The productivity of workers at a shoe factory in
pairs of shoes per hour) can be modeled using the
function p(h) = -4h + 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?

Answer:

3/8.

Step-by-step explanation:

First convert days to hours:

2 days = 2 * 24 = 48 hours.

The greatest common factor of 18 and 48 = 6 so the required fraction is

18/48

= (18/6) / (48/6)

= 3/8.

Parameterize the surface (I'll call it S) by

r(u, v) = (1 - u) (1 - v) i + u (1 - v) j + v k

with 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1.

Take the normal vector to this surface to be

n = ∂r/∂u × ∂r/∂v = ((v - 1) i + (1 - v) j) × ((u - 1) i - u j + k) = (1 - v) (i + j + k)

with magnitude

||n|| = √3 (1 - v)

Then in the integral, we have

[tex]\displaystyle\iint_SG(x,y,z)\,\mathrm ds = \int_0^1\int_0^1 G((1-u)(1-v),u(1-v),v) \|\mathbf n\| \,\mathrm du\,\mathrm dv \\\\= \sqrt3 \int_0^1\int_0^1uv(1-v)^2\,\mathrm du\,\mathrm dv \\\\= \boxed{\frac1{8\sqrt3}}[/tex]

Alternatively, if you're not familiar with parameterizing surfaces, you can use the "projection" formula:

[tex]\displaystyle\iint_S G(x,y,z)\,\mathrm ds = \int_{S_{xy}}G(x,y,z)\sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2}\,\mathrm dx\,\mathrm dy[/tex]

where I write [tex]S_{xy}[/tex] to mean the projection of the surface onto the (x, y)-plane, and z = f(x, y). We would then use

x + y + z = 1   ==>   z = f(x, y) = 1 - x - y

and [tex]S_{xy}[/tex] is the triangle,

{(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}

Then the integral becomes

[tex]\displaystyle\int_0^1\int_0^{1-x}y(1-x-y)\sqrt{1+(-1)^2+(-1)^2}\,\mathrm dy\,\mathrm dx \\\\= \sqrt3\int_0^1\int_0^{1-x} y(1-x-y)\,\mathrm dy\,\mathrm dx \\\\= \frac{\sqrt3}{24} \\\\= \boxed{\frac1{8\sqrt3}}[/tex]

Answer:

let x represent the bigger number

x+x-47=125

2x-47=125

2x=125+47

2x=172

2x/2=172/2

x=86

the smaller number=x-47

86-47

39

therefore the answer is a) 39 and 86

Answer:

A

Step-by-step explanation:

To find the sum of 125, you have to add the numbers.

39+86 = 125

To find the difference of 47, you have to subtract the numbers.

86-39 = 47

Answer:

[tex]8^{298} \\8^{3(n-1)+1}[/tex]

Step-by-step explanation:

Answer:

8^298

Step-by-step explanation:

n = 1, 8^(1 + 0 * 3)

n = 2, 8^(1 + 1 * 3)

n = 3, 8^(1 + 2 * 3)

n = 4, 8^(1 + 3 * 3)

The exponent of 8 is 1 added to product of 1 less than the term number multiplied by 3.

n = n, 8^(1 + [n - 1] * 3) = 8^(1 + 3n - 3) = 8^(3n - 2)

For n = 100, the exponent is

3n - 2 = 3(100) - 2 = 300 - 2 = 298

Answer: 8^298

Answer:

Step-by-step explanation:

[tex]hope \: it \: helps[/tex]

CarryOnLearning

Answer: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]

Step-by-step explanation:

[tex]f(x)=10x^{3}\\y=10x^{3}[/tex]

switch the x and y:

[tex]x=10y^{3}[/tex]

Now solve for y:

[tex]x=10y^{3} \\\frac{x}{10} =y^{3} \\\sqrt[3]{\frac{x}{10} } =y\\[/tex]

Therefore, the inverse of that function is: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]

Answer:

[tex]\frac{3v}{a^{2}} = h[/tex]

Step-by-step explanation:

[tex]v = \frac{1}{3} a^{2} h[/tex]

[tex]3v = a^{2} h[/tex]

[tex]\frac{3v}{a^{2}} = h[/tex]

Answer:

16 years

Step-by-step explanation:

Given that :

Earth's distance from sun = 93 million miles

Number of years to complete an orbit = 1 year

Average orbiting distance of new asteroid = 1488 million miles

Number of years to complete an orbit = x

93,000,000 Miles = 1

1488000000 miles = x

Cross multiply :

93000000x = 1488000000

x = 1488000000 / 93000000

x = 16 years

Period taken to orbit the sun = 16 years

Answer: 64 Earth years...

Answer:

[tex]3x^{2} -3x-11 = 0[/tex]

Step-by-step explanation:

Answer:

1d = -3

2b = 2

2c = 1

3a = 3

3d = 4

Step-by-step explanation:

Polynomial 1: [tex]x^2-8x+15[/tex]

Multiply the leading coefficient, 1, and the last term, 15. You get: 15.

Then, list out the factors of 15 and the addends of -8 until you get two of numbers that are the same:

Factors of 15: -5 * -3

Addends of -8: -5 + -3

Replace the -8x with -5x - 3x:

[tex]x^2-5x-3x+15[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex](x^2-5x)-(3x+15)[/tex]

[tex]x(x-5)-3(x-5)[/tex]

[tex](x-5)(x-3)[/tex]

Looking at the answer (ax + b)(cx + d), d would correspond with -3.

Polynomial 2: [tex]2x^3-8x^2-24x[/tex]

First factor out the x:

[tex]x(2x^{2}-8x-24)[/tex]

Divide the polynomial inside by 2 and place the 2 outside with the x:

[tex]2x(x^2-4x-12)[/tex]

Then find the factors of 1*-12 and the addends of -4 and see which two numbers match:

Factors of -12: -6 * 2

Addends of -4: -6 + 2

Replace the -8x with -6x + 2x:

[tex]2x(x^2-6x+2x-12)[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex]2x((x^2-6x)+(2x-12))[/tex]

[tex]2x(x(x-6)+2(x-6))[/tex]

[tex]2x((x+2)(x-6))[/tex]

[tex]2x(x+2)(x-6)[/tex]

Looking at the answer (2x)(ax + b)(cx + d), b & c would correspond with 2 & 1.

Polynomial 3: [tex]6x^2+14x+4[/tex]

Divide the polynomial by 2:

[tex](2)(3x^2+7x+2)[/tex]

Find the factors of 3*2 and the addends of 7 and see which two numbers match:

Factors of 6: 6 * 1

Addends of 7: 6 + 1

Replace the 7x with 6x + x:

[tex](2)(3x^2+6x+x+2)[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex](2)((3x^2+6x)+(x+2))[/tex]

[tex](2)(3x(x+2)+(x+2))[/tex]

[tex](2)((3x+1)(x+2))[/tex]

[tex](2)(3x+1)(x+2)[/tex]

Then multiply the 2 with the (x+2) and here's your final answer:

[tex](3x+1)(2x+4))[/tex]

Looking at the answer (ax + b)(cx + d), a & d correspond with 3 & 4.

Hope that helps (●'◡'●)

(This took a while to write, sorry about that)

Answer: 3x - 2

Step-by-step explanation:

First to solve this, we need to know some basic information such as:

1. (-) × (-) = +

2. (+) × (-) = -

3. (+) × (+) = +

Therefore, 6x-(3x+2)​

= 6x - 3x - 2

= 3x - 2

The answer to the question after removing the bracket will be 3x - 2.

Answer:

75.5

Step-by-step explanation:

First, the picture is not to scale.

The Area of the bottom (2) rectangle is 33

base x height = A

11 x 3 = 33      (where did I get 3? Total height of shape is 8. Trapezoid is 5)

                      (8-5 = 3)

Area of the trapezoid:

A = [tex]\frac{h (B_{1} + B_{2}) }{2}[/tex]

  =  [tex]\frac{(5)(6 + 11)}{2}[/tex]

  =  [tex]\frac{5(17)}{2}[/tex]

  = [tex]\frac{85}{2}[/tex]

  = 42.5

42.5 + 33 = 75.5

Answer:

0.0498

Step-by-step explanation:

In this question,

x~exponential

we have

mean = 1/λ = 8

from here we cross multiply, when we do

such that

λ = 1/8

probability of x functioning in 8 months

= e^-λx

= e^-1/8x12

= e^-1.5

= 0.2231

i got this value through the use of a scientific calculator

then the probability that these two are greater than 12

= 0.2231²

= 0.04977

= approximately 0.0498

therefore the probability that both components are functioning in 12 months is 0.0498

Answer:

[tex]B = \frac{3V}{h}[/tex]

Step-by-step explanation:

Given

[tex]V = \frac{1}{3}Bh[/tex]

Required

Solve for B

We have;

[tex]V = \frac{1}{3}Bh[/tex]

Multiply by 3

[tex]3V = Bh[/tex]

Make B the subject

[tex]B = \frac{3V}{h}[/tex]

Answer:

What do you need help with

Step-by-step explanation:

Answer:

from math import comb

n = 100

x = 20

p = 0.26

q = 0.76

print(comb(n, x)*(p**x)*(q**(n-x)))

Step-by-step explanation:

Given that :

Number of trials, n = 100

P(success), p = 26% = 0.26

P(success)' = 1 - p = 1 - 0.26 = 0.74

Chance that sample has 20 successes = x

This problem meets the condition for a binomial probability distribution :

p(x = 20)

Recall :

P(x = x) = nCx * p^x * q^(n-x)

Using python :

comb is an built in function which calculate the combination of two arguments it takes ; and returns the combination value.

** mean raised to the power and

* is used for multiplication

The Python code as per the given question is provided below.

Program explanation:

The number of trials,

Probability of success,

Size of array generated,

The output that shows chances of 20 success,

Program code:

import numpy as np

S=sum(np.random.binomial(100,0.26,2000)==20)/2000

S

Learn more about Python expression here:

https://brainly.com/question/21645017

[tex]\bar{x} = 0[/tex]

[tex]\bar{y} =\dfrac{136}{125}[/tex]

Step-by-step explanation:

Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:

[tex]f(x) = x^2 + 1[/tex]

[tex]g(x) = 6x^2[/tex]

The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:

[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]

[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]

The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by

[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]

[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]

[tex]\:\:\:\:\:\:\:= 0[/tex]

The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by

[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]

[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]

[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]

Answer:

it's and equilateral triangle because

all sides are equal

Answer:

equilateral triangle i have a math proffesor helping me

Step-by-step explanation:

I have a math proffesor helping me

Answer:

65 solve theprob

Step-by-step explanation:

sinolove ko po yan paki brainly

Answer:

a = 0.0040 m/s², v = 14.4 m/s.

Step-by-step explanation:

Given that,

The distance between Kathmandu and Khanikhola, d = 26 km = 26000 m

Time, t = 1 hour = 3600 seconds

Let a is the acceleration of the bus. Using second equation of motion,

[tex]d=ut+\dfrac{1}{2}at^2[/tex]

Where

u is the initial speed of the bus, u = 0

So,

[tex]d=\dfrac{1}{2}at^2\\\\a=\dfrac{2d}{t^2}\\\\a=\dfrac{2\times 26000}{(3600)^2}\\\\a=0.0040\ m/s^2[/tex]

Now using first equation of motion.

Final velocity, v = u +at

So,

v = 0+0.0040(3600)

v = 14.4 m/s

Hence, this is the required solution.

Answers:

=============================================

Explanation:

The angle theta is between pi and 3pi/2, excluding both endpoints.

This places theta in the third quadrant (Q3) between 180 degrees and 270 degrees. The third quadrant is in the southwest.

Plot point A at the origin. 12 units to the left of this point, will be point B. So B is at (-12,0). Then five units lower is point C at (-12,-5). Refer to the diagram below. Notice how triangle ABC is a right triangle.

The angle theta will be the angle BAC, or simply angle A.

Since cos(theta) = -12/13, this indicates that

AB = -12 = adjacent

AC = 13 = hypotenuse

Technically, AB is should be positive, but I'm making it negative so that we can then say

cos(angle) = adjacent/hypotenuse

cos(theta) = AB/AC

cos(theta) = -12/13

------------------

If you apply the pythagorean theorem, you should find that BC = 5, which I'll  make negative since we're below the x axis. Then we can say

sin(theta) = opposite/hypotenuse

sin(theta) = BC/AC

sin(theta) = -5/13

------------------

If you divide sine over cosine, then you'll get 5/12. The 13's cancel out. This is the value of tangent.

Or you could say

tan(theta) = opposite/adjacent

tan(theta) = BC/AB

tan(theta) = (-5)/(-12)

tan(theta) = 5/12

------------------

To find csc, aka cosecant, you apply the reciprocal to sine

sin = -5/13 which means csc = -13/5

sec, or secant, is the reciprocal of cosine

cos = -12/13 leads to sec = -13/12

and finally cotangent (cot) is the reciprocal of tangent

tan = 5/12 leads to cot = 12/5

------------------

Note: everything but tan and cot is negative in Q3.

Answer:

the second one

Step-by-step explanation:

Answer:

[tex]AC = 87[/tex]

Step-by-step explanation:

Given

[tex]AB = 3x + 4[/tex]

[tex]BC = 4x -1[/tex]

[tex]AC = 8x - 9[/tex]

Required

The value x

Since A, B and C are collinear, then;

[tex]AC = AB + BC[/tex]

This gives:

[tex]8x - 9 =3x+4+4x-1[/tex]

Collect like terms

[tex]8x - 3x - 4x = 9 + 4-1[/tex]

[tex]x = 12[/tex]

We have:

[tex]AC = 8x - 9[/tex]

[tex]AC = 8*12 - 9[/tex]

[tex]AC = 87[/tex]

Answer:

B."5, -3, -4, 1, -1, 6, -4"

Step-by-step explanation:

We are given that

13,5,4,9,7,14,4

We have to find the deviation.

Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]

Using the formula

[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]

[tex]Mean,\mu=\frac{56}{7}=8[/tex]

Deviation=[tex]x_i-\mu[/tex]

         [tex]x_i-\mu[/tex]

13          5

5           -3

4           - 4

9            1

7             -1

14            6

4            - 4

Hence, option  B is correct.

Answer:

Top left: not a function

Top right: not a function

Bottom left: function

Bottom right: not a function

Step-by-step explanation:

A function is a relationship where each x value has it's own y value ( note that domain = x values and range = y values)

For the one on the top left.

S and n have more than one y value.

Because s and n have more than one y value the relation is not a function

For the one of the top right.

There x value "c" has multiple y values therefore the relation is not a function

For the one on the bottom left

Each x value has it's own y value therefore it is a function ( note that the y values can repeat. It's only the x values that can't repeat. )

For the one on the bottom right

The x value "-5" has multiple y values therefore the relation is not a function

Answer:

9.48

Step-by-step explanation:

Answer:

The slope of the line is -6.

Answer:

400 + .03(250,000) = $7900

Step-by-step explanation: