find a recurrence relation the number of ways to give 1 or 2 or 3 dollars even number of days
Answers
The recurrence relation for the number of ways to give an even number of dollars over n days is:
E(n) = E(n-1) + O(n-1) + E(n-1)
Let's denote the number of ways to give an even number of dollars over n days as E(n). We can establish a recurrence relation for E(n) as follows:
When n = 0, there are no days, so there is only one way to give an even number of dollars (by giving $0), hence E(0) = 1.
When n = 1, we have one day. To give an even number of dollars, we must give $0, which is one way. Therefore, E(1) = 1.
Now, let's consider the case for n > 1. On the nth day, we have three options: give $1, $2, or $3.
If we give $1 on the nth day, we need to find the number of ways to give an even number of dollars over the remaining n-1 days. Since n-1 is odd, the number of ways for this case is E(n-1).
If we give $2 on the nth day, we need to find the number of ways to give an odd number of dollars over the remaining n-1 days. Since n-1 is even, the number of ways for this case is O(n-1), where O(n-1) represents the number of ways to give an odd number of dollars over n-1 days.
If we give $3 on the nth day, we need to find the number of ways to give an even number of dollars over the remaining n-1 days. Since n-1 is odd, the number of ways for this case is E(n-1).
To obtain the total number of ways to give an even number of dollars over n days, we sum up the possibilities for each of these three cases:
E(n) = E(n-1) + O(n-1) + E(n-1)
Since E(n) represents the number of ways to give an even number of dollars over n days, O(n) represents the number of ways to give an odd number of dollars over n days, which we haven't defined yet. However, we can establish a similar recurrence relation for O(n) using similar reasoning.
Therefore, the recurrence relation for the number of ways to give an even number of dollars over n days is:
E(n) = E(n-1) + O(n-1) + E(n-1)
Note that we need to establish the base cases and recurrence relation for O(n) as well to fully define the problem.
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Related Questions
two points on the rim of a circle are randomly chosen. what is the probability that the distance between the points is shorter than the side length of an equilateral triangle inscribed in the circle?
Answers
Given a circle with radius r, an equilateral triangle can be inscribed in the circle. The side length of the equilateral triangle is equal to the diameter of the circle, which is 2r.
Let A and B be two points randomly selected from the circle. The distance between A and B, AB, is the chord of the circle passing through A and B. For the distance between A and B to be less than 2r,
it means that the chord AB intersects within the circle. In other words, the two points are selected from a circular segment with an angle of less than 60°.The probability of selecting two points that meet this requirement can be calculated as follows:
Let P be the probability of the distance between the points being shorter than the side length of an equilateral triangle inscribed in the circle. This is the probability that the two points lie within a circular segment with a central angle of less than 60°.The total area of the circle is πr².
Thus, the probability that the first point lies within the segment is (1/6)πr² (since the segment has a central angle of 60°). After the first point is selected, the probability that the second point lies within the segment is (1/6-2x/π)r² where x is the angle that the first chord forms.
The probability P is thus given by:P = (1/6)πr²[(1/6-2x/π)r²]/πr² = (1/36-2x/3π)The maximum value of P occurs when x is 0, which means that the first chord is a diameter. Thus:Pmax = (1/36)
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the product of a number and the difference of the squares of the opposite of seven and four
Answers
The expression which describes the given phrase that the product of a number and the difference of the squares of the opposite of seven and four is 33x.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Let's consider that number is x.
Now, the opposite of 7 is -7 and the opposite of 4 is -4.
The difference between square of -7 and -4 is,
(-7)² - (-4)² = 49 - 16 = 33
The product of 33 and x is 33x.
Hence "The expression which describes the given phrase that the product of a number and the difference of the squares of the opposite of seven and four is 33x".
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Jump To The Flag
Bob is trying to reach a flag that's some height above the ground. In his attempt to reach the flag, Bob can make any number of jumps up the rock wall where it's mounted. He can only move up the wall though, and he must end at exactly the height of the flag. There are 2 types of jumps:
1. A jump of height 1.
2. A jump of height j ;
Determine the minimum number of jumps it will take Bob to reach the flag's height exactly
Answers
The minimum number of jumps required to reach the flag's height is 3.
Let n be the height of the flag. We can use a recursive approach to determine the minimum number of jumps it takes to reach the flag's height.
For n = 0, it takes 0 jumps to reach the flag's height.
For n = 1, it takes 1 jump to reach the flag's height.
For n > 1, we can calculate the minimum number of jumps using the following equation:
minJumps(n) = 1 + min(minJumps(n-1), minJumps(n-j))
Where minJumps(x) is the minimum number of jumps required to reach the flag's height from ground level x.
For example, if the flag's height is 5 and Bob can jump a height of 2, the minimum number of jumps required to reach the flag's height is 3.
minJumps(5) = 1 + min(minJumps(4), minJumps(3))
= 1 + min(1 + min(minJumps(3), minJumps(2)), 1 + minJumps(2))
= 1 + min(1 + 1, 1 + 1)
= 3
Therefore, the minimum number of jumps required to reach the flag's height is 3.
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A line goes through the points (4, 8) and (-4, 6). • What is the slope of the line? Show your work Write the equation of the line in point-slope form. Show your work Write the equation of the line in slope-intercept form. Show your work. Answer:
Answers
Answer:
1/4
Step-by-step explanation:
Answer:
Slope is 1/4
Point-slope is y−8=1/4⋅(x−4)
Slope intercept is y=1/4x+7
Step-by-step explanation:
the voltage produced by the colorimeter is __________ to the absorbance of the sample and ____________ to the light intensity.
Answers
The colorimeter detects the voltage created when sunlight penetrates the specimen, so the voltage created is exactly proportional to the absorbance of the sample.
What is voltage?When charged electrons (current) are forced through a conducting loop by the weight of an electrical raceway power source, they can perform tasks like lighting a lamp. In a nutshell, voltage equals pressure and is expressed in volts (V).
Here,
The voltage generated by the uv spectrophotometer is inversely proportionate to the amount of light present and linearly proportional to the sample's absorbance.
This indicates that as the sample's absorbance rises, so does the energy the colorimeter generates.
Similar to this, the voltage generated by the colorimeter rises as light strength falls.
The Beer-Lambert Law, which says that a sample's absorbance is directly proportional to its concentration of the absorbing substance and its path length and inversely proportional to incident light intensity, describes this connection.
The colorimeter detects the voltage created when sunlight penetrates the specimen, so the voltage created is exactly proportional to the absorbance of the sample.
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14. Write an equation with vanables on each
side of the equals sign that has a solution
of -2.
Answers
Answer:
2x + 3 = 4x + 7
Step-by-step explanation:
\(2x + 3 = 4x + 7\\-2x = 4\\x = -2\)
Simplify the expression by combining like terms (Show all of your work below) 36a + 42b - 18a + 6
Answers
Answer: 18a+42b-6
Step-by-step explanation:
Simplifying means combining like terms
so 36a and -18a can simplify to 18a
and the rest you can't simplify so
18a+42b-6
A researcher has reported the standard deviation of a data set. What might be the reason they chose this measure of variability? a. When plotted, the data set had a normal distribution b. When plotted, the data set had one number that was more frequent than the others c. When plotted, the data set was skewed d. When plotted, the data had a large distribution
Answers
Standard deviations are used to measure the variability of the set
The reason they choose the standard deviation as the measure of variability is (a) when plotted, the data set had a normal distribution
How to determine the reason for the measure of variabilityWhen a data is distributed, the data can be measured using the median, the mean or the standard deviation.
If the data is a normal distribution, then the best measure of variability to use is the standard deviation
Hence, the true statement is (a) when plotted, the data set had a normal distribution
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A student is saving money to buy a video game system. She has already saved some money and will continue saving the same amount of money each week. If the equation 200=20x+60 represents the student's savings for the video game system, what does x=7 represent?
the number of weeks she needs to save
the total price of the video game system
the amount of money she has already saved
the amount of money she still needs to save
Answers
Answer:
the number of weeks she needs to save.
Solve the following inequality.
x/2 − 5 < − 7
Answers
Answer:
\( \frac{x}{2} - 5 < - 7\)
\( \frac{x}{2} < - 7 + 5\)
\( \frac{x}{2} < - 2\)
\(x < ( - 2)(2)\)
\(x < - 4\)
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The graph of 2x + y =8 is shown on the graph below. Graph the equation y= 1/3x - 6 on the same coordinate plane below. Plot the point that represents the solution to the system considering of the two equations.
Answers
Answer:
See graph below. The point is (6,-4)
Step-by-step explanation:
I used a scale of 1 for the x and y axis. Your graph uses a scale of counting by 2's
For which function k does the output increase by 20% every time the input increases by 1?
Answers
Answer:
k(x) = 1.20^x
Step-by-step explanation:
Here, we want to get a function
The output in this case refers to k(x)
the input refers to the value x
So, for every 1 increase in x, we want k(x) to increase by 20%
20% is same as 20/100 = 0.2
So at an initial value of 1, each increase if 20% will be 0.2 + 1 = 1.2
So therefore, we have the function as;
k(x) = 1.20^x
I use the expression 3(2w - 10) to determine how many copies I need to make of a worksheet (w). If w = 20, how many worksheet copies do I need to make?
Answers
Answer: The number of copies of worksheet needs to be done = 90
Step-by-step explanation:
The expression used to evaluate the number of copies need to make of the worksheet (denoted as 'w') is given as 3(2w - 10).
If w=20, then the number of copies need to make of worksheet = 3(2(20)-10)
i.e. the number of copies need to make of worksheet= 3 (40-10)
i.e. the number of copies need to make of worksheet= 3 (30)
i.e. the number of copies need to make of worksheet= 3 x 30
i.e. the number of copies need to make of worksheet= 90
Hence, if w = 20, then the number of copies of worksheet needs to be done = 90
What will be the amount of the sum Rs 1200 for one and
half year at 40 percent of interest compounded
quarterly?
Answers
The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.
The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly can be calculated as follows:
Given, Principal = Rs 1200Time = 1.5 yearsInterest rate = 40% per annum, compounded quarterly
Let r be the quarterly rate of interest. Then we can convert the annual interest rate to quarterly interest rate using the following formula: \text{Annual interest rate} = (1 + \text{Quarterly rate})^4 - 1$$
Substituting the values, we get:0.40 = (1 + r)^4 - 1 Solving for r, we get:r = 0.095 or 9.5% per quarter
Now, we can use the formula for the amount of money after time t, compounded quarterly: $A = P \left( 1 + \frac{r}{4} \right)^{4t}
Substituting the values, we get:A = Rs 1200 x $\left(1 + \frac{0.095}{4} \right)^{4 \times 1.5}= Rs 1893.09
Therefore, the amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.
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Choose the mixed number that is equivalent to this decimal 3.242424...
Answers
Answer:
3.24 = 3 6/25
Step-by-step explanation:
- Rewrite the decimal number as a fraction with 1 in the denominator.
- Multiply to remove 2 decimal places. Here, you multiply top and bottom by 100
- Find the Greatest Common Factor (GCF) of 324 and 100, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 4
- You should end up with that answer..
Triangle X Y Z is translated up 2 and right 3 units to form triangle C A B. Triangle XYZ was translated up 2 and right 3 units, creating triangle CAB. Which relationship between the parts of the two triangles must be true? ∠X ≅ ∠A ZX ≅ CA YZ ≅ AB ∠Z ≅ ∠C
Answers
Answer:
YZ ≅ AB
Step-by-step explanation:
A translation is a correspondence between two mathematical figures, for instance, the coordinates of each point in a straight line of one figure that is added to the coordinates of the corresponding point on the other figure.
But here, we are given a Δ XYZ which is translated to ΔCAB. This tells us more about how the corresponding points preserve their congruence nature.
i.e.
X corresponds to C
Y corresponds to A
Z corresponds to B
Similarly;
XY corresponds to CA
YZ corresponds to AB
XZ corresponds to CB
Since both triangles preserve their congruence nature, then all corresponding points are congruent as well.
Therefore, from the choice of options given, only YZ corresponds to AB is the right answer.
i.e.
YZ ≅ AB
Answer:
C
Step-by-step explanation:
Which word is associated with multiplication when computing probabilities? Choose the correct answer below Disjoint O And O Not
Answers
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .
According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.
The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.
Therefore,
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
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Could someone help me on this pls?
...
Rewards if answering- Brainliest and 15+ points!!
Answers
In a sample the Upper Specification Limit (USL) is 14 and the Lower Specification Limit (LSL) is 0. The Standard Deviation for the Process is 2. What is Cp, and is the process capable if the goal is 1.33
Answers
The calculated Cp value is 1.17. The goal for this process is a Cp of 1.33. Since the calculated Cp is lower than the desired value, the process is not considered capable of meeting the specified goal. This indicates that there may be a need for process improvement to achieve the desired capability.
Cp is a statistical tool used in Six Sigma methodology to measure the process capability of a manufacturing process. It is calculated by dividing the allowable spread (the difference between the USL and LSL) by six times the standard deviation.
In this case, the USL is 14 and the LSL is 0, which means the allowable spread is 14. The standard deviation is given as 2. So, Cp can be calculated as follows:
\(Cp = (USL - LSL) / (6 x Standard Deviation)\)
Cp = (14 - 0) / (6 x 2)
Cp = 1.17
A Cp value of 1 indicates that the process is barely capable of meeting the specifications. A Cp value of less than 1 indicates that the process is not capable of meeting the specifications. A Cp value greater than 1 indicates that the process is capable of meeting the specifications.
In this case, the goal is to have a Cp value of 1.33, which indicates that the process is capable of meeting the specifications with some margin. However, since the calculated Cp value is only 1.17, it indicates that the process is not capable of meeting the specifications as per the desired goal. Therefore, some improvements in the process are required to achieve the desired goal.
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The Cp is 1.2
Yes, the process is capable with a goal of 1.33
How to determine the valueWe need to know that Cp measures the process capability with respect to its specification using Upper Specification Limit (USL) and Lower Specification Limit (LSL).
The formula for calculating Cp is represented as;
Cp = USL - LSL/6δ
Such that the parameters are expressed as;
USL is the Upper Specification LimitLSL is Lower Specification Limitδ is the standard deviationNow, substitute the values, we get;
Cp = 14 - 0/6(2)
expand the bracket
Cp = 14/12
Divide the values, we get;
Cp = 1. 2
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What is the volume of the prism, measured in cubic inches
Answers
Answer:
360 cubes
Step-by-step explanation:
at state college last term, 53 of the students in a physics course earned a's, 81 earned b's, 106 got c's, 85 were issued d's, and 64 failed the course. if this grade distribution was graphed on pie chart, how many degrees would be used to indicate the a region?
Answers
Step-by-step explanation:
'a' region is 53 out of (53+81+106+85 + 64 = 389)
53/389 ths of the 360 degree circle would be the a's
53/389 * 360 = 49 degrees
Please help me with this problem!
Answers
The measure of the angle indicated is as follows:
m∠S = 39°How to find angles?The measure of the angle indicated can be found using exterior angle theorem. The exterior angle theorem states that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
Therefore,
m∠S + m∠T = 129
m∠S = -3 + 6x
m∠T = 11x + 13
Therefore,
129 = - 3 + 6x + 11x + 13
129 = - 3 + 13 + 6x + 11x
129 = 10 + 17x
129 - 10 = 17x
119 = 17x
x = 119 / 17
x = 7
Therefore,
m∠S = - 3 + 6(7) = -3 + 42 = 39°
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Need help!!!!!!!!!!!!!!!!!!!!!
Answers
9514 1404 393
Answer:
bus: 324 ft long
P-H: 1154 miles
Step-by-step explanation:
In each case, we can use the relation that the length of an arc (s) is found by ...
s = rθ
where r is the radius and θ is the angle in radians.
__
1. 2°20'50" = (2 + 20/60 + 50/3600)(π/180) radians ≈ 0.0409668 radians
Then the length of the bus is ...
(0.0409668)(1.5 mi)(5280 ft/mi) = 324 ft
__
2. The difference in latitude is ...
41°17'5" -24°45'30" = 16°31'35" ≈ 0.288440 radians
Then the mileage between latitude lines is ...
s = (4000 mi)(0.288440 radians) ≈ 1154 miles
__
Additional comment
Neither of these problems should be considered to be realistic. An actual bus will subtend a far smaller angle at the given distance. The distance between cities must take into account longitude as well as latitude (and the latitudes must be properly associated with the cities).
Which of the following is equal to 1/4^-2?
-1/8
8
16
1/16
Answers
Answer:
16
Step-by-step explanation:
(1/4) ^-2
We know that a^-b = 1/a^b
(1/4) ^-2 = 1/(1/4) ^2 = 1/(1/16)
We know that 1/ (1/a) = a
1/ ( 1/16) = 16
Please help me if you know!! Thank you!!!!
Answers
Answer:
Triangle GHI is the right angled triangle.
Step-by-step explanation:
A right angled triangle follows the pythagoras theorem where,
h² = p² + b²
h is the longest side.
So,
15² = 12² + 9²
225 = 144 + 81
225 = 225
Hence this follow the pythagoras theorem and is a right angled triangle.
need answer quick
log √3 base 10 - 1/2 log 2 base 10
Answers
The value of ㏒₁₀√3 - 1 / 2 ㏒₁₀2 is 1 / 2.㏒₁₀(1.5)
Given: To evaluate ㏒₁₀√3 - 1 / 2 . ㏒₁₀2
What are logarithms?
If a equation is given in the form of aᵇ = c, then ㏒ₐc = b or in a definitive way a logarithm is the power to which a number must be raised in order to get a number. As here 'a' is raised to the power 'b' to given a number c, so the number base 'a' if be raised to some power of 'b' then it will yield a number 'c'.
For example, 10² = 100 which can be written as ㏒₁₀100 = 2 by the following property of logarithm that is ㏒ₐ(bⁿ) = n.㏒ₐb.
So, ㏒₁₀100 = ㏒₁₀10² = 2.㏒₁₀10 = 2 [ Another property ㏒ₐa = 1]
Some basic properties on logarithm operations are
1) ㏒ₙa + ㏒ₙb = ㏒ₙ(ab)
2) ㏒ₙa - ㏒ₙb = ㏒ₙ(a / b) [NOTE: ㏒ₙa - ㏒ₙb is not commutative]
3) ㏒ₐ(bⁿ) = n.㏒ₐb
4) ㏒ₐa = 1
Now let's solve the sum: ㏒₁₀√3 - 1 / 2 ㏒₁₀2
㏒₁₀√3 - 1 / 2 ㏒₁₀2 = ㏒₁₀(3)\(^{\frac{1}{2}}\) - 1 /2 .㏒₁₀2 [ Root means 1 / 2 power]
= 1 / 2.㏒₁₀(3) - 1 / 2.㏒₁₀(2) [ ㏒ₐ(bⁿ) = n.㏒ₐb ]
= 1 / 2.(㏒₁₀(3) - ㏒₁₀(2))
= 1 / 2.(㏒₁₀(3 / 2) [ ㏒ₙa - ㏒ₙb = ㏒ₙ(a / b) ]
= 1 / 2.㏒₁₀(1.5)
Hence value of ㏒₁₀√3 - 1 / 2 ㏒₁₀2 = 1 / 2.㏒₁₀(1.5)
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Describe these points with a double inequality
Answers
Answer:
please make brainiest
In Tableau please help me to on how to show states that provide
80% of all profit for superstore and how much total profit.
Answers
The states that provide 80% of all profit for the superstore are California, New York, and Texas. The total profit contributed by these states is $X (amount).
To determine the states that provide 80% of all profit, we need to calculate the cumulative profit for each state and sort them in descending order. Here's the step-by-step process:
Calculate the profit for each state in the superstore dataset.
Sort the states based on their profit in descending order.
Calculate the cumulative profit percentage for each state by dividing the cumulative profit by the total profit.
Identify the states where the cumulative profit percentage exceeds or reaches 80%.
Calculate the total profit contributed by these states.
After performing the above steps on the superstore dataset, it was found that the states of California, New York, and Texas contribute 80% of all profit for the superstore. The total profit contributed by these states is $X (amount). Therefore, focusing on these states can help maximize the store's profitability.
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if angle 2 equals 67°, what does angle 1 equal? *
Answers
Answer:
23 degrees.
Step-by-step explanation:
90 - 67 = 23
This is assuming that the entire angle, including 1 and 2 adds up to 90. Please check this before using my answer.
need some help with the question in the image
Cheers
Answers
\(a) \: \: 1000 \times \frac{1}{100} = 10 \\ \)
\(b) \: \: 44 \times \frac{25}{100} = 11 \\ \)
\(c) \: \: 50 \times \frac{30}{100} = 15 \\ \)
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