Answer:
P(A/D) = 0.5714
Step-by-step explanation:
Let's call A the event that a chip is produced by Plant A, B the event that a chip is produced by Plant B and D the event that the chip is defective
So, the likelihood or probability P(A/D) that a chip came from plant A given that the chip is defective is calculated as:
P(A/D) = P(A∩D)/P(D)
Where P(D) = P(A∩D) + P(B∩D)
Then, the probability P(A∩D) that a chip is produced by plant A and it is defective is calculated as:
P(A∩D) = 0.4*0.02 = 0.008
Because, Plant A produces 40% of the chips and 2% of the chips produced by plant A are defective.
At the same way, the probability P(B∩D) that a chip is produced by plant B and it is defective is calculated as:
P(B∩D) = 0.6*0.01 = 0.006
So, P(D) and P(A/D) are equal to:
P(D) = 0.008 + 0.006 = 0.014
P(A/D) = 0.008/0.014 = 0.5714
it means that if a randomly chosen chip produced by the company is defective, the likelihood that the chip came from plant A is 0.5714
What is true about the function graphed below?
see image v v v
A. The coordinates of the vertex are (3, 0).
B. The function graphed is look at the picture.
C. The axis of symmetry is the x-axis.
D. The axis of symmetry is the y-axis.
Answer:
D. The axis of symmetry is the y-axis.
Step-by-step explanation:
The vertex is at coordinates (0, 3). Since this parabola opens vertically, its axis of symmetry is the x=coordinate of the vertex: x = 0. That is the equation of the y-axis.
The axis of symmetry is the y-axis.
DEFINE PARALLELLOGRAM
Answer:
Parallelograms are shapes that have four sides with two sides that are parallel. For example, some shapes that are parallelograms are squares, rectangle, rhombus and rhomboid.
Step-by-step explanation:
No explanation :)
Final answer:
A parallelogram is a quadrilateral with parallel and congruent opposite sides, congruent opposite angles, and diagonals that bisect each other.
Explanation:
A parallelogram is a four-sided polygon, also known as a quadrilateral, where opposite sides are parallel and equal in length. There are several properties that define a parallelogram:
Opposite sides are congruent (equal in length).Opposite angles are congruent (equal in measure).Consecutive angles are supplementary (their measures add up to 180 degrees).The diagonals of a parallelogram bisect each other.Each diagonal divides the parallelogram into two congruent triangles.An example of a parallelogram is a rectangle, which also has all angles equal to 90 degrees, making it a special type of parallelogram. Another example is a rhombus, which has all sides of equal length. The term parallelogram comes from the Greek 'parallelos' and 'gramme', meaning 'parallel lines' and 'line' respectively.
what is the slope of the line y=8 ?
Answer:
0
Step-by-step explanation:
It is a horizontal line, the slope is 0 and it crosses the y-axis at 8
The line is a horizontal line, which has a slope that is equal to zero (0).
Given the following equation:
[tex]y = 8[/tex]To calculate or determine the slope of the given line:
The slope of a line can be defined as the gradient of a line.
In Mathematics, a slope is typically used to describe both the direction and steepness of an equation of a straight line.
Generally, the standard form of an equation of line is given by the following formula;
[tex]y = mx+b[/tex]
Where:
x and y are the points. m is the slope. b is the intercept.Comparing the two equations, we can deduce that the slope of the given line is equal to zero (0).
This ultimately implies that, the line is a horizontal line, which would cross the y-axis of a graph at point 8.
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What is the domain of f(x) = 3x – 22
Answer: 7.3333
Step-by-step explanation:
What is the formula for margin of error?
ME = StartFraction z times StartRoot s EndRoot Over StartRoot n EndRoot EndFraction
ME = StartFraction z times StartRoot s EndRoot Over n EndFraction
ME = StartFraction z times s Over StartRoot n EndRoot EndFraction
ME = StartFraction z times s Over n EndFraction
ANSWER IS:
C) ME = StartFraction z times s Over StartRoot n EndRoot EndFraction
Answer:
Margin of error = Critical value x Standard error of the sample.
Step-by-step explanation:
The margin of error can be calculated in two ways, depending on whether you have parameters from a population or statistics from a sample: Margin of error = Critical value x Standard deviation for the population. Margin of error = Critical value x Standard error of the sample.
Its C. ME= (z*s)/ sqrt n
Using a proportion, what can you infer about the number of households in her town that have more than three children?
Answer:
About 296 households have more than three children.
Step-by-step explanation:
The complete question is:
Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below. Children in 50 Households Number of Children Number of Households 0 5 1 11 2 13 3 10 4 9 5 2 Using a proportion, what can you infer about the number of households in her town that have more than three children? About 242 households have more than three children. About 269 households have more than three children. About 296 households have more than three children. About 565 households have more than three children.
Solution:
The data provided for the number of children and number of households is:
Number of Children (X) Number of Households (f (X))
0 5
1 11
2 13
3 10
4 9
5 2
TOTAL 50
Compute the probability of households having more than three children as follows:
P (More than 3 children) = P (4 children) + P (5 children)
[tex]=\frac{9}{50}+\frac{2}{50}[/tex]
[tex]=\frac{11}{50}[/tex]
[tex]=0.22[/tex]
Let the random variable Y be defined as the number of households having more than three children.
The probability of the random variable Y is, p = 0.22.
The entire population, i.e. total number of addresses in Carmen's town with numbers ranging from zero to five children, consists of N = 1,346 households.
Compute the expected number of households having more than three children as follows:
[tex]E(Y) =N\times p[/tex]
[tex]=1346\times 0.22\\=296.12\\\approx 296[/tex]
Thus, about 296 households have more than three children.
De una cesta de manzanas se pudren 2/3 . Comemos las 4/ 5 del resto y las 25 restantes las utilizamos para hacer mermelada. ¿Cuántas manzanas había en la cesta?
Google translation
2/3 of a basket of apples rot. We eat 4/5 of the rest and use the remaining 25 to make jam. How many apples were in the basket
Answer:
375
Step-by-step explanation:
Since the basket was full, ⅔ rot so the remaining for any use will be 1-⅔=⅓
Since we only eat 4/5 of this remaining quantity, we use the 1-4/5=1/5 of ⅓ for making jam
1/5 of ⅓=1/5*⅓=1/15
If 1/15 equals 25 pieces then the full basket had
25*15/1=375 pieces
the plane that delta airlines uses to travel from New York to Los Angeles has a total of 80 seats. On the most recent flight, only 4/5 of the seats were filled with passengers. Of those filled with passagers 3/4 were people traveling for business. How many people on the flight were traveling for business?
Answer:
48
Step-by-step explanation:
If only 4/5 of the 80 seats were filled, then 4/5*80=64 of the seats were filled. Of those filled, if 3/4 were travelling for business, then 3/4*64=48 of the people were travelling for business. Hope this helps!
Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 16 13 18 11 15 14 Choose the correct time series plot. (i) Time Series ValueWeek(t) (ii) Time Series ValueWeek(t) (iii) Time Series ValueWeek(t) (iv) Time Series ValueWeek(t) Plot (i) What type of pattern exists in the data? Horizontal Pattern Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Week Time Series Value Forecast 1 16 2 13 3 18 4 11 15.67 5 15 14 6 14 14.67 MSE: 7.74 The forecast for week 7: 13.33 Use = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Week Time Series Value Forecast 1 16 2 13 16 3 18 15.4 4 11 15.92 5 15 14.94 6 14 14.95 MSE: 8.17 The forecast for week 7: 14.76 Compare the three-week moving average forecast with the exponential smoothing forecast using = 0.2. Which appears to provide the better forecast based on MSE? Three-week moving average Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. Use trial and error to find a value of the exponential smoothing coefficient that results in a smaller MSE than what you calculated for = 0.2. Find a value of for the smallest MSE. Round your answer to three decimal places. = 0.157
This answer involves time series analysis concepts, specifically focusing on three-week moving averages and exponential smoothing methods. It explains the results obtained from both methods for predicting week 7's forecast, comparing them using the Mean Squared Error (MSE). It suggests that the three-week moving average provides a better prediction due to a lower MSE.
Explanation:The question asked is a problem in time series analysis, a category of statistics that involves the use and interpretation of data points ordered in time. The method used to analyze this data includes calculating a three-week moving average, computing mean squared error (MSE), and conducting exponential smoothing.
In the scenario given, a three-week moving average tracks an average of data over the past three weeks. It showed a forecast for week 7 as 13.33 with an MSE value of 7.74. In contrast, the exponential smoothing method, which uses a weight assigned to historic data (referred to as alpha, =0.2 in this case) forecasted a higher value of 14.76 with a slightly greater MSE of 8.17.
Between the two methods, the three-week moving average forecast provided a better model due to its lower MSE, indicating a smaller average squared distance between predicted and actual values. Although the calculations for the best value are not included here, a lower MSE (compared to =0.2) was obtained with the value =0.157. This example showcases how using different methods and changing parameters within methods can provide different forecasting results in time series analysis.
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Simplify the Square root of 72a6b3c2
Toxaphene is an insecticide that has been identified as a pollutant in the Great Lakes ecosystem. To investigate the effect of toxaphene exposure on animals, groups of rats were given toxaphene in their diet. An article reports weight gains(in grams) for rats given a low dose (4ppm) and for control rats whose diet did not include the insecticide. The sample standard deviation for 23 female control rats was 32g and for 20 female low-dose rats was 54g. Does this data suggest that there is more variability in low-dose weight gains than in control weight gains? Assuming normality, carry out a test of hypotheses at significance level .05.
Answer:
Check the explanation
Step-by-step explanation:
The details of the given samples are as follows:
Low dose. Number numbers of rats 20
The standard deviation . [tex]S_1[/tex]=54g
Control:
Number of rats [tex]N_2[/tex]=23
The standard deviation [tex]S_1[/tex]=32g
[tex]H_0[/tex]: there is no more variability in low — dose weight gains than in the control weight gins
[tex]H_1[/tex]: There is mere In-viability in low — dose weight gains than in control weight gains
>4 The level of significance.
a= 0.05 The test statistic to test the above hypothesis is Larger variance Smaller variance
The critical value of F (19.22) dr and at 0.05
significance level is 2.0837
The P-Value is 0.01 The test significance value is greater the the critical level is 20837.
Also. the 8-value is less then the significance level Hence, we reject the null hypothesis.
Therefore, we conclude that there is sufficient evidence to conclude that there is more variability in low — dose weight gains than in control weight gains .
(1 point) Suppose that f(x) and g(x) are given by the power series f(x)=6+7x+3x2+5x3+⋯ and g(x)=7+8x+3x2+4x3+⋯. By multiplying power series, find the first few terms of the series for the product h(x)=f(x)⋅g(x)=c0+c1x+c2x2+c3x3+⋯.
Answer:
f(x).g(x) = c0+c1x+c2x2+c3x3+⋯.
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...…...
Step-by-step explanation:
Suppose that f(x) and g(x) are given by the power series
f(x)=6+7x+3x2+5x3+⋯ and
g(x)=7+8x+3x2+4x3+⋯
By multiplying power series ,
f(x).g(x) = (6+7x+3x2+5x3+⋯).(7+8x+3x2+4x3+⋯)
= 6(7+8x+3x2+4x3+⋯)+7x(7+8x+3x2+4x3+⋯)+3x2(7+8x+3x2+4x3+⋯) + 5x3(7+8x+3x2+4x3+⋯)+......
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
f(x).g(x) = c0+c1x+c2x2+c3x3+⋯.is the form
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...……
In this problem, power series f(x) and g(x) are multiplied together term by term to produce the product h(x). The first few terms of the h(x) series are found by sequentially multiplying the corresponding terms of f(x) and g(x). The procedures produced the first four terms as 42, 98, 170, and 356 respectively.
Explanation:In the field of mathematics, specifically calculus, you can multiply two power series together term by term. In this case, function f(x) = 6 + 7x + 3x2 + 5x3 + ⋯ and g(x) = 7 + 8x + 3x2 + 4x3 + ⋯ are provided. When you multiply these two power series, the product h(x) = f(x) ⋅ g(x) is obtained by multiplying each corresponding term in the series of f(x) and g(x) together.
To find the first few terms we consider it like
First term, c0: f0*g0 = 6*7 =42Second term, c1: f1*g0 + g1*f0 = 7*6 + 8*7 = 98Third term, c2: f2*g0 + f1*g1 + g2*f0 = 18*3*6 + 7*8 + 21*6 = 170Fourth term, c3: f3*g0 + f2*g1 + f1*g2 + f0*g3 = 30*7 + 18*8 + 21*7 + 6*0 = 356and so on for the subsequent terms.
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Your friend brings 12 chocolate cupcakes and 12 vanilla cupcakes to school. Students will take turns picking a pair of cupcakes at random. What is the probability that the first student will pick 2 vanilla cupcakes?
Answer:
Answer = 11/46
Step-by-step explanation:
which is greater, 7 or 24/4
Answer:
7
Step-by-step explanation:
24/4=6. 7>6
is The polar form of a complex number is unique?
Answer:
no
Step-by-step explanation:
The angle in the polar form of a complex number can have any multiple of 2π radians added to it, and the number will be the same number. That is, there are an infinite number of representations of a complex number in polar form.
Final answer:
The polar form of a complex number is not unique due to the angle component, which can vary by multiples of full rotations (2π). However, when considering the principal value of the angle, the polar form becomes unique.
Explanation:
The polar form of a complex number is not entirely unique, the reason being that the angle (θ) in the polar form can be expressed as θ + 2πk, where k is any integer.
This is because complex numbers are represented in the complex plane, which is similar to a circle, where angles that differ by full rotations (2π radians) represent the same point.
However, the magnitude (or modulus) and the principal value of the angle (typically between -π and π) combine to give a unique representation of a complex number in polar form.
Matty jogs 9 km/hr. Compute Matty's speed in m/s.
Step-by-step explanation:
1km = 9000 m
1 min = 60 sec
So 60 min = 3600 sec
In this way Matty jogs 9000m /3600sec
Matty's speed of 9 km/hr is equivalent to 2.5 m/s when converted using the relationship where 1 km equals 1000 meters and 1 hour equals 3600 seconds.
Explanation:To compute Matty's speed in meters per second (m/s), we need to convert from kilometers per hour (km/h) to m/s. To do this, we can use the conversion rate where 1 km equals 1000 meters, and 1 hour equals 3600 seconds.
First, we convert Matty's speed to meters:
9 km/h = 9 × 1000 m/h = 9000 m/h.
Then, we convert hours to seconds:
9000 m/h × (1 h / 3600 s) = 9000 m / 3600 s = 2.5 m/s.
Therefore, Matty's speed in meters per second is 2.5 m/s.
The number of people who enter an elevator on the ground floor is a Poisson random variable with mean 10. If there are N floors above the ground floor and if each person is equally likely to get off at any one of these N floors, independently of where the others get off, compute the expected number of stops that the elevator will make before discharging all of its passengers.
Answer:
Expected no of stops=N(1-exp(-10/N)
Step-by-step explanation:
Using equation
X=∑[tex]I_{m}[/tex]
where m lies from 1 to N
solve equation below
E(X)=N(1-exp(-10/N)
Given Information:
Distribution = Poisson
Mean = 10
Required Information:
Expected number of stops = ?
Answer:
[tex]E(N) = N(1 - e^{-0.1N} )[/tex]
Explanation:
The number of people entering on the elevator is a Poisson random variable.
There are N floors and we want to find out the expected number of stops that the elevator will make before discharging all of its passengers.
Mean = μ = 10
The expected number of stops is given by
[tex]E(N) = N(1 - e^{-mN} )[/tex]
Where m is the decay rate and is given by
Decay rate = m = 1 /μ = 1/10 = 0.10
Therefore, the expected number of stops is
[tex]E(N) = N(1 - e^{-0.1N} )[/tex]
If we know the number of floor (N) then we can the corresponding expected value.
A is a 7 x 7 matrix with three eigenvalues. One eigenspace is two-dimensional, and one of the other eigenspaces is three dimensional. Is it possible that A is not diagonalizable? Justify your answer
Yes, it is possible for a 7 x 7 matrix to not be diagonalizable even if it has three eigenvalues.
Explanation:Yes, it is possible for a 7 x 7 matrix to not be diagonalizable even if it has three eigenvalues. A matrix is diagonalizable if and only if it has n linearly independent eigenvectors, where n is the size of the matrix. In this case, since we have one eigenspace two-dimensional and one eigenspace three-dimensional, we have a total of 5 linearly independent eigenvectors. Since 5 is less than 7, the matrix is not diagonalizable.
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Yes, it is possible that matrix A is not diagonalizable. For a square matrix to be diagonalizable, it must have a complete set of eigenvectors.
Explanation:Yes, it is possible that matrix A is not diagonalizable. For a square matrix to be diagonalizable, it must have a complete set of eigenvectors. In this case, we have a 7 x 7 matrix with three eigenvalues, but only two eigenspaces are given (a two-dimensional eigenspace and a three-dimensional eigenspace). Since we don't have eigenvectors for all the eigenvalues, matrix A is not guaranteed to be diagonalizable.
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Write a logical argument which determines what I ate for dinner. Number eachstep in your argument and cite which rule you use for each step.a. I did not have a coupon for buns or I did not have a coupon for hamburger.b. I had hamburgers or chicken for dinner.c. If I had hamburgers for dinner then I bought buns.d. If I did not have a coupon for buns then I did not buy buns.e. If I did not have a coupon for hamburger then I did not buy buns.
Answer:
88
Step-by-step explanation:
this is my answer it will help you
You roll a six-sided die twice. What is the probability of rolling a 3 and then a 5?
My guess is that it is 2/12 chance to get it, or 16.6
Answer:
1/36
Step-by-step explanation:
Multiply the two independent probabilities to find the compound probability.
P(3 and 5) =
1
6
×
1
6
=
1
36
farmer ed has 3000 meters of fencing and wants to enclose a rectangle plot that borders on a river. if farmer ed does not fence the side along the river what is the largest area that can be enclosed
Answer:
area = 1500× 750 = [tex]1125000 m^2[/tex]
Step-by-step explanation:
we know area of rectangle
for length = l m
and width = b m
[tex]A = lb[/tex]
and perimeter
[tex]Perimeter = 2 (length + width)[/tex]
but one side length measures is not required because of the river so
He does not use the fence along the side of the river
so we use this formula
Perimeter = P = L + 2 b
Perimeter is 3000 m
[tex]so \ \ 3000 = l +2b[/tex]
[tex]l = 3000 - 2b[/tex]
so area will be
[tex]A = (3000-2b)b[/tex]
it is a quadratic function whose max or min will
occur at the average of the Solutions.
on Solving (3000 - 2b)b = 0
3000 - 2b = 0 or b=0
2b =3000
[tex]b =\frac{3000}{2} \\b = 1500 m[/tex]
or [tex]b = 0 m[/tex]
The average of the values are [tex]\frac{(0+1500)}{2} = 750[/tex]
so for max area we use b= [tex]750 m[/tex]
The Length is then L=3000 - 2(750) = 3000 - 1500 = 1500
for max area
length = 1500 m
bredth = 750 m
area = 1500× 750 = [tex]1125000 m^2[/tex]
The largest area that can be enclosed by Farmer Ed with 3000 meters of fencing along a river (with only three sides fenced) equals 1,125,000 square meters by using principles of mathematical optimization.
Explanation:In this question, Farmer Ed wants to maximize the area of a rectangle with only three sides fenced, since one side borders on a river. We can use the principles of optimization in mathematics to solve this problem.
With 3000 meters of fencing for three sides, if we denote one side perpendicular to the river as X and the side parallel to the river (which forms the base of the rectangle) as Y, then, the perimeter would be Y+2X which is equal to 3000 meters. So, Y = 3000-2X.
The area A of a rectangle is length times width, or, in this case, A = XY. Substituting Y from the equation above: A = X(3000-2X) = 3000X - 2X^2. To maximize this area, we need to find values of X for which this equation has its maximum value.
The maximum or minimum of a function can be found at points where its derivative is zero. So, we take the derivative of A with respect to X, set it equal to zero, and solve for X.
The derivative, dA/dX is 3000 - 4X. Setting this equal to 0 gives X = 3000/4 = 750. So, the maximum area that Farmer Ed can enclose is when X is 750, and Y is 3000 - 2X = 1500, so the maximum area is 750 * 1500 = 1,125,000 square meters.
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Commuting. there are two routes he could take to work. Aneighbor who has lived there a long time tells him Route Awill average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way to go, driving each route 20 days. He finds that Route Atakes an average of 40 minutes, with stan- dard deviation 3 minutes, and Route B takes an average of 43 minutes, with standard deviation 2 minutes. His- tograms of travel times for the routes are roughly sym- metric and show no outliers. a.Find a 95% confidence interval for the difference in average commuting time for the two routes. b.Should the man believe the old-timer s claim that he can save an average of 5 minutes a day by always driving Route A
Answer:
a)We are 95% confident that the average commuting time for route A is between 1.3577 and 4.6423 minutes shorter than the average committing time for rout B.
(b) No, because the confidence internal does not contain —5, which corresponds with an average of 5 minutes shorter for route A.
Step-by-step explanation:
Given:
n_1 = 20
x_1= 40
s_1 = 3
n_2 = 20
x_2= 43
s_2 = 2
d_f = 33.1
c = 95%. 0.95
(a) Determine the t-value by looking in the row starting with degrees of freedom df = 33.1 > 32 and in the column with c = 95% in the Student's t distribution table in the appendix:
t[tex]\alpha[/tex]/2 = 2.037
The margin of error is then:
E = t[tex]\alpha[/tex]/2 *√s_1^2/n_1+s_2^2/n_2
E = 2.037 *√3^2/20+s_2^2/20
= 1.64
The endpoints of the confidence interval for u_1 — u_2 are:
(x_1 — x_2) — E = (40 — 43) — 1.6423 = —3 — 1.6423= —4.6423
(x_1 - x_2) + E = (40 — 43) + 1.6423 = —3 + 1.6423= —1.3577
a)We are 95% confident that the average commuting time for route A is between 1.3577 and 4.6423 minutes shorter than the average committing time for rout B.
(b) No, because the confidence internal does not contain —5, which corresponds with an average of 5 minutes shorter for route A.
Point A is at (-2, -7) and point M is at (2.5, -1.5).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?
Answer:
B = (7, 4)
Step-by-step explanation:
B = 2M -A = 2(2.5, -1.5) -(-2, -7)
B = (5+2, -3+7)
B = (7, 4)
__
Derivation
You know the midpoint is calculated from ...
M = (A+B)/2
Solving for B, we get ...
2M = A+B
B = 2M-A . . . . the formula we used above
Answer:
Give more points
Step-by-step explanation:
Further, Boris must also take into consideration the chicken calorie specifications which, as you know, are imposed by customers and competitors. The target for the chicken calorie content is 475 calories---with a tolerance level of 50 calories in each direction. The upper control limit of the X-bar chart is: (Please round up) a) More than 520 calories but less than or equal to 540 calories. b) More than 540 calories but less than or equal to 560 calories. c) More than 560 calories but less than or equal to 580 calories. d) More than 580 calories but less than or equal to 600 calories. e) None of the above.The lower control limit of the X-bar chart is:a) More than 415 calories but less than or equal to 430 calories.b) More than 430 calories but less than or equal to 445 calories.c) More than 445 calories but less than or equal to 460 calories.d) More than 460 calories but less than or equal to 475 calories.The process capability index, Cp, is:a) Negative.b)Less than 1.c)More than 1 but less than 1.3d)More than 1 but less than 1.4.e)None of the above.The process capability index, Cpk, is:a) Negative.b) Less than 1.c) More than 1 but less than 1.05d) More than 1 but less than 1.08e) None of the above.
Answer:
a, a, b,b
Step-by-step explanation:
Upper bound: 475+50= 525
lower bound: 475-50= 425
Cp= (Upper bound-lower bound)/ 6σ
Cp= (525-525)/ (6× 50)
Cp= 0.33
Cpk is minimum of two following values: (Upper bound-mean)/ 3σ, (mean -lower bound)/ 3σ
Cpk in this case is: Min (0.33,0.33)
The Cp and Cpk values are calculated from the actual process values. Here target Cp and Cpk value is 0.33
Roster's Chicken can monitor their caloric content using an X-chart with control limits calculated at either three or four standard deviations from the mean. The analysis reveals that grilled chicken breast is more energy-dense than tortilla chips. After consuming 16 tortilla chips, significant portions of the daily values (DV) for fat, sodium, and fiber remain for other meals.
Control Limits for X-Chart
To design an X-chart for monitoring the caloric content of Roster's Chicken, we need to establish the upper and lower control limits based on the given parameters.
Part a) Control Limits with Four Standard Deviations
The average caloric content of the chicken breast is 420 calories with a standard deviation of 20 calories. For a sample size of 25, the standard error is:
Standard Error = σ / √n = 20 / √25 = 20 / 5 = 4
Therefore, the four standard deviation limits from the target mean of 420 calories are:
Upper Control Limit (UCL) = 420 + 4 * 4 = 420 + 16 = 436 calories
Lower Control Limit (LCL) = 420 - 4 * 4 = 420 - 16 = 404 calories
Part b) Control Limits with Three Standard Deviations
Using the same standard error, the three standard deviation limits are:
Upper Control Limit (UCL) = 420 + 3 * 4 = 420 + 12 = 432 calories
Energy Density Comparison
A serving of grilled chicken breast (4 oz) has about 190 calories. In comparison, 16 tortilla chips typically have around 140 calories. Chicken breast is more energy-dense because it has more calories per ounce compared to tortilla chips, which makes it a denser source of calories.
Percentage Daily Values (DV) in 16 Tortilla Chips
If 16 tortilla chips contribute 10% DV of fat, 8% DV of sodium, and 4% DV of dietary fiber, the remaining percentages for a healthy diet would be:
• Fat: 100% - 10% = 90% DV remaining
• Sodium: 100% - 8% = 92% DV remaining
• Fiber: 100% - 4% = 96% DV remaining
Complete Question:- Roster's Chicken advertises "lite" chicken with 30% fewer calories than standard chicken. When the process for "lite chicken breast production is in control, the average chicken breast contains 420 calories, and the standard deviation in caloric content of the chicken breast population is 20 calories. Roster's wants to design an X-chart to monitor the caloric content of chicken breasts, where 25 chicken breasts would be chosen at random to form each sample. a) What are the lower and upper control limits for this chart? These limits are chosen to be four standard deviations from the target. Upper Control Limit (UCL): 436 calories (enter your response as an integer) Lower Control Limit (LCL): 404 calories (enter your response as an integer) b) What are the limits with three standard deviations from the target? Upper Control Limit (UCL): calories (enter your response as an integer)
Determine whether the following statement is true or false.
f(g(x)) = f(x) · g(x)
Answer:
False.Step-by-step explanation:
f(g(x)) = f of g of x
f(x) · g(x) = f at x times g at x, which is not the same thing.
From a point along a straight road, the angle of elevation to the top of a hill is . From farther down the road, the angle of elevation to the top of the hill is . How high is the hill?
Complete Question:
From a point along a straight road, the angle of elevation to the top of a hill is 33° . A distance of 200 ft farther down the road, the angle of elevation to the top of the hill is 20°. How high is the hill?
Answer:
The hill is 165.87 ft high
Step-by-step explanation:
Check the file attached below for a pictorial understanding of the question
[tex]tan \theta = \frac{opposite}{Adjacent}[/tex]
From ΔABC
[tex]tan 33 = \frac{y}{x} \\[/tex]
[tex]y = x tan 33[/tex]..........(1)
From ΔABD
[tex]tan 20 = \frac{y}{x + 200} \\[/tex]
[tex]y = (x + 200) tan 20[/tex]............(2)
Equating (1) and (2)
[tex]x tan 33 = (x+200) tan20\\xtan33 = xtan20 + 200tan20\\0.649x = 0.364x + 72.794\\0.649x - 0.364x = 72.794\\0.285x = 72.794\\x = 72.794/0.285\\x = 255.42 ft[/tex]
Substitute the value of x into equation (1)
[tex]y = 255.42 tan 33[/tex]
y = 165.87 ft
The height of the hill is 550 feet.
Given:
- [tex]\(\theta_1 = 31^\circ\)[/tex]
- [tex]\(\theta_2 = 24^\circ\)[/tex]
- [tex]\(d = 320\) feet[/tex]
We use the formula for the height of the hill \(h\):
[tex]\[h = \frac{d \tan(\theta_2) \tan(\theta_1)}{\tan(\theta_1) - \tan(\theta_2)}\][/tex]
First, we calculate [tex]\(\tan(31^\circ)\)[/tex] and [tex]\(\tan(24^\circ)\)[/tex]:
[tex]\[\tan(31^\circ) \approx 0.6009\][/tex]
[tex]\[\tan(24^\circ) \approx 0.4452\][/tex]
Now, substitute these values into the formula:
[tex]\[h = \frac{320 \times 0.4452 \times 0.6009}{0.6009 - 0.4452}\][/tex]
Calculate the numerator:
[tex]\[320 \times 0.4452 \times 0.6009 \approx 85.676256\][/tex]
Calculate the denominator:
[tex]\[0.6009 - 0.4452 \approx 0.1557\][/tex]
Now, divide the numerator by the denominator:
[tex]\[h = \frac{85.676256}{0.1557} \approx 550.41\][/tex]
Rounding to the nearest foot, the height of the hill is:
550 feet.
Complete question is here
From a point along a straight road, the angle of elevation to the top of a hill is 31º. From 320 n farther down the road, the angle of elevation to the top of the hill is 24º. How high is the hill? Round to the nearest foot.
Safety regulations state that roller coasters cannot operate safely in high winds. Throughout the day, ride operators measure the wind speed at several random locations along the track to verify that the speed is below an established threshold value, allowing the ride to operate safely. The collected data is used to conduct a one-sample z -test of the null hypothesis that the mean wind speed is moderate against the alternative that the mean wind speed is too high. If the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions. Choose the correct description of a type I error and a type II error in this context.
Answer:
Type I error would be to conclude that the mean wind speed is too high and decide to shut down the ride but in actual the wind speed was moderate and it is safe to do riding.
Type II error would be to conclude that the mean wind speed is moderate and decide to go on riding but in actual the wind speed is too high and it unsafe to go on riding and should be shut down.
Step-by-step explanation:
We are given that the collected data is used to conduct a one-sample z -test of the null hypothesis that the mean wind speed is moderate against the alternative that the mean wind speed is too high.
If the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions.
So, Null Hypothesis, [tex]H_0[/tex] : The mean wind speed is moderate.
Alternate Hypothesis, [tex]H_A[/tex] : The mean wind speed is too high.
Also, it is provided that if the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions.
Now, Type I error states the Probability of rejecting null hypothesis given the fact that it was true or Probability of rejecting the true hypothesis.
So, in the given context, Type I error would be to conclude that the mean wind speed is too high and decide to shut down the ride but in actual the wind speed was moderate and it is safe to do riding.
On the other hand, Type II error states the Probability of accepting null hypothesis given the fact that it was false or Probability of accepting the false hypothesis.So, in the given context, Type II error would be to conclude that the mean wind speed is moderate and decide to go on riding but in actual the wind speed is too high and it unsafe to go on riding and should be shut down.
Help fast!!! Pls!!!!!
Answer:
The height is 5 and the base is 9
Step-by-step explanation:
The area of a parallelogram is given by
A = bh
45 =x(x+4)
Distribute
45 =x^2+4x
Subtract 45 from each side
45-45 =x^2 +4x-45
0 = x^2 +4x-45
Factor
What two numbers multiply to -45 and add to 4
9+-5 = -45
9-5 =4
0=(x+9) (x-5)
Using the zero product property
0= x+9 0 = x-5
x=-9 x=5
Since length cannot be negative
x=5 is the solution
x=5
x+4 = 5+4 =9
The line AB has midpoint (2,5).
A has coordinates (1, 2).
Find the coordinates of B.
Answer:
[tex] X_m = \frac{A_x +B_x}{2}= \frac{1+B_x}{2}= 2[/tex]
And we can solve for [tex] B_x[/tex] and we got:
[tex] 1+B_x = 4[/tex]
[tex]B_x = 3[/tex]
[tex] Y_m = \frac{A_y +B_y}{2}= \frac{2+B_y}{2}= 5[/tex]
And we can solve for [tex] B_x[/tex] and we got:
[tex] 2+B_y = 10[/tex]
[tex]B_y = 8[/tex]
So then the coordinates for B are (3,8)
Step-by-step explanation:
For this case we know that the midpoint for the segment AB is (2,5)
And we know that the coordinates of A are (1,2)
We know that for a given segment the formulas in order to find the midpoint are given by:
[tex] X_m = \frac{A_x +B_x}{2}= \frac{1+B_x}{2}= 2[/tex]
And we can solve for [tex] B_x[/tex] and we got:
[tex] 1+B_x = 4[/tex]
[tex]B_x = 3[/tex]
[tex] Y_m = \frac{A_y +B_y}{2}= \frac{2+B_y}{2}= 5[/tex]
And we can solve for [tex] B_x[/tex] and we got:
[tex] 2+B_y = 10[/tex]
[tex]B_y = 8[/tex]
So then the coordinates for B are (3,8)
The coordinates of point B are (4, 8).
Explanation:To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M(xm, ym) of a line segment with endpoints A(x1, y1) and B(x2, y2) are given by:
xm = (x1 + x2) / 2
ym = (y1 + y2) / 2
In this case, we are given that the midpoint M is (2, 5) and A is (1, 2). We can substitute these values into the formula:
2 = (1 + x2) / 2
5 = (2 + y2) / 2
Now, we can solve for x2 and y2:
x2 = 4
y2 = 8
Therefore, the coordinates of point B are (4, 8).
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A travelling salesman sells milkshake mixing machines and on average sells 8.9 machines per month. He needs to sell at least 3 machines each month order to stay in business, otherwise he will shut down. Using the Poisson distribution, what is the probability he will have to shut down after this month
Answer:
0.67% probability he will have to shut down after this month
Step-by-step explanation:
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^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
On average sells 8.9 machines per month.
So [tex]\mu = 8.9[/tex]
Using the Poisson distribution, what is the probability he will have to shut down after this month
If he sells less than 3 machines.
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-8.9}*8.9^{0}}{(0)!} = 0.0001[/tex]
[tex]P(X = 1) = \frac{e^{-8.9}*8.9^{1}}{(1)!} = 0.0012[/tex]
[tex]P(X = 2) = \frac{e^{-8.9}*8.9^{2}}{(2)!} = 0.0054[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0001 + 0.0012 + 0.0054 = 0.0067[/tex]
0.67% probability he will have to shut down after this month