A production line operation is designed to fill cans with tomato sauce with a mean weight of 20 ounces. A sample of 25 cans is selected to test whether overfilling or under filling is occurring in the production line and they should stop and adjust it. Sample statistics (mean and standard deviation) are calculated. Assume the population of interest is normally distributed.



Let the p-value be 0. 067 for this sample. At 0. 05 level of significance, it can be concluded that the mean filling weight of the population is :_________



a. Significantly different than 20 ounces


b. Not significantly different than 20 ounces


c. Significantly less than 20 ounces


d. Not significantly less than 20 ounces

Answer: ME

Step-by-step explanation:

Answer: 84 yd²

Step-by-step explanation:

First find the area of the entire rectangle.

7 × 16 = 112 yd²

Then find area of the cut-out triangle.

\(\frac{1}{2}\)bh = \(\frac{1}{2}\)(7)(8) = 28 yd²

To find the area of the shaded area:

rectangle - triangle = shaded area

112 - 28 = 84 yd²

The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

Learn more about bisection method at: brainly.com/question/30320227

#SPJ11

Answer:

9/100

Step-by-step explanation:

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

The next number in the sequence is 0.5, which corresponds to option B. ½.

To find the next number in the sequence 16, 8, 4, 2, 1, ?, observe the pattern and identify the rule that governs the sequence.

If we look closely, we notice that each number in the sequence is obtained by dividing the previous number by 2. Specifically:

8 = 16 / 2

4 = 8 / 2

2 = 4 / 2

1 = 2 / 2

Therefore, the pattern is that each number is obtained by dividing the previous number by 2.

Following this pattern, the next number in the sequence would be obtained by dividing 1 by 2:

1 / 2 = 0.5

Hence, the next number in the sequence is 0.5.

Among the given options, the closest option to 0.5 is B. ½.

Therefore, the answer is B. ½.

Learn more about sequence here:

https://brainly.com/question/30262438

#SPJ11

The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

To know more about perimeter , visit:

https://brainly.com/question/25092270

#SPJ1

Answer:

y = \(\frac{-14}{27}\)

Step-by-step explanation:

27y + 5 = -9 -> subtract -9 and 5

(-9) - 5 = -14

27y = -14 divide 27 and -14

(-14)/27

You are then left with

y = \(\frac{-14}{27}\)

\(answer \\ k = - 4 \\ solution \\ 2x + y - 6 = 0 \\ (5 \: k) \: is \: a \: solution \: so \\ x = 5 \: and \: y = r \\now \\ 2x + y - 6 = 0 \\ or \: 2 \times 5 + r - 6 = 0 \\ or \: 10 + r - 6 = 0 \\ or \: 10 - 6 + r = 0 \\ or \: 4 + r = 0 \\ or \: r = 0 - 4 \\ r = - 4 \\ hope \: it \: helps\)

Answer:

d = 16.7 in

Step-by-step explanation:

Since C = πd, d = C/π.          52.438 in

Here, with C = 52.438, d = ----------------- = 16.7 in

                                                  3.14

\({\boxed{\boxed { \tt {d=16.7 in}}}}\)

Since C=πd = c/π 52.438 in

C=52.438 , d = ________= 16.7 in

3.14

#CarryOnLearning

#LetsJustTheSummer

Answer:

The side length of the cube is 9.

Step-by-step explanation:

To find the volume of a cube you use the equation V=E³, although edge can mean length.

Since we already know the volume though, we have to do this equation backwards, and find the cubed root of 729.

To do this we do \(\sqrt[3]{729\\}\) which will give us our answer of 9 cubic inches.

Hope this helped!

Answer:

19 tickets

Step-by-step explanation:

Nadine sold two kinds of tickets to her class play

The student tickets cost $3

Adult tickets cost $5.50

Nadine sold a total of 25 tickets for $90

We are required to find the number of students tickets that were sold

Let x represent the number of tickets sold to students

Let y represent the number of tickets sold to adults

x + y= 25

x= 25-y..........equation 1

Since the total cost of the ticket is $90

3x + 5.50y=90..........equation 2

Substitute 25-y for x in equation 2

3(25-y) + 5.50y= 90

75-3y+5.50y= 90

75+2.5y= 90

Collect the like terms

2.5y= 90-75

2.5y=15

Divide both sides by 2.5

2.5y/2.5=15/2.5

y= 6

Substitute 6 for y in equation 1

x= 25-y

x= 25-6

x= 19

Hence Nadine sold 19 student tickets

Answer:

100

Step-by-step explanation:

take 100 multiplied by half or 50% and it gives you 50.

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of phones produced abroad and y represent the number of phones produced locally.

The company can provide 6000 hours of labor each week and it takes 30 hours to produce the cellphone abroad and at the local factory it takes 20 hours, hence:

30x + 20y = 6000            (1)

Also, there is a total resource of $12000 each week, the cost of producing abroad is $20 and the cost of producing locally is $60. Hence:

20x + 60y = 12000           (2)

Multiply equation 1 by 3 and subtract equation 2 from the result. This gives:

70x = 6000

x = 600/7 ≈ 86

Put x = 86 in equation 1:

30(86) + 20 y = 6000

20y = 3420

y = 171

86 phones should be produced abroad and 171 phones locally

Answer:

a. 10560

b. 63360 in.

c. 10000 m

d. 100000 cm

e. 3.107 miles

f. 42.165 km

Step-by-step explanation:

a. 2 miles contain how many feet?

1 mile = 5280 ft

2 miles × 5280 ft / mile = 10560 ft

b. 1 mile contains how many inches?

1 ft = 12 in

1 mile × 5280 ft/mile × 12 in./ft = 63360 in.

c. 10 kilometers contain how many meters?

1 km = 1000 m

10 km × 1000 m/km = 10000 m

d. 1 kilometer contains how many centimeters?

1 km × 1000 m/km × 100 cm/m = 100000 cm

e. How many miles are in a "5k" (five-kilometer) race?

1 in. = 2.54 cm

5 km =

= 5 km × 1000 m/km × 100 cm/m × 1 in. / (2.54 cm) × 1 ft / (12 in.) × 1 mile / (5280 ft)

= 3.107 miles

f. A marathon is 26.2 miles. How many kilometers is this?

26.2 miles =

26.2 miles × 5280 ft / mile × 0.3048 m/ft × km / (1000 m) = 42.165 km

(a)   The standard time for the work cycle is 3485.39 min.

(b)   The worker's efficiency is approximately 8505.6%.

(c)    The worker's performance on the portion of the cycle he controlled is approximately 1.96%.

(a)    To determine the standard time for the work cycle, we need to consider the allowances for personal and machine-related factors.

Given:

Normal time of the work cycle (T) = 5.39 min

Operator-controlled portion (O) = 0.84 min

PFD allowance factor (PFD) = 16% (0.16)

Machine allowance factor (MAF) = 3000

The total allowances can be calculated as follows:

Total Allowances = (PFD allowance factor * machine allowance factor) + machine allowance factor

= (0.16 * 3000) + 3000

= 480 + 3000

= 3480

Standard time for the work cycle (ST) = T + Total Allowances

= 5.39 + 3480

= 3485.39 min

Therefore, the standard time for the work cycle is 3485.39 minutes.

(b)    To calculate the worker's efficiency, we need to determine the number of units produced and compare it to the standard time.

Given:

Number of units produced during an 8-hour shift = 85

Standard time for the work cycle = 3485.39 min

Shift duration = 8 hours = 480 min

Total units produced during the shift = (Number of units produced per cycle) * (Number of cycles per shift)

= 85 * (480 / T)

= 85 * (480 / 5.39)

= 85 * 89.0

= 7565

Efficiency = (Total units produced / Total units that could be produced) * 100

= (7565 / (480 / T)) * 100

= (7565 / (480 / 5.39)) * 100

= (7565 / 89.0) * 100

= 8505.6

Therefore, the worker's efficiency is approximately 8505.6%.

(c)    To determine the worker's performance on the portion of the cycle he controlled, we need to calculate the actual time spent on the operator-controlled portion and compare it to the standard time.

Given:

Total time lost due to personal needs and delays = 42 min

Operator-controlled portion (O) = 0.84 min

Actual time spent on the operator-controlled portion = O + Total time lost

= 0.84 + 42

= 42.84 min

Worker's performance = (Standard time for operator-controlled portion / Actual time spent on operator-controlled portion) * 100

= (O / (O + Total time lost)) * 100

= (0.84 / (0.84 + 42)) * 100

= (0.84 / 42.84) * 100

= 1.96

Therefore, the worker's performance on the portion of the cycle he controlled is approximately 1.96%.

learn more about Work Cycle.

brainly.com/question/30088159

#SPJ11

Answer:

1

Step-by-step explanation:

Anything to the power of zero is = 1

Answer: the answer is 1

Step-by-step explanation:

The statement asserts that there is at least one student who listens to all of their professors.

The statement "Some students listen to every one of their professors" can be understood as follows:

1. Sx: x is a student.

This predicate defines Sx as the property of x being a student. It indicates that x belongs to the group of students.

2. Pxy: x is a professor of y.

This predicate defines Pxy as the property of x being a professor of y. It indicates that x is the professor of y.

3. Lxy: x listens to y.

This predicate defines Lxy as the property of x listening to y. It indicates that x pays attention to or follows the teachings of y.

The statement states that there exist some students who listen to every one of their professors. This means that there is at least one student who listens to all the professors they have.

The logical representation of this statement would be:

∃x(Sx ∧ ∀y(Pyx → Lxy))

Breaking down the logical representation:

∃x: There exists at least one x.

(Sx: x is a student): This x is a student.

∀y(Pyx → Lxy): For every y, if y is a professor of x, then x listens to y.

In simpler terms, the statement asserts that there is at least one student who listens to all of their professors.

Learn more about representation here:

https://brainly.com/question/32896268

#SPJ11

Answer:

a. 9ab

b. 9a

C. 4a

d. 2a^2b^2

e. -8c^3

f. 12x^3y^3

g. 25a^2

h. 2b^2

I. -2ab^2

Step-by-step explanation:

Hope this helps! Mark brainliest please worked a long time

Fill the blanks this way

1. Given

2. Segment addition postulate

3. Substitution property of equality

4. Substraction property of equality

5. Division property of equality

\(3\dfrac{1}{10}=\dfrac{3\cdot10+1}{10}=\dfrac{30+1}{10}=\boxed{\frac{31}{10}}\)

Answer:

4

Step-by-step explanation:

at x=3

since x=3 means x>= 1

use x+1 = 3+1=4

The central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

To find the central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

If you want the central angle in degrees, you can convert it using the fact that there are 2π radians in a full circle (360 degrees):

Central angle (in degrees) = (Arc length / Radius) * (180 / π)

Make sure to use consistent units for the arc length and radius, such as meters or centimeters, to obtain accurate results.

To know more about central angle:

https://brainly.com/question/29150424

#SPJ4

In linear equation , the car y's price changes the most.

What are a definition and an example of a linear equation?

According to the question

a)  Car x : £ 10320  ≈  £ 10300        10320 - 10300 = 20

    Car y  : £ 15430 ≈ £ 15400          15430 - 15400 = 30

    Car z   :  £ 17490 ≈  £ 17500        17490 - 17500  = 10

                   10 < 20 < 30

so the car y's price changes the most.

b) this car's price change £ 30

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

Answer:

x⁴ - 11x² + 28

= x⁴ - 4x² - 7x² + 28

= x²(x² - 4) - 7(x² - 4)

= (x² - 7)(x² - 4)

\( = (x - \sqrt{7} )(x + \sqrt{7} )(x - 2)(x + 2)\)

The number of unique random numbers which need to be selected from the table of random digits is: C. 800.

A random number can be defined as a numerical value that's unique and cannot be predicted based on past or present numerical values.

Based on the information given, the total number of objects are 1,200 and they are to be placed into three (3) equally sized treatment groups.

Each group = 1200/3

Each group = 400 objects.

Selection = 400 × 2

Unique selection = 800 random numbers.

Read more on random sample here: https://brainly.com/question/17831271

#SPJ1

For 8% p-value cutoff , Melissa should use 92% confidence interval

A confidence interval calculated for a treatment effect measure shows the range in which the true treatment effect is likely to fall.

A smaller sample size or higher variability will result in a wider confidence interval with a larger margin of error. The interval width is also influenced by the level of confidence. If you want a higher level of certainty, the interval should be wider.

The width of the confidence interval and the size of the p value are related.

The narrower the interval, the smaller the p value. The confidence interval, on the other hand, provides useful information about the likely magnitude of the effect under consideration as well as the accuracy of the estimate.

To know more about Confidence interval here

https://brainly.com/question/24131141

#SPJ4

Answer:

-6

Step-by-step explanation:

A parabola is vertex form is written as

y = a(x-h)^2 +k  where (h,k) is the vertex

Substituting in the vertex

y = a(x-5)^2 +5

We know a point on the parabola so we can find a

-1 = a( 6-5)^2 +5

-1 =a(1)^2+5

-1 = a +5

Subtract 5 from each side

-1-5 = a

-6 =a

If we have a population that doesn't follow the normal distribution, we must choose a minimum sample size of 30 to ensure an approximately normal (symmetric) distribution.

        According to the Central Limit Theorem (CLT), a minimum sample size of 30 is required to ensure a normal distribution, regardless of the shape of the population distribution.

       In this case, a minimum sample size of 30 will suffice for a normal distribution, regardless of the population's shape, as long as the sample is random and the population's standard deviation is known or greater than 30.

      Therefore the minimum sample size of 30 we should select in order to have an approximately normal distribution (symmetric).

To learn more about normal distribution visit: https://brainly.com/question/4079902

#SPJ11