There are k types of coupons. independently of the types of previously collected coupons, each new coupon collected is of type i with probability pi, ki =1 pi = 1. if n coupons are collected, find the expected number of distinct types that appear in this set. (that is, find the expected number of types of coupons that appear at least once in the set of n coupons.)
Answers
Let X be the expected number of distinct types of coupons in the collection of k coupons X = X1 + X2 + ……. + Xx.
Related Questions
the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds, find the frequency when the tension is 72 pounds.
Answers
[tex]\bf f=k\sqrt{t}\quad \textit{we also know that } \begin{cases} f=300\\ t=8 \end{cases}\implies 300=k\sqrt{8} \\\\\\ \cfrac{300}{\sqrt{8}}=k\implies \cfrac{300}{\sqrt{2^2\cdot 2}}=k\implies \cfrac{300}{2\sqrt{2}}=k\implies \cfrac{150}{\sqrt{2}}=k \\\\\\ \textit{and we can \underline{rationalize} it to }\cfrac{150\sqrt{2}}{2}\implies 75\sqrt{2}=k[/tex]
[tex]\bf thus\qquad f=\stackrel{k}{75\sqrt{2}}\sqrt{t}\implies \boxed{f=75\sqrt{2t}}\\\\ -------------------------------\\\\ \textit{now, when t = 72, what is \underline{f}?}\qquad f=75\sqrt{2(72)}[/tex]
Answer:
when the tension is 72 pounds , the frequency is 900 hertz
Step-by-step explanation:
Hello, I think I can help you with this.
you can easily solve this by using a rule of three.
According to the question data:
the pitch, or frequency, of a vibrating string varies directly with the square root of the tension.in mathematical terms it is:
f ∝ √T
where f is the pitch or frequency and T is the tension
Step 1
if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds
300 hertz ∝ √8 pounds
300⇔√8
what is the frequency when the tension is 72 pounds
x⇔√72
Step 2
Let
300⇔√8
x⇔√72
the relation is
[tex]\frac{300}{\sqrt{8} } =\frac{x}{\sqrt{72} }\\\\ Now, solve\ for\ x\\\\\\\frac{300*\sqrt{72} }{\sqrt{8} } =x\\x=\frac{300*\sqrt{72} }{\sqrt{8} } \\x=\frac{300*\sqrt{8*9}}{\sqrt{8}} \\x=\frac{300*\sqrt{8}*\sqrt{9}}{\sqrt{8}} \\x=300*\sqrt{9}\\x=300*3\\x=900[/tex]
when the tension is 72 pounds , the frequency is 900 hertz
have a good day.
Farmer Jack needs 1,800 square feet of garden space to have enough corn for a year. His garden space is currently 10 5⁄6 feet by 18 feet. How much more land does farmer Jack need to plant the rest of his corn?
Answers
Farmer Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.
Explanation:To find out how much more land Farmer Jack needs to plant the rest of his corn, we need to calculate the area of his current garden and subtract it from the required area of 1,800 square feet. Farmer Jack's garden is 10 5/6 feet by 18 feet, so we can multiply these two dimensions to get the area of his current garden. Then, we subtract this area from 1,800 to find out how much more land he needs:
Area of Farmer Jack's garden: 10 5/6 feet * 18 feet = 197 1/3 square feet
More land needed by Farmer Jack: 1,800 square feet - 197 1/3 square feet = 1,602 2/3 square feet
Farm Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.
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The width of a rectangle is 3 4 the length. The perimeter is 252 cm. What is the width of the rectangle? A) 36 cm B) 48 cm C) 54 cm D) 72 cm
Answers
the perimeter is P = 252 cm = 2(W) + 2L = 2(3/4)L + 2L, in terms of L only.
Then (6/4)L + 2L = 252 cm. Clear out the fraction by mult. all terms by 4:
6L + 8L = 252 cm, or 14L = 252 cm. Solving for L, L = 252 cm / 14 = 18
The length, L, is 18, and the width, W, is (3/4)(18 cm) = 13.5 cm (answer)
Find tanθ exactly if sinθ=-9/41, and θ is in the fourth quadrant
Answers
now, we know the angle is in the IV quadrant, therefore the opposite side or "y" is negative, thus
[tex]\bf sin(\theta )=-\cfrac{9}{41}\implies sin(\theta )=\cfrac{\stackrel{opposite}{-9}}{\stackrel{hypotenuse}{41}} \\\\\\ \textit{so, now let's find the \underline{adjacent side} then} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\bf \pm\sqrt{41^2-(-9)^2}=a\implies \pm\sqrt{1600}=a\implies \pm 40=a \\\\\\ \stackrel{\textit{in the IV quadrant}}{+40=a}\\\\ -------------------------------\\\\ tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan(\theta)=\cfrac{-9}{40}[/tex]
Find the radius of convergence of the power series \sum_{n=1}^\infty \frac{x^n}{\root 9 \of n}
Answers
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{\sqrt[9]{n+1}}}{\frac{x^n}{\sqrt[9]n}}\right|<1[/tex]
We have
[tex]\displaystyle|x|\lim_{n\to\infty}\frac{\sqrt[9]n}{\sqrt[9]{n+1}}=|x|\sqrt[9]{\lim_{n\to\infty}\frac n{n+1}}=|x|<1[/tex]
which means the radius of convergence for this power series is 1.
choose the equation below that represent the line that passes through the point (7,-2) and has a slope of -3
Answers
y+2=-3x+21
y= -3x+19
Let f(X)=1/x+1
Use the limit definition of the derivative to find:
i) f(-4)
ii) f(-3)
iii) f(1)
iv) f(3)
Answers
[tex]\bf \cfrac{\frac{-h}{x^2+xh+2x+h+1}}{h}\implies \cfrac{-h}{x^2+xh+2x+h+1}\cdot \cfrac{1}{h} \\\\\\ \lim\limits_{h\to 0}~\cfrac{-1}{x^2+xh+2x+h+1}\implies \cfrac{-1}{x^2+x(0)+2x+0+1} \\\\\\ \lim\limits_{h\to 0}~\cfrac{-1}{x^2+2x+1}[/tex]
The local home improvement store wants to increase their inventory. Last year 40 lawn mowers cost them $4,776.
At the same cost, how much would 120 lawn mowers cost them this year?
Answers
Then cross-multiply to get 40x = 120(4776) or 40x = 573120. Now divide each side by 40 to isolate the variable.
X = 14328.
120 lawn mowers would cost $14,328.
Answer:14,328
Step-by-step explanation:
The price of a technology stock has risen to $9.73 today. Yesterday's price was $9.60 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
Write 7.085 × 10-14 as an ordinary number
Answers
To convert [tex]7.085 * 10^-{14}[/tex] to an ordinary number, move the decimal point 14 places to the left, resulting in 0.00000000000007085.
Explanation:To write [tex]7.085 * 10^-{14}[/tex] as an ordinary number, you need to move the decimal point 14 places to the left because the exponent is negative. This means the number is very small. The process is similar to changing other numbers from scientific to standard notation, for example, changing [tex]7.5 x 10^{-3}[/tex] to 0.0075 by moving the decimal point three places to the left.
For [tex]7.085 * 10^-{14}[/tex], you will end up with 0.00000000000007085. The number has thirteen zeros after the decimal point and before the 7085 because we move the decimal 14 places.
Use this equation to find dy/dx. 9y cos(x) = x2 + y2
Answers
9y×-sin(x) + cos(x) 9dy/dx
differentiate RHS
2x+2ydy/dx
equate LHS - RHS
-9ysin(x) +9cos(x)|dy/dx = 2x + 2y|dy/dx
9cos(x)dy/dx - 2ydy/dx = 2x + 9ysin(x)
(9cos(x) -2y) |dy/dx = 2x+9ysin(x)
dy/dx = (2x+9ysin(x) ) / (9cos(x) -2y)
Final answer:
The derivative dy/dx for the equation 9y cos(x) = x² + y² is found by applying implicit differentiation. Rearranging terms after differentiation, dy/dx is obtained as the fraction (9y sin(x) + 2x) / (9 cos(x) - 2y).
Explanation:
The question asks for the derivative of dy/dx using the equation 9y cos(x) = x2 + y2. To find dy/dx, we can apply implicit differentiation, which implies taking the derivative of both sides with respect to x while treating y as a function of x (y(x)).
Let's differentiate both sides:
The left side: d/dx [9y cos(x)] = d/dx [9y] cos(x) + 9y d/dx[cos(x)] = 9(dy/dx) cos(x) - 9y sin(x)
The right side: d/dx [x2 + y2] = 2x + 2y(dy/dx)
Equating both the derivatives, we have:
9(dy/dx) cos(x) - 9y sin(x) = 2x + 2y(dy/dx)
Now, solving for dy/dx gives us:
dy/dx = (9y sin(x) + 2x) / (9 cos(x) - 2y)
"suppose we are comparing the implementations of algorithm a and algorithm b on the same machine. for inputs of size n, algorithm a runs in 2n steps, and algorithm b runs in 5√n steps. for which values of n does algorithm a beat algorithm b?"
Answers
The solution is : n = 9
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Explanation:
To find the answer we need to check at what point the running time of algorithm A is equal the running time of B:
1000*n*n = n*n*n*n*n
1000 = n*n*n = n^3
n = ∛(1000) = 10 (when n equals ten A equal B)
For any integer greater than ten B > A and for any integer smaller than ten B < A.
The greatest integer for which B < A is nine, therefore nine is our answer.
A B
1000n^2 n^5
n = 8 64000 < 32768
n = 9 81000 < 59049
n = 10 100000 = 100000
n = 11 121000 > 161051
n = 12 144000 > 248832
therefore nine is our answer.
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For [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex], Algorithm A (which runs in [tex]\( 2n \)[/tex] steps) beats Algorithm B (which runs in [tex]\( 5\sqrt{n} \)[/tex] steps).
To determine for which values of [tex]\( n \)[/tex] Algorithm A beats Algorithm B in terms of running time, we compare their complexities:
Algorithm A runs in [tex]\( 2n \)[/tex] steps.
Algorithm B runs in [tex]\( 5\sqrt{n} \)[/tex] steps.
Algorithm A beats Algorithm B if [tex]\( 2n < 5\sqrt{n} \)[/tex].
Let's solve this inequality step by step:
1. Square both sides to eliminate the square root (valid since [tex]\( n \geq 0 \)[/tex]):
[tex]\[ (2n)^2 < (5\sqrt{n})^2 \][/tex]
[tex]\[ 4n^2 < 25n \][/tex]
2. Bring all terms to one side to form a quadratic inequality:
[tex]\[ 4n^2 - 25n < 0 \][/tex]
3. Factorize the quadratic inequality if possible:
[tex]\[ n(4n - 25) < 0 \][/tex]
4. Find the values of [tex]\( n \)[/tex] that satisfy the inequality:
[tex]\( n(4n - 25) < 0 \)[/tex] holds when one factor is negative, and the other is positive:
[tex]\( n < 0 \)[/tex] and [tex]\( 4n - 25 > 0 \)[/tex]: No valid solutions since [tex]\( n \geq 0 \)[/tex].
[tex]\( n > 0 \)[/tex] and [tex]\( 4n - 25 < 0 \)[/tex]:
[tex]\[ 4n < 25 \Rightarrow n < \frac{25}{4} = 6.25 \][/tex]
[tex]\( n < 0 \) and \( 4n - 25 < 0 \)[/tex]: All [tex]\( n \geq 0 \)[/tex] satisfy this condition.
5. Determine the integer values of [tex]\( n \)[/tex]:
Since [tex]\( n \)[/tex] must be non-negative, the integer values of [tex]\( n \)[/tex] that satisfy [tex]\( 4n^2 - 25n < 0 \)[/tex] are [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex].
Brianna built a rectangular flower garden. The garden is 10 feet long and 8 feet wide. What is the area of Briannas flower garden?.
Answers
10 × 8 = 80
Explain why you think slope-intercept form makes sense as a name for y = mx +
b. explain why you think point-slope form make sense as a name for y - y1 = m(x - x1)
Answers
The slope-intercept form y = mx + b shows how the slope and y-intercept values are used in the equation, while the point-slope form y - y₁ = m(x - x₁) defines a line using a point and the slope.
Explanation:The slope-intercept form, y = mx + b, makes sense as a name because it explicitly shows how the slope and y-intercept values are used in the equation.
The 'm' represents the slope, which describes the steepness of the line, and the 'b' represents the y-intercept, which indicates where the line intersects the y-axis.
For example, in the equation y = 2x + 3, the slope is 2 and the y-intercept is 3.
The point-slope form, y - y₁ = m(x - x₁), is called so because it defines a line using a single point (x₁, y₁) and the slope 'm'. This form makes it easier to determine the equation of a line when given a point and the slope.
For instance, in the equation y - 2 = -3(x - 4), the point (4, 2) and the slope -3 are used to specify the line equation.
Name the property of equality that justifies: If x = 3 and y = x + 5, then y = 8
Answers
Hope this helps!
Solve the quadratic equation of 2x^2-5x+1=0
Answers
[tex]x = (5 + \sqrt{17} ) \div 4[/tex]
OR
[tex]x = (5 - \sqrt{17} ) \div 4[/tex]
If a drug has a concentration of 350 mg per 10 mL, how many milliliters are needed to deliver 2 grams of the drug? Express your answer rounded to the nearest milliliter.
Answers
To deliver 2 grams of a drug with a concentration of 350 mg per 10 mL, convert 2 grams to milligrams (2000 mg), and then divide this value by the concentration in mg/mL (350 mg/10 mL) to find the volume in milliliters. After calculation, this results in approximately 6 milliliters, when rounded to the nearest milliliter.
Explanation:To calculate how many milliliters are needed to deliver 2 grams of the drug when the concentration is 350 mg per 10 mL, we start with the conversion of grams to milligrams since the concentration is provided in milligrams. Remember, 1 gram equals 1000 milligrams:
Convert 2 grams to milligrams: 2 grams × 1000 = 2000 mg.Determine how many milliliters provide 350 mg: 10 mL corresponds to 350 mg.Calculate the proportion: (2000 mg) / (350 mg/mL) = Number of milliliters needed.Perform the calculation: 2000 / 350 = 5.71428571 mL.Round to the nearest milliliter: Approximately 6 mL.Therefore, approximately 6 milliliters of the drug are needed to deliver a dose of 2 grams.
Z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s , ∂z ∂t , ∂z ∂u when s = 1, t = 4, u = 5
Answers
[tex]y(1,4,5)=100[/tex]
[tex]z_s=z_xx_s+z_yy_s=(4x^3+2xy)(1)+x^2(tu^2)[/tex]
[tex]z_s(1,4,5)=1,024,000[/tex]
[tex]z_t=z_xx_t+z_yy_t=(4x^3+2xy)(2)+x^2(su^2)[/tex]
[tex]z_t(1,4,5)=1,331,200[/tex]
[tex]z_u=z_xx_u+z_yy_u=(4x^3+2xy)(-1)+x^2(2st)[/tex]
[tex]z_u(1,4,5)=-450,560[/tex]
Latrell bought 4 bags of powdered sugar. He got a total of 5 1/2 cups of sugar. How many cups of sugar were in each bag?
Answers
[tex]\bf \stackrel{mixed}{5}\frac{1}{2}\implies \cfrac{5\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{11}{2}}\\\\ -------------------------------\\\\ \cfrac{\quad\frac{11}{2} \quad }{4}\implies \cfrac{\quad\frac{11}{2} \quad }{\frac{4}{1}}\implies \cfrac{11}{2}\cdot \cfrac{1}{4}\implies \cfrac{11}{8}\implies \stackrel{cups}{1\frac{3}{8} }[/tex]
Each bag contained 1.375 cups of sugar.
To find out how many cups of sugar were in each bag that Latrell bought, we need to divide the total amount of sugar by the number of bags. Latrell has a total of 5 1/2 cups of sugar, which is the same as 5.5 cups when converted to a decimal. He bought 4 bags of sugar. Therefore, the calculation we need to perform is:
5.5 cups / 4 bags = 1.375 cups per bag
So, each bag contained 1.375 cups of sugar.
A cube has an edge if 4 feet. The edge is increasing at a rate of 2 feet per minute. Express the volume of the cube as a function
Answers
so 16^3=4096
To find the volume of a cube with an edge length that is increasing with time, express the edge length as a function of time and substitute this into the volume formula. In the given problem, the edge length is increasing 2 feet per minute, thus the volume V of the cube at any given time can be expressed as V = (4 + 2t)³.
Explanation:The volume of a cube is calculated by raising the edge length to the power of three (V = e³). For this problem, we know that the edge e is increasing at a rate of 2 feet per minute. Therefore, we can express e as a function of time t, where e = 4 + 2t. Substituting this back into our volume equation, we receive the volume V of the cube as a function of time t: V = (4 + 2t)³.
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how do you solve 3 - 1 3/4
Answers
To make this "easier" for you to solve
You can solve the "mixed fraction" (1 3/4)
So, 1 3/4 = 7/4 (or you can say 3/4)
Our problem becomes: 3 - 3/4
Now, 3 - 3/4 = 9/4
Answer: 9/4
Good luck on your assignment and enjoy your day
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PLEASE ANSWER
Solve the Equation
-2=3x/5+1
Answers
-2 - 1 = 3x/5
-3 = 3x/5
-3 * 5 = 3x
-15 = 3x
x = -15/3
x = -5
the letters that spell WAIKIKI are each written on separate tiles laying face down on a table. A tile is selected at random, the letter is recorded, and then the letter is placed face down on the table. Then the process repeats. What is the theoretical probability of choosing a tile with the letter A?
A. 1/7
B. 1/4
C. 2/7
D. 3/7
Answers
Answer:
the Answer is. A 1/7
Step-by-step explanation:
i did the test
Effie's store has 10,908 more comic book than Brody's. Brody's store has 45,607 coming books. How many books do Effie's and Brody's store have together?
Show your work...
Answers
Mr. River's car averages 25 3/4 miles per gallon. Express the miles per gallon as a decimal
Answers
10 POINTS!!! I WILL GIVE BRAINLIEST!
Bens barbeque charges a setup fee to $52 for catering a barbeque party plus an additional $6.25 per person. Robert is planning to hire Ben's barbeque to cater a picnic. Robert has no more than $175 to spend on the picnic. What is the greatest number of people who can attend the picnic? (*WRITE AND SOLVE AN INEQUALITY TO SOLVE THIS PROBLEM*)
Answers
123/6.25=19.68
you can't have 19.68 people, so the max amount of people that could attend would be 18. Hope it helped:)
two hundred eighty-four thousand, one hundred eighty-seven in expanded form
Answers
It is 200000+ 80000 + 4000 + 100 + 80 + 7.
Hope This Helps You!
Good Luck :)
- Hannah ❤
Find a formula for the function whose graph is given below.
Answers
^^^^^^^^^^^^^^^^
The equation of parabola is y = ( x - 2 )² + 3
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k - p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
The vertex of the parabola is given as A ( 2 , 3 )
Now ,
The equation of parabola is given by
y = a ( x - h )² + k
where the vertex of the parabola is A ( h , k )
a = 1
So , substituting the values of vertex in the equation of parabola , we get
y = ( x - 2 )² + 3
Hence , the equation of parabola is y = ( x - 2 )² + 3
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A picture has a width that is 17 inches shorter than the length, and its total area is 480 square inches. Find the dimensions of the picture.
Answers
Final answer:
To find the dimensions of the picture, set up an equation using the length and width. Solve the equation to find the dimensions: length = 32 inches, width = 15 inches.
Explanation:
To find the dimensions of the picture, let's assume the length is x inches. According to the problem, the width is 17 inches shorter than the length, so the width would be (x - 17) inches. The total area of the picture is given as 480 square inches. We can set up an equation using the length and width: x(x - 17) = 480. Solve this quadratic equation to find the dimensions of the picture.
Expanding the equation, we get x^2 - 17x - 480 = 0. Factoring the quadratic equation, we find (x + 15)(x - 32) = 0. Therefore, the possible values for x are -15 and 32. Since the length cannot be negative, we discard -15. Thus, the length of the picture is 32 inches and the width is (32 - 17) = 15 inches.
Final answer:
The dimensions of the picture are 32 inches in length and 15 inches in width.
Explanation:
To find the dimensions of the picture, we need to establish equations based on the information provided. Let the length of the picture be L inches and the width be W inches.
Given that:
The width is 17 inches shorter than the length: W = L - 17.The total area of the picture is 480 square inches: L × W = 480.Plug the width expression from step 1 into the area equation from step 2 to form a quadratic equation:
L(L - 17) = 480
Solving this quadratic equation will give us the value of L. Once we have L, we can use the first equation to get W. Let's solve the quadratic equation:
L² - 17L - 480 = 0
Factoring the quadratic, we find that (L - 32)(L + 15) = 0. So L can be either 32 or -15. Since a length cannot be negative, L must be 32 inches, and W, therefore, is 32 - 17 = 15 inches.
The dimensions of the picture are therefore 32 inches by 15 inches.
What is the concentration of nitrate ions in a 0.125 M Mg(NO3)2 solution
Answers
Mg(NO₃)₂ --> Mg²⁺ + 2NO₃⁻
Each mole of the Mg(NO₃)₂ will dissociate into 2 moles of NO₃⁻. Thus, to determine the concentration of the nitrate ions, we multiply the given value of two.
M = (0.125M)(2) = 0.250M
ANSWER: 0.250 M
We have that the concentration of the nitrate ions is mathematically given as
M= 0.250M
The concentration of the nitrate ionsQuestion Parameters:
Generally the equation for the Reaction is mathematically given as
Mg(NO₃)₂ --> Mg²⁺ + 2NO₃⁻
Each mole of the Mg(NO₃)₂ will dissociate into 2 moles of NO₃⁻.
the concentration of the nitrate ions is
M = (0.125M)(2)
M= 0.250M
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