.
b.The value of the van decreases by 80% each year since its purchase.
d.Each year since its purchase, the value of the van is 80% of the value of the previous year.
Step-by-step explanation:
From the above question, we are given the Exponential function
V(t)=10,000(0.8)^t
Verifying the given options:
a.The value of the van decreases by 20% each year since its purchase.
Option a is correct , this is because, the Exponential function above is and Exponential Decrease.
The formula is given as:
V(t) = 10000(1 - r) ^t
Where r = Decreasing rate
Comparing
= 1 - r = 0.8
= 1 - 0.8 = r
r = 0.2
Converting to percentage
= 0.2 × 100 = 20%
Option a is correct
b.The value of the van decreases by 80% each year since its purchase.
Let solve for t = 1 and t = 2
V(t) = 10000(0.8) ^t
When t = 1
= 10000× 0.8¹
= 8000
When t = 2
= 10000× 0.8²
= 6400
Confirming option d
For year 2
= 80% × year 1
Year 1 = 8000
= 80% × 8000 = 6400
Option b is correct
c.The value of the van decreases by $2,000 each year since its purchase.
Option C is incorrect
d.Each year since its purchase, the value of the van is 80% of the value of the previous year.
Option d is correct because
Let solve for t = 1 and t = 2
V(t) = 10000(0.8) ^t
When t = 1
= 10000× 0.8¹
= 8000
When t = 2
= 10000× 0.8²
= 6400
Confirming option d
For year 2
= 80% × year 1
Year 1 = 8000
= 80% × 8000 = 6400
Option d is correct
e.Each year since its purchase, the value of the van is 0.8 times the value of the previous year.
Option e is incorrect
From the options given in the question, the correct statements are,
Options a, b, and d.
someone please help!
Answers
IT IS THE THIRD ONE:
3+8.486
because I find it like that
Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have? 6 ounces 12 ounces 18 ounces 27 ounces Please help cuz im in a pretest and my brain is ded
Answers
Complete question :
The graph below shows the percentages of ingredients in a salad mix.
A pie chart titled Percentages in salad mix. 40 percent is iceberg, 27 percent is romaine, 15 percent is spinach, 12 percent is arugula, 6 percent is carrots.
Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have?
Answer:
18 ounces
Step-by-step explanation:
From the pie chart ;
The percentage of each Salad mixture in the mix is given ;
Romaine lettuce occupies 27% of the total salad mix ;
The total of amount of ounce of the entire salad mix is 64 ounce
Therefore, number of ounces of Romaine lettuce in the salad mix is ;
27% of 64
0.27 * 64
17.28
= 18 ounces
What is the equation of the line that passes through the point (4,-3)(and has a slope of 11?
Answers
Answer: -3 = 11(4) + b
Step-by-step explanation: y = mx + b, -3 is the y, 11 is the slope (m), 4 is the x, b is the y-intercept which is unknown unless you solve for it.
PLEASE help, i’ll give brainliest
Answers
Step-by-step explanation: I think it is 18 tell me if I am wrong
The regular price of a skateboard is p. Which expression represents the price of the skateboard when it is on sale for 25% off? Select all that apply.
Answers
Answer: The expression represents the price of the skateboard when it is on sale for 25% off = 0.75p
Step-by-step explanation:
Given: Regular price of a skateboard is p.
Discount = 25% off = 0.25p
Now, the price of the skateboard when it is on sale for 25% off = p - Discount
= p -0.25p
= (1-0.25)p
= 0.75p
Hence, the expression represents the price of the skateboard when it is on sale for 25% off = 0.75p
Answer: The expression represents the price of the skateboard when it is on sale for 25% off = 0.75p
Step-by-step explanation:
8-(-4)=
What’s the answer?
Answers
it says i need 20 characters to submit ;-;
anyone know this? I need help with this badly
Answers
Answer:
Step-by-step explanation:
no
Alfredo has 3 times as many sneakers as Jessy. Lucia has 5 more sneakers than Jessy. Together they have 20 pairs. Find the number of sneakers each person has.
please show work
Answers
Answer:
Step-by-step explanation:
H
Answer:
15
Step-by-step explanation: 3x5=15
so thx 4 the points
At T-Shirts R Us, the cost to make new shirts is $1.50 per shirt plus a $50 set-up fee. At T-Shirt Planet, the set-up fee is $75 and $1 per shirt. Find the number of shirts you can order so that the cost at both companies is the same.
Answers
Answer: The number of shirts you can order = 40
Step-by-step explanation:
Let x = Number of shirts
At T-Shirts R Us,
Total cost = 50+1.50x
At T-Shirt Planet,
Total cost = 75+x
As per given, when the cost at both companies is the same then
[tex]1.50x+50=x+70\\\\\Rightarrow\ 1.50x-x=70-50\\\\\Rightarrow 0.50x=20\\\\\Rightarrow\ x=\dfrac{20}{0.50}=40[/tex]
Hence, the number of shirts you can order = 40
Pleeease help meeeeee
Answers
Answer:
It would have to either be A or B
Step-by-step explanation:
the 2 triangles are similar. if the perimeter of triangle abc is 28, find the value of x
Answers
so 10 + x - 4 + x - 1.5 = 35
4.5 + 2x = 35
2x = 30.5
x = 15.25
Find the simple interest for 3 years at a rate of 5% on $200
Answers
Answer:
The simple interest is $30
Step-by-step explanation:
To find this, we use the simple interest formula
Mathematically, this is;
I = PRT/100
P is the principal = $200
R is the rate = 5%
T is the time = 3 years
Substituting these values, we have;
I = (200 * 5 * 3)/100
I = $30
Please help as soon as possible
Answers
Answer:
Step-by-step explanation:
the answer is No its not similar
because the factors don't work
PLEASE HELLPPP MEEEEE
Answers
Answer:
2x - 3y = 24
Step-by-step explanation:
You use the formula Ax ± By = C.
This is the standard linear equation form.
What percent of 18 is 24?
Answers
Answer:
133.33%
Step-by-step explanation:
you can find this by doing 24/18x100, which is equal to 133.33
Answer:
133%
Step-by-step explanation:
We're going to divide [tex]\frac{24}{18}[/tex].
That equals about 1.33 repeating.
Next, we're multiplying that decimal by 100.
That gets us 133.
IM BEING TIMED PLZ HURRY AND THANKS What is the sum of a° + c°
Answers
Answer:
300°
Step-by-step explanation:
a° is 180°
c° is 120° (from 180° = 60° + c°)
PLZ: show work, solve for x:
Answers
x+11/-2=-8
x+11/-2 x -2= -8 x -2
x+11= 16
X+11-11=16-11
x = 5
Hard Equation that equals 1-25
Answers
Answer:
8000000000000000000000000000000000
Answer:
5X5=
-X4=
-+25=
-divide by 5=
Step-by-step explanation:
hope thats ok for you please mark me as brainliest
12a+10 find the algebraic expression
Answers
Answer:
2(6a+5)
Step-by-step explanation:
Factor 12a+10
12a+10
=2(6a+5)
Answer:
2(6a+5)
Step-by-step explanation:
HELP!!!!!!! Solve the equation |x-1|+3=2
Answers
The absolute value of x-1 is x+1
Our new equation: x+1+3=2
X+4=2
Then you have to isolate the variable
X+(-4+4)=(2-4)
Answer: X=-2
can someone pls help!!!
Answers
3n+4=10
answer= n=2
c+2=18
Jake said he can find 630 ÷ 10 by taking the 0 off of 630 to get 63. Jake finds 35.270 ÷ 10 using the same method and gets 35.27. Use the drop-down menus to complete the statement about why Jake is correct or incorrect.
Answers
Answer:
Jake is incorrect with his methodology for solving these problems
Step-by-step explanation:
Jake is incorrect with his methodology for solving these problems. This is because dividing a number by 10 requires moving the decimal point one digit to the left. When dividing 630 by 10, removing the zero works because by moving the decimal one digit to the left we would simply drop the zero and the decimal would not be needed leaving the answer as 63. However, this does not work on numbers that already have a decimal such as 35.270. This number divided by 10 would be 3.527 but simply removing the 0 like Jake states would give us the incorrect answer of 35.27
Answer:
Step-by-step explanation:
1/3 divided by 4
2/5 divided by 4
4/7 divided by 4
2/5 divided by 3
5/6 divided by 5
5/8 divided by 10
Answers
2. 2/5 divided by 4 is 0.1
3. 4/7 divided by 4 is 0.1428
4. 2/5 divided by 3 is 0.1333
5. 5/6 divided by 5 is 0.1666
6. 5/8 divided by 10 is 0.0625
Answer:
1. 0.0833
2. 0.1
3. 0.1428
4. 0.1333
5. 0.1666
6. 0.0625
whats 4 +4
guys pls help
Answers
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
A person can bike 48 miles in 2 hours. At this rate how long will it take this person to travel 66 miles? Show work please!!!
Answers
Answer:
Convert to a decimal by dividing the numerator by the denominator.
2.75 hours
plz helps so i can pass
Answers
Answer:
C
Step-by-step explanation:
did it on edge
3х +2у = -5
Чx - Зу = 16
Answers
3х +2у = -5 Xx - Pe = 16
I don’t understand help plzz
Answers
Answer:
Slope/m=1/2, y-intercept=-4
Step-by-step explanation:
Y=mx+b is slope-intercept form. So in the equation y=1/2x-4, m stands for the slope, and in the equation 1/2 is in the place of m. B stands for the y-intercept, and in its place is -4.
Ahem, I'm writing with a mouse, excuse the scraggly lines and writing on the graph.
Which one of these transformations would produce an image that is not congruent to its pre-image? (4 points)
A translation of (x − 1, y − 3)
A rotation of 90 degrees about the origin
A rotation followed by a translation
A dilation followed by a reflection
Answers
Answer:
A dialation followed by a reflection
Step-by-step explanation:
When you dialate a shape it changes the size which makes the shape similar but not congrouent.
The option “a dilation followed by a reflection” will produce an image that is not congruent to its pre-image option, fourth is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
As we know, the translation will shift the object.
If rotate the image with 90 degree about origin will change the orientation of the image but shape will remains same.
A dilation followed by reflection will change the image because the transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller.
Thus, the option "a dilation followed by a reflection" will produce an image that is not congruent to its pre-image option fourth is correct.
Learn more about the geometric transformation here:
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