A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 419 gram setting. It is believed that the machine is underfilling the bags. A 15 bag sample had a mean of 409 grams with a standard deviation of 22. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answers
Answer:
We reject the null hypothesis, and accept the alternative hypothesis.
So, it means that the machine is under filling the bags
Step-by-step explanation:
Given
Null Hypothesis
\(H_0:\mu = 419\) --- works correctly at 419g
Alternate Hypothesis
\(H_0:\mu < 419\) --- under fills the bag
\(n =15\) --- the sample
\(\bar x = 409\) --- the mean
\(\sigma = 22\) --- the standard deviation
\(\alpha = 0.05\) --- the significance level
Required
What is the decision rule
Since n is less than 30, we make use of t test
\(t = \frac{\bar x - \mu}{\sigma/\sqrt n}\)
\(t = \frac{409 - 419}{22/\sqrt{15}}\)
\(t = \frac{-10}{22/ 3.87}\)
\(t = \frac{-10}{5.58}\)
\(t = -1.792\)
Calculate df
\(df = n-1\)
\(df = 15-1\)
\(df = 14\)
Calculate the p value from the Student's t-distribution at df = 14 and \(t = -1.792\)
\(p =0.047\)
Given that: \(\alpha = 0.05\)
Since \(p < \alpha\)
So, it means that the machine is under filling the bags
Related Questions
Please help me quick
Answers
The product of the ages 2 years from today is 924
System of equationLet the ages of the three cousins be x, y and z. If the product of their ages is 1716, hence;
xyz = 1716
If the product of their ages last year is 1320, then;
(x-1)(y-1)(z-1) = 1320
Two years ago, the product of their ages will be;
(x-2)(y-2)(z-2) = 1320- (1716-1320)
(x-2)(y-2)(z-2) = 1320-396
(x-2)(y-2)(z-2) =924
Hence the product of the ages 2 years from today is 924
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please
Find the surface area of the prism.
Answers
The following lots of Commodity Z were available for sale during the year. Beginning inventory 9 units at $50 First purchase 16 units at $50 Second purchase 21 units at $59 Third purchase 16 units at $62 The firm uses the periodic system, and there are 23 units of the commodity on hand at the end of the year. What is the ending inventory balance at the end of the year according to the FIFO method?
Answers
According to the FIFO method, the ending inventory balance for Commodity Z is $1,405
How much inventory is left under FIFO?FIFO means that earlier inventory is sold first and later inventory would be the last goods left.
Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:
= (16 x 62) + (7 x 59)
= 992 + 413
= $1,405
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a geologist has collected 14 specimens of basaltic rock and 14 specimens of granite. the geologist instructs a laboratory assistant to randomly select 23 of the specimens for analysis. (a) what is the pmf of the number of granite specimens selected for analysis? (round your probabilities to four decimal places.) x 9 correct: your answer is correct. 10 correct: your answer is correct. 11 correct: your answer is correct. 12 correct: your answer is correct. 13 correct: your answer is correct. 14 correct: your answer is correct. p(x) 0.0974 incorrect: your answer is incorrect. 0.1384 incorrect: your answer is incorrect. 0.1612 incorrect: your answer is incorrect. 0.1612 incorrect: your answer is incorrect. 0.1384 incorrect: your answer is incorrect. 0.0974 incorrect: your answer is incorrect. (b) what is the probability that all specimens of one of the two types of rock are selected for analysis? (round your answer to four decimal places.) 0.0974 incorrect: your answer is incorrect. (c) what is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value? (round your answer to four decimal places.)
Answers
The standard deviation is 1.0319
x values between 10.4681 and 12.5319 are respectively ( 11 , 12 )
The probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value is 0.6740
How to solve thisWe are given that: a geologist has collected 14 specimens of basaltic rock and 14 specimens of granite.
Thus total rocks = N = 14 +14 = 28
The geologist instructs a laboratory assistant to randomly select 23 of the specimens for analysis.
Thus sample size = n = 23
Part a) What is the pmf of the number of granite specimens selected for analysis?
x = the number of granite specimens selected
Thus M = Number of granite specimens = 14
Thus x can have the following values:
x n-x = 23-x
9 14
10 13
11 12
12 11
13 10
14 9
We can select a minimum 9 granite specimens, so that total becomes 9 granite specimens + 14 basaltic rock = 23
and maximum 14 granite specimens, so that total becomes 14 granite specimens + 9 basaltic rock = 23
Here x = the number of granite specimens selected follows Hypergeometric distribution with parameters N = 28 ,M=14 , n = 23 .
P(X=9) =0.02037
Similarly, we find all next probabilities:
x P(x)
9 0.0204
10 0.1426
11 0.3370
12 0.3370
13 0.1426
14 0.0204
Part b) What is the probability that all specimens of one of the two types of rock are selected for analysis?
the probability that all specimens of one of the two types of rock are selected
That is:
P( All 14 are granite specimens and rest 9 are basaltic rock OR All 14 are basaltic rock and rest 9 are granite specimens)=......?
That is:
P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) =......?
From above table in part a) , we have:
P( 14 granite specimens) = 0.0204 , that means
P(14 granite specimens , 9 basaltic rock) = 0.0204
and
P( 9 granite specimens)=0.0204
That is:
P( 14 basaltic rock , 9 granite specimens) = 0.0204
Thus
P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) =0.0204 + 0.0204
P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) = 0.0408
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The local government is concerned with the population of a new predatory fish, the tiger gar, which was first observed in Lake Richmond about 5 years ago. The following table shows the approximate number of tiger gars living in the lake since 2016:
2016 2017 2018 2019 2020 2021
322 399 507 618 785 975
Using the TI-nspire calculator, write an exponential function that models the population of tiger gar in the lake. (Round all numbers to the nearest hundredth.)
y=blank(blank)x
Answers
The exponential function that models the population of tiger gar in the lake is given as follows:
\(y = 322.63(1.25)^x\)
How to define an exponential function?An exponential function has the definition presented as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.Considering x as the number of years since 2016, the points are given as follows:
(0, 322), (1, 399), (2, 507), (3, 618), (4, 785), (5, 957).
Inserting these points into an exponential regression calculator, the equation is given as follows:
\(y = 322.63(1.25)^x\)
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A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the standard deviation of sample mean
Answers
Answer:
\( \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) \)
And the standard deviation for the sample mean would be given by:
\( \sigma_{\bar X}= \frac{1.5}{\sqrt{25}}= 0.3\)
Step-by-step explanation:
For this case we know that the amount of cheese inserted into the ravioli is normally distributed. And we have the following info given;
\( \bar X =15\) the sample mean
\(s= 1.5\) the sample deviation
\( n=25\) the sample size
And for this case we know that the sample size is large enough in order to apply the central limit theorem and the distribution for the sample mean would be given by:
\( \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) \)
And the standard deviation for the sample mean would be given by:
\( \sigma_{\bar X}= \frac{1.5}{\sqrt{25}}= 0.3\)
Complete the table shown below. f(x) = 2x2 - 8x + 6 1 0 2 y 3 4. 6 X= y = Z
Answers
Answer:
x = 6, y = -2, z = 0
Step-by-step explanation:
To find x, we have to plug 0 into f(x). Therefore, x = f(0) = 2 * 0² - 8 * 0 + 6 = 6. Similarly, to find y, we have to plug 2 into f(x) so y = f(2) = 2 * 2² - 8 * 2 + 6 = -2. Finally, z = f(3) = 2 * 3² - 8 * 3 + 6 = 0.
Answer:
6, -2, 0
Step-by-step explanation:
After the party, a bag of ice weighs 7/8 pound. Before the party, the bag of ice weighed 3 times as much. How many pounds did the bac
party?
Drag the pointer to its correct location on the number line to show the weight of the bag of ice before the party.
3
4
Weight of Bag of Ice Before Party
2
4
Finish Late
Answers
The weight before the party could be any positive number
The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:
x - weight used at the party = 7/8
We know that the weight used at the party is the weight before the party minus the weight after the party.
So we can substitute 3x for the weight before the party:
3x - (7/8) = weight used at the party
We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.
So we can set up another inequality:
weight used at the party ≤ 3x
Putting it all together:
3x - (7/8) ≤ 3x
Simplifying:
-(7/8) ≤ 0
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The bottom number. I need written in a way where there is no number above the square root symbol. (The number 3 that’s above the square root symbol) I need it like simplified to where there is no number above the square root symbol
Answers
1) We need to remember that a radical can be rewritten as a power.
2) So in this case, to rewrite it as a square root, we need to raise it to the 3/2 power so that we get an index of 2
\(\begin{gathered} ^{} \\ (-8\sqrt[3]{63})^{\frac{3}{2}}\Rightarrow(-8\cdot63^{\frac{1}{3}})^{\frac{3}{2}}=-8^{\frac{3}{2}}\cdot63^{\frac{1}{2}}=-8^{\frac{3}{2}}\sqrt[]{63} \end{gathered}\)3) Hence, if we raise it to the 3/2 exponent we can rewrite it as -8 raised to 3/2 times the square root of 63.
Find two square numbers that total 45
Answers
x^2+^2=45
if ×=3 and y=6
then 9+36=45
Algebraic expression for 4less then 3x
Answers
When 'x' is 5, the Algebraic expression 3x - 4 evaluates to 11.
To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.
First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.
Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.
In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.
To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:
3(5) - 4
This simplifies to:
15 - 4 = 11
So, when 'x' is 5, the expression 3x - 4 evaluates to 11.
In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.
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Note the complete question:
Algebraic expression for 4 less than the product of 3 and some number
What is the algebraic expression for "4 less than the product of 3 and some number?
Please help me understand the meaning of how to calculate.
Marriage Prospects Data released by the Census Bureau in 1986 indicated the likelihood that never-married women would eventually marry. The data indicated that the older the woman, the less the likelihood of marriage. Specifically, two statistics indicated that women who were 45 and never-married had an 18 percent chance of marriage and women 25 years old had a 78 percent chance of marriage. Assume that a linear fit to these two data points provides a reasonable approximation for the function p=f(a), where p equals the probability of marriage and a equals the age of a never- married woman. (a) Determine the linear function p=f(a). (b) Interpret the slope and p intercept. (c) Do the values in part b seem reasonable? (d) If the restricted domain on this function is 20 sa s 50, determine f(20), f(30), f(40), and f(50).
Answers
Answer:
See below
Step-by-step explanation:
Using the two pairs of (a, p) to determine the function:
(45, 18) and (25, 78)The function would be:
f(a) = ma + b, where m is slope, b is p-interceptSlope is:
m = (78 - 18)/(25 - 45) = -50/20 = -2.5p-intercept:
18 = -2.5*45 + bb = 18 + 112.5 = 120.5So the function is:
(a)
f(a) = -2.5a + 120.5(b) Slope is negative, indicating the lower probability at greater age. P-intercept of 120.5 is of the non-real case as for zero age it gives more than 100% probability.
(c) The domain needs restriction in line with law, so minimum age and maximum to be determined in order not to have unrealistic outcome. It should be ok between 18 and 48.
(d) The values at given points:
f(20 = -2.5*20 + 120.5 = 70.5f(30) = -2.5*30 + 120.5 = 45.5f(50) = -2.5*50 + 120.5 = -4.5 (negative probability for the age of 50 is not real)Which point is at 4/3 on the number line?
Answers
Answer:
Hi there!
Step-by-step explanation:
Its 1.3
the diameter of a circle is 8. what is the area of the circle in terms of π?
Answers
Answer:
Step-by-step explanation:
radius r = 8/2 = 4
area of circle = πr² = 16π units²
Select the correct answer.
If no denominator equals zero, which expression is equivalent to 15/x-6 + 7/x+6?
A.
OB.
OC.
OD.
22 +132
²36
22-48
236
22
C.36
22 +48
²36
Answers
The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).
Given expression is,
[15 / (x - 6)] + [7 / (x + 6)]
Cross multiplying the two fractional expressions,
= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]
= [15x + 90 + 7x - 42] / [x² - 6²]
= (22x + 48) / (x² - 36)
Hence the equivalent expression is D.
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Which describes the effect of the transformations on the graph of f(x) = x2 when changed to f(x) = 1/4(x - 3)2 - 9?
A) stretched vertically, shifted left 3 units, and shifted up 9 units
B) stretched vertically, shifted right 3 units, and shifted down 9 units
C) compressed vertically, shifted left 3 units, and shifted up 9 units
D) compressed vertically, shifted right 3 units, and shifted down 9 units
This is not part of the equation its just to help
"(x- 3)2 -9"
2 is a exponent
Note: The photo does not show full equation
Answers
Answer:
B
Step-by-step explanation:
P=x-2 ÷ x+1 for what value of x is P undefined
Answers
Answer:
x = - 1
Step-by-step explanation:
P = \(\frac{x-2}{x+1}\)
the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.
x + 1 = 0 ( subtract 1 from both sides )
x = - 1
P is undefined when x = - 1
Describe the relationship between the terms in each arithmetic sequence. Then write the next three terms in each sequence.
B
0, 5, 10, 15, …
a.
2 is added to each term; 17, 19, 21
b.
5 is added to each term; 20, 25, 30
c.
5 is added to each term; 25, 30, 35
d.
10 is added to each term; 25, 35, 45
Answers
Answer:
Answer b)
Step-by-step explanation:
In the sequence 0, 5, 10, 15,...
5 is added to each term in order to get the next one. Therefore the next three terms would be; 20, 25, 30.
This agrees with answer b) in the list of possible answers.
for the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.
14. distance to the closest movie theater
16. number of competing computer spreadsheet software packages
Answers
Answer:
14: quantitative continuous
16: quantitative discrete
Step-by-step explanation:
Distance can be any non-negative real number, hence it is continuous.
The number of packages has to be a positive integer, hence is discrete.
Decide whether each expression or fraction shows another way to write 3 Choose True or False for each expression or fraction. 3+ True False 15+ True 0 False 19 5 True False 7 5 를 O True O False ] 55+ 8 + 8 + + True 0 False
Answers
Answer:
Explanation:
Given the below mixed fraction;
\(3\frac{4}{5}\)We can also express it as an improper fraction by multiplying the whole number by the denominator and adding the result to the numerator. We'll have;
\(3\frac{4}{5}=\frac{19}{5}\)Let's go ahead and simplify each of the given expressions or fractions in order to decide which of them is the same as the above fraction.
1. For the 1st expression;
\(\begin{gathered} 3+\frac{4}{5}=\frac{15+4}{5}=\frac{19}{5} \\ \end{gathered}\)From the above, we can see that the given expression is the same as our above fraction, so we'll choose ''True''
2. For the 2nd expression;
\(\frac{15}{5}+\frac{4}{5}=\frac{15+4}{5}=\frac{19}{5}\)From the above, we can also see that the given expression is the same as our above fraction, so we'll choose ''True''
3. The fraction 19/5 is the same as the improper fraction we had above, so we'll choose ''True''
4. The fraction 3 4/5 or 19/5 can not be reduced to 7/5, so we'll choose "False" here
5. For the 5th expression;
\(\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{4}{5}=1+1+1+\frac{4}{5}=3+\frac{4}{5}=\frac{15+4}{5}=\frac{19}{5}\)From the above, we can also see that the given expression is the same as our above fraction, so we'll choose ''True''
Which of the following questions are statistical? A. How many hours did you sleep last night. B. How many hours did the students in your class sleep last night. C. How many hours did your friend spend reading last night. D. How many hours did your teacher spend reading on Saturday.
Answers
This is a statistical question because you get multiple answers. The other choices can just be answered with a definitive answer. Statistical question are those that have data with variabilty, meaning many different values
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Umberto plants a garden with an area of 16 square feet. What is the area of the garden in square inches
Answers
Answer:
2,304 inches
Step-by-step explanation:
1 square foot = 144 square inches
16 x 144 = 2,304 square inches
Suppose that a recent poll found that 40% of adults in a certain country believe that the overall state of moral values is poor. If a survey of a random sample of 20 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values.
complete parts (a) through (e) below.
Click here to view the table for the binomial probability distribution.
Click here to view the table for the cumulative binomial probability distribution.
(a) Find and interpret the probability that exactly 12 of those surveyed feel the state of morals is poor.
The probability that exactly 12 of those surveyed feel the state of morals is poor is
(Round to four decimal places as needed
Answers
Answer:
0.0355 = 3.55% probability that exactly 12 of those surveyed feel the state of morals is poor. This means that there is a low probability of finding this exact value.
Step-by-step explanation:
For each adult surveyed, there are only two possible outcomes. Either they think that the state of morals is poor, or they do not. One adult's opinion is independent of other adults. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
40% of adults in a certain country believe that the overall state of moral values is poor.
This means that \(p = 0.4\)
Sample of 20 adults
This means that \(n = 20\)
(a) Find and interpret the probability that exactly 12 of those surveyed feel the state of morals is poor.
This is P(X = 12).
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 12) = C_{20,12}.(0.4)^{12}.(0.6)^{8} = 0.0355\)
0.0355 = 3.55% probability that exactly 12 of those surveyed feel the state of morals is poor. This means that there is a low probability of finding this exact value.
Triangle ABC is dilated about the origin to create triangle A′B′C′.
Triangle ABC with vertices at A negative 13 comma negative 4, B negative 6 comma negative 4, and C negative 6 comma 4 and triangle A prime B prime C prime with vertices at A prime negative 32.5 comma negative 10, B prime negative 15 comma negative 10, and C prime negative 15 comma 10.
Determine the scale factor used to create the image.
three fourths
2
one half
2.5
Answers
The scale factor of the dilation of the triangle is k = 2.5
Given data ,
Let the triangle be represented as ΔABC
Now , the coordinates of the triangle are
A ( -13 , -4 ) , B ( -6 , -4 ) and C ( -6 , 4 )
Now , the dilated triangle is given by ΔA'B'C'
where the coordinates are
A' ( -32.5 , -10 ) , B' ( -15 , -10 ) and C' ( -15 , 10 )
So , the scale factor k is given by
k = -32.5 / -13
k = 2.5
Hence , the dilation factor is k = 2.5
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1: Solve and Graph: 5-3(x - 1)> 2
2: Solve and Graph: 2x - 3> 7 or x+5<2
3: Solve for x: |1x-5|=13
Answers
Answer:
3) x=18 , -8
Step-by-step explanation:
hi
hope it helps you
Milkayla withdraws 20 on 4 different
Answers
Answer:
20 times 4 = 20
Step-by-step explanation:
Please mark as brainliest
David has a bank account which pays interest at the rate of 1.5% per year, compounded annually. Determine what amount David
must have in the bank, given that he would like to draw an annual salary of $32,635.15 from his account at the end of each year
for 30 years. Round to the nearest cent.
Answers
Answer: the amount that David must have in the bank is $783243.6
Step-by-step explanation:
We would apply the formula for determining present annuity. It is expressed as
PV = R[1 - (1 + r)^- n]r
Where
PV represents the present value of the investment.
R represents the regular payments made(could be weekly, monthly)
r = represents interest rate/number of interval payments.
n represents the total number of payments made.
From the information given,
r = 1.5/100 = 0.015
n = 30 years
R = $32,635.15
Therefore,
PV = 32635.15[1 - (1 + 0.015)^- 30]/0.015
PV = 32635.15[1 - (1.015)^- 30]/0.015
PV = 32635.15[1 - 0.64]/0.015
PV = 32635.15[0.36]/0.015
PV = 32635.15 × 24
PV = $783243.6
a. $783,760.48
on edgen
I need to know this please answer asap
Answers
Answer:
y=-1/2x+1
Step-by-step explanation:
Tony invested $9538 in an account at 8% compounded daily. Identify the compound
interest C after 1 years.
Answers
9514 1404 393
Answer:
$794.30
Step-by-step explanation:
The account balance for principal P invested at rate r compounded daily for t years is ...
A = P(1 +r/365)^(365t)
We have P=$9538, r=0.08, t=1, and we want the value of P-A, the interest earned.
P-A = P(1 +0.08/365)^365 -1) = $9538(1.08327757 -1) ≈ $794.30
The interest earned in one year is $794.30.
The distances between Centerville, Springfield, and Capital City form a right triangle. The distance between Centerville and Springfield is 913 kilometers and the distance between Springfield and Capital City is 976 kilometers.
Anwell travels from Centerville to Springfield, then on to Capital City. Yue travels directly from Centerville to Capital City. How much farther does Anwell travel than Yue?
Answers
Answer:
Step-by-step explanation:
x+9
x0+
10
Anwell travels a distance of 552.533 km more than Yue.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Given that,
The distances between Centerville, Springfield, and Capital City form a right triangle.
The triangle is given below.
This is a right angled triangle, where the hypotenuse is the distance between Centerville and Capital city.
Using Pythagoras Theorem,
Hypotenuse² = (Leg 1)² + (Leg 2)²
x² = (913)² + (976)²
x² = 1786145
x = √1786145 = 1336.467
Distance that Yue travels = 1336.467 km
Distance Anwell travels = 913 km + 976 km = 1889 km
Difference = 1889 km - 1336.467 km = 552.533 km
Hence Anwell travels 552.533 km more than Yue.
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