A
(a) You're looking for
[tex]P(X\le 8) = \displaystyle \sum_{x=0}^8 P(X=x)[/tex]
where
[tex]P(X=x) = \begin{cases}\dfrac{\lambda^x e^{-\lambda}}{x!}&\text{if }x\in\{0,1,2,\ldots\}\\0&\text{otherwise}\end{cases}[/tex]
Customers arrive at a mean rate of 6 customers per 10 minutes, or equivalently 12 customers per 20 minutes, so
[tex]\lambda = \dfrac{12\,\rm customers}{20\,\rm min}\times(20\,\mathrm{min}) = 12\,\mathrm{customers}[/tex]
Then
[tex]\displaystyle P(X\le 8) = \sum_{x=0}^8 \frac{12^x e^{-12}}{x!} \approx \boxed{0.155}[/tex]
(b) Now you want
[tex]P(X\ge4) = 1 - P(X<4) = 1 - \displaystyle\sum_{x=0}^3 P(X=x)[/tex]
This time, we have
[tex]\lambda = \dfrac{6\,\rm customers}{10\,\rm min}\times(10\,\mathrm{min}) = 6\,\mathrm{customers}[/tex]
so that
[tex]P(X\ge4) = 1 - \displaystyle \sum_{x=0}^3 \frac{6^x e^{-6}}{x!} \approx \boxed{0.849}[/tex]
B
(a) In other words, you're asked to find the probability that more than 1 customer shows up in the same minute, or
[tex]P(X > 1) = 1 - P(X \le 1) = 1 - P(X=0) - P(X=1)[/tex]
with
[tex]\lambda = \dfrac{6\,\rm customers}{6\,\rm min}\times(1\,\mathrm{min}) = 1\,\mathrm{customer}[/tex]
So we have
[tex]P(X > 1) = 1 - \dfrac{1^0 e^{-1}}{0!} - \dfrac{1^1 e^{-1}}{1!} \approx \boxed{0.264}[/tex]
C
(a) Similar to B, you're looking for
[tex]P(X \le 1) = P(X=0) + P(X=1)[/tex]
with
[tex]\lambda = \dfrac{12\,\rm customers}{6\,\rm min}\times(1\,\mathrm{min}) = 2\,\mathrm{customers}[/tex]
so that
[tex]P(X\le1) = \dfrac{2^0e^{-2}}{0!} + \dfrac{2^1e^{-2}}{1!} \approx \boxed{0.406}[/tex]
Please help with questions 1-4.
Observe the quantities, ie. see what happens if you increase one or decrease the other.
To simplify imagination, expose one quantity. I will expose y.
1.
[tex]-\frac{y}{4}=2x\implies y=-8x[/tex]
So what is their variation or proportion? If I increase x then y is getting more and more negative. So is this direct or inverse or nothing? It is direct.
2.
[tex]14x=\frac{14}{y}\implies y=x, y\neq0[/tex] again if I increase x then y will match, will also increase. This is again direct.
3.
[tex]y=\frac{13}{x}, x\neq0[/tex] this time if I increase x, y will get smaller. When x is exactly 13, y will be 1 and when x is 10000, y will be 0.0013. This is inverse. One quantity gets really small when other quantity gets really big.
4.
[tex]y=x-2[/tex] if I increase x then y will also increase even though by slightly less (-2) it will still increase. However since there is no multiplication this is not a direct variation nor is it inverse. It is nothing/no-variation.
Hope this helps :)
15. Five boys went to see the CIRCUS. Four of them had Rs.5 each and the fifth boy had Re.1 more than the entrance ticket price. IF with the whole amount (which the 5 boys had), the boys were able to just buy the entrance ticket for all the 5, cost of the entrance ticket per person was
Answer:
20+(x+1) = 5x
x=21/4
x= 5.25
The entrance ticket per person can be calculated using algebraic equation. We have create the algebraic expression as per the question.
The entrance ticket per person is Rs. 5.25.
Given:
Total boys are 5
4 boys has 5 rupee each so total rupee are [tex]=5\times 4=20[/tex].
Let the entrance ticket per boy is [tex]x[/tex].
One boy had 1 rupee more than entrance ticket [tex](x+1)[/tex].
Write the algebraic expression to calculate the entrance ticket per person.
[tex]5x=20+(x+1)\\5x=20+x+1\\5x-x=20+1\\4x=21\\x=5.25[/tex]
Thus, the entrance ticket per person is Rs. 5.25.
Learn more about algebraic expression here:
https://brainly.com/question/953809
PLEASE HELP !! (2/5) -50 POINTS-
Answer:
[tex]X=\begin{bmatrix}5\\ 14\\ -10\end{bmatrix}[/tex]
Step-by-step explanation:
Our approach here is to isolate X, and simplify this solution. We want to begin by subtracting matrix 2, as shown below, from either side - the first step in isolating X. Afterwards we can multiply either side by the inverse of matrix 1, the co - efficient of X, such that X is now isolated. We can then simplify this value.
Given,
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ \:\:\:3&-2&-1\end{bmatrix}[/tex] : Matrix 1
[tex]\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}[/tex] : Matrix 2
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X+\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}=\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}[/tex] ( Subtract Matrix 2 from either side )
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X=\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}-\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}[/tex] ( Simplify )
[tex]\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}-\begin{bmatrix}3\\ -1\\ 8\end{bmatrix} = \begin{bmatrix}6-3\\ 4-\left(-1\right)\\ 5-8\end{bmatrix}=\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}[/tex] ( Substitute )
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X=\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}[/tex] ( Multiply either side by inverse of Matrix 1 )
[tex]X=\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}^{-1}\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}=\begin{bmatrix}5\\ 14\\ -10\end{bmatrix}[/tex] - let's say that this is Matrix 3. Our solution would hence be Matrix 3.
If Q(x) = x2 – 2 – 2, find Q(-3).
Answer: A (10)
Step-by-step explanation:
Plug in Q(-3) into formula x^2-x-2
(-3)^2-(-3)-2= 9+3-2
=10
If (x - 2) and (x + 1) are factors of
x + px? + qx + 1, what is the sum of p and q?
Answer:
p + q = -3
Step-by-step explanation:
First we need to take the original equation, and factor it to a form that's easier to get two binomial factors from (i.e., let's get a quadratic):
x^3 + px^2 + qx + 1
= x (x^2 + px + q) + 1
Now that we have factored out the x, we have a quadratic trinomial which we know can be broken down into two linear binomials. The problem gives us two linear binomials, so let's take a look.
(x - 2) (x + 1) = (x^2 + px + q)
x^2 - 2x + x -2 = x^2 + px + q
Now let's solve.
x^2 - x - 2 = x^2 + px + q
-x - 2 = px + q
From here, we can easily see that p = -1 (the coefficient of x) and q = -2.
Hence, p + q = -1 + -2 = -3.
Cheers.
Which statement about this function is true?
O A.
The value of a is positive, so the vertex is a minimum.
OB.
The value of a is negative, so the vertex is a minimum.
OC.
The value of a is negative, so the vertex is a maximum.
OD
The value of a is positive, so the vertex is a maximum.
Answer:
b
Step-by-step explanation:
The value of a is negative, so the vertex is a minimum.
Yooo I just had MAD diarrhea D:
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = - 8p^2 + 24,000p. What unit
price should be established for the dryer to maximize revenue? What is the maximum revenue?
The unit price that should be established to maximize revenue is $|
(Simplify your answer.)
Here we have a problem of maximization and quadratic equations.
The unit prize that maximizes the revenue is $1,500, and the maximum revenue is $18,000.
We know that the revenue equation is:
R(P) = - 8p^2 + 24,000p
Where the variable p is the price.
Now we want to find the value of p that maximizes the revenue.
To do it, we can see that the revenue equation is a quadratic equation with a negative leading coefficient.
This means that the arms of the graph will go downwards, then the maximum point of the graph will be at the vertex.
Remember that for an equation like:
y = a*x^2 + b*x+ c
The x-value of the vertex is at:
x = -b/(2*a)
Then for the equation:
R(P) = - 8p^2 + 24,000p
The vertex is at:
p = -(24,000)/(2*-8) = 1,500
The value of p that maximizes the revenue is p = $1,500
To get the maximum revenue, we need to evaluate the revenue equation in that p value.
R(1,500) = - 8*(1,500)^2 + 24,000*1,500 = 18,000
And the revenue equation is in dollars, then the maximum revenue is 18,000 dollars.
If you want to learn more, you can read:
https://brainly.com/question/18269297
p = 1500 $ the unit price
R(p) = 18000000 $ maximum revenue
We will use two different procedures to calculate the maximum revenue.
That is equivalent to solve the problem and after that to test the solution
The first one is:
R(p) = - 8*p² + 24000*p
we realize that R(p) is a quadratic function ( a parabola) of the form:
y = a*x² + b*x + c ( c = 0 in this case)
We also know that as the coefficient of p² is negative the parabola opens downwards then the vertex is a maximum value for R(p), and the x coordinate of p is:
x = p = - b/2*a then by substitution
p = - ( 24000)/ 2 ( - 8)
p = 1500 $ and for that value of p
R(p) = - 8 ( 1500)² + 24000* (1500) = - 18000000 + 36000000
R(p) = 18000000 $
The second procedure is solving with the help of derivatives.
R(p) = - 8*p² + 24000*p
Tacking derivatives on both sides of the equation we get:
R´(p) = -16p + 24000
If R´(p) = 0 then -16p + 24000 = 0
p = 24000/ 16 p = 1500
if we check for the second derivative
R´´(p) = -16 -16 < 0 therefore there is a maximum value for R(p) when p = 1500, and that value is:
By substitution in R(p)
R(p) = -8 *(1500)² + 24000* 1500
R(p) = - 18000000 + 36000000
R(p) = 18000000 $
MY
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
Col
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
MY
11 cm
Pro
Pro
Теа
5 cm
11 cm
cm2
2 of 4 OOO
Help
Step-by-step explanation:
Hi, there!!!
According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,
So, let's simply work with it,
Firstly, finding the area of rectangle,
length = 11cm.
breadth = 11cm.
now, area= length× breadth.
or, a = 11cm× 11cm.
a= 121cm^2
Now, let's work out the area of circle.
radius= 5cm
and pi. = 3.14 {using pi value as 3.14}
now,
area of a circle = pi× r^2
or, a= 3.14×5^2
or, a = 78.5 cm^2.
Therefore, The area of a circle is 78.5cm^2.
Now lastly finding the area of shadedregion,
area of shaded region = area of rectangle - area of circle.
or, area of shaded region = 121cm^2 - 78.5cm^2
Therefore, the area of shaded region is 42.5 cm^2.
Hope it helps...
woman has 7 coworkers' man. How many different possible groups of four people could do the project, if one out of three is women? g
Answer: 24ways
Step-by-step explanation:
Given data:
No of men in the workplace = 7
No of women in the workplace = 1
How many ways can a group of 4 people carry out a project if on out of the 3 must be a woman.
Solution.
A group of 4 can carry out the project with one be a woman
This means there must be 3 males and 1 female in the group
= 4p3
= 24ways
The project can be carried out by 4 groups in 24 ways
Intro to Translations
Acellus
Find the image of the given point
under the given translation.
P(-1,2)
T(x, y) = (x + 2, y - 4)
P' = ([?], [])
Enter the number that belongs
in the green box.
Answer:
(1,-2)
Step-by-step explanation:
P(-1,2) and (x, y) -> (x + 2, y - 4). Plugging in x and y in the transformation, the transformed points are (-1+2, 2-4) = (1,-2)
Convert degrees to radians
Answer:
it's answer is
[tex] \frac{25}{18} [/tex]
4. Create your own scenario for the variable expression below. Then, suggest values for the variables and solve. 14x + 12y
Answer:
Cost of pencil = $20
Cost of copy = $6
Step-by-step explanation:
Statement.
Gill buys 14 copy and 12 pencils and pays a total $324, if the value of 1 copy and 1 pencil is $26, find cost of copy and pencil.
Computation:
Assume.
Cost of copy = x
Cost of pencil = y
So,
x + y = 26.......Eq1
And
14x + 12y = 324.........Eq2
From Eq1 ad Eq2
Cost of pencil = $20
So,
Cost of copy = $6
Niall and Zayn buy 14 concert tickets for them and their friends to go see 5sos and 12 concert tickets for them and their friends to go see Little Mix with a total cost of $648. If the value of 1 5sos ticket and 1 Little Mix ticket is $52, and the Little Mix ticket is $4 more than the 5sos ticket, find cost of both tickets.
5sos = x
Little Mix = y
52 / 2 = 26
26 - 2 = 24
26 + 2 = 26
x = 24
y = 28
5sos tickets = $24 each
Little Mix tickets = $26 each
Find the value of the logarithm. log 122
Answer:
2.086
Step-by-step explanation:
Log 122 is equal to 2.086
Write all the factors of 32
Matj
Answer
Answer: 1, 2, 4, 8, 16, and 32.
Step-by-step explanation:
Factors are what we can multiply to get the number.
Factors of 32:
1 x 32=32
2 x 16=32
4 x 8=32
Therefore, the factors of 32 are 1, 2, 4, 8, 16, and 32.
Your friend Stacy has given you the following algebraic expression: "Subtract 20
times a number n from twice the cube of the number. What is the expression that your
friend is saying?
Answer:
Expression = 2n³ - 20n
Step-by-step explanation:
Find:
Expression
Computation:
Assume given number is 'n'
Cube of number = n³
Twice of cube = 2n³
Subtract number = 20n
Expression = 2n³ - 20n
I can’t figure this out, true or false?
Answer:
False.
Step-by-step explanation:
Because 4 is a constant .Yeah
Find the solution of the system of equations.
2x – 10y = -28
-10x + 10y = -20
GbA
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
2x - 10y = - 28 → (1)
- 10x + 10y = - 20 → (2)
Adding (1) and (2) term by term eliminates the term in y, that is
- 8x = - 48 ( divide both sides by - 8 )
x = 6
Substitute x = 6 into either of the 2 equations and evaluate for y
Substituting into (1)
2(6) - 10y = - 28
12 - 10y = - 28 ( subtract 12 from both sides )
- 10y = - 40 ( divide both sides by - 10 )
y = 4
Solution is (6, 4 )
Suppose that Y1, Y2,..., Yn denote a random sample of size n from a Poisson distribution with mean λ. Consider λˆ 1 = (Y1 + Y2)/2 and λˆ 2 = Y . Derive the efficiency of λˆ 1 relative to λˆ 2.
Answer:
The answer is "[tex]\bold{\frac{2}{n}}[/tex]".
Step-by-step explanation:
considering [tex]Y_1, Y_2,........, Y_n[/tex] signify a random Poisson distribution of the sample size of n which means is λ.
[tex]E(Y_i)= \lambda \ \ \ \ \ and \ \ \ \ \ Var(Y_i)= \lambda[/tex]
Let assume that,
[tex]\hat \lambda_i = \frac{Y_1+Y_2}{2}[/tex]
multiply the above value by Var on both sides:
[tex]Var (\hat \lambda_1 )= Var(\frac{Y_1+Y_2}{2} )[/tex]
[tex]=\frac{1}{4}(Var (Y_1)+Var (Y_2))\\\\=\frac{1}{4}(\lambda+\lambda)\\\\=\frac{1}{4}( 2\lambda)\\\\=\frac{\lambda}{2}\\[/tex]
now consider [tex]\hat \lambda_2[/tex] = [tex]\bar Y[/tex]
[tex]Var (\hat \lambda_2 )= Var(\bar Y )[/tex]
[tex]=Var \{ \frac{\sum Y_i}{n}\}[/tex]
[tex]=\frac{1}{n^2}\{\sum_{i}^{}Var(Y_i)\}\\\\=\frac{1}{n^2}\{ n \lambda \}\\\\=\frac{\lambda }{n}\\[/tex]
For calculating the efficiency divides the [tex]\hat \lambda_1 \ \ \ and \ \ \ \hat \lambda_2[/tex] value:
Formula:
[tex]\bold{Efficiency = \frac{Var(\lambda_2)}{Var(\lambda_1)}}[/tex]
[tex]=\frac{\frac{\lambda}{n}}{\frac{\lambda}{2}}\\\\= \frac{\lambda}{n} \times \frac {2} {\lambda}\\\\ \boxed{= \frac{2}{n}}[/tex]
3x7-12-2=7?
I have no clue please help...
Answer:
X = 28/3, or 9 1/3 or 9.3
Step-by-step explanation:
Answer:
Step-by-step explanation:
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
Step-by-step explanation:
4x - 13 = x + 5 Add 13 to both sides
4x = x + 18 Subtract x
3x = 18 Divide by 3
x = 6
HELP
PLSFind all the missing elements:
Answer:
a = 6.7 , c = 2.0
Step-by-step explanation:
For side aTo find the missing side a we use the sine rule
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]From the question
B = 58°
b = 6
A = 109°
Substituting the values into the above formula we have
[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex][tex] |a| \sin(58) = 6\sin(109) [/tex]Divide both sides by sin 58°
[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]a = 6.728791
a = 6.7 to the nearest tenthFor side cTo find side c we use the sine rule
That's
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]C = 13°
[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex][tex] |c| \sin(58) = 6 \sin(13) [/tex]Divide both sides by sin 58°
[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]c = 1.591544
c = 2.0 to the nearest tenthHope this helps you
Answer:
B=58 a=6.7 c=1.6
Step-by-step explanation:
It was right on Acellus
Sorry I cant give a better explanation but this unit is killing me.
Need Help
*Please Show Work*
Hi there! :)
Answer:
y = -2x + 3
Step-by-step explanation:
We can write an equation in slope-intercept form. Use the slope formula to find the rate of change in the table:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in values from the table:
[tex]m = \frac{5 - 7}{-1 - (-2)}[/tex]
Simplify:
m = -2 (rate of change)
Use a point from the table (-2, 7) and the slope to solve for the equation for the linear function:
7 = -2(-2) + b
7 = 4 + b
7 -4 = b
b = 3
Rewrite:
y = -2x + 3 is the equation for the linear function.
Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed Show Your Work
Answer:
The removed number is 11.
Step-by-step explanation:
Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :
[tex]let \: x = total \: values[/tex]
[tex] \frac{x}{5} = 7[/tex]
[tex]x = 7 \times 5[/tex]
[tex]x = 35[/tex]
Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :
[tex]let \: y = removed \: number[/tex]
[tex] \frac{35 - y}{4} = 6[/tex]
[tex]35 - y = 6 \times 4[/tex]
[tex]35 - y = 24[/tex]
[tex]35 - 24 = y[/tex]
[tex]y = 11[/tex]
Okay, let's slightly generalize this
Average of [tex]n[/tex] numbers is [tex]a[/tex]
and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.
Solution:
If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]
Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]
For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .
so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]
or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]
Simplify the equation, and solve for [tex]x[/tex] to get,
[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]
Hope you understand it :)
Consider the line =−−7x4y−6.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
4/7
Step-by-step explanation:
Original equation, in general form: -7x - 4y - 6
Rearrange to get: 4y = -7x - 6
Divide both sides by 4 to get: y = -7/4(x) - 1.5
To find the slope of a line perpendicular to another line, take the original gradient, and find the negative inverse
So for here,
Original gradient: -7/4
Negative: 7/4
Negative Inverse: 4/7 (which is our gradient)
Done!
A team wishes to purchase 10 shirts of the same color. A store sells shirts in 3 different colors. What must the inventory of the store be in order to conclude that there are at least 10 shirts in one of the three colors?
Answer:
30
Step-by-step explanation:
What is the difference between a line graph and a scatter plot?
Step-by-step explanation:
scatter plot s are similar to line graphs in that they start with mapping quantitive data points. The difference is that with a scatter plot, the decision is made the the individual points should not be connected directly together with a line but, instead express a trend
Lesson 9.6: Steady-State Analysis.) Consider a particular data set of 100,000 stationary waiting times obtained from a large queueing system. Suppose your goal is to get a confidence interval for the unknown mean. Would you rather use (a) 50 batches of 2000 observations or (b) 10000 batches of 10 observations each?
Answer:
I would rather use:
(b) 10,000 batches of 10 observations each.
Step-by-step explanation:
It is easier to have 10,000 batches of 10 observations each than to have 50 batches of 2,000 observations. Human errors are reduced with fewer observations. For example, Hadoop, a framework used for storing and processing big data, relies on batch processing. Using batch processing that divides the 100,000 stationary waiting times into 10 observations with 10,000 batches each is more efficient than having 2,000 observations with 50 batches each.
I need help plotting this on number line
Answer:
Step-by-step explanation:
1 What is the product of 2r^2- 5 and 3r
Answer:
Step-by-step explanation:
3r(2r^2 - 5)
6r^(2 + 1) - 5*3r
6r^3 - 15r