Answer:
P(blue and green) = P(blue)*P(green) = (5/8)(2/8) = 10/64
The probability that the first ball is blue and the second is green, with no replacement, is approximately 0.179 or 17.9%.
Explanation:The subject of this question pertains to probability, specifically the concept of dependent events in the realm of combinatorics. The problem involves an urn with 8 balls of different colors. The question asks us to find the probability that a blue ball is drawn first and a green ball second, with no replacement.
Firstly, we calculate the individual probabilities. The probability of drawing a blue ball first is 5/8, because there are 5 blue balls out of a total of 8. Since the blue ball isn't replaced, there are now 7 balls left in the urn, and therefore, the probability of drawing a green ball next is 2/7. To find the combined probability, we multiply the individual probabilities: (5/8) * (2/7) = 10/56 = 0.1786 (rounded). So the probability that the first ball is blue and the second is green is approximately 0.179 or 17.9%.
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MODELING EXPONENTIAL GROWTH
1. You put $3,800 dollars in a savings account. The bank will provide 1.8% interest every year. Write and solve a model that describes how much money will be in the account in 15 years.
2. Suppose you deposit $2000 into a savings account that pays an interest annual rate of 4% if no money is added or withdrawn from the account, how much will be in the account after 3 years? What about 18 years? How many years will it take for the account to contain 3000 (for this now you know the total amount, you need to find t time)?
Answer:
1. M = C*1.018^t
After 15 years: M = 4965.93
2. After 3 years: M = 2249.728
After 18 years: M = 4051.633
Time to achieve 3000: t = 10.338 years
Step-by-step explanation:
1. Since the money gets increased every year at a rate of 1.8% after one year it'll be the initial amount multiplied by 1.018, so:
After one year:
M = C*1.018
After two years:
M = C*1.018*1.018 = C*(1.018)²
After three years:
M = C*(1.018)²*1.018 = C*(1.018)³
And so on, therefore:
M = C*(1.018)^t
Where M is the final amount, C is the initial amount and t is the time elapsed in years. For this case we have:
M = 3800(1.018)^15 = 4965.92626
2. Applying the same line of thought as above, we have:
M = C*(1.04)^t
After 3 years:
M = 2000*(1.04)^3 = 2249.728
After 18 years:
M = 2000*(1.04)^18 = 4051.633
To obtain 3000:
3000 = 2000*(1.04)^t
2000*(1.04)^t = 3000
1.04^t = 3000/2000
1.04^t =1.5
log(1.04^t) = log(1.5)
t*log(1.04) = log(1.5)
t = log(1.5)/log(1.04) = 10.338 years
which number doesn't belong?
9 16 25
43
Answer:
43
Step-by-step explanation:
Square root of 9 is 3
Square root of 16 is 4
Square root of 25 is 5
Square root of 43 is not a whole number.
Answer:
43
Step-by-step explanation:
The first three numbers are perfect squares:
9 = 3²
16 = 4²
25 = 5²
43 is not a perfect square.
HELP ME ASAP PLEASE!!!WILL MARK BRAINLIEST!!!
What’s x?
#3 only. But if u wanna do #5 then go ahead lol
Answer:
x=10.85
Step-by-step explanation:
you add 85 and 31 equaling 116.
13x-21=116
+21 =+21
13x=137
13x= 13x
x=10.85
which is the rate of change for the interval between -6 and -3 on the x-axis ?
Answer:
Its -2.
Step-by-step explanation:
Answer:
A. -2
Step-by-step explanation:
Please Help Me!! I can’t figure this out!!
Answer:
a=12 ft, b=12 ft
Step-by-step explanation:
-Length A and length B are equal since the right angle triangle is also an isosceles triangle.
-We use the Law of sines to calculate the two lengths:
[tex]\frac{a}{Sin \ A}=\frac{b}{Sin \ B}=\frac{12\sqrt{2}}{Sin\ 90\textdegree}\\\\a=b=12\sqrt{2} \ Sin \ 45\textdegree\\\\a=b=12\ ft[/tex]
Hence, length a is equal to length b which is equal to 12 ft
What is the degree of the monomial?
8x
Answer:
1
Step-by-step explanation:
when a variable does not have an exponent the degree is always one. Ex: 8x is the same as 8x to the power of 1
You purchased a car for $23,000 and can expect the car to depreciate at an average annual rate of 9%. What will the value of your care be 6 years after purchasing it
Answer:
$13,060.99
Step-by-step explanation:
We can use the following formula to solve:
[tex]A=P(1-r)^t[/tex]
P = principal value
r = rate (decimal)
t = time (years)
First, change 9% into a decimal:
9% -> [tex]\frac{9}{100}[/tex] -> 0.09
Now, just plug the values into the equation:
[tex]A=23,000(1-0.09)^6[/tex]
[tex]A=13,060.99[/tex]
The value of the car after 6 years will be $13,060.99
Frank has twice as many CDs as Vanessa. Lois has 4 less than 2 times as many CDs as Frank. If there is a total of 115 CDs for all 3 people, how many CDs does each person have?
Answer:
Frank, Vanessa, Lois have 34, 17, 64 disks respectively
Step-by-step explanation:
In this question, we are to calculate the number of disks each of the 3 has.
Let the number of disks owned by Frank be x
for vanessa, she has half of what frank has and that would be x/2
Lois has 4 less than 2 times what Frank has, that would be 2x - 4
adding the 3, we have a total of 115 disks
This means that;
x + x/2 + (2x-4) = 115
Multiply throughout by 2;
that gives;
2x + x + 4x - 8 = 230
7x -8 = 230
7x = 230+ 8
7x = 238
x = 238/7
x = 34 disks
Frank has 34
Vaness has 34/2 = 17
Lois have 2x - 4 = 2(34) - 4 = 68 - 4 = 64 disks
Answer:
So Frank has 34 CDs, Vanessa has 17 CD's and Lois has 64 CDs
Step-by-step explanation:
Let's call the amount of CDs that Frank has by 'F', that Vanessa has by 'V' and that Lois has by 'L'. Then, we can write the following equations:
F = 2*V
L = 2*F - 4
F + V + L = 115
If we use the values of F and L in the third equation, we have that:
2*V + V + 2*(2*V) - 4 = 115
7*V = 119
V = 17 CD's
Now we can find F:
F = 2*V = 34 CDs
And then we find L:
L = 2*F - 4 = 68 - 4 = 64 CDs
So Frank has 34 CDs, Vanessa has 17 CD's and Lois has 64 CDs
Marquise has 200200200 meters of fencing to build a rectangular garden.
The garden's area (in square meters) as a function of the garden's width www (in meters) is modeled by:
A(w)=-w^2+100wA(w)=−w
2
+100wA, left parenthesis, w, right parenthesis, equals, minus, w, squared, plus, 100, w
What is the maximum area possible?
Answer:
2500 Square meters
Step-by-step explanation:
Given the garden area (as a function of its width) as:
[tex]A(w)=-w^2+100w[/tex]
The maximum possible area occurs when we maximize the area. To do this, we take the derivative, set it equal to zero and solve for w.
A'(w)=-2w+100
-2w+100=0
-2w=-100
w=50 meters
Since Marquise has 200 meters of fencing to build a rectangular garden,
Perimeter of the proposed garden=200 meters
Perimeter=2(l+w)
2(l+50)=200
2l+100=200
2l=200-100=100
l=50 meters
The dimensions that will yield the maximum area are therefore:
Length =50 meters
Width=50 meters
Maximum Area Possible =50 X 50 =2500 square meters.
a web music store offers two versions of a popular song. the size of the standard version is 2.9 megabytes (MB). the size of the high-quality version is 4.8 MB. yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 6188 MB. How many downloads of the standard version were there?
Answer:
280 downloads
Step-by-step explanation:
-let x denote the number of standard version downloads.
-Given that the high-quality version was downloaded four times as often as the standard version it is denoted as 4x
-This can then be expressed as:
[tex]x(2.9)+4x(4.8)=6188\\\\2.9x+19.2x=6188\\\\22.10x=6188\\\\x=280[/tex]
Hence, the number of standard version downloads is 280
A student decided to start saving money.On the first day he saved 1 cent, on the second day an additional 2 cents, on day 3 he saved 4 cents. Each day he doubled the amount he saved the previous day. How much would he be saving on day 20?
(Hint: The first term of the geometric sequence is 0.01 and the common ratio is 2. What is the 20th term?)
Question 1 options:
A-$3.80
B-$10,485.75
C-$5,242.88
D-$10,485.76
Answer:
The correct option is option (B).
He would be saving $10,485.75.
Step-by-step explanation:
We know that,
1 cent =$ 0.01.
Geometric sequence:
The first term of the sequence be a and common ratio n, then [tex]n^{th}[/tex] term of the sequence is [tex]T_n=a(r)^{n-1}[/tex] .The sum of the sequence is[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex] where r>1
[tex]=\frac{a(1-r^n)}{1-r}[/tex] where r<1
=na where r=1
Here first term(a)= $0.01, r= 2 , n=20
[tex]S_n=\frac{0.01(2^{20}-1)}{2-1}[/tex]
=10,485.75
He would be saving $10,485.75.
What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?
Answer:
there is one zero: 5/16
Step-by-step explanation:
i used photomath
Write 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 using an exponent.
Answer:
9
[tex] {9}^{8} [/tex]
An automobile dealer agrees to discount the $10,288 sticker price of a new car by 5% for a customer. What is the price of the car for the customer?
Answer: 514.4
Step-by-step explanation:
10, 288 x 5 ÷ 100
What is 240,000 divided by 1962.5 ?
Answer:
122.293
Step-by-step explanation:
PLEASE HELP
A circle has radius 50 cm. Which of these is closest to its area?
Captionless Image
1. A
2. B
3. C
4. D
Answer:
C.) [tex]7,854[/tex] [tex]cm^2[/tex]
Step-by-step explanation:
use the area of a circle formula:
[tex]A=\pi r^2[/tex]
Insert the radius:
[tex]A=\pi *50^2[/tex]
Simplify exponents:
[tex]A=\pi *2500[/tex]
Simplify pi:
[tex]A=3.14*2500\\A=7850[/tex]
Option C is the closest to 7850.
Finito.
Admission to a baseball game is $4.00 for general admission and $4.50 for reserved seats. The receipts were $5150.00 for 1255 paid admission. How many of each ticket were sold?
Answer:
995 general admission tickets and 260 reserved seat tickets
Step-by-step explanation:
We can solve this by using Simultaneous equations.
General admission is $4.00 and each Reserved seat is $4.50.
Let g represent the number of General admission tickets and r represent the number of Reserved seat tickets.
The total amount paid for 1255 tickets is $5150.00.
This means two things:
1. The total number of tickets is 1255, which means if we add the general admission tickets and the number of reserved seat tickets, we will get 1255:
g + r = 1255 ________________ (1)
2. The total price of all tickets is $5150.00, which means if we multiply the number of general admission tickets by the price of general admission tickets and we multiply the number of reserved seat tickets by the price of reserved seat tickets and add them up, we will get $5150:
(4.00*g) + (4.50*r) = 5150 _________(2)
=> g + r = 1255 __________________(1)
(4.00*g) + (4.50*r) = 5150 _________(2)
From (1):
g = 1255 - r _______ (3)
Putting (3) in (2):
{4.00*(1255 - r)} + (4.50*r) = 5150
5020 - 4.00r + 4.50r = 5150
5020 + 0.50r = 5150
=> 0.50r = 5150 - 5020
0.50r = 130
r = 130 / 0.50 = 260
Putting the value of r in (3):
g = 1255 - 260 = 995
Hence, 995 general admission tickets and 260 reserved seat tickets were sold.
Final answer:
To find the number of general admission and reserved seat tickets sold, set up and solve a system of equations using the given information.
Explanation:
Given:
General admission tickets cost $4.00.
Reserved seat tickets cost $4.50.
Total receipts were $5150.00 for 1255 paid admissions.
To solve:
Let x be the number of general admission tickets sold.
Let y be the number of reserved seat tickets sold.
Form the equations: x + y = 1255 and 4x + 4.50y = 5150.
Solve the system of equations to find x and y.
Answer: 705 general admission tickets and 550 reserved seat tickets were sold.
The math team has 11 boys, 10 girls, and 1 coach. What is the ratio of coach to students?
Group of answer choices
11/1
1/21
1/11
21/1
Answer: 1:21
Step-by-step explanation:
We know that if they say students they mean both boys and girls so we add 11 and 10 to make 21 and since its, (COACH,) and then student we do 1:21 and not 21:1!
1/21
Step-by-step explanation:
First we need to figure out how many students are in the class.
10 + 11 = 21
Then we need to make a ratio
1/21
For every 21 students there is 1 coach
If you look at the question it says from coach to students so we do 1 coach to 21 students which is why 21/1 is wrong
Hope this helps can I have brainliest
A bag contains white marbles and blue marbles, 65 in total. The number of white marbles is 8 more than 2 times the number of blue marbles. How many white marbles are there?
Answer:
NOTE: THIS IS AN EXAMPLE
Step-by-step explanation:
Let the Yellow Marbles be “X” and Red Marbles be “Y”
Total is 65, so X+Y = 65
Since we know that Yellow Marbles are 5 more than 4 times red marbles, let us convert that in terms of X and Y as well.
i.e, X = 4Y+5
Now replace X with (4Y+5) in the first equation we wrote above.
(4Y+5)+Y = 65
i.e, 5Y+5 = 65
5Y = (65–5),
5Y = 60
Therefore Y = 60/5 = 12
we know total is 65
So X= 65-Y
X=65–12 = 53
Therefore, the number of Yellow Marbles are 53 and the Red ones are 12.
What is 3/2 times 14
Answer:
21
Step-by-step explanation:
3/2×14=21
Answer:
21
Step-by-step explanation:
1093999 nearest to million
Answer:
1,000,000
Step-by-step explanation:
Because you are rounding down because it is not enough to round up.
What is the range of y = sin θ
A. [-1, 1]
B. [0, infinite]
C. all real numbers
D. 2pi
Answer:
A
Step-by-step explanation:
range is the possible y values
sin x and cos x parent graphs all have range from [-1, 1].
factors a, b, c, d affect the graph of asin(bx+c)+d
since a and b = 1 and c and d = 0, the range is default [-1,1]
T=s+.50 T=0.25s+1.70 In the equation above t and a represent the weight in tons of a sedan and of a truck, respectively. What is the weight of a sedan in tons
Answer :
The weight of a sedans in tons is 2.1 tons.
Step-by-step explanation:
Given : Equations [tex]T=s+0.50[/tex] and [tex]T=0.25s+1.70[/tex] where T and s represents the weight in tons of a sedan and of a truck, respectively.
To find : What is the weight of a sedan in tons ?
Solution :
Solving equations,
[tex]T=s+0.50[/tex] ......(1)
[tex]T=0.25s+1.70[/tex] .....(2)
As LHS is equate we equate RHS,
[tex]s+0.50=0.25s+1.70[/tex]
[tex]s-0.25s=1.70-0.50[/tex]
[tex]0.75s=1.2[/tex]
[tex]s=\frac{1.2}{0.75}[/tex]
[tex]s=1.6[/tex]
Substitute in equation (1),
[tex]T=1.6+0.50[/tex]
[tex]T=2.1[/tex]
Therefore, the weight of a sedans in tons is 2.1 tons.
Hannah planted flowers next to the school playground. She planted 2 daisies, 3 sunflowers and 4 tulips.
What is the ratio of the number of daisies she planted to the total number of flowers she planted?
Answer:
the ratio is 2:9
Step-by-step explanation:
there are a total of 9 flowers, she planted 2 daisies
What 4 out 100 in percent
Answer:
4%
Step-by-step explanation:
Answer:
4%
Step-by-step explanation:
How much is 4 out of 100 written as a percentage? Convert fraction (ratio) 4 / 100
What is the center of the circle given by the equation (x + 5)2 + (y - 8)2 = 1?
A.
(5, -8)
B.
(-5, -8)
C.
(5, 8)
D.
(-5, 8)
Circle equation: (x + h)² + (y - k)² = r²
The center can be found by looking at (h, k) in the equation.
We are given the equation (x + 5)² + (y - 8)² = 1
The center is (h, k) so, it is (-5, 8)
Best of Luck!
Answer:
he center is (h, k) so, it is (-5, 8)
Step-by-step explanation:
x2 + 4x - 21 = 0 quadratic formula
Answer:
0
Step-by-step explanation:
x2 +4x-21=0. solve for x
[tex]x = \frac{7}{2} [/tex]
[tex]x = 3 \frac{1}{2} \ x = 3.5[/tex]
Solve the equation 264 = 2(x+26)
A leaf blower runs on a mixture of oil and gas. The ratio is 40 to 1. How many ounces of gas does the leaf blower need for 4 ounces oil??
Answer:
160
Step-by-step explanation:
you need to multiply the ounces of gas by 4 like you did to the oil.
Answer:
160 oz
Step-by-step explanation:
However, I personally think this does not make sense. A leaf blower should take more gas than oil, right? For this reason, I will provide an additional answer.
If the ratio of gas to oil is 40:1, then you would multiply by 4 to get 4 oz oil and 160 oz gas.
Alternate answer:
If the ratio of oil to gas is 40:1, then you divide by 10 on both sides to get 4 oz oil and .1 oz gas.
Alt answer: .1 oz
The graph of the function f(x) = (x+6)(x+2) is shown.
Which statements describe the graph? Check all that
apply.
The vertex is the maximum value.
The axis of symmetry is x= -4.
The domain is all real numbers.
The function is increasing over (-0, -4).
The function is negative over (-6, -2).
Intro
Done
Answer: Is 2, 3 and 5
Step-by-step explanation:
I just completed the assignment on Edge
By analyzing the quadratic function, we can see that:
1) true2) true3) true4) false5) true.Which statements are correct?
Here we have the quadratic function:
f(x) = (x + 6)*(x + 2)
Let's analyze each statement to see which ones are correct.
1) "The vertex is the maximum value."
True, the leading coefficient is positive, so the parabola opens up, meaning that the vertex is the minimum.
2) " The axis of symmetry is x= -4."
The two roots are x = -6 and x = -2, the axis of symmetry is right between these two values, so it is at x = -4, so this is true.
3) "The domain is all real numbers."
For all quadratic functions, this is true.
4) "The function is increasing over (-0, -4)"
(I don't know what -0 means, the segment (-0, -4) does not exist, so i will take this as false).
5) "The function is negative over (-6, -2)."
This is true, the two roots are at -6 and -2, so between these values the function must be negative.
If you want to learn more about quadratic functions, you can read:
https://brainly.com/question/1214333