The probability that exactly 3 of those games were won by the colonies is 25%.
We are given that;
Number of colonies= 4
Number of games= 3
Now,
To find the probability of exactly 3 wins out of 4 games, we can use the binomial probability formula1:
P(X = 3) = nCx * p^x * q^(n-x)
where n is the number of trials (4 games), x is the number of successes (3 wins), p is the probability of success (0.5), q is the probability of failure (1 - p = 0.5), and nCx is the combination of n things taken x at a time.
P(X = 3) = 4C3 * 0.5^3 * 0.5^(4-3) P(X = 3) = (4! / (3! * (4-3)!)) * 0.125 * 0.5 P(X = 3) = (24 / (6 * 1)) * 0.0625 P(X = 3) = 4 * 0.0625 P(X = 3) = 0.25
Therefore, by the probability the answer will be 25%.
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the capacity of P vessel is 12l and that of Q vessel is 18l. Write the capacities of different vessels which completely fill P vessel with exact number of filling.
i) The capacities of different vessels which completely fill P vessel with exact number of fillings are:
One vessel of 12 ITwo vessels of 6 I eachThree vessels of 4 I eachFour vessels of 3 I eachSix vessels of 2 I eachTwelve vessels of 1 I eachHow to explain the information(ii) The capacities of different vessels which completely fill Q vessel with exact number of fillings are:
One vessel of 18 I
Two vessels of 9 I each
Three vessels of 6 I each
Six vessels of 3 I each
Nine vessels of 2 I each
Eighteen vessels of 1 I each
(iii) The common capacities of vessels which completely fill P as well as Q vessels with exact number of fillings are:
Two vessels of 6 I each
Three vessels of 4 I each
Six vessels of 2 I each
Twelve vessels of 1 I each
(iv) The greatest capacity of vessel that completely fills P as well as Q vessels with exact number of fillings is 6 I.
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Use a number line to illustrate:
1.) p – q
p + (-q)
If the equation is true: p – q = p + (-q)
The illustration of p - q and p + (-q) using a number line is added as an attachment
Illustrating the expression using a number lineFrom the question, we have the following parameters that can be used in our computation:
p - q
Also, we have
p + (-q)
The above expressions mean that
To add two numbers (positive and negative), we can start from a point p, and then count backwards on the number line in q terms
Using the above as a guide, we have the following:
The illustration using a number line is added as an attachment
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please if you know this help me i would appreciate it.
The reduced row echelon form of the matrix is:
[tex]\left[\begin{array}{ccc}-1144/259&\\-321/259\\25/74\end{array}\right][/tex]
Solving Echelon MatrixGiven the matrix below
[tex]\left[\begin{array}{ccc}7&-1&-3 |-63\\0&-6&-2 |-20\\0&1&1 | 6\end{array}\right][/tex]
Divide the first row by 7:
[tex]\left[\begin{array}{ccc}1&-1/7&-3/7 |-9\\0&-6&-2 |-20\\0&1&1 | 6\end{array}\right][/tex]
Add 1/7 times the first row to the second row:
[tex]\left[\begin{array}{ccc}1&-1/7&-3/7 |-9\\0&-37/7&-17/7 |-107/7\\0&1&1 | 6\end{array}\right][/tex]
Add 3/7 times the second row to the first row:
[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&1&1 | 6\end{array}\right][/tex]
Add 17/37 times the second row to the third row:
[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&0&20/37 | 25/37\end{array}\right][/tex]
Multiply the third row by 37/20:
[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&0&1 | 25/74\end{array}\right][/tex]
Add 3/7 times the third row to the second row:
[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&0 |-321/259\\0&0&1 | 25/74\end{array}\right][/tex]
Add 16/37 times the third row to the first row:
[tex]\left[\begin{array}{ccc}1&0&0 |-1144/259\\0&-37/7&0 |-321/259\\0&0&1 | 25/74\end{array}\right][/tex]
Multiply the second row by -7/37:
[tex]\left[\begin{array}{ccc}1&0&0 |-1144/259\\0&1&0 |321/259\\0&0&1 | 25/74\end{array}\right][/tex]
This is the reduced row echelon form of the given matrix.
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Evaluate the following question given below
The solution is, simplification of the expression is; 71.19.
Here, we have,
the given expression is:
(5/2)^4/2 * (3/2)^6
=(5/2)^2 * (3/2)^6
as we know that, 4/2 = 2.
now, we have,
(5/2)^2 * (3/2)^6
=5²/2² ^ 3⁶/2⁶
= 5² * 3⁶ / 2² * 2⁶
=5² * 3⁶ / 2 ^ (2+6)
=5² * 3⁶ / 2 ^8
=25 * 729/ 256
=18225/ 256
=71.19
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just needs to be solved can't figure it out thanks
1. The balances for each type of investment at the end of the third year are:
Treasury bond: $13,964.18CD: $3,429.57Stock plan: $9,973.02Savings account: $6,783.622. The total gain from all of the investments combined is $4,150.39.
How to calculate the valuea. Treasury bond:
Balance = Principal * (1 + (interest rate/100))^time
Balance = $12,000.00 * (1 + (5.35%/100))³
Balance = $13,964.18
CD:
Balance = Principal * (1 + (interest rate/100))^time
Balance = $3,000.00 * (1 + (4.75%/100))³
Balance = $3,429.57
Stock plan:
Principal = 0.3 * $30,000.00 = $9,000.00
Year 1: Increase of 9%, so balance = $9,000.00 * (1 + (9%/100)) = $9,810.00
Year 2: Decrease of 5%, so balance = $9,810.00 * (1 - (5%/100)) = $9,319.50
Year 3: Increase of 7%, so balance = $9,319.50 * (1 + (7%/100)) = $9,973.02
Savings account:
Balance = Principal * (1 + (interest rate/100))^time
Balance = $6,000.00 * (1 + (3.90%/100))³
Balance = $6,783.62
b. Treasury bond: Gain = $13,964.18 - $12,000.00 = $1,964.18
CD: Gain = $3,429.57 - $3,000.00 = $429.57
Stock plan: Gain = $9,973.02 - $9,000.00 = $973.02
Savings account: Gain = $6,783.62 - $6,000.00 = $783.62
Total gain from all investments combined = $1,964.18 + $429.57 + $973.02 + $783.62 = $4,150.39
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You saved $30,000.00 and want to diversify your monies. You invest 40% in a Treasury bond for 3 years at 5.35% APR compounded annually. You
place 10% in a CD at 4.75% APR for 3 years compounded annually. 30% you invest in a stock plan and the remainder is in a savings account at
3.90% APR compounded annually. The stock plan increases 9% the first year, decreases in value by 5% the second year, and increases by 7% the
third year.
1. What are the balances for each type of investment at the end of the third year?
2. What is your total gain from all of the investments combined?
what is the surface area of the cylinder with height 7in and radius 2in? round your answer to the nearest tenth
Answer:
113.1 in²
Step-by-step explanation:
A = 2πrh + 2πr²
r = 2 in
h = 7 in
A = 2π(2)(7) + 2π2² = 113.1 in²
A plane leaves an airport and flies 19 km east then 24 km south. How far is the plane from the airport?
Answer: 30.6 km away
Step-by-step explanation:
The main thing this problem requires is Pythagoras' theorem. So set the problem up by marking the airport as (0,0) on a graph. Then move 19 units to the right, and 24 units down and make a point. Now you have the two short lengths of a right-angle triangle, so all that's left is to solve for the hypotenuse. So using the formula [tex]a^{2} + b^{2} = c^{2}[/tex] you would end up with [tex]19^{2} + 24^{2} =c^{2}[/tex]. Then you get: 361+576=[tex]c^{2}[/tex]
solve for c and you get about 30.6 km!
Hope this helps!
$11,335
is invested, part at 9%
and the rest at 6%
. If the interest earned from the amount invested at 9%
exceeds the interest earned from the amount invested at 6%
by $865.35
, how much is invested at each rate? (Round to two decimal places if necessary.)
Answer:
Let x be the amount invested at 9% and y be the amount invested at 6%
.According to the problem:
x + y = 11,335 ----(1) (the total amount invested is $11,335)0.09x - 0.06y = 865.35 ----(2) (the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 6% by $865.35)
We can use these two equations to solve for x and y.
Multiplying equation (1) by 0.06, we get
:0.06x + 0.06y = 680.10 ----(3)
Subtracting equation (3) from equation (2), we get:
0.03x = 185.25
x = 6,175
Substituting x = 6,175 into equation (1), we get:
y = 5,160
Therefore, $6,175 is invested at 9% and $5,160 is invested at 6%.
Step-by-step explanation:
The function f(x) is defined as f(x) = 1/x + 5x3, Find the value of f(2).
The value of f(2) is 40.5
The given function is f(x) = 1/x + 5[tex]x^3[/tex], and we need to find the value of f(2).
To do this, we substitute x=2 into the function and simplify:
f(2) = 1/2 + 5([tex]2^3[/tex])
= 1/2 + 5(8)
= 1/2 + 40
= 40.5
Therefore, the value of f(2) is 40.5.
The function f(x) has two parts: 1/x and 5[tex]x^3[/tex]. The first part of the function, 1/x, is a decreasing function that approaches zero as x gets larger. The second part of the function, 5[tex]x^3[/tex], is an increasing function that grows rapidly as x gets larger.
When we substitute x=2 in the function f(x), we get f(2) = 1/2 + 5([tex]2^3[/tex]) = 40.5. This means that at x=2, the value of the function is 40.5.
This result tells us that the function f(x) has a positive value at x=2. Moreover, since the second part of the function grows faster than the first part, the value of the function f(x) will increase as x gets larger. This means that as x increases, the value of f(x) will increase more and more rapidly.
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Find the formula for the Riemann sum obtained by dividing the interval [0, 1] into n equal
subintervals and using the right endpoint for each c. Then take the limit of these sums as n → ∞
to calculate the area under the curve f(x) = 21x + 21x³ over [0, 1].
The area under the curve over [0, 1] is…..
The area under the curve over [0, 1] is 15.75.
How to solveTo find the Riemann sum, divide [0, 1] into n equal subintervals of width Δx = 1/n.
Using the right endpoint, c = iΔx = i/n. The Riemann sum is:
Σ[f(c)Δx] = Σ[(21(i/n) + 21(i/n)³)(1/n)] from i=1 to n.
To find the area under the curve, take the limit as n→∞:
Area = lim(n→∞) Σ[(21(i/n) + 21(i/n)³)(1/n)].
Find the answer by using the method of definite integration.
Area = ∫(21x + 21x³)dx from 0 to 1 = [10.5x² + 5.25x⁴] from 0 to 1 = 10.5(1)² + 5.25(1)⁴ - 0 = 15.75.
The area under the curve over [0, 1] is 15.75.
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30 POINTS!! HELP PLEASE.....
Match the given situation to analyze whether they are a part of internal control accounting.
company policies help employees
to carry out their daily operations
verbal job descriptions are enough
to state an employee’s accountability
bank reconciliation needs to be
prepared for verification
transactions need not be authorized
by the management in advance
organization’s financial data in the
computer should be in password
protected files
Answer:
Company policies help employees to carry out their daily operations. - Yes, part of internal control accounting.
Bank reconciliation needs to be prepared for verification. - Yes, part of internal control accounting.
The organization's financial data in the computer should be in password-protected files. - Yes, part of internal control accounting.
Step-by-step explanation:
10. Given ADEF, find m/E.
Round your answer to the nearest hundredth of a degree.
E
6
D
4
Find the missing degree E>
After considering all the given data we conclude that the measure of m∠E is 54.46° under the condition that ADEF is a right angled triangle.
We already know that ADEF is a right angled triangle having sides EF = 6 and FD = 4, we can apply the Pythagorean theorem to evaluate the length of the hypotenuse AD.
AD = √(6² + 4²)
= √52)
≈ 7.21
Now we can apply the sine function to find the measure of angle E.
sin(E) = opposite/hypotenuse = EF/AD
E = arcsin(EF/AD)
≈ 54.46°
Therefore, m∠E ≈ 54.46°.
The Pythagorean Theorem is considered a fundamental relation in the context of Euclidean geometry comparing the three sides of a right triangle.
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Translation
AABC is translated 4 units to the right and 5 units down. Answer the questions to
find the coordinates of A after the translation.
1. Give the rule for translating a point 4 units right and 5 units down. (2 points)
(x,y) → (x
y
)
The rule for this translation. and the coordinates of the image point are (x, y) = (x + 4, y - 5); (7, -6)
a, Write the rule for this translation.From the question, we have the following parameters that can be used in our computation:
translated to the right 4 units and down t units
Mathematically, this can be expressed as
(x, y) = (x + 4, y - 5)
b. What are the coordinates of the image point?Given that
A = (3, -1)
And, we have
(x, y) = (x + 4, y - 5)
This means that
A' = (3 + 4, -1 - 5)
Evaluate
A' = (7, -6)
So, the image point is A' = (7, -6)
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Question
ABC is translated 4 units to the right and 5 units down. Answer the questions to find the coordinates of A after the translation.
A = (3, –1)
A lottery has a very large number of tickets, one in every 500 of which entitles the purchaser to prize. Find the minimum number of tickets the agent must sell to have 95% chance of selling at least one prize winning ticket.
The minimum number of tickets the agent must sell to have a 95% chance of selling at least one prize-winning ticket is 368 tickets
To unravel this issue, we are able to utilize the concept of likelihood. Let's begin with discovering the likelihood of not offering any prize-winning tickets with one ticket:
- The likelihood of not winning with one ticket is 499/500 (since there's as it were one winning ticket out of 500).
- The likelihood of not winning with n tickets is (499/500)[tex]^n[/tex](since the probabilities are autonomous and we duplicate them together).
Presently, we need to discover the least number of tickets the specialist must offer to have a 95% chance of offering at the slightest one prize-winning ticket. In other words, we need to discover the least esteem of n such that:
- The likelihood of not winning with n tickets is less than or rises to 5% (or 0.05).
- This can be identical to (499/500)[tex]^n[/tex]≤ 0.05.
We will illuminate for n utilizing logarithms:
- Take the normal logarithm of both sides:
ln[(499/500)[tex]^n[/tex]] ≤ ln(0.05).
- Utilize the logarithmic property of types to bring down the example:
n ln(499/500) ≤ ln(0.05).
- Fathom for n by partitioning both sides by ln(499/500) and taking the ceiling work (since n must be an entire number):
n = ceil[tex][ln(0.05) / ln(499/500)].[/tex]
Employing a calculator, we get
n = ceil[tex][ln(0.05) / ln(499/500)][/tex]≈ 368
In this manner, the specialist must offer at the slightest 368 tickets to have a 95% chance of offering at the slightest one prize-winning ticket.
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What is the slope of line represented by 5x-12y=24
Answer:
5/12
Step-by-step explanation:
add 12 y to both sides:
5x = 24 + 12y
subtract 24 from both sides:
12y = 5x - 24
divide all by 12:
y = (5/12)x - 2.
slope is the number in front of x.
slope is (5/12).
A new car is purchased for $41, 000 and over time its value depreciates by one half every 3 years. What is the value of the car 4 years after it was purchased, to the nearest hundred dollars?
The value of the car 4 years after it was purchased is $16,270.86.
What is the value of the car after 4 years?
Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.
The equation that would be used to determine the value of car with the passage of time would be an exponential equation.
Value of the car after t years = [tex]p(1 -r)^{\frac{t}{3}[/tex]
Where:
p = purchase price of the car r = rate of depreciation t = number of yearsValue of the car after 4 years = [tex]41,000(1 -0.5)^{\frac{4}{3}[/tex] = $16,270.86
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The owner of a pet shop predicts that 10 out of 20 new puppies are male. He randomly selects 10 of the puppies, and notes that all 10 are male. Which of the following conclusions BEST supports his findings?
Select one:
a.
All 20 puppies are male.
b.
Less than 10 of the puppies are male.
c.
More than 10 of the puppies are male.
d.
10 of the puppies are male and 10 are female.
What’s 6-x=3 in pre algebra
Answer:3
Step-by-step explanation:
subtract 3 from 3 and repeat on the other side of the equal sign. So 6 minus 3 equals 3.
How much kinetic energy does i-6 kg bowling ball have when it's rolling at 60 mph 7.1 m/s then when it's rolling at 14 mph 6.2 m per second??
Find the inverse of this function: f(n)= -4/N-1 -1
a) f^-1(n)= 4/-n-1
b) f^-1(n)= 4/-n-1 +1
c) f^-1(n)= -4/n+3 +1
d) f^-1(n)= 2/n+1 +1
Thank you!!!!!!!! <3
Answer:
The correct answer is b) f^-1(n)= 4/-n-1 +1.
b
Step-by-step explanation:
I think parentheses are missing :
y = -4/(n-1) - 1 switch n and y then solve for y
n = -4/(y-1) - 1 add 1 to both sides of the equation
n+1 = - 4/(y-1) multiply through by y -1
(y-1)(n+1) = - 4 divide through by (n+1)
y -1 = - 4/ (n+1) add 1 to both sides
y = - 4/ (n+1 ) + 1 <=====this is the inverse function y = -4/(n-1) -1
equivalent to 4 / (-1-n) + 1 by putting the ' - ' in the denominator
If a trader Gaines 15% interest by selling an article for 1560.00 what is the cost price for the article
$1356.52 is the cost price of the article.
To find the cost price of the article, we can utilize the concept of calculating the original amount based on a percentage increase.
Let's assume the cost price of the article is "x" dollars.
The trader gained a 15% interest, which means the selling price is 115% of the cost price. In other words, the selling price is 115% of "x".
To calculate the selling price, we can set up the following equation:
115% of x = 1560
To convert the percentage to a decimal, we divide it by 100:
1.15 * x = 1560
Now we can solve for x by dividing both sides of the equation by 1.15:
x = 1560 / 1.15
Using a calculator, we find:
x ≈ 1356.52
Therefore, the approximate cost price of the article is $1356.52.
This means that the trader purchased the article for around $1356.52 and then sold it for $1560.00, resulting in a 15% gain.
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Find the perimeter of a field that has length 2/x+1 and width 5/x^2-1
The perimeter of the field is 4x + 6/(x + 1)(x - 1).
Given that a field has a width of 5/x²-1 and the length is 2/x+1,
We need to find the perimeter,
A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle,
Perimeter of a rectangle = 2(l+w)
= 2(5/x²-1+2/x+1)
= 2((2(x-1)+5)/(x + 1)(x - 1)
= 4x + 6/(x + 1)(x - 1)
Hence the perimeter of the field is 4x + 6/(x + 1)(x - 1).
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Helppp please
Thorium 234 is a radioactive isotope that decays according to the eqaution At=A0e^-10.498t, where A0 is the initial amount present and At is the amount present after t years. is the amount present after t years. If you begin with 1000 grams of strontium 90,
(a) How much thorium 234 will be left after 0.5 years? Round your answer to the nearest tenth of a gram.
------------------- grams
(b) When will 115 grams of thorium 234 be left? Round your answer to the nearest tenth of a year.
-------------------- years
if you need to see the picture here is too. Thank u.
a) Approximately 778.7 grams of thorium 234 will be left after 0.5 years.
b) Approximately 2.1 years will have passed when 115 grams of thorium 234 are left.
(a) To find the amount of thorium 234 left after 0.5 years, we can use the equation:
[tex]A_t = A_0 e^{(-10.498t)}[/tex]
where A₀ is the initial amount, which is 1000 grams, t is the time in years, and At is the amount after t years.
Substituting t = 0.5, we get:
[tex]At = 1000 e^{(-10.498\times0.5)} = 778.7 \ grams[/tex]
Therefore, approximately 778.7 grams of thorium 234 will be left after 0.5 years.
(b) To find the time at which 115 grams of thorium 234 will be left, we can use the same equation and solve for t:
[tex]A_t = A_0 e^{(-10.498t)[/tex]
Dividing both sides by A₀ and taking the natural logarithm of both sides, we get:
ln(At/A₀) = -10.498t
Substituting At = 115 grams and A₀ = 1000 grams, we get:
ln(115/1000) = -10.498t
Solving for t, we get:
t = (ln(115/1000)) / (-10.498) ≈ 2.1 years
Therefore, approximately 2.1 years will have passed when 115 grams of thorium 234 are left.
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Jodi is making cookies. The recipe calls for 2½ cups of flour and flour and 1¼ cups of sugar She wants to double the reape, but she only has a ½-cup measuring cup. How many ½ cups of flour will she need to make 2 batches of cookies?
Jodi will need 10 half-cup measurements of flour to make 2 batches of cookies.
To double the recipe, Jodi needs to multiply the amounts of each ingredient by 2.
The original recipe calls for 2½ cups of flour. Doubling this amount gives:
2½ cups * 2 = 5 cups of flour
We may divide the total amount of flour required (5 cups) by the quantity in each 12-cup measurement to get the number of 1-1/2 cups Jodi needs.
5 cups / ½ cup = 10
Therefore, Jodi will need 10 half-cup measurements of flour to make 2 batches of cookies.
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Sanjay tried to find the median from the following dot plot, which shows how far he went on his recent walks. However, he made a mistake.
Answer:
Do you wish for the mistake to be pointed out? If so, can you please provide the dot plot so I can answer this question?
Step-by-step explanation:
Gabe has eight dollars the game at the arcade cost 2$ dollars instead of one dollar write ordered pairs to represent the amount of money left after playing different numbers of games.
The ordered pairs representing the amount of money left after playing variable number of games is :
(Number of games played, Amount of money left)
(0, 8)
(1, 6)
(2, 4)
(3, 2)
(4, 0)
Ordered pairsOrdered pairs gives a tabular description of data as the values of two or more variables change.
Here, the amount Gabe has before playing a game is $8 and the cost per game is $2 .
Hence, the amount he has left decreases by $2 for every increase in number of games played.
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what is 1975f= t 1758+Q2
To solve for f, we can rearrange the equation:
1975f = t1758 + Q2
First, we can isolate f by dividing both sides of the equation by 1975:
f = (t1758 + Q2) / 1975
So the final answer is:
f = (t1758 + Q2) / 1975
I need help with this quickly of 100 students,27 are taking caculus,26 are taking french and 13 are doing both. If a student is picked at random,what is the prob that the student is taking calculus OR french? Put the aneswer in decimal form rounded to two decimal places.
The required probability that a student is taking calculus or French, rounded to two decimal places, is 0.40.
The probability that a student is taking calculus or French is calculated by adding the number of students taking calculus and the number of students taking French and then subtracting the number of students taking both calculus and French. This gives us the number of students taking either calculus or French. We then divide this number by the total number of students, which is 100.
The number of students taking calculus is 27.The number of students taking French is 26.The number of students taking both calculus and French is 13.So, the number of students taking either calculus or French is 27 + 26 - 13 = 40.
The probability that a student is taking either calculus or French is 40 / 100 = 0.40 = 40%.
Therefore, the probability that a student is taking calculus or French, rounded to two decimal places, is 0.40.
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Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.
Answer:
[-infinity, 4]
Step-by-step explanation:
-9x + 3 >= -33
-9x >= -36
x<=4 (sign switched because of dividing both sides by a negative integer in an inequality)
Therefore, x is less than or equal to 4
[ - infinity, 4]
A 12-sided die is rolled. The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a 7.
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The probability of rolling a 7 is
(Type an integer or a simplified fraction.)
Ans4863
Step-by-step explanation: