Answer:
(a) 0.6579
(b) 0.2961
(c) 0.3108
(d) 240
Step-by-step explanation:
The random variable X can be defined as the number of particles in a suspension.
The concentration of particles in a suspension is 50 per ml.
Then in 5 mL volume of the suspension the number of particles will be,
5 × 50 = 250.
The random variable X thus follows a Poisson distribution with parameter, λ = 250.
The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.
The mean of the approximated distribution of X is:
μ = λ = 250
The standard deviation of the approximated distribution of X is:
σ = √λ = √250 = 15.8114
Thus, [tex]X\sim N(250, 250)[/tex]
(a)
Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:
[tex]P(235<X<265)=P(\frac{235-250}{15.8114}<\frac{X-\mu}{\sigma}<\frac{265-250}{15.8114})[/tex]
[tex]=P(-0.95<Z<0.95)\\=P(Z<0.95)-P(Z<-0.95)\\=P(Z<0.95)-[1-P(Z<0.95)]\\=2P(Z<0.95)-1\\=(2\times 0.82894)-1\\=0.65788\\\approx 0.6579[/tex]
Thus, the value of P (235 < X < 265) = 0.6579.
(b)
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{5}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{5}})[/tex]
[tex]=P(-0.28<Z<0.28)\\=P(Z<0.28)-P(Z<-0.28)\\=P(Z<0.28)-[1-P(Z<0.28)]\\=2P(Z<0.28)-1\\=(2\times 0.64803)-1\\=0.29606\\\approx 0.2961[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.2961[/tex].
(c)
A 10 mL sample is withdrawn.
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{10}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{10}})[/tex]
[tex]=P(-0.40<Z<0.40)\\=P(Z<0.40)-P(Z<-0.40)\\=P(Z<0.40)-[1-P(Z<0.40)]\\=2P(Z<0.40)-1\\=(2\times 0.65542)-1\\=0.31084\\\approx 0.3108[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.3108[/tex].
(d)
Let the sample size be n.
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{n}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{n}})[/tex]
[tex]0.95=P(-z<Z<z)\\0.95=P(Z<z)-P(Z<-z)\\0.95=P(Z<z)-[1-P(Z<z)]\\0.95=2P(Z<z)-1\\P(Z<z)=\frac{1.95}{2}\\\\P(Z<z)=0.975[/tex]
The value of z for this probability is,
z = 1.96
Compute the value of n as follows:
[tex]z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241[/tex]
Thus, the sample selected must be of size 240.
The length of a rectangle is four more than three times it’s width. The perimeter is 64 inches
Answer:
Length: 25, Width: 7
Step-by-step explanation:
Let the width be represented by w. We can then assume that the length is equivalent to 3w+4
So, we can set the equation 2(3w+4)+2(w). Simplify to 8w+8=64
Simplify the equation and solve for w, which is 7
Plug into the the length, which is 3w+4
Answer:
Length: 25 inches
Width: 7 inches
Step-by-step explanation:
Perimeter = 2L + 2W
Length: 3w + 4
Width: w
64 = 2(3w + 4) + 2w
64 = 6w + 8 + 2w
64 = 8w + 8
56 = 8w
w = 7
Length: 3(7) + 4 = 25
Width: 7
-1 2/3 divided by 6 need helo asap
Answer:
-5/18
Step-by-step explanation:
-1 2/3 is equal to -5/3 and if you follow the keep change flip rule, keep -5/3 change the division sign to multiply and then flip the fraction (6/1 to 1/6) and then multiply.
-5/3 * 1/6 = -5/18
60 5/6 + 54 1/3 + 56 1/6 + 59 1/3 pls help
Answer: Is 174.333333333 Hope this helps! and pls give me brainliest i need it
Step-by-step explanation:
line A and B are parallel. line C and D are parallel. Line D is perpendicular to line B . therefore line C is ? to line A
Answer:
C is Perpendicular to A
Step-by-step explanation:
Solve the equation 3(x+1 )-2=x+5
Answer:
x=2
Step-by-step explanation:
first, let's distribute.
3(x+1)-2=x+5
3x+3-2=x+5
then, let's combine like terms.
3x+1=x+5
now, we subtract x on both sides.
2x+1=5
subtract 1 on both sides.
2x=4
divide by 2 on both sides.
x=2
Gabrielle’s age is two times Mikhail’s age. The sum of their ages is 36. What is Mikhail’s age?
Enter the sum of numbers as a product of their GCF.
30 + 36
The sum of the numbers as a product of their GCF is
Their GCF is 6 and the sum is 66
Step-by-step explanation:
A line has slope 3 and y-intercept 4.
Which answer is the equation of the line?
O y = 3x + 4
Oy= 3x -4.
O y= 3/4x-4
O y = 4x + 3
Answer:
y = 3x +4
Step-by-step explanation:
In slope-intercept form, the equation of a line is ...
y = mx + b
Where m is the slope (3) and b is the y-intercept (4).
Putting the given numbers in the equation, it becomes ...
y = 3x +4
Write the equation of a line that passes through two points (3, 4) and (4, -2).
Answer:
y=-6x+22
Step-by-step explanation:
Equation is declining so its a negative
Mid point on x axis between the two is 22
Graph the image of the given triangle after the transformation that has the rule (x, y)→(x−5, y+6). Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
Answer:
Step-by-step explanation:
Transformation involves changing the position of a shape in the coordinate.
See attachment for the image of the triangle
Assume the triangle is triangle ABC.
The coordinates of ABC are:
[tex]\mathbf{A = (-1,-4)}[/tex]
[tex]\mathbf{B = (-2,-7)}[/tex]
[tex]\mathbf{C = (5,-6)}[/tex]
The transformation rule is given as:
[tex]\mathbf{(x,y) \to (x -5,y+6)}[/tex]
So, we have:
[tex]\mathbf{A' = (-1 -5,-4+6)}[/tex]
[tex]\mathbf{A' = (-6,2)}[/tex]
[tex]\mathbf{B' = (-2 -5,-7+6)}[/tex]
[tex]\mathbf{B' = (-7,-1)}[/tex]
[tex]\mathbf{C' = (5 -5,-6+6)}[/tex]
[tex]\mathbf{C' = (0,0)}[/tex]
So, the coordinates of the new triangle would be:
[tex]\mathbf{A' = (-6,2)}[/tex]
[tex]\mathbf{B' = (-7,-1)}[/tex]
[tex]\mathbf{C' = (0,0)}[/tex]
See attachment for the image of ABC
Read more about transformations at:
https://brainly.com/question/12463306
How do you do this question?
================================================
Explanation:
Choice A is true assuming we have [tex]a_n = (-1)^n*b_n[/tex]
In this case, [tex]a_n = (-1)^n*\frac{1}{\sqrt{n}}[/tex] and [tex]b_n = \frac{1}{\sqrt{n}}[/tex]
--------
Choice B is false. See choice A above.
--------
Choice C is true. The sequence [tex]\{b_n\}[/tex] is decreasing. As n gets larger, [tex]b_n[/tex] gets smaller. This is because the denominator is growing larger with the numerator held constant.
--------
Choice D is false. This contradicts choice C.
--------
Choice E is true since the denominator is growing forever
This is similar to [tex]\displaystyle \lim_{n \to \infty} \frac{1}{n} = 0[/tex]
--------
Choice F is true due to choices C and E being true.
--------
Choice G is false because it contradicts choice F.
3x-29=6x-7 what is x
Answer:
Step-by-step explanation:
You want to get x on one side and the constants on the other. First subtract both sides by 3x to get:
-29 = 3x - 7
Now add 7 to both sides to get:
-22 = 3x
Divide each side by 3 to get:
x = -22/3
Which is the best approximate solution of the system of linear equations y=1.5x -1 and y=1
Answer:
(1 1/3, 1)
Step-by-step explanation:
1.5x-1=1
1.5x=2
x=1 1/3
y=1
(1 1/3, 1)
Please help ASAP HELP!
Answer:
Step-by-step explanation:
You equal both angles to each other and solve. You should get x=5, the you plug in x giving you 44 for both angles and 88 for ABC
The value of y is directly PROPORTIONAL to the value of x. If y=44 when x= 240, what is the value of y when x=84?
If you need the answer in fraction form, then it would be 77/5
This is equivalent to the mixed number 15 & 2/5
======================================================
Work Shown:
y = k*x ..... general direct proportion equation
44 = k*240 .... plug in x = 240 and y = 44
240k = 44
k = 44/240
k = 11/60 .... divide both parts by 4
y = k*x .... go back to the general form
y = (11/60)x .... plug in the k value we found earlier
y = (11/60)*84 .... plug in x = 84
y = 15.4
---------------
Extra info:
15.4 = 15 + 0.4
15.4 = 15 + 4/10
15.4 = 15 + 2/5
15.4 = 15 & 2/5 .... mixed number form
and
15.4 = 15 + 2/5
15.4 = 75/5 + 2/5
15.4 = (75+2)/5
15.4 = 77/5 ... improper fraction
Use the domain and range of each of the following relations to determine which is a function.
{(-4,3), (-2,-1), (-4,8)}
{-4, 3), (-2.-1), (-7, 8)}
{-4,-2,-7, 7}
{-4,3). (-2, -1). (-2, -8), (-7,8)}
Answer:
A) Not a function
B) Function
C) Function
D) Not a function
Step-by-step explanation:
If the relation has two of the same x-values (that equal different y-values), it is not a function. In other words, if each input value leads to only one output value, classify the relation as a function.
{(-4,3), (-2,-1), (-4,8)} = Not a function
{-4, 3), (-2.-1), (-7, 8)} = Function
{-4,-2,-7, 7} = Function (I think?)
{-4,3). (-2, -1). (-2, -8), (-7,8)}= Not a function
The value of a stock over a 12 year period form 2003 to 2015 is shown in the line graph. Which statement is not supported by the graph?
Answer:
an individual who invested in the market in 2006 has yet to regain the losses incurred in 2008
Step-by-step explanation:
Which of the following is a point on the graph of y-7=3(x-5)
carol feeds her bird the same amount of food every day. over the past 7 days, her bad of bird food has decreased by 1 3/4 cups.
Answer:
12.25 or 12 1/4
Step-by-step explanation:
Every day, the bird at 1.75 or 1 and 3/4. so, this would also equal to 1.75*1 day.
So, 7 days, the bird would eat, 1.75*7 days.
1.75*7=12.25
Answer:
12.25 or 12 1/4
Step-by-step explanation:
Every day, the bird at 1.75 or 1 and 3/4. so, this would also equal to 1.75*1 day.
So, 7 days, the bird would eat, 1.75*7 days.
1.75*7=12.25
I needdddd helpppp !! Quickkkk !!
P = 2l + 2w
A rectangle has a width of x and a length of
x + 2. The perimeter is 20 inches. Find the value of the width and the length of the rectangle.
A. Width=9, Length=11
B. Width=6, Length=8
C. Width=4,Length=6
D. Width=3, Length=5
Answer:
width= 4, length= 6
Step-by-step explanation:
use perimeter formula and substitute values
so formula becomes:
20= 2(x+2) + 2(x)
expand the brackets and that gives us
20= 2x+4 +2x
so
16=4x
x= 4
so width is x which is 4
and length is x+2 which is 6
Find the distance between the two numbers on a number line. Write your answer as a decimal.
-1.85 , 7.36
Answer:
9.21
Step-by-step explanation:
I'm pretty sure you just add the two numbers as positive numbers :/
The required distance on the number line between the points -1.85 and 7.36 is 9.21.
Given that,
To determine the distance between the two numbers on a number line points are -1.85 and 7.36.
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
On the number line, -1.85 lies on the left of the zero, and 7.36 lies on the right so the required distance would be the addition of the two points. So,
Distance = 7.36 - (-1.85)
Distance = 7.36 + 1.86
Distance = 9.21
Thus, the required distance on the number line between the points -1.85 and 7.36 is 9.21.
Learn more about number line here:
brainly.com/question/17683084
#SPJ5
Help me please does anyone know this answer
Answer:
There are 150 new employees in the sample space.
There are 30 new employees in each event.
There is a 20% probability that you choose a new employee that has been assigned to orientation group C
Step-by-step explanation:
Bill hikes 8 miles in 3 hours. At this rate. how many miles will he hike after 2 hours?
Answer:
5 1/3 miles
Step-by-step explanation:
We can use a ratio to solve
8 miles x miles
------------ = --------
3 hours 2 hours
Using cross products
8*2 = 3x
16 = 3x
Divide by 3
16/3 = 3x/3
5 1/3 miles =x
Answer: [tex]5 \frac{1}{3}[/tex] miles
For the rate of 8 miles in 3 hours, you divide.
For the rate of - miles in 2 hours, multiply.
8 x 2 = 3x
16 = 3x
Now, we have to divide by 3x by 3.
3x divided by 3 = 5 1/3
Answer = 5 1/3
what are the measures of angles a,b,c ?
Answer:
a=30 , b=60, c=105
Step-by-step explanation:
a=30 [Being vertically opposite angle]
Now,
a+b+90=180 [Being the sum of interior angles of a triangle]
or, 30+b+90=180
or, b+120=180
or, b=180-120
so, b= 60
Again,
c+75= 180 [Being linear pair]
or, c=180-75
so, c= 105
5 yüz binlik 2 binlik 4 yüzlükten oluşan
altı basamaklı doğal sayı kaçtır?
Answer:
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Solve for x in the triangle. Round your answer to the nearest tenth.
Answer: x ~34.31 (rounded)
HELP QUICK WILL GIVE BRAINLIEST
Answer:
I gave the answers to the first four problems.
Step-by-step explanation:
1) LAB=40°
2) angle 3= 57°
3) x=25°
4) y= 29°
Please help hurry!! This is due in 30 minutes and I need help with domain and range.
240 in a ratio of 3:5?
The number who needs to be made into a ratio = 240
Total number of parts = 3 + 5
= 8 parts
Each part = 240 ÷ 8
= 30
Then three parts = 30 × 3 = 90
Five parts = 30 × 5 = 150
Then , the ratio will be = 90 : 150
Therefore , 240 in a ratio of 3 : 5 = 90 : 150 .
At a local festival, general admission was $3 for students and $5 for adults. 331 people came to the festival and they sold a total of $1431 tickets. How many students came to the festival?
Answer:112
Step-by-step explanation:
I did it and we doing the same test rn haha. What did you get for the grant one?