Answer:
0.0207 = 2.07% approximate probability of finding at least 157 defects
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
n instances of a Poisson distribution can be approximated to a normal distribution, with [tex]\mu = n\lambda, \sigma = \sqrt{\lambda}\sqrt{n}[/tex]
The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle.
This means that [tex]\lambda = 1.33[/tex]
Suppose that we inspect 100 Volkswagen vehicles at random.
This means that [tex]n = 100[/tex]
Mean and standard deviation:
[tex]\mu = n\lambda = 100*1.33 = 133[/tex]
[tex]\sigma = \sqrt{\lambda}\sqrt{n} = \sqrt{1.33}\sqrt{100} = 11.53[/tex]
What is the approximate probability of finding at least 157 defects?
Using continuity correction(Poisson is a discrete distribution, normal continuous), this is [tex]P(X \geq 157 - 0.5) = P(X \geq 156.5)[/tex], which is 1 subtracted by the p-value of Z when X = 156.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{156.5 - 133}{11.53}[/tex]
[tex]Z = 2.04[/tex]
[tex]Z = 2.04[/tex] has a p-value of 0.9793.
1 - 0.9793 = 0.0207
0.0207 = 2.07% approximate probability of finding at least 157 defects
What is equal to 30- 6v - 13w
Which histogram represents the following data set?
31, 67, 8, 37, 12, 87, 14, 34, 105, 57, 42, 8, 16, 54, 17, 20, 72, 23,
27, 63, 24, 52, 14, 44, 27, 5, 28, 22, 33, 15, 6, 36, 41, 21, 46
Answer:
Option A
Step-by-step explanation:
Histogram shows the range of data on the x-axis while the frequency of occurrence is on the y-axis.
We have the following ranges from the Histogram ;
0 to 11
11 to 22
22 to 33
33 to 44
44 to 55
55 to 66
66 to 77
77 to 88
88 to 99
99 to 110
From the given set of data, the frequency according to the range is as follows;
0 to 11; 4
11 to 22; 8
22 to 33; 7
33 to 44; 6
44 to 55; 4
55 to 66; 2
66 to 77; 2
77 to 88; 1
88 to 99; 0
99 to 110; 1
The only Histogram that corresponds to these frequency is option A
What do you know to be true about the values of p and ?
p"
q
601
454
45
A. p> 9
B. p<9
C. p= 9
D. Can't be determined
f(x) = 4x3 + 7x2 – 2x – 1
g(x) = 4x – 2
Find (f - g)(x).
please help
9514 1404 393
Answer:
(f-g)(x) = 4x^3 +7x^2 -6x +1
Step-by-step explanation:
(f -g)(x) = f(x) -g(x)
= (4x^3 +7x^2 -2x -1) -(4x -2)
= 4x^3 +7x^2 +(-2-4)x +(-1+2)
(f -g)(x) = 4x^3 +7x^2 -6x +1
insert a digit in place of each ... to make a number that is divisible by 6
4 . . . 6
Answer:
2
Step-by-step explanation:
If the measure of angle 2 is 920 and the measure of angle 4 is 2
what is the value of x?
14.
23
Step-by-step explanation:
the value of x will be 920
What is the gradient of the blue line?
5
4
3
2
1
-5 -4 -3 -2 - 1 0 1. 2. 3. 4. 5
- 1
- 2
- 3
- 4
- 5
The line starts at (-5,3) and finishes (5,0.5)
Answer:
The gradient is -0.25
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-5,3)[/tex]
[tex](x_2,y_2) = (5,0.5)[/tex]
Required
The gradient (m)
This is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{0.5-3}{5--5}[/tex]
[tex]m = \frac{-2.5}{10}[/tex]
[tex]m = -0.25[/tex]
Johnny tripled his baseball card collection. Then he added 6 more cards to the collection. Now he has 24 cards. How many cards did he start with?
9514 1404 393
Answer:
6
Step-by-step explanation:
Work backward.
If he has 24 after adding 6, he had 18 before that addition.
If he had 18 after tripling his collection, he had 18/3 = 6 cards to start with.
__
Note that this is the same process you would use if you started with an equation.
3c +6 = 24 . . . . where c is the number of cards Johnny started with
3c = 24 -6 = 18 . . . . . subtract 6 from the final number
c = 18/3 = 6 . . . . . . . . divide the tripled value by 3 to see the original value
Johnny started with 6 cards.
Find the solution set.
The solution set for 5v2 – 125 = 0
Answer:
5v2 – 125 = 0
5(v2−25)=0
v2−25=0
a couple more steps and the answer is...
v=-5
find 9 rational no. between 8/7 and 17/10.
Answer:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
Step-by-step explanation:
We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]
We make the denominators of both fractions same. So,
[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]
and
[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]
The rational number are:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
An 8-oz bottle of hair spray costs $4.46. Find the unit price in cents per ounce
Answer:
55.75 cents per ounce
Step-by-step explanation:
Take the cost and divide by the number of ounces
We want cents per ounce so change dollars to cents
446 / 8
55.75 cents per ounce
Coliform bacteria are randomly distributed in a river at an average concentration of 1 per 20cc of water. What is the variance of the number of Coliform bacteria in a sample of 40cc of water
Answer:
[tex]Var = 1.9[/tex]
Step-by-step explanation:
Given
[tex]p = \frac{1}{20}[/tex] i.e. 1 per 20cc of water
[tex]n = 40[/tex] -- sample size
Required
The variance
This is calculated using:
[tex]Var = np(1 - p)[/tex]
So, we have:
[tex]Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})[/tex]
[tex]Var = 40 * \frac{1}{20} * \frac{19}{20}[/tex]
[tex]Var = 2 * \frac{19}{20}[/tex]
[tex]Var = \frac{38}{20}[/tex]
[tex]Var = 1.9[/tex]
14. The Elizabeth Tower is 320 feet tall. At what time or times during your ride on the London Eye are you at the same height as the top of the tower? Show your work. (4 points: 2 points for finding the correct time(s), 2 points for work shown)
Answer:
Ok so on a clock there is 12 numbers where 12 is on top so at 12 am and 12 pm noon and midnight you will be at the top of the clock
Hope This Helps!!!
During the ride on the London Eye, you will be at the same height as the top of the Elizabeth Tower at approximately 21 minutes and 43.16 seconds after the start of the ride.
To determine the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower (commonly known as Big Ben), we need to consider the height of the London Eye and its rotational motion.
Given that the Elizabeth Tower is 320 feet tall, we need to find the position of the London Eye when its height aligns with the top of the tower.
The London Eye has a height of 443 feet, and it completes one full rotation in approximately 30 minutes (or 1800 seconds). This means that it moves at a constant angular velocity of 360 degrees per 1800 seconds.
To find the time(s) when the heights align, we can set up a proportion:
(Height of the Elizabeth Tower) / (Height of the London Eye) = (Angle covered by the London Eye) / 360 degrees
Substituting the given values:
320 / 443 = (Time to align) / 1800
Simplifying the equation:
(Time to align) = (320 / 443) * 1800
Calculating the value:
(Time to align) ≈ 1303.16 seconds
Converting the time to minutes and seconds:
(Time to align) ≈ 21 minutes and 43.16 seconds
Therefore, during the ride on the London Eye, you will be at the same height as the top of the Elizabeth Tower at approximately 21 minutes and 43.16 seconds after the start of the ride.
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A line contains the points (3,1) and (-6,4) what is the equation for this line in slope intercept form
Answer:
y = (-1/3)x + 2
Step-by-step explanation:
Since points (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation. Thus, intercept is 2.
Answer:
m = -⅓
Step-by-step explanation:
m = (y2- y1)/(x2 - x1)
m = (4 -1)/(-6-3)
m = -⅓
Lolz please help me I would gladly appreciate it
Pentagon has sum of 540°
Công ty T vừa đưa vào sản xuất một loại sản phẩm mới với định mức giờ máy là 2 giờ/sản phẩm. Tài liệu về sản phẩm trong năm như sau (đồng):
Chi phí nguyên vật liệu trực tiếp/sp
30.000
Chi phí nhân công trực tiếp/sp
27.000
Chi phí sản xuất chung/sp
12.000(25% là biến phí)
Bao bì/sp (ở khâu SX)
5.000
Lương quản lý và bán hàng
83.300.000
Quảng cáo
34.700.000
Chí phí khác bằng tiền
30.000.000
Vốn đầu tư bình quân
1.200 triệu
ROI mong muốn
16%
Tổng số giờ máy hoạt động cho sản xuất
40.000 giờ
Yêu cầu:
1. Hãy định giá bán theo biến phí?
2. Để sản xuất sp mới này, Cty tự chế tạo 1 chi tiết để lắp vào sản phẩm với thông tin như sau:
- Biến phí sản xuất của Chi Tiết = 40% biến phí sp
- KH TSCĐ cho việc sản xuất chi tiết là 42.000.000đ
- Chi phí quản lý chung phân bổ cho việc sản xuất chi tiết là 19.040.000đ.
Có một doanh nghiệp khác đến chào hàng chi tiết với giá chỉ bằng 70% so với giá thành cty tự sản xuất và đảm bảo đủ số lượng, chất lượng theo yêu cầu. Các phương tiện sản xuất chi tiết có thể cho thuê 13.000.000đ/năm. Cty nên tự sản xuất hay mua ngoài?
Answer:
??????
Step-by-step explanation:
Can you help me answer this question? Screenshot is added.
9514 1404 393
Answer:
(c)
Step-by-step explanation:
[tex]\displaystyle\sqrt[3]{xy^5}\sqrt[3]{x^7y^{17}}=\sqrt[3]{x^{1+7}y^{5+17}}=\sqrt[3]{x^6x^2y^{21}y}=\sqrt[3]{x^6y^{21}}\sqrt[3]{x^2y}\\\\=\boxed{x^2y^7\sqrt[3]{x^2y}}[/tex]
What is the distance between -10.2 and 5.7?
Answer:
15.9
Step-by-step explanation:
The distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
Two numbers on a number line:
-10.2 and 5.7
As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
Indicating the above numbers on a number line:
= 5.7 -(-10.5)
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= 5.7 + 10.5
= 15.9
Thus, the distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.
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Find the value of x in each case:
which of the following is a geometric sequence -3,3,-3,3... 11,16,21,26, ... 6, 13, 19, 24, ... -2,6,14,22, ...
Answer:
p and q are two numbers.whrite down an expression of
If the angles (4x + 4)° and (6x – 4)° are the supplementary angles, find the value of x.
Answer:
18
Step-by-step explanation:
Supplementary angles means sum of angles is 180.
4x + 4 + 6x - 4 = 180
4x + 6x + 4 - 4 = 180
10x = 180
x = 180 / 10
x = 18
Answer:
x=18 degree
Step-by-step explanation:
If they are supplementary angles, then their sum = 180 degree
4x+4 + 6x-4 =180
4x+6x + 4-4 = 180
10x = 180
x=180/10
x=18
solve the inequality x(x+6) >16
please show steps and interval notation!
Answer:
x > 2, x < -8
Interval notation:
( -infinity, -8) U (2, infinity)
Step-by-step explanation:
x(x+6) > 16
distribute x into x+6, multiply
x^2 + 6x > 16
bring 16 to left side, subtract
x^2 + 6x - 16 > 0
factors of -16 that add to +6 is -2 and +8
(x - 2)(x + 8) > 0
solve for x:
x < -8, x > 2
Interval notation:
( -infinity, -8) U (2, infinity)
A small insurance company has determined that on average it receives 6 property damage claims per day. P left parenthesis X equals k right parenthesis space equals space fraction numerator lambda to the power of k e to the power of negative lambda end exponent over denominator k factorial end fraction k space i s space t h e space g i v e n space n u m b e r space o f space e v e n t space o c c u r r e n c e s lambda space i s space t h e space a v e r a g e space r a t e space o f space e v e n t space o c c u r r e n c e s What is the probability that the company will receive 7 property damage claims on a randomly selected day? Answer choices are rounded to the hundredths place.
Answer:
The probability that the company will receive 7 property damage claims on a randomly selected day is 0.137
Step-by-step explanation:
Given,
[tex]\lambda=6[/tex],
The probability mass function of Poisson distribution is used for evaluating the probability of the company will receive 7 property damages claims on any selected day is,
[tex]\begin{aligned}P(X=K)&=e^{-6} \times \dfrac{6^7}{7!}\\&=0.002478\times\dfrac{279936}{5040}\\&=\dfrac{693.89136}{5040}\\P(X=7)&=0.1365927874\\P(X=7)&=0.137\; (\rm{rounded \;off})\end{aligned}[/tex]
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What is the measure of angle WZY? 54.5° 71° 125.5° 180°
Answer:
71
Step-by-step explanation:
The measure of angle WXY will be thee ame as the measure of the intercepted arc, 109°.
W and Y are both tangent to the circle; this means angle XWZ and angle XYZ are both 90°.
Every quadrilateral has a total measure of 360°; to find the measure of WZY, we subtract:
360-90-90-109 = 71°
The measure of angle WZY (∠WZY) is; 71°
What is the measure of the angle?From the attached image, we can say that the measure of ∠WXY will be the same as the measure of the intercepted arc, 109°.
Now, W and Y are both tangent to the circle and this means that ∠XWZ and ∠XYZ are both equal to 90°.
Now, every quadrilateral has a total internal sum of angles as 360°.
Thus, ∠WZY is gotten from;
∠WZY = 360 - (90 + 90 + 109)
∠WZY = 71°
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Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist. b. What are the speeds of the two cyclists? _______________
Answer:
4r + 4(r + 3) = 68
r = 7 miles per hour
r + 3 = 10 miles per hour
Step-by-step explanation:
distance = rate * time
a)
4r + 4(r + 3) = 68
Distribute
4r + 4r + 12 = 68
8r + 12 = 68
8r = 56
r = 7 miles per hour
r + 3 = 10 miles per hour
1) Prepare a post merger financial position for METRO using the pooling of interest method.
Answer:
Metro and Medec
METRO
Post-merger Financial Position, using the pooling of interest method:
Pre-merger Financial Positions:
Metro (RM ‘000)
Assets
Current assets 120
Fixed assets 830
Total assets 950
Liabilities and Equities
Current liabilities 40
Long term debt 200
Common stock (RM1 par) 480
Capital surplus 120
Retained earnings 110
Total liabilities and equity 950
Earnings available to
common stockholders 230
Common Dividends 150
Addition to Retained Earnings 80
Step-by-step explanation:
Pre-merger Financial Positions:
Metro (RM ‘000) Medec(RM ‘000)
Assets
Current assets 50 70
Fixed assets 650 180
Total assets 700 250
Liabilities and Equities
Current liabilities 30 10
Long term debt 140 60
Common stock (RM1 par) 400 80
Capital surplus 50 70
Retained earnings 80 30
Total liabilities and equity 700 250
Earnings available to
common stockholders 100 130
Common Dividends 50 100
Addition to Retained Earnings 50 30
Exchange ratio = 1:2
Find the angle between the vectors ????=????+???? and ????=−????+????. (Give an exact answer. Use symbolic notation and fractions where needed.)
Answer:
The angle between them is 60 degrees
Step-by-step explanation:
Given
[tex]a = 2i + j -3k[/tex]
[tex]b = 3i - 2j -k[/tex]
Required
The angle between them
The cosine of the angle between them is:
[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]
First, calculate a.b
[tex]a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)[/tex]
Multiply the coefficients of like terms
[tex]a \cdot b =2 * 3 - 1 * 2 - 3 * -1[/tex]
[tex]a \cdot b =7[/tex]
Next, calculate |a| and |b|
[tex]|a| = \sqrt{2^2 + 1^2 + (-3)^2[/tex]
[tex]|a| = \sqrt{14[/tex]
[tex]|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}[/tex]
[tex]|b| = \sqrt{14}[/tex]
Recall that:
[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]
This gives:
[tex]\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}[/tex]
[tex]\cos(\theta) = \frac{7}{14}[/tex]
[tex]\cos(\theta) = 0.5[/tex]
Take arccos of both sides
[tex]\theta =\cos^{-1}(0.5)[/tex]
[tex]\theta =60^o[/tex]
Last year there were two hundred and forty seven thousand, three hundred and seventy two weddings in the UK.
Write this as a number
Answer:
247372
Step-by-step explanation:
two hundreds forty seven thousand, three hundred and seventy two
The number of weddings in the UK in numerical form will be 247,372.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Last year there were two hundred and forty-seven thousand, three hundred and seventy-two weddings in the UK.
Convert the statement into a number. Then we have
⇒ 247,372
The number of weddings in the UK in numerical form will be 247,372.
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What is the value of x
Answer:
52/3
Step-by-step explanation:
Use basic Thales therom,
[tex]\frac{3x}{4x}=\frac{3x+7}{5x-8}\\\\\frac{3}{4}=\frac{3x+7}{5x-8}\\[/tex]
Cross multiply,
3*(5x-8)=4*(3x+7)
3*5x - 3*8 = 4*3x + 4*7
15x - 24 = 12x +28
Add 24 to both sides
15x = 12x + 28 + 24
15x = 12x + 52
Subtract 12x from both sides
15x-12x =52
3x = 52
Divide both sides by 3
x = 52/3
The volume, V, of a sphere in terms of its radius, r, is given by , V(r)=4/3(pie)r^3. Express r as a function of V, and find the radius of a sphere with volume of 150 cubic feet. Round your answer for the radius to two decimal places.
r(V)=
A sphere with volume 150 cubic feet has radius
_________ feet.
Step-by-step explanation:
If
[tex]V=\dfrac{4\pi}{3}r^3[/tex]
then we can solve for r as
[tex]r = \sqrt[3]{\dfrac{3V}{4\pi}}[/tex]
If the volume of the sphere is 150 ft^3, then the radius is
[tex]r = \sqrt[3]{\dfrac{3(150\:\text{ft}^3)}{4\pi}} = 3.30\:\text{ft}[/tex]
The radius of the given sphere with a volume of 150 cubic feet is 2.29 feet, correct to two decimal places.
Given that
the volume of a sphere = 150 cubic feet.
the radius of the sphere=????
what is a Sphere?a round solid figure, or its surface, with every point on its surface equidistant from its center.
as we know,
the volume of a sphere
[tex]V=\frac{4}{3} *\pi *r^3[/tex]
[tex]r = \sqrt[3]{\frac{3V}{4\pi } }[/tex][tex]r = \sqrt[3]{\frac{3*150}{4\pi } }[/tex][tex]=2.29 feet[/tex]
therefore, the radius of the given sphere is 2.29feet
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