Answer:
27:-3×9
51:-3×17
In 27 and 51 the common one is 3 and hence it is the greatest common factor.✓✓
if you want smallest or lowest common factor then you have to take the common 3 as one and multiply like this:-3×9×17=459 is the Lowest common factor.
*mark me brainliest
How many 1/4 cup servings are in 2 1/2 cups of yogurt?
Answer:
10
Step-by-step explanation:
Hope it helps! :D
Answer:
6
Step-by-step explanation:
1 1/2 divided by 1/4
1 2/4 divided by 1/4
6/4 divided by 1/4
How many times does 1/4 go into 6/4?
Use the image below to answer the questions that follow:
** I can't upload the image but the Whole Math problem is in the Link I added to make it easier! **
(The image is Half of a house on one side of the graph)
Question 1. What type of symmetry would be used to complete the image of the house?
Question 2. What is the equation of the line of symmetry (or the point of symmetry if there is one) for the image?
Question 3. Use the rules of symmetry to determine 13 ordered pairs that would need to be plotted so that they can be connected by lines to complete the image of the house
Question 4. Complete the image of the house by plotting the points from the previous question and connecting the dots. You may copy the image into a drawing program to complete this task electronically, or you may print the image and upload a hand-drawn image to this document. Be sure to label the points.
Answer:
I can't please the question is sooo hard but can you give steps
Find the missing side lengths. Leave your answers as radicals in simplest form.
Please help!!!! Due today please help!!!!!!
Answer:
[tex]m = 10\sqrt 3[/tex]
[tex]n = 10[/tex]
Step-by-step explanation:
Required
Find m and n
Considering the given angle, we have:
[tex]\sin(60) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(60) = \frac{m}{20}[/tex]
Make m ths subject
[tex]m = 20 * \sin(60)[/tex]
[tex]\sin(60) =\frac{\sqrt 3}{2}[/tex]
So, we have:
[tex]m = 20 *\frac{\sqrt 3}{2}[/tex]
[tex]m = 10\sqrt 3[/tex]
Considering the given angle again, we have:
[tex]\cos(60) = \frac{Adjacent}{Hypotenuse}[/tex]
This gives:
[tex]\cos(60) = \frac{n}{20}[/tex]
Make n the subject
[tex]n = 20 * \cos(60)[/tex]
[tex]\sin(60) =\frac{1}{2}[/tex]
So, we have:
[tex]n = 20 *\frac{1}{2}[/tex]
[tex]n = 10[/tex]
Determine the period of the following trigonometric function.
Answer:
[tex]\displaystyle 1\frac{1}{4}\pi[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = 4cos\:(1\frac{3}{5}x - 1\frac{3}{10}\pi)} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{13}{16}\pi} \hookrightarrow \frac{1\frac{3}{10}\pi}{1\frac{3}{5}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{-\frac{3}{4}\pi} \hookrightarrow \frac{2}{1\frac{3}{5}}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle \boxed{y = 4sin\:(1\frac{3}{5}x + 1\frac{1}{5}\pi)} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{3}{4}} \hookrightarrow \frac{-1\frac{1}{5}\pi}{1\frac{3}{5}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{4}\pi} \hookrightarrow \frac{2}{1\frac{3}{5}}\pi \\ Amplitude \hookrightarrow 4[/tex]
Keep in mind that although this IS a sine function, if you plan on writing your equation as a function of cosine, then by all means, go right ahead. As you can see, the photograph farthest to the right displays the trigonometric graph of [tex]\displaystyle y = 4cos\:1\frac{3}{5}x,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph farthest to the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph farthest to the right] is shifted [tex]\displaystyle \frac{13}{16}\pi\:units[/tex]to the left, which means that in order to match the sine graph [photograph farthest to the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{13}{16}\pi\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{13}{16}\pi} = \frac{1\frac{3}{10}\pi}{1\frac{3}{5}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4cos\:(1\frac{3}{5}x - 1\frac{3}{10}\pi).[/tex]Intermediate, the centre photograph displays the trigonometric graph of [tex]\displaystyle y = 4sin\:1\frac{3}{5}x.[/tex]Again, just like before, we must figure out the appropriate C-term that will make this sine graph horisontally shift and map onto the sine graph in the leftward photograph. So, between the two photographs, we can tell that the centre sine graph is shifted [tex]\displaystyle \frac{3}{4}\pi\:units[/tex]to the right, which means that in order to match the leftward sine graph, we need to shift the graph BACKWARD [tex]\displaystyle \frac{3}{4}\pi\:units,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{3}{4}\pi} = \frac{-1\frac{1}{5}\pi}{1\frac{3}{5}}.[/tex]So, the sine graph is [tex]\displaystyle y = 4sin\:(1\frac{3}{5}x + 1\frac{1}{5}\pi).[/tex]Now, the amplitude is obvious to figure out because it is the A-term. Moreover, the midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Which of the following names a line segment in the drawing?
When the Bureau of Labor Statistics conducts a survey, it begins by partitioning the U.S. adult population into 2007 groups called primary sampling units. Assume that these primary sampling units all contain the same number of adults. If you randomly select one adult from each primary sampling unit, is the result a simple random sample? Why or why not? If it is not a simple random sample, what type of sample is it?
The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.
What is Probability and Non-Probability Sampling?It is not always possible to interview or survey an entire population. Therefore, in many research studies, a portion of the population that is expected to represent the population is drawn and surveyed instead. The portion that is drawn is called the sample, and the method used to draw the sample is called the sampling method. Broadly, there are two types of sampling methods. The probability sampling method is a method wherein all members of the population have an equal probability to be selected to be included in the sample. The non-probability sampling method is a method wherein not all members of the population have an equal probability to be selected to be included in the sample. Instead, members are recruited into the sample based on the researcher's subjective and personal judgment.
Simple Random Sampling Method:
Simple random sampling method, sometimes abbreviated as SRS, is the purest form of probability sampling. Figuratively, it is like putting the names of the entire population in a hat and drawing each member from the hat with a blindfold. Therefore, every member of the population has an equal chance of being included in the sample.
Two-stage Cluster Sampling Method:
In the first stage of a two-stage cluster sampling method, the population is first divided into subgroups called clusters. For instance, the population is divided into subgroups based on geographic location. Unlike strata in stratified sampling, clusters are heterogeneous and each cluster is supposed to represent the heterogeneity of the population. These clusters are also known as primary sampling units or PSUs. In the second stage, the simple random sampling method is used to draw individuals from each of the PSUs to be included in the study sample.
Hence, The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.
For more references on Probability and Non-Probability Sampling, click;
https://brainly.com/question/28016369
#SPJ1
simplify the following expression 4 + 3 . 7
what is the inverse of y=4-3x and is it a function
Answer:
y=(x+4)/3
Step-by-step explanation:
Answer:
x + 4 / 3
Step-by-step explanation:
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. a. What is the mean or expected number of customers that will arrive in a five-minute period
Answer:
The mean number of customers that will arrive in a five-minute period is 2.
Step-by-step explanation:
a. What is the mean or expected number of customers that will arrive in a five-minute period
For one minute, the mean is of 0.4 customers.
So, using proportions, for 5 minutes, the mean is of 5*0.4 = 2 customers.
The mean number of customers that will arrive in a five-minute period is 2.
It is believed that the average amount of money spent per U.S. household per week on food is about $99, with standard deviation $13. A random sample of 16 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. State the null and alternative hypotheses for this test, the test statistic and determine if the results significant at the 5% level.
Answer:
The null hypothesis is [tex]H_0: \mu = 99[/tex]
The alternate hypothesis is [tex]H_a: \mu > 99[/tex]
The test statistic is [tex]z = 0.31[/tex]
The pvalue of the test is 0.3783 > 0.05, which meas that the results are not significant at the 5% level.
Step-by-step explanation:
It is believed that the average amount of money spent per U.S. household per week on food is about $99. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average.
At the null hypothesis, we test if the mean is the national average of 99, that is:
[tex]H_0: \mu = 99[/tex]
At the alternate hypothesis, we test if the mean is greater than the national average of 99, so:
[tex]H_a: \mu > 99[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
99 is tested at the null hypothesis:
This means that [tex]\mu = 99[/tex]
A random sample of 16 households in a certain affluent community yields a mean weekly food budget of $100. Standard deviation of $13.
This means that [tex]n = 16, X = 100, \sigma = 13[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{100 - 99}{\frac{13}{\sqrt{16}}}[/tex]
[tex]z = 0.31[/tex]
The test statistic is [tex]z = 0.31[/tex].
Determine if the results significant at the 5% level.
The pvalue of the test is the probability of finding a sample mean above 100, which is 1 subtracted by the pvalue of z = 0.31.
Looking at the ztable, z = 0.31 has a pvalue of 0.6217
1 - 0.6217 = 0.3783
The pvalue of the test is 0.3783 > 0.05, which meas that the results are not significant at the 5% level.
Do you want to buy the 101 disc CD charger for 108 and also the digital camera for 364 if the sales tax is 6.5 what is your after-tax total
Answer: 441.32 currency units
Step-by-step explanation:
The CD changer costs 108 currency units and the Camera costs 364 currency units.
First add these up to find out the total price:
= 108 + 364
= 472 currency units
The sales tax is 6.5% and this needs to be deducted from the total to get the after-tax total:
= 472 * ( 1 - 6.5%)
= 441.32 currency units
Tell whether the following lengths are possible to be sides of a right triangle. if it is a triangle, state whether if it is a acute, right or obtuse
a. 2,2,2
b. 4,6,10
c. 7,24,25
d. 1, √3, 2
Answer:
A) an equilateral triangle with acute angles (60°)
B) isn't the lengths of a triangle
C) is a right triangle
D) is a right triangle
Step-by-step explanation:
A) 2,2,2, all sides and angles are all equal
B) applying cos rule to get the angles, an angle will be zero and a triangle can't have zero angle, thus the lengths are not that of a triangle
C) it's a right triangle as the dimensions are a pythagorean triple
D) it's a right triangle as the dimensions are a pythagorean triple
If m∠ABJ = 28, ∠ABC ≅ ∠DBJ, find m∠JBC.
Answer:
Step-by-step explanation:
If m∠ABJ = 28 and ∠ABC ≅ ∠DBJ, then we can set up the following equation:
m∠ABC = m∠DBJ
Since angles ∠ABC and ∠DBJ are congruent, they have the same measure, so the equation above is true.
Since we are trying to find m∠JBC, we can use the fact that the measure of an angle is equal to the sum of the measures of the other two angles in the triangle to set up another equation:
m∠JBC = m∠ABC + m∠ABJ
Substituting the value for m∠ABC from the first equation into the second equation, we get:
m∠JBC = m∠DBJ + m∠ABJ
Substituting the given value of m∠ABJ into this equation, we get:
m∠JBC = m∠DBJ + 28
Since m∠ABJ = m∠DBJ, we can substitute m∠ABJ in for m∠DBJ:
m∠JBC = m∠ABJ + 28
Substituting the given value of m∠ABJ into this equation, we get:
m∠JBC = 28 + 28
Solving this equation, we find that m∠JBC = 56.
Therefore, the measure of angle ∠JBC is 56 degrees.
About 25% of the students in Mr. Goodman's Clas got an A on their last math test. Of those, 50% are girls. The class has 12 girls and 16 boys. Is it reasonable to say 6 girls got an A on the test?
A) No, because 6 is not 25% of 28
B) No, because 6 girls is 50% Of all the girls in the class, and not all girls got A’s
C) Yes, because 50% of 12 is 6
D) Yes, because more girls than boys got A’s
Answer:
Hello, the answer is 6, C.
Step-by-step explanation:
50 percent of 12 is 6.
A coin is tossed and a number cube is rolled at the same time. What is the probability that the coin will land on tails and the number cube will land on 4?
a. 1/12
b. 1/6
c. 1/4
d. 5/12
DIRECTIONS: Use this information to answer Parts A and B. The width of a rectangle is shown. The length is twice the width. Part A 5-1x Write an expression for the perimeter listing each side separately.
Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.
Define perimeter.In geometry, a shape's perimeter, or overall length, is referred to as its perimeter. The lengths of all a shape's sides and edges are added up to determine its perimeter.
Here,
Given : length = 5 - 1(x) or
=> length = 5-x
Width is twice the length
thus,
=>Width = 2(5-x)
=>Width = 10-2x
So ,To find the perimeter
We use,
=> Perimeter = 2(length + width)
=> Perimeter = 2( 5-x + 10-2x )
=> Perimeter = 2( 15 -3x)
=> Perimeter = 30 -6x
Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.
To know more about perimeter, visit
brainly.com/question/6465134
#SPJ1
Which of the following statements is true about the number 3/20
Answer:
0.15
Step-by-step explanation:
I just put the fraction in decimal form since there is no photo.
A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs. The null hypothesis is that there is no difference in the population means (i.e. the difference is zero). The alternative hypothesis is that there is a difference (i.e. the difference is not equal to zero). He randomly selects a sample of 9 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40. He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90. He is using an alpha value of .10 to conduct this test. Assuming that the populations are normally distributed and that the population variances are approximately equal, the degrees of freedom for this problem are _______.
Answer:
The degrees of freedom for this problem are 21
Step-by-step explanation:
Degrees of freedom:
When testing an hypothesis involving two samples, the number of degrees of freedom is given by:
[tex]df = n_1 + n_2 - 2[/tex]
In which [tex]n_1[/tex] is the size of the first sample and [tex]n_2[/tex] is the sample of the second sample.
In this question:
Samples of 9 and 14, so [tex]n_1 = 9, n_2 = 14[/tex]
The degrees of freedom for this problem are
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 9 + 14 - 2 = 21[/tex]
The degrees of freedom for this problem are 21
The required degree of freedom is 21.
Given that,
He randomly selects a sample of 9 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40.
He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90.
He is using an alpha value of .10 to conduct this test.
We have to find,
The degrees of freedom for this problem are.
According to the question,
Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample.
Degrees of freedom are commonly discussed in relation to various forms of hypothesis testing in statistics, such as a chi-square.
When testing an hypothesis involving two samples, the number of degrees of freedom is given by,
[tex]Degree \ of \ freedom = n_1+n_2-2[/tex]
Where, [tex]n_1[/tex] is the size of the first sample and [tex]n_2[/tex] is the sample of the second sample.
[tex]n_1 = 9 \ and\ n_2 = 14[/tex]
Therefore,
[tex]Degree \ of \ freedom = 9+14-2\\\\Degree \ of \ freedom = 21[/tex]
Hence, The required degree of freedom is 21.
To know more about Degree of Freedom click the link given below.
https://brainly.com/question/23452965
I have a question which says:
Increase 32 by 4.4%
Answer:
increase amount = 32× 4.4%
= 32 × 4.4 ÷ 100
= 32 × 44 ÷ 1000
= 1.408
32 increased by 4.4% = 32 + 1.408 = 33.408
What is the inverse of the function
f(x)=X+3?
Answer:
x-3
Step-by-step explanation:
hope i helped, tell me if you get it right! :)
The door to the house is 2 meters and 4 centimeters tall. How many centimeters tall is it?
Answer:
200 CENTIMETRES
Step-by-step explanation:
Need Help! To Pass :/
Answer:
180 degrees counter-clockwise and 180 degrees clockwise
Step-by-step explanation:
Cuál es el radio de un círculo con diámetro de 47 mm
Respuesta:
23,5 milímetros
Explicación paso a paso:
Dado :
Diámetro del círculo = 47 mm
Radio del círculo = diámetro / 2
Por lo tanto, Radio = 47 mm / 2
Radio = 23,5 mm
100 POINTS PLEASE HELP!!! PICTURE IS ATTACHED.
The simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
How simplification of an expression work?The given expression is [tex](a^0 b^-4 cde^3)^2[/tex]
We know that any number raised to the power of 0 is 1.
Therefore,[tex]a^0 = 1[/tex].
Also, any number raised to the power of -1 is its reciprocal.
Therefore, [tex]b^-4 = 1/b^4[/tex]
Simplifying the above expression we get
[tex](1*1/b^4 * cde^3)^2 = (cde^3/b^4)^2[/tex]
Now, we apply the rule that [tex](a^m * a^n) = a^(m+n)[/tex]
So, [tex](cde^3/b^4)^2 = c^2 d^2 e^6 / b^8)[/tex]
Hence the simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
Please note, when an exponent is raised to another exponent, we can multiply the exponents, so [tex](a^m)^n = a^(m*n)[/tex]
To know more about simplification visit: https://brainly.com/question/28996879
#SPJ1
There is a proportional relationship between the weight and total cost of a bag of lemons. One bag weighs 2.4 pounds and costs $5.28. Another bag weighs 2.7 pounds and costs $5.94. Describe how you would graph the proportional relationship i need help asp
There is a directly proportional relationship between the weight and total cost of bag of of lemons.
What is constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
When two variables are directly or indirectly proportional to one another, their relationship may be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.
As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant.
Given data :
One bag weighs 2.4 pounds and cost $5.28.
Another bag weighs 2.7 pounds and cost $5.94
2.4k = 5.28
k= 2.2
2.7k = 5.94
k = 2.2
k > 1
The weight and total cost of bag of of lemons is directly proportional, so when weight of lemon increases, the cost of lemon also increases.
Therefore, there is a directly proportional relationship between the weight and total cost of bag of of lemons.
Learn more about constant of proportionality refer to :
brainly.com/question/28413384
#SPJ1
Garth is packing boxes with books. The list shows how many books are in each of 10 boxes.
6, 14, 6, 18, 9, 9, 12, 10, 11, 15
Which statement is true about the number of books packed to a box?
The median number of books to a box is 8.
The median number of books to a box is 9.
The mean number of books to a box is 11.
The mean number of books to a box is 12.
Answer:
The mean number of books to a box is 11.
Step-by-step explanation:
Given - Garth is packing boxes with books. The list shows how many books are in each of 10 boxes.
6, 14, 6, 18, 9, 9, 12, 10, 11, 15
To find - Which statement is true about the number of books packed to a box?
Solution -
Mean of number of books is equal to
= (6+ 14+ 6+ 18+ 9+ 9+ 12+ 10+ 11+ 15)/10
= 110/10
= 11
∴ we get
The mean number of books to a box is 11.
For Median -
Firstly, arrange the data into increasing order
6, 6, 9, 9, 10, 11, 12, 14, 15, 18
Now, we know that,
If total data(n) is even then median is the average of value at (n/2)th place and [(n/2 + 1]th place
Here n = 10
So,
Median is average of 10 and 11
i.e. Median = (10+11)/2
= 21/2 = 10.5
So,
Median number of books to a box is 10.5
∴ we get
The correct option is - The mean number of books to a box is 11.
Answer:
The mean number of books to a box is 11.
Step-by-step explanation:
New York City is 2.727272.% of the United States' population. NYC's population is 9 million people. What is the population of the United Sates?
The population of US is 330 million approx.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." The number "%" is used to symbolize it.
Given
population of new york = 2.727272% population of US
population of new york = 9 million
population of US = 1/2.727272% of new york
population of US = 36.6666 x 90,00,000
population of US = 33,00,00,087.9 = 330 million approx
Hence population of US is approx 330 million.
Learn more about percent;
https://brainly.com/question/28840349
#SPJ1
Solve the inequality: -16< 4(2x + 8) <40
Answer:
-6 < x <1 , (-6, 1)
Step-by-step explanation:
I need the answer to this question
Answer:
it is not factorable
Step-by-step explanation:
There are no factors of 24 that will make -4, so it is not factorable
Your firm bottles water in plastic bottles labeled for 16.9 ounces. The specifications are 16.75 ounces to 17.05 ounces. Your filling process has an average fill of 16.90 ounces with a standard deviation of 0.04 ounces. Which of the following statements are TRUE? I The Cp calculation indicates that the process is capable. II The Cpk calculation is less than the Cp calculation. III The process is centered, so the Cp calculation should be used. I only II only III only I and III II and III
Answer:
From the statements in the question, I and III is CORRECT
Step-by-step explanation:
First we take down the given data from the question for substitution;
Process mean = 16.9 ounces
Lower specification limit = 16.75 ounces
Upper specification limit = 17.05 ounces
Standard deviation = 0.04
Now, we get our Cpk;
Cpk = MINIMUM( (Upper specification limit - mean ) / 3 × Standard deviation), (mean - Lower specification limit) / 3 × Standard deviation) )
so we substitute
Cpk = MINIMUM( ((17.05 ounces - 16.9 ounces) / 3 × 0.04 ounces ), (( 16.9 ounces - 16.75 ounces) / 3 × 0.04 ) )
Cpk = MINIMUM( 0.15 / 0.12 ), ( 0.15 / 0.12 )
Cpk = MINIMUM( 1.25, 1.25 )
Cpk = 1.25
Next the Cp;
Cp = ( Upper specification limit - Lower specification limit ) / ( 6 × standard deviation )
we substitute
Cp = ( 17.05 ounces - 16.75 ounces ) / ( 6 × 0.04 ounces )
Cp = 0.3 / 0.24
Cp = 1.25
Hence;
Cpk calculation is not less than Cp calculation.
Since Cp is greater than 1, the process is cable.
Since the actual process mean is also 16.90 ounces, then the process is centered.
Therefore, From the statements in the question, I and III is CORRECT
The correct statement is "the Cp calculation indicates that the process is capable" and "the process is centered, so the Cp calculation should be used" and this can be determined by using the formula of Cpk and Cp.
GIven :
Your firm bottles water in plastic bottles labeled for 16.9 ounces. The specifications are 16.75 ounces to 17.05 ounces. Your filling process has an average fill of 16.90 ounces with a standard deviation of 0.04 ounces.The formula of Cpk is given below:
[tex]\rm Cpk = minimum\left( \dfrac{Upper \;specification \;limit - mean}{ 3 \times Standard \;deviation)}, \dfrac{ mean - Lower\; specification\; limit} { 3 \times Standard \;deviation}\right )[/tex]
Now, substitute the known terms in the above formula.
[tex]\rm Cpk = minimum \left(\dfrac{17.05-16.9}{3\times 0.04},\dfrac{16.9-16.75}{3\times 0.04}\right)[/tex]
[tex]\rm Cpk = minimum \left(\dfrac{0.15}{0.12},\dfrac{0.15}{0.12}\right)[/tex]
Cpk = 1.25
Now, the formula of Cp is given below:
[tex]\rm Cp = \dfrac{Upper\; specification\; limit - Lower\; specification \;limit} { 6 \times standard \;deviation }[/tex]
Now, substitute the known terms in the above formula.
[tex]\rm Cp = \dfrac{17.05-16.75}{6\times 0.04}[/tex]
Cp = 1.25
So, the correct statement is "the Cp calculation indicates that the process is capable" and "the process is centered, so the Cp calculation should be used".
Therefore, the correct option is D) I and III.
For more information, refer to the link given below:
https://brainly.com/question/15351734