This probability is approximately [tex]\frac{1}{e}[/tex], which is around 0.37, that we collect all n coupons in exactly n weeks.
The probability of collecting all n coupons in exactly n weeks is very low, as it is dependent on getting a unique coupon every week for n weeks. This is known as the "Coupon Collector's Problem".
The probability can be calculated using the formula:
[tex](1/n) * (1 - (1 - \frac{1}{n})^n)[/tex]This formula can be broken down as follows:
1/n represents the probability of getting the first unique coupon in the first week, it's 1/n because there are n different types of coupons and all of them are equally likely to be in a box.
[tex](1 - (1 - \frac{1}{n})^n)[/tex]represents the probability of getting the remaining n-1 unique coupons in the next n-1 weeks.[tex](1 - \frac{1}{n} )[/tex] represents the probability of not getting a unique coupon in any given week. And raising it to the power of n gives the probability of not getting a unique coupon in n weeks.So, by subtracting this probability of not getting a unique coupon in n weeks from 1, we get the probability of getting at least one unique coupon in n weeks.
Finally, by multiplying the probability of getting the first unique coupon [tex]\frac{1}{n}[/tex] with the probability of getting at least one unique coupon in the next n-1 weeks, we get the overall probability of collecting all n coupons in exactly n weeks.
Therefore, the probability is approximately [tex]\frac{1}{e}[/tex], which is around 0.37, this is a very low probability, and in practice it would take a much longer time to collect all n coupons.
For more such questions on probability
https://brainly.com/question/11034287
#SPJ4
what is the value of (x - y) (x - y) if xy = 3 and x2 y2 = 25?
The value of (x - y)(x - y), if xy = 3 and x² + y² = 25, is 19.
A binomial is an expression represented by the sum or a difference of two algebraic terms. Generally, we can express it as a+b. If we square this binomial, (a + b)², it can be expanded into a² + 2ab + b².
xy = 3
x² + y² = 25
Now, (x - y)(x - y) = x² + y² -xy -xy
(x - y)(x - y) = x² + y² -2xy
Now put the values of x² + y² and xy
(x - y)(x - y) = 25 - 2 × 3
(x - y)(x - y) = 25 - 6
(x - y)(x - y) = 19
To know more about binomial, here
https://brainly.com/question/13870395
#SPJ4
on a recent trip to the beach, jaya collected seashells. the lengths of the seashells were measured, in inches. the 5 number summary of seashell lengths are shown below min median max 2 3.5 5 6.2 7 a) % of the length of seashells collected by jaya were between 3.5 and 7 inches b) 25% of the length of seashells collected by jaya were between 2 and inches. c) % of the length of seashells collected by jaya were more than 5 inches. d)* the range of lengths of seashells collected by jaya was inches.
a) Not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches.
b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.
c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.
d) The range of lengths of seashells collected by Jaya was = 4.2 inches.
In statistics, the range is the difference between the highest and lowest values for a particular data collection.
For instance, if the provided data set is 2,5,8,10,3, the range is 10 - 2 = 8.
As a result, the range may alternatively be defined as the difference between the highest and lowest observations.
a) It is not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches based on the information provided.
b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.
c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.
d) The range of lengths of seashells collected by Jaya was 6.2 - 2 = 4.2 inches.
For more questions on Range of data
https://brainly.com/question/15953457
#SPJ4
BC is a radius of circle C and AB is tangent to circle C. Find the value of x
The length of the side AC of the right-angle triangle will be 117 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The tangent and radius of the circle intersect at the right angle. Then the value of 'x' is given as,
AC² = AB² + B²
x² = 45² + 108²
x² = 2025 + 11664
x² = 13689
x = 117 units
The length of the side AC of the right-angle triangle will be 117 units.
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
#SPJ1
find the coordinates of the intersecrion of the diagnonals of abcd with vertices A (-4,9), B (3,9), C(2,3), D(-5,3)
Answer:
Step-by-step explanation:
The diagonals of a quadrilateral divide it into two congruent triangles. In this case, the diagonals of quadrilateral ABCD with vertices A (-4,9), B (3,9), C(2,3), D(-5,3) are AC and BD.
To find the intersection point of the two diagonals, we can use the equations of the two lines.
The equation of line AC can be represented as y = mx + b, where m is the slope of the line and b is the y-intercept.
m = (y2-y1)/(x2-x1)
m = (3-9)/(2-(-4)) = -6/6 = -1
b = y1 - mx1
b = 9 - (-1)(-4) = 9+4 = 13
The equation of the line is y = -x + 13
Similarly, the equation of line BD can be represented as y = nx + c, where n is the slope of the line and c is the y-intercept.
n = (y4-y3)/(x4-x3) = (3-9)/(-5-3) = -6/8 = -3/4
c = y3 - nx3
c = 3 - (-3/4)(-5) = 3 + 15/4 = 27/4
The equation of the line is y = -3/4 x + 27/4
Now we can find the point of intersection (x,y) by solving the following system of equations
-x + 13 = -3/4 x + 27/4
Multiply the equation 1 by 4
-4x + 52 = -3x + 27
Add 3x to both sides
-x + 52 = 27
Subtract 27 from both sides
-x = -25
x = 25
Now we can substitute this value of x in any of the equation to find the value of y
y = -x + 13
y = -25 + 13
y = -12
So, the coordinates of the intersection of the diagonals of quadrilateral ABCD are (25,-12).
Please help I am not sure of the answer be exact with it
The system of equations that represents the given situation is:
q + d = 35
q*0.25 + d*0.10 = 4.90
How to write the system of equations?Here we want to write a system of equations that represents the given situation.
First, let's define the two variables:
q = number of quarters.
d = number of dimes.
There are 35 coins in total, so the first equation is:
q + d = 35
And the value of these coins is $4.90, then the second equation is:
q*0.25 + d*0.10 = 4.90
Then the system of equations is:
q + d = 35
q*0.25 + d*0.10 = 4.90
Learn more about systems of equations at
https://brainly.com/question/13729904
#SPJ1
Write the standard form of the equation of each line given the slope and
y-intercept.
9) Slope = 3, y-intercept = -9
10) Slope = -7, y-intercept = 10
12. Julie had $400 in her savings account at the beginning of the summer. Each week she took
$20 out of her account. Stephen had $100 in his account at the beginning of summer. Each
week he added $30 to his account. After how many weeks did Julie and Stephen have the same
amount in their accounts?
y=400-20x
y=100-30x
Use pascal's triangle to expand the binomial
(4x + 3y)³
Answer:
[tex]\boxed{x^4+4x^3y+6x^2y^2+4xy^3+y^4\\}[/tex]
Step-by-step explanation:
Pascal’s triangle defines the coefficients which appear in binomial expansions. That means the nth row of Pascal’s triangle comprises the coefficients of the expanded expression of the polynomial (a + b)ⁿ
To create Pascal's triangle for any n in (a + b)ⁿ ,
To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern.Here is Pascal's triangle for the first 5 rows. The first row is row 0
Row #
0 1
1 1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
[tex]\textrm{ Here row 0 represents $(a + b)^0$ }[/tex] = [tex]\boxed{\textbf{1}}[/tex]
[tex]\textrm{Row 1 corresponds to $(a + b)^1$} =[/tex] [tex]\boxed{1}\;a + \boxed{1}\;b[/tex]
[tex]\textrm{Row 2 corresponds to $(a + b)^2$} = \boxed{1}\;a^2 + \boxed{2} \;ab +\boxed{1}\;b^2[/tex]
[tex]\textrm{Row 3 corresponds to $(a + b)^3$} = \boxed{1}\;a^3 + \boxed{3}\;a^2b + \boxed{3}\;ab^2 + \boxed{1}\;b^3[/tex]
[tex]\textrm{Row 4 corresponds to $(a + b)^4$} = \boxed{1}\;b^4 + \boxed{4} \;a^3b +\boxed{6}\;a^2b^2 + \boxed{4} \;ab^3 + \boxed{1} \;b^4[/tex]
For the specific problem, (4x + 3y)³ use coefficients of row 3 and use 4x instead of a and 3y instead of b
[tex]\mbox{\normal(4x + 3y)^3= \boxed{1}\;(4x)^3 + \boxed{3}\;(4x)^2(3y) + \boxed{3}\;4x(3y)^2 + \boxed{1}\;(3y)^3}[/tex]
[tex]= \boxed{x^4+4x^3y+6x^2y^2+4xy^3+y^4\\} \;\;\; \textrm{ANSWER}[/tex]
Step-by-step explanation:
l don't know how to solve
it
consider the function f(x)={2xif x<2if x≥2 evaluate the definite integral ∫6−1f(x)dx
The value of the given integration is =25, where the function is defined.
Integrals are the values of the function that are discovered through the integration process. Integration is the process of obtaining f(x) from f'(x). When all the little data are combined, problems with displacement and motion, area and volume, and other issues develop. Integrals assign numbers to functions in a way that describes these issues. We can determine the function f given the derivative f' of the function f. Here, the function f is referred to as integral of f' or antiderivative of f.
if the function f(x) defined as
[tex]f(x)=\left \{ {2 \ if \ {x < 2} \atop {x\ if\ x\geq 2}} \right.[/tex]
then find out the-
[tex]\int_{-1}^{6}f(x) dx[/tex]
To find out the integral break it -1 to 2 and 2 to 6, where our function is defined as-
[tex]let\ I=\int_{-1}^{2}f(x)dx +\int_{2}^{6}f(x)dx\\\\I=\int_{-1}^{2}2dx+\int_{2}^{6}xdx\\\\=[2x]_{-1}^{2}+[x^2/2]_{2}^{6}\\\\= [4+1]+[18+2]=5+20\\=25 .[/tex]
Hence, the value of the given integration is =25, where the function is defined.
learn more about integration.
https://brainly.com/question/18125359
#SPJ4
help please i hate math
The measure of angle POQ is 118°.
What are triangles?Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Given ΔPQR
∠R = 62°
QS and PT are altitudes,
Take ΔQRS
∠R = 62°
∠QSR = 90°
so, ∠SQR + ∠QSR + ∠R = 180°
∠SQR = 180 - 90 - 62
∠SQR = 28°
Taking ΔPRT
∠R = 62°
∠PTR = 90°
so, ∠RPT + ∠PTR + ∠R = 180°
∠RPT = 180 - 90 - 62
∠RPT = 28°
now let ∠TPQ = x° and ∠SQP = y°
in ΔPQS,
∠SPQ = 28 + x
∠PQS = y°
∠QSP = 90°
∠QSP + ∠PQS + ∠SPQ = 180°
90 + y + 28 + x = 180
x + y = 180 - 90 - 28
x + y = 62°
now in ΔPOQ
∠OPQ = x°, ∠OQP = y°
∠POQ + ∠OPQ + ∠OQP = 180°
∠POQ + x + y = 180
sunstitute value of x + y = 62°
∠POQ = 180 - 62
∠POQ = 118°
Hence the value of angle POQ is 118°.
Learn more about triangles;
https://brainly.com/question/2773823
#SPJ1
Consider the following liquids: d = 0.8146 g/mL 1-pentanol Isopropyl alcohol d=0.7851 g/mL 2-pentanol Hexane You have two unknown samples, each known to be one of the above liquids. a. In determining the density of the first unknown, you weighed a 5.00 mL sample of the d 0.8098 g/mL d 0.660 g/mL liquid, and found the mass to be 3.310 g. What is the identity of the unknown? Explain. b. For the second unknown, a 5.00 mL sample weighed 4.061 g. Based on this data, what can you conclude about the identity of unknown number two? Explain. 3. A perfect cube of jade has a mass of 15.00 g. If jade's density is 3.25 g/ml, determine the edge length of the jade cube.
The identity of the unknown is hexane, the second unknown is isopropyl alcohol, and the edge length of the jade cube is approximately 1.87 cm.
a. To determine the identity of the first unknown, we can compare the calculated density with the known densities of the liquids. The calculated density can be found by dividing the mass of the sample (3.310 g) by its volume (5.00 mL), giving us a density of 0.6620 g/mL.
Since the calculated density (0.6620 g/mL) is closest to the density of hexane (0.7851 g/mL), it is likely that the first unknown is hexane.
b. To determine the identity of the second unknown, we can use the same approach as in part a. By dividing the mass of the sample (4.061 g) by its volume (5.00 mL), we find the calculated density to be 0.8122 g/mL.
This density is closest to the density of isopropyl alcohol (0.7851 g/mL), so it is likely that the second unknown is isopropyl alcohol.
c. To find the edge length of the jade cube, we can use the formula for the volume of a cube: V = l^3. We know the mass of the cube (15.00 g) and its density (3.25 g/mL), so we can find its volume by dividing the mass by the density:
V = m/d = 15.00 g / 3.25 g/mL = 4.62 mL = 4.62 cm^3
Since the volume is equal to the edge length cubed, we can find the edge length by taking the cube root of the volume:
l = cuberoot(V) = cuberoot(4.62 cm^3) = approximately 1.87 cm.
To know more about volume, here
https://brainly.com/question/28058531
#SPJ4
bilal's fishing line was on a spool with a radius of 4 cm 4 cm4, start text, space, c, m, end text. suddenly, a fish pulled on the line, and the spool spun 16 1616 times before bilal began to reel in the fish. what is the distance the fish pulled the fishing line?
The fish pulled the fishing line at a distance of 402.92 cm ≈ 402 cm.
We can use the formula for the circumference of a circle to find the distance the fishing line was pulled:
C = 2πr
Where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius of the spool.
The circumference of the spool is:
C = 2 × 3.14 × 4 = 25.12 cm
So, the distance the fishing line was pulled is:
25.12 × 16 = 402.92 cm
So, the fish pulled the fishing line at a distance of 402.92 cm ≈ 402 cm.
To know more about circumference of a circle, here
https://brainly.com/question/15334188
#SPJ4
--The given question is incorrect; the correct question is
"Bilal's fishing line was on a spool with a radius of 4cm. Suddenly, a fish pulled on the line, and the spool spun 16 times before Bilal began to reel in the fish. What is the distance the fish pulled the fishing line?"--
Question in picture. Pls answer soon 30 points!
Answer: 25.13cm
Step-by-step explanation:
Answer:
31.4 cm
Step-by-step explanation:
C=2πr
Plug in numbers: C= 2 * 3.14 * 5
Consider the linear system:x + y - z = 2x + 2y + z = 3x + y + (k^2-5)z = kwhere k is an arbitrary constant. For which value(s) of k does this system have a unique solution? For which value(s) of k does the system have infinitely many solutions? For which value(s) of k is the system inconsistent?This question is from Linear Algebra with Applications Fourth Edition Author Otto Bretscher Page 6 #26. This is something we have not gone over in class yet. I'm not sure where to even start! Should I just pick any constant for k? Please work out all steps.
The system will have solution when an arbitrary constant have infinitely many solutions when a-2b+c =0
What is Linera Alegebra?
The study of the planes and lines, vector spaces, and mappings needed for linear transforms is known as linear algebra. It was first defined in the 1800s to help solve systems of linear equations and is a relatively new subject of research.
Given,
x + y - z = 2x + 2y + z = 3x + y + (k^2-5)z
[tex]\left[\begin{array}{ccc}1&1&-1\\1&2&1\\1&1&R^{2}-5 \end{array}\right] \left[\begin{array}{ccc}2\\3\\R\end{array}\right] = (A:B)[/tex]
Apply [tex]R_{2}[/tex] ⇒ R2 -R1, R3⇒R3-R1
[tex]\left[\begin{array}{ccc}1&1&-1\\0&1&2\\0&0&R^{2}-4 \end{array}\right]\left[\begin{array}{ccc}2\\1\\R-2\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}1&1&-1\\0&1&2\\0&0&(K-2)(R+2)\end{array}\right] \left[\begin{array}{ccc}2\\1\\R-2\end{array}\right][/tex]
(1) For K = -2 the system has no solution as we get
[tex]\left[\begin{array}{ccc}1&1&-1\\0&1&2\\0&0&0\end{array}\right] \left[\begin{array}{ccc}2\\1\\-4\end{array}\right][/tex]
(2)For k =2 the system has infinite solution as we get
[tex]\left[\begin{array}{ccc}1&1&-1\\0&1&2\\-0&0&0\end{array}\right] \left[\begin{array}{ccc}2\\1\\0\end{array}\right][/tex]
(3) for K ∈ R, R∉ (-2,2) Here the system will have unique solution as doe above here we have
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}A\\B\\C\end{array}\right][/tex]
Apply R2 = R2- 4R1
R3 = R3 -7R1
R1 To get
[tex]\left[\begin{array}{ccc}1&2&3\\0&-3&-6\\0&-6&-12\end{array}\right] \left[\begin{array}{ccc}A\\B-4A\\C-7A\end{array}\right][/tex]
Apply R2= R2 /3 To get
[tex]\left[\begin{array}{ccc}1&2&3\\0&1&2\\0&-6&-12\end{array}\right] \left[\begin{array}{ccc}A\\4A-B/3\\C-7A\end{array}\right][/tex]
Apply R1 = R1 - 2(R2)
[tex]\left[\begin{array}{ccc}1&0&-1\\0&1&2\\0&0&0\end{array}\right] \left[\begin{array}{ccc}-5A+2B/3\\4A-B/3\\A-2B+C\end{array}\right][/tex]
The system will have solution when an arbitrary constant have infinitely many solutions when a-2b+c =0
To learn more about Linear Equation visit:
brainly.com/question/29739212
#SPJ4
BF is a median of △BEC . If EC = 15, find FC
The required measure of the segment CF in the given triangle is 7.5 units.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.
Here,
The median of the triangle is the line joining the midpoint of the side to the opposite vertex, so if f is the midpoint then,
CF = EC/2
CF = 15 / 2
CF = 7.5 units
Thus, the required measure of the segment CF in the given triangle is 7.5 units.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
This table shows the low and high temperatures in four different regions in a state.
Answer:
The answer is the east region
suppose there are ten five- and six-year-olds attending a birthday party. when a 30-year-old mother walks into the room with an infant in her arms, what happens to the standard deviation of ages in the room? (changes or stays approximately the same) changes what happens to the median of ages in the room? (gets bigger; gets smaller; stays approximately the same
The standard deviation of ages in the room increases, while the median of ages stays approximately the same.
Standard deviation is a measure of the variability of a set of data points. The addition of a 30-year-old mother and an infant to the group of ten five- and six-year-olds increases the spread of the ages, thus increasing the standard deviation.
The median, on the other hand, is the middle value in a set of data points. Since the median only depends on the order of the values, not their magnitude, adding a mother and an infant to the group of children does not significantly affect the median age in the room, which would still be close to 5 or 6 years old.
Learn more about standard deviation
brainly.com/question/20450242
#SPJ4
I NEED HELP ASAP!!!!
How many boxes would Alan have to sell to earn less than $2050?
Answer:
4357
Step-by-step explanation:
what region R in the xy-plane minimizes the value of ! r (x^2 y^2 − 9) dA ?
To minimize our double integral, we want to find the region over which the function we are integrating has negative values
x^2 +y^2 − 9</= 0
Solving the inequality
x^2 +y^2 </= 9
We can verify this solution by graphing. f(x,y) = x^2 +y^2 − 9
Our function is a paraboloid. Only the negative values of f(x, y) are graphed here.
We can see that f(x, y) is negative below the circle in the x-y plane given by the formula x^2 + y^2 <= 9. If we were to include any points outside of this region in our integral, we would add positive values of f(x, y) to our double integral and the integral wouldn't be minimized
therefore, R : x^2 +y^2 </= 9
Learn more about paraboloid here :
https://brainly.com/question/17018480
#SPJ4
Need help with 11th grade math
Answer:
[tex]\left(-\frac{3}{5},\frac{4}{5} \right)[/tex]
Step-by-step explanation:
We have to find [tex]n\in\mathbb{N}[/tex] such that [tex]\frac{1-n^2}{1+n^2} \neq 0[/tex] and [tex]\frac{2n}{1+n^2} \neq 0[/tex].
If we choose [tex]1\neq n\in\mathbb{N}[/tex] [tex]\left(\frac{1-n^2}{1+n^2},\frac{2n}{1+n^2} \right)[/tex] is a rational point not on the x-axis or y-axis but on the unit circle.
Let [tex]n=2[/tex]
[tex]\left(\frac{1-2^2}{1+2^2},\frac{2*2}{1+2^2} \right)[/tex]
[tex]\left(\frac{1-4}{1+4},\frac{4}{1+4} \right)[/tex]
[tex]\left(-\frac{3}{5},\frac{4}{5} \right)[/tex]
(2/5) and (1/2). What’s the constant of proportionality?
Answer:
4/5
Step-by-step explanation:
The constant of proportionality is the number that relates the two quantities in a proportion. In the proportion (2/5) and (1/2), the constant of proportionality is the same for both fractions. To find the constant of proportionality, you can divide the two fractions and compare the results.
For example:
(2/5) / (1/2) = (2/5) * (2/1) = 4/5
So the constant of proportionality is 4/5.
The col Villeda are buying a new car. The cash price is $35,000.00. They will make a down payment of 20% or 5,000. The balance will be covered an installment loan. The loan will be repaid in 48 monthly payment of $651. The annual percentage rate for loan is
The annual percentage rate, APR, for the loan is about 5.486%
What is an annual percentage rate?The annual percentage rate is the cost of a loan or interest on an investment per year during the loan term or period.
Price of the car = $35,000.00
The down payment = 20% of $35,000 = $7,000
The installment loan details include;
The number of installment = 48 monthly installment
The amount paid each month = $651
The total payment, A= 48 × 651 = 31248
The equal monthly installment (EMI) formula is presented as follows;
[tex]EMI = P\cdot \frac{r\cdot (1+r)^n}{(1+r)^n -1}[/tex]
Where;
EMI = The equal monthly installment paid = $651
P = The principal amount of the loan
r = The interest rate
n = Number of payments to be made = 48
The principal is therefore;
P = $35,000.00 - $7,000.00 = $28,000.00
Therefore;
The
[tex]651 = 28000\times \frac{r\cdot (1+r)^{48}}{(1+r)^{48} -1}[/tex]
Using an online calculator and by trial and error, or by graphing we get;
The Annual Percentage Rate, APR = 5.846%Learn more on installment payment on a loan here: https://brainly.com/question/29221275
#SPJ1
Solve the system of equation by substitution
2x -3y = -24
x + 6y = 18
*Pls use step by step explanation
Answer:
y = 4
x= -6
Step-by-step explanation:
Substitution; so pretty much finding one equation and substituting it into the second
Let's find the equation of the top one... we'll find X (you can find either x or y though)
2x - 3y = -24
We'll add 3y to both sides
2x = 3y - 24
Dividing by 2 on both sides
x = (3y-24)/2... Simplifying it to x = 1.5y - 12
Let's put it into x + 6y = 18. Since we found X
1.5y - 12 + 6y = 18
Let's add 12
1.5y + 6y = 30
Combining like terms
7.5y = 30
Lastly, we'll divide by 7.5
y = 4
So now that we finally found Y, we can use either equation to solve for X. I'll do both to show both equations end up with the same X
2x-3y =-24
2x-3(4)=-24
2x-12=-24
2x=-12
x=-6
---------
x+6y=18
x+6(4)=18
x+24=18
x=-6
do waiters or waitresses earn larger tips? to answer this question, a restaurant consultant undertook a preliminary study. the study involved measuring the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selected waitress from each of 50 restaurants during a 1-week period. what conclusions can be drawn from these data?
From these data, it is difficult to draw any meaningful conclusions about which waiters and waitresses earn larger tips.
The data only measure the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selected waitress from each of the 50 restaurants during a 1-week period, which does not provide a large enough sample size to draw any meaningful conclusions. In order to draw more reliable conclusions, a larger, more comprehensive study should be conducted that measures the tips for multiple waiters and waitresses from each restaurant over a longer period of time.
Learn more The data:
https://brainly.com/question/964590
#SPJ4
What is the missing number in the factor tree?
A) 9
B) 8
C) 5
D) 2
. in order to identify when the process is malfunctioning, how many items should be tested so that the probability that one or more items are found defective is at least 99%?
The number of items that should be tested so that the probability that one or more items are found defective is at least 99% is:
234 items.
To determine the number of items that need to be tested to have a 99% probability that one or more items are found defective, we need to use the binomial distribution and its cumulative distribution function (CDF).
The binomial distribution is used to model the number of successful outcomes in a fixed number of independent trials, where each trial has a probability of success p.
Let's assume that the probability of finding a defective item is p.
To find the minimum number of items that need to be tested, we need to solve the equation:
1 - (1 - p)^n >= 0.99Where n is the number of items tested and (1 - p)^n is the probability that none of the items are defective.
To solve this equation, we can use a numerical method or a spreadsheet software, or we can use an approximate formula:
n >= log(1 - 0.99) / log(1 - p)For a typical value of p = 0.01 (1% defect rate), the minimum number of items that need to be tested is approximately:
n >= log(0.01) / log(0.99) = log(0.01) / -0.01005033585350145n >= 233So, in this case, it would be advisable to test at least 234 items to have a 99% probability that one or more items are found defective.
Learn more about binomial distribution at: brainly.com/question/14565246
#SPJ4
How can you calculate the terms of pi if the total surface area of a solid cylinder of radius is 3 cm and height is 4 cm?
Answer:
yes. see below
Step-by-step explanation:
area of a cylinder = top circle + bottom circle + lateral
lateral = perimeter of the circle * height = 2π*4 * 10 =80π
area of a circle = πr² = 9π
top & bottom =18π
total = 80π+18π =98π
MODELING WITH MATHEMATICS You push your younger cousin on a tire swing one time and then allow your
cousin to swing freely. On the first swing, your cousin travels a distance of 14 feet. On each successive swing,
your cousin travels 75% of the distance of the previous swing. What is the total distance your cousin swings?
56 feet is the total distance your cousin swings. This can be solved by using the concept of explicit formula.
What is explicit formula?From the term of the series, it is simple to get the explicit formula for the arithmetic sequence. For the mathematical series a, a + d, a + 2d, a + 3d,.......a + (n - 1)d, and the nth component in the sequence provides the explicit formula. Consequently, a = a + (n - 1)d serves as the explicit formula for the arithmetic series.
Given that,
You push your younger cousin on a tire swing one time and then allow your cousin to swing freely. On the first swing, your cousin travels a distance of 14 feet.
So, a₁ = 14 feet
the second swing the person travels a distance that is 75% of the first, hence, a₂ = 0.75 a₁
On the third swing it is a₃ = 0.75 a₂
since, a₂ = 0.75 a₁ and a₃ = 0.75 a₂
Now, using explicit formula we find that,
a₂ = 0.75 a₁ = 14 × 0.75
a₃ = 0.75 a₂ = 0.75 × (14 × 0.75) = 14 × (0.75)²
a₄ = 0.75 a₃ = 0.75 × 14 × (0.75)³
Thus, the general formula becomes: a(n) = 14 × (0.75)ⁿ
Now use formula for the Sum of infinite geometric series to calculate the total distance: S = a₁ / (1 - r)
S = 14 / ( 1 - 0.75)
S = 14 / 0.25
S = 56 feet
56 feet is the total distance your cousin swings.
To know more about explicit formula refer to:
https://brainly.com/question/28354530
#SPJ1
determine if the equation is exact. if it is, then solve it. (3x^2y 3)dx (x^3-5)dy=0
Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1
for function
Φ(x) = x^m
then
dΦ/dx (x) = m*x^(m-1)
d²Φ/dx² (x) = m*(m-1)*x^(m-2)
then
for a expression
3x^2 (d^2y/dx^2) + 11x(dy/dx) - 3y = 0
3x^2*m*(m-1)*x^(m-2) + 11*x* m*x^(m-1) - 3*x^m = 0
3*m*(m-1)*x^m + 11*m*x^m- 3*x^m = 0
dividing by x^m
3*m*(m-1) + 11*m - 3 =0
3*m² + 8 m - 3 =0
m= [-8 ± √(64 + 4*3*3)]/2 = (-8±10)/2
m₁ = -9 , m₂= 1
then Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1
learn more about of equation here
https://brainly.com/question/14529768
#SPJ4
(a) A straight duct extends in the z direction for a length L and has a square cross section, bordered by the lines x = plusminus B and y = plusminus B. A colleague has told you that the velocity distribution is given by v_z = (P_0 - P_1)B^2/4 mu L [1 - (x/B)^2] [1 - (y/B)^2] (3B.3-1) Since this colleague has occasionally given you wrong advice in the past, you feel obliged to check the result. Does it satisfy the relevant boundary conditions and the relevant differential equation?
A straight duct extends in the z direction for a length L and has a square cross section, bordered by the lines x = plus minus B and y = plus minus B
z direction
f(x,y) = x² - y² subject to x² + y² = 1 g(x,y) = x² + y²- 1
δf(x,y)/ δx = 2*x δg(x,y)/ δx = 2*x
δf(x,y)/ δy = - 2*y δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ* δg(x,y)/ δx
2*x = λ*2*x
δf(x,y)/ δy = λ* δg(x,y)/ δy
- 2*y = λ*2*y
Then, solving
2*x = λ*2*x x = λ*x λ = 1
- 2*y = λ*2*y y = - 1
x² + y²- 1 = 0 x² + ( -1)² - 1 = 0 x = 0
Point P ( 0 ; -1 ) ; then at that point
f(x,y) = x² - y² f(x,y) = 0 - ( -1)² f(x,y) = - 1 minimum
b) f( x, y ) = 3*x + y g ( x , y ) = x² + y² = 10
δf(x,y)/ δx = 3 δg(x,y)/ δx = 2*x
δf(x,y)/ δy = 1 δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ * δg(x,y)/ δx ⇒ 3 = 2* λ *x (1)
δf(x,y)/ δy = λ * δg(x,y)/ δy ⇒ 1 = 2*λ * y (2)
learn more about of direction here
https://brainly.com/question/24188659
#SPJ4
