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The productivity of workers at a shoe factory (in pairs of shoes per hour) can be modeled using the function p(h) = -2/7h + 5, where h is the number of hours. If a worker must create at least 3 pairs of shoes per hour for the company to be profitable, how long should the worker's shift be?

Answers

Answer 1

Answer:

Answer:

no more than 7 hours

Step-by-step explanation:

You want p(h) ≥ 3, so ...

p(h) ≥ 3

-2/7h +5 ≥ 3

2 ≥ 2/7h . . . . . . add 2/7h -3

7 ≥ h . . . . . . . . . multiply by 7/2

The worker's shift should be 7 hours or less.

Answer 2

Answer:

Final answer:

The equation is solved by equating it to 3 and solving for h (hours). It results in a maximum work shift of 7 hours to maintain an average productivity of at least 3 pairs of shoes per hour.

Explanation:

The question deals with a linear function that models the productivity rate of workers in a shoe factory. The function is p(h) = -2/7h + 5 which presents the productivity (p) in pairs of shoes per hour, depending on the hours worked (h). If the company requires a minimum productivity of 3 pairs of shoes per hour to stay profitable, we want to find the maximum value of h such that p(h) is equal to or greater than 3.

To solve, equate the function to 3, that is: 3 = -2/7h + 5. By simplifying, you obtain: -2/7h = 3 - 5 = -2. Then, divide both sides by -2/7, we get h = -2 / (-2/7) = 7 hours.

Therefore, for the company to stay profitable, the worker's shift should not exceed 7 hours.

Learn more about Linear Function here:

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The length of a rectangle is represented by (6x − 2), and the width is represented by (x − 1). Which expression best represents the area of the rectangle? A) 6x2 + 8x + 2 B) − 8x + 2 C) 6x2 − 8x + 2 D) 6x2 − 8x − 2

Answers

Answer: Area = $6x^(2)-8x+2$

Step-by-step explanation:

The formula for calculating the area of a rectangle is given by :

Area = Length x width

length = $(6x-2)$

Width = $(x-1)$

Therefore :

Area = $(6x-2)(x-1)$

Expanding the equation , we have

Area = $6x(x-1) -2(x-1)$

Area = $6x^(2)-6x$ $-2x + 2$

Area = $6x^(2)-8x+2$

What is the range of h?

Answers

Answer:

Image?

Step-by-step explanation:

Answer:

where is the image

Step-by-step explanation:

2 PointsThese dot plots show the lengths (in feet) from a sample of crocodiles and

alligators

Crocodi

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Alligator

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Length

What are the differences between the centers and spreads of these

distributions?

Select two choices: one for the centers and one for the spreads

D A Centers: The crocodiles have a lower median length than the

alligators

B. Centers: The crocodiles have a greater median length than the

alligators

c. Spreads: The lengths of the alligators are more spread out

D. Spreads. The lengths of the crocodiles are more spread out

PREVIOUS

SEO

Answers

Answer:

(B) Centers: The crocodiles have a greater median length than the alligators

Step-by-step explanation:

The question is incomplete without the diagram. Find attached the diagram used in solving the question

Centers: this is the median of the distribution

Spread: this is the variation of the data distribution. The range can be used to find the spread. If the range is large, the spread is larger and If the range is small, the spread is smaller.

Range = highest value - lowest value

From the diagram:

Median of crocodile = 17

Median of the alligator = 9

Therefore, for Centers: The crocodiles have a greater median length than the alligators (option B)

Spread for crocodile data = from 15 to 19

Range = 19-15 = 4

Spread for alligator data = from 7 to 15

Range = 15-7 = 8

For Spreads: The lengths of the alligators are more spread out.

Answer: b and c

Step-by-step explanation:

Which pair of variables would most likely have a negative correlation?A. the time spent driving in a car and the number of miles driven

B. the height of a dog in inches and the number of ounces of food the dog eats per day

C. the number of sit-ups completed and the number of calories burned during a workout

D. the time spent reading a book and the number of pages remaining to be read in the book

Answers

The pair of variables that will most likely have a negative correlation are D. the time spent reading a book and the number of pages remaining to be read in the book.

Negative Correlation

This means that the variables involved move in the opposite direction from each other.
Means that as one variable increases, the other decreases and vice versa.

If you spend a longer time reading a book, you would read more pages which would reduce the number of pages left to be read. The time taken to read the book is therefore negatively correlated with the number of pages left.

In conclusion, option D is correct.

Find out more on negative correlation at brainly.com/question/2476038.

Answer: D

Step-by-step explanation:

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.) f(x) = x9 − 9, x1 = 1.6

Answers

Answer:

Iteration 1: $x_(2)=1.446$

Iteration 2: $x_(3)=1.337$

Step-by-step explanation:

Formula for Newton's method is,

$x_(n+1)=x_n-(f\left(x_n\right))/(f'\left(x_n\right))$

Given the initial guess as $x_(1)=1.6$ , therefore value of n = 1.

Also, $f\left(x\right)=x^(9)-9$ .

Differentiating with respect to x,

$(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9-9\right)$

Applying difference rule of derivative,

$(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9\right)-(d)/(dx)\left(9\right)$

Applying power rule and constant rule of derivative,

$(d)/(dx)\left(f\left(x\right)\right)=\left(9x^(9-1)\right)-0$

$(d)/(dx)\left(f\left(x\right)\right)=9x^(8)$

Substituting the value,

$x_(1+1)=x_1-(f\left(x_1\right))/(f'\left(x_1\right))$

$x_(2)=1.6-(f\left(1.6\right))/(f'\left(1.6\right))$

Calculating the value of $f\left(1.6\right)$ and $f'\left(1.6\right)$

Calculating $f\left(1.6\right)$

$f\left(1.6\right)=\left(1.6\right)^(9)-9$

$f\left(1.6\right)=59.71947674$

Calculating $f'\left(1.6\right)$ ,

$f'\left(1.6\right)=9\left(1.6\right)^(8)$

$f'\left(1.6\right)=386.5470566$

Substituting the value,

$x_(2)=1.6-(59.71947674)/(386.5470566)$

$x_(2)=1.446$

Therefore value after second iteration is $x_(2)=1.446$

Now use $x_(2)=1.446$ as the next value to calculate second iteration. Here n = 2

Therefore,

$x_(2+1)=x_2-(f\left(x_2\right))/(f'\left(x_2\right))$

$x_(3)=1.446-(f\left(1.446\right))/(f'\left(1.446\right))$

Calculating the value of $f\left(1.446\right)$ and $f'\left(1.446\right)$

Calculating $f\left(1.446\right)$

$f\left(1.446\right)=\left(1.446\right)^(9)-9$

$f\left(1.446\right)=18.63851065$

Calculating $f'\left(1.446\right)$ ,

$f\left(1.446\right)=9\left(1.446\right)^(8)$

$f\left(1.446\right)=172.0239252$

Substituting the value,

$x_(3)=1.446-(18.63851065)/(172.0239252)$

$x_(3)=1.337$

Therefore value after second iteration is $x_(3)=1.337$

Final answer:

To calculate two iterations of Newton's Method, use the formula xn+1 = xn - f(xn)/f'(xn). Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, calculate f(xn) and f'(xn) at x1 and then use the formula to find x2 and x3.